EXPLORING POTENTIAL ENERGY SURFACES AND REACTION MECHANISMS OF
INORGANIC MOLECULES BY COMPUTATIONAL METHODS
Except where reference is made to the work of others, the work described in this dissertation is
my own or was done in collaboration with my advisory committee. This dissertation does not
include proprietary or classified information.
________________________________
Hyun Joo
Certificate of Approval:
________________________________ ___________________________________
William E. Hill Michael L. McKee, Chair
Professor Professor
Chemistry and Biochemistry Chemistry and Biochemistry
_______________________________ ___________________________________
Thomas R. Webb German Mills
Associate Professor Associate Professor
Chemistry and Biochemistry Chemistry and Biochemistry
_________________________________
Stephen L. McFarland
Acting Dean
Graduate School
EXPLORING POTENTIAL ENERGY SURFACES AND REACTION MECHANISMS OF
INORGANIC MOLECULES BY COMPUTATIONAL METHODS
Hyun Joo
A Dissertation
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Doctor of Philosophy
Auburn, Alabama
December 16, 2005
iii
EXPLORING POTENTIAL ENERGY SURFACES AND REACTION MECHANISMS OF
INORGANIC MOLECULES BY COMPUTATIONAL METHODS
Hyun Joo
Permission is granted to Auburn University to make copies of this dissertation at its discretion,
upon request of individuals of institutions and at their expense. The author reserves all
publication rights.
_________________________
Signature of Author
_________________________
Date of Graduation
iv
VITA
Hyun Joo, the first son of Sucheon Joo (father) and Soonyoung Yoo (mother), was born
on February 10, 1971 in Yeosu, South Korea.  He received his early education in his hometown,
graduated from Suncheon high school and then went to college in Seoul.  After graduating from
Hanyang University with a B.S. in Chemistry, he entered the graduate program in the same
University and obtained an M.S. degree in inorganic chemistry in February 1999.  After
graduation, he worked as a research scientist in Molecular Simulation Institute at Soongsil
University for one year and then at Hanyang University until July 2001.  In August 2001, he
joined Dr. Michael L. McKee?s research group at Auburn University and conducted research on
potential energy surfaces and reaction mechanisms of inorganic and organic molecules.  At
Auburn, he met Geum Jhun Martha Lee, daughter of Young Ik Lee and Ok Hee Kim, and married
on December 28, 2002.  In October 2004, they had a son, Michael Lee Joo.
v
DISSERTATION ABSTRACT
EXPLORING POTENTIAL ENERGY SURFACES AND REACTION MECHANISMS OF
INORGANIC MOLECULES BY COMPUTATIONAL METHODS
Hyun Joo
Doctor of Philosophy, December 16, 2005
(M.S. Hanyang University-Seoul, Korea, 1999)
(B.S. Hanyang University-Seoul, Korea, 1997)
169 Typed Pages
Directed by Michael L. McKee
Various computational methods have been applied in order to explore potential energy
surfaces (PES) and reaction mechanisms.   Theoretical background and computational methods
are introduced in chapter 1.  Chapters 2-5 report four different studies exploring potential energy
surfaces of inorganic and organic molecules in order to understand reaction mechanisms.
Chapter 2 reports an investigation of the singlet and triplet potential energy surfaces of
BCP isomers.  From constructed PES, intramolecular rearrangment mechanisms are studied,
possible dissociation pathways are discussed, a conical intersection is located, and Renner-Teller
species are investigated.
Chapter 3 reports the dissociation mechanism of phosphorus-containing hyponitrites at
the B3LYP level. The cis-hyponitrite, XON=NOX (X=PF
2
, OPF
2
), is predicted to concertedly
vi
decompose to N
2
 plus phosphorus-containing radicals or to N
2
O plus the ?-oxo phosphorus
species.  The trans-hyponitrite can only decompose to N
2
 plus the phosphorus-containing radicals
because there is a very high barrier for rearrangement to cis-hyponitrite.  However, the silver
cation is predicted to reverse the order of the two transition states through stronger interactions
with the oxygen atoms in the transition state of the N
2
O-producing pathway.
Chapter 4 explains the reactions mechanism of ?stable? bis(amino)silylene with
halomethanes and reports that the reactions occur via a radical mechanism.  To explain the
discrepancy of the theoretical model chemistry with experimental observations, substituent
effects on the nitrogen atoms and halogen effects on the halomethanes are investigated which
explain experimental observations.
In Chapter 5, the reaction of atomic carbon with formaldehyde is reported.  The possible
singlet excited carbene (
1
B
1
) formation pathways are investigated by analyzing the singlet and
triplet potential energy surfaces of ketene.  The production of 
1
B
1
 methylene from deoxygenation
by 
1
D carbon and potential energy surface crossing along the C-C and C-O bond stretching are
considered.
vii
ACKNOWLEDGMENTS
I would like to express my most sincere gratitude to Dr. Michael L. McKee for his
guidance and encouragement over four years.  He has been more than a mentor for his
generosity, patience, help and understanding toward me during my graduate life in Auburn.
I am deeply indebted to all my committee (Dr. Hill, Dr. Mills, and Dr. Webb) for their
careful examination, helpful comments and advice on the dissertation.  I am deeply grateful to
Dr. Philip B. Shevlin for his guidance and mentorship.  I would like to thank all the faculty of the
Department of Chemistry and Biochemistry for their hospitality and encouragement on my
graduate study.
I would also like to thank Dr. Nida McKee for her help and generosity through my living
in Auburn.  Sincere appreciation is extended to Dr. Younghi Kwon for his help and
encouragement, and to Nick, Lauren, Tyler, and Ohyun Kwon for their friendship and sharing
valuable time in Auburn.  All my friends, whom I cannot mention one by one, would be given
my appreciation from my heart.
Special great thanks are expressed to my mother who provided me with generous
support and endless love through my life, and to my sisters and brother for their support.  I also
express sincere appreciation to my parents-in-law, and sister-in-law for their support and
encouragement.  Finally, I would like to dedicate this dissertation to my beloved wife, who
supports me most to meet this challenge, and to my son who has given me the greatest pleasure
and hope in my life.
viii
Style manual or journal manual used: Journal of the American Chemical Society
Computer software used: Mac-MS word 2001, CS ChemDraw Std. 7.0 for Mac
ix
TABLE OF CONTENTS
LIST OF FIGURES  ????????????????????????????.
LIST OF TABLES  ????????????????????????????..
CHAPTER 1  GENERAL INTRODUCTION  ??????????????????
1.1  The Born-Oppenheimer approximation and potential energy surface  ?.
1.2  Potential energy surface crossing and non-crossing rule  ??????.
1.3  Conical intersection  ?????????????????????
1.4. Molecular Orbital (MO) Theory  ????????????????
1.5  Hartree-Fock (HF) method  ?????????.?????????
1.6  Basis set  ?????????.???????????????.?
1.7  Electron correlation methods  ?????????.????????
1.8  Compound models  ?????????.????????????
1.9  References  ?????????.???????????????.
CHAPTER 2  AN INVESTIGATION OF THE BCP POTENTIAL ENERGY SURFACE
2.1  Introduction  ..???????????????????????..
2.2  Computational details  ?????????.???????????
2.3  Results and Discussions   .????????.??????????..
2.4  Conclusions  ?????????.??????????????...
2.5  References  ????????????????????????..
xii
xv
1
2
4
5
8
9
11
16
24
27
30
30
31
33
50
52
x
CHAPTER 3  AN EXPERIMENTAL AND THEORETICAL EVALUATION OF THE
REACTIONS OF SILVER HYPONITRITE WITH PHOSPHORUS
HALIDES. IN SEARCH OF THE ELUSIVE PHOSPHORUS-
CONTAINING HYPHONITRITES  ???????????????...
3.1  Introduction  ???????????????????????..
3.2  Experimental  ...??????????????????????.
3.3  Computational methods  ???????????????????
3.4  Results and Discussion  ???????????????????.
3.5  Conclusions  ???????????????????????..
3.6  References  ...???????????????????????.
CHAPTER 4  COMPUTATIONAL STUDY OF THE ?STABLE?
BIS(AMINO)SILYLENE REACTION WITH HALOMETHANES.  A
RADICAL OR CONCERTED MECHANISM? ???????????
4.1  Introduction  ...??????????????????????...
4.2  Computational details  ?......????????...????????..
4.3  Results and Discussion ???????????????.???.....
4.4  Conclusions ...?????????????????????.?...
4.5  References  ..???????????????????????..
CHAPTER 5  COMPUTATIONAL STUDY OF CARBON ATOM (
3
P AND 
1
D)
REACTION WITH CH
2
O: THEORETICAL EVIDENCE OF THE 
1
B
1
METHYLENE PRODUCTION BY C (
1
D) ?????????????.
5.1  Introduction  ....??????????????????????..
5.2  Computational details  ...??????????????????..
57
57
59
64
66
84
85
89
89
92
93
118
120
125
125
127
xi
5.3  Results and Discussion  .....??????????????????
5.4  Conclusions  ..???????????????????????
5.5  References  ..???????????????????????..
128
146
148
xii
LIST OF FIGURES
CHAPTER 1
Figure 1. (a) One-dimensional potential energy curves showing linear Jahn-Teller
distortion. (b) Renner-Teller (Type A) potential energy surface curves  ...
CHAPTER 2
Figure 1. Optimized geometric parameters of stationary points at the DFT level with
the CAS level in parentheses  ??????????????????
Figure 2. Schematic potential energy surface for the BCP system  ?.?.????..
Figure 3. Schematic drawing for revolution of the phosphorus atom around the B-C
core on the singlet PES  ????????????????????.
Figure 4. (a) State crossing from the 
3
A? surface to 
3
A? surface via linear T34 (
3
P)
(b) State crossing through a conical intersection  .??????????
Figure 5. Orbital crossing diagram around the conical intersection  ....??????
CHAPTER 3
Figure 1. Calculated geometries for species on the following PES F
2
PON=NOPF
2
(A), F
2
P(O)ON=NOPF
2
 (B), and F
2
P(O)ON=NOP(O)F
2
 (C) at the
B3LYP/SBS level ??????????????????????..
Figure 2. Reaction profiles of free energies for the reaction of A in THF solution at
the B3LYP/LBS//B3LYP/SBS level  .?????...???????.?.
6
35
39
41
43
44
68-70
73
xiii
Figure 3. Reaction profiles of free energies for the reaction of B in THF solution at
the B3LYP/LBS//B3LYP/SBS level  ????.??????????
Figure 4. Reaction profiles of free energies for the reaction of C in THF solution at
the B3LYP/LBS//B3LYP/SBS level  ??????????????..
Figure 5. Illustration of possible catalytic effect of Ag
+
 on the cis?trans
isomerization of F
2
PON=NOPF
2
  ???????????????...
Figure 6. Optimized geometries of F
2
P(O)ON=NOP(O)F
2
 with Ag(I) at the
B3LYP/SBS level  ?????????????????????...
Figure 7. Comparison of the free energy reaction profiles for C in THF with C
catalyzed by Ag(I) in THF  ??????????????????.
CHAPTER 4
Figure 1. (a) ?(e) Geometries optimized at the B3LYP/6-31+G(d) level  ????.
Figure 2. Schematic reaction free energy profile for the reaction of A with ClCH
3
at the B3LYP/LBS//B3LYP/SBS level  ?????????????.
Figure 3. Schematic reaction free energy profile for the reaction of A with BrCH
3
at the B3LYP/LBS//B3LYP/SBS level  ????????????.?
Figure 4. Schematic reaction free energy for the reaction of A with ICH
3
 at the
B3LYP/LBS//B3LYP/SBS level  ???.????????????...
Figure 5. Orbital interactions are depicted that are analyzed by NBO in Table 9  ?
Figure 6. Geometries (B3LYP/6-31+G(d)) of reactants CH
2
Cl
2
, CHCl
3
, and CCl
4
and the transition states for the initiation steps  ??????????..
Figure 7. Transition vectors of the two transition states (Cl-TS3 and Br-TS3)  ?...
74
75
77
78
80
96-100
106
107
108
110
115
117
xiv
CHAPTER 5
Figure 1. Optimized geometries of singlet ketene at the DFT and CAS level  ??.
Figure 2. Optimized geometries of triplet ketene at the DFT and CAS level  ??...
Figure 3. Optimized geometries of four lowest state methylenes at the DFT and
CAS level  ????????????????????????...
Figure 4. Triplet Potential free energy surface at the MCPT level  .....????.?.
Figure 5. Singlet Potential free energy surface at the MCPT level  ..??...???.
Figure 6. Two singly occupied orbitals (a) a?, (b) a? orbital  ..???..?????.
Figure 7. The orbital crossing diagram  ?????????????????..
131
132
134
136
140
141
143
xv
LIST OF TABLES
CHAPTER 2
Table 1. Important electronic configurations of ground state diatomic fragments of
BCP and minimum energy isomers of BCP at the CASPT2 level  ???.
Table 2. Relative Energies (in kcal/mol) of species on the potential energy surface
of BCP  ??????????????????????????
Table 3. Energies  relative to T2 (in kcal/mol) and reference weights (Rw)
obtained by using the level shift (LS) technique  ??????????
Table 4. Calculated bond dissociation energies (in kcal/mol)  ????????..
Table 5. Wiberg Bond Index calculated at the DFT level  ??????????
Table 6. NBO stabilization energies associated with electron delocalization
(kcal/mol) at the DFT level  ??????????????????
Table 7. Heats of formation (kcal/mol) of ground state diatomic fragments and S1
Table 8. Heats of formation (kcal/mol) of S1 at 0K and 298K by different
reactions  ?????????????????????????..
Table 9. Vibrational Frequencies (cm
-1
) and Renner-Teller Constants of Triplet
Linear Species  ???????????????????????
Table 10. Calculated Vibrational Frequencies (cm
-1
)  and IR intensities (km/mol) of
S1, S2, T1 and T2
 
 ?????????????????????...
34
38
41
45
46
47
48
48
49
49
xvi
CHAPTER 3
Table 1. Relative Enthalpies and Free Energies (kcal/mol) on the Potential Energy
Surface of F
2
PON=NOPF
2
 at the B3LYP/LBS//B3LYP/SBS Level  ??
Table 2. Relative Enthalpies and Free Energies (kcal/mol) on the Potential Energy
Surface of F
2
P(O)ON=NOPF
2
 at the B3LYP/LBS//B3LYP/SBS Level  ...
Table 3. Relative Enthalpies and Free Energies (kcal/mol) on the Potential Energy
Surface of F
2
(O)PON=NOP(O)F
2
 at the B3LYP/LBS//B3LYP/SBS Level
Table 4. Natural Population Analysis (NPA) Charges for Stationary Points at the
B3LYP/SBS Level  ?????????????????????.
Table 5. Binding Energies, Enthalpies, and Free Energies (kcal/mol) of Ag(I) with
F
2
P(O)ON=NOP(O)F
2
  ????????????????????
Table 6. Reaction Enthalpies and Free Energies (kcal/mol) for Radical
Recombinations  ??????????????????????..
Table 7. Atomic Mulliken Spin Densities and NPA Charges of Radical Species
Calculated at the B3LYP/SBS Level  ??????????????..
Table 8. Kinetic and Thermodynamic Data (kcal/mol) for the Concerted N
2
-
Producing Pathway  ?????????????????????.
CHAPTER 4
Table 1. Calculated Electronic Energies (hartrees), Zero-Point Energies, Heat
Capacity Corrections to 298K (kcal/mol), Entropy (cal/mol?K) and Spin-
Squared Values (<S
2
>) are Calculated at the B3LYP/SBS Level  ???.
Table 2. Natural Atomic Charges (NPA) and Mulliken Spin Densities (MSD) of
X-Si(NHCH)
2
, (X=ep, CH
3
, Cl, Br, I) Radicals Calculated at the
B3LYP/SBS Level  ?????????????????????.
71
71
72
76
79
81
82
83
94
101
xvii
Table 3. Relative Energies, Enthalpies, and Free Energies (kcal/mol) in the
Reaction Profile for the Reaction of A with ClCH
3
  ????????...
Table 4. Relative Energies, Enthalpies, and Free Energies (kcal/mol) in the
Reaction Profile for the Reaction of A with BrCH
3
  ????????
Table 5. Relative Energies, Enthalpies, and Free Energies (kcal/mol) in the
Reaction Profile for the Reaction of A with ICH
3
  ?????????
Table 6. Bond Dissociation Energies (BDE), Bond Dissociation Enthalpies at 0K
(BDE
0
) and at 298K (BDE
298
) Calculated at the
B3LYP/LBS//B3LYP/SBS Level (kcal/mol)  ???????????.
Table 7. Comparison of Free Energies of Activation (kcal/mol) for Concerted
Oxidative Addition with Halogen Abstraction Reaction for A + XCH
3
  ?
Table 8. Predicted Differences in Free Energies of Activation (??G
298
, kcal/mol)
for Formation of CH
3
 and I-Si Radical from ClCH
3
 and BrCH
3
 at
B3LYP/LBS//B3LYP/SBS Level  ???????????????..
Table 9. Orbital Interaction Energies (kcal/mol) from Second Order Perturbation
Theory Analysis in NBO Analysis at the HF/LBS Level  ??????..
Table 10. Comparison of Activation Energies, Enthalpies, and Free Energies
(kcal/mol) in the Initiation Steps for the Reaction of A with ClCH
3
,
CH
2
Cl
2
, CHCl
3
 or CCl
4
 and for the Reaction of SiM with ClCH
3
 and
CH
2
Cl
2
  ??????????????????????????
CHAPTER 5
Table 1. Calculated electronic energies (a.u.) at DFT, CAS and MCPT level along
with ZPC (kcal/mol), H
corr
 (kcal/mol), entropy (S) (cal?K
-1
mol
-1
), spin
squared value (<S
2
>), reference weight of dominant configuration (c
i
2
),
101
102
102
109
109
110
110
117
xviii
and electronic states  ?????????????????????
Table 2.  Relative enthalpies (kcal/mol) of C
2
H
2
O triplet isomers at 0K (?H
0
),
298K (?H
298
) and free energies at 298K (?G
298
) calculated at the MCPT
level with thermodynamic corrections at the DFT level  ???????
Table 3.  Relative enthalpies (kcal/mol) of C
2
H
2
O singlet isomers at 0K (?H
0
),
298K (?H
298
) and free energies at 298K (?G
298
) calculated at the MCPT
level with thermodynamic corrections at the DFT level  ???????
Table 4. Important valence electron configurations of four lowest electronic state
methylene and four singlet species obtained at CAS level  ??????
Table 5. Reaction enthalpies at 0K (?H
0
) and 298K (?H
298
) and free energies at
298K (?G
298
) at MCPT level (in kcal/mol)  ????????????
129
135
139
145
146
1
CHAPTER 1
GENERAL INTRODUCTION
The concept of a potential energy surface (PES) comes from the Born-Oppenheimer
approximation which states that the motion of electrons is much faster than that of nuclei and that
those motions can be separated.
1-3
  We can think of the electrons as being subject to the
electrostatic field of the stationary nuclei.  The electronic wave function is obtained by solving
the Schr?dinger equation for a given nuclear configuration.  On the other hand, the nuclei are
subject to a potential which is the sum of the nuclear repulsion and the average field due to the
electrons.  The wave function for the nuclei is thus obtained by solving a Schr?dinger equation in
which the nuclei are subject to a potential which is the sum of the electronic energy and
electrostatic potential of the nuclei.  This potential, which is a function of the nuclear geometry, is
called the potential energy function or potential energy surface for nuclear motion.  For a non-
linear (linear) molecule containing N atoms, the potential energy function is a function of 3N-6
(3N-5) variables.  Such functions cannot be represented graphically except for diatomic
molecules.  It is possible to portray the potential energy function for a polyatomic molecule only
by constraining some of the variables.  Because the potential energy function for a polyatomic
molecule cannot be fully represented graphically, it is often referred to as a potential energy
hypersurface.
The potential energy surface plays a central role in our understanding of the dynamics of
chemical reactions.  For example, the activation barrier can be understood in terms of the
variation of potential energy along the reaction coordinate, and the dynamics of a chemical
2
reaction can be understood fully only in terms of motion of the nuclei on a potential energy
surface.  Any theoretical treatment of the dynamics, whether classical, semi-classical or quantum,
requires some form of potential energy surface.  A potential energy surface can be obtained
experimentally from vibrational-rotational spectroscopy or theoretically from quantum
mechanical calculations.  It is extremely difficult to derive information about the potential energy
surface for a polyatomic molecule where the potential is not a curve but a multidimensional
surface.  Therefore, quantum mechanical calculations are generally applied to obtain the potential
energy surface of molecules.
Due to the rapid development of computer technology, computational chemistry has been
one of the fastest growing fields of chemistry.  Computational chemistry provides reliable
information to help chemists not only analyze and interpret experimental data but also predict
chemical and physical properties of molecules and design new molecules.  The goal of this
dissertation is to explore the potential energy surface of molecules and to explain reaction
mechanisms by using various computational methods.  This chapter presents the theoretical
background and features of the potential energy surface and quantum mechanical methods which
have been utilized in the study for this dissertation.
1.1  The Born-Oppenheimer approximation and potential energy surface
If one could solve the Schr?dinger equation for a molecule, one would be able to obtain
all the information about the molecule consistent with the postulates of quantum mechanics.
However, the Schr?dinger equation can be solved exactly for only a limited number of simple
systems and the use of quantum mechanics to obtain a description of a molecule is based on a
number of approximations.  One of the most important approximations related to application of
quantum mechanics to molecules is the Born-Oppenheimer approximation.
1-3
  The basic idea
behind this approximation is that the movements of electrons and nuclei are on different time
3
scales.  Thus we expect the electrons to be able to move much faster than nuclei.  This allows us
to solve the Schr?dinger equation by separating the motion of electrons from that of nuclei.  The
mathematical description of this separation follows.
The time-independent Schr?dinger equation for the motion of the electrons and the
nuclei in a molecule is of the form
[
?
()
?
() () (,) ()] (,) (,)TRTrVRVRrVr RrERr
nuc el nn ne ee
++ + + =??.                                         (1)
?
()TR
nuc
 is the kinetic energy operator for the nuclei at positions R, 
?
()Tr
el
 is the kinetic energy
operator for the electrons at positions r, VR
nn
() is the electrostatic potential energy of the nuclei,
VRr
ne
(,) is the potential energy of the electrons in the field of the nuclei and Vr
ee
() is the inter-
electron repulsion.  Nuclei are much heavier than electrons and thus nuclear motion is very slow
compared with electronic motion and a reasonable approximation is to separate the two types of
motion.  This is the Born-Oppenheimer separation in which the total wavefunction ?(,)Rr  is
written as the product of an electronic wave function ?(,)Rr  and a nuclear wave function ?()R :
??(,) (,)()Rr Rr R= ? .                                                                                                  (2)
[
?
()
?
() () (,) ()](,)() (,)()TRTrVRVRrVr RrRERrR
nuc el nn ne ee
++ + + =????                (3)
The electronic wavefunction ?(,)Rr  is the solution to the electronic Schr?dinger equation,
[
?
() (,) ()](,) ()(,)Tr V Rr Vr Rr WR Rr
el ne ee
++ =??,                                                                (4)
with eigenvalue WR() which is the electronic energy depending on the nuclear coordinates R.
The rest of the Schr?dinger equation can be written as
[
?
() () ()](,)() (,)()T R V R W R Rr R E Rr R
nuc nn
++ =????.                                             (5)
The nuclear kinetic energy operator is of the form of
?
()TR
h
M
nuc
k
k
k
=? ?
?
2
2
2
8
1
?
                                                                                                         (6)
where the summation k runs over the nuclei of mass M
k
.  Thus
4
?
()(,)() (,) ()
() (,)
{ ( , )}{ ( )}
TR RrR Rr
h
M
R
R
h
M
Rr
h
M
Rr R
nuc
k
k
k
k
k
k
k
k
k
k
??
?
?
?
?
?
?
?
?
?
=? ?
?
?
?
?
?
?
+? ?
?
?
?
?
?
?
???
?
?
?
2
2
2
2
2
2
2
2
8
1
8
1
8
2
                                                      (7)
In equation (7), the second and third terms can be shown to be negligible.  For example, in the
second term, ?
k
Rr
2
?(,) is a second order derivative of the electronic wave function with respect
to the nuclear coordinates and will be of the same order of magnitude as the derivative with
respect to electronic coordinates ?
i
Rr
2
?(,).  However 
h
m
Rr
2
2
2
8?
??(,) is of the same order of
magnitude as the energy of one of the electrons.  The second term in equation (7) is thus of the
order of m/M
k
 where m is mass of an electron and can be neglected.  Similarly, the third term can
be neglected.  Therefore,
?
()(,)() (,)
?
()()TR RrR RrTRR
nuc nuc
?????                                                                                 (8)
and finally we can rewrite equtation (5) as
[
?
() () ()]() ()TRVRWR RER
nuc nn
++ =??.                                                                                 (9)
which is called the nuclear Schr?dinger equation.  The sum of two terms
UR V R WR
nn
() () ()=+ in equation (9) is known as the potential energy function or potential
energy surface.
1.2  Potential energy surface crossing and non-crossing rule
When computing multiple potential energy surfaces for a system, it is possible to have
points where two potential energy surfaces UR() have the same energy.  What happens at this
point is of great interest to chemists and will be discussed in this section.  The non-crossing rule
was put forward by Hund
4
 and formulated by von Neumann and Wigner.
5
  It states that in a
5
diatomic molecule for an infinitely slow change of internuclear distance, potential energy curves
corresponding to electronic states of the same symmetry cannot cross.  When two wave functions
are mixed to form a better wave function, the new energies repel each other.  As two potential
energy surfaces come close together along the reaction coordinate, the two wave functions are
mixed and they split apart.  The point of nearest approach is called an avoided crossing point.
The avoided crossing points arise because the adiabatic electronic states around the
avoided crossing point are often mixtures of molecular orbitals of two states.  The mixing of the
two molecular orbitals causes two states to repel each other and results in separation of two
states.  A surface where the actual intersections are substituted for the avoided crossing is called a
diabatic surface.  If the nuclei are assumed to move slowly, then they are likely to follow a single
adiabatic surface.  If the nuclei have sufficient velocity, however, then the Born-Oppenheimer
approximation breaks down and the nuclei may effectively ignore the gap in the avoided crossing
and simply cross over to the other adiabatic surface, adopting that configuration.  This is termed
non-adiabatic behavior.  However two potential energy surfaces can cross if their symmetries are
sufficiently different.  Hund wrote that if two potential energy surfaces cross, the electronic state
must be degenerate at the crossing point.
4
1.3  Conical intersection
Conical intersections occur when two surfaces cross.  At the point of intersection the
two surfaces are degenerate, and it is at this point that a molecule can cross from one electronic
state to another.  Until recently conical intersections were thought to be very rare. However over
the last 10 years, it has been established that conical intersections are ubiquitous.
6,7
  In fact, many
photochemical reactions have been shown to involve conical intersections.
7
  A conical
intersection is called ?conical? because in a reduced space called the ?branching space? the
equations for the two surfaces look like the geometric equations for a cone.  The branching space
6
is just two special normal modes from the total of 3N-6 (3N-5) allowed to a non-linear (linear)
molecule.  The branching space modes are special in that they break the degeneracy of the two
intersecting surfaces, while in all other modes this degeneracy remains.  Near a conical
intersection we say that the two surfaces couple or mix and at a conical intersection the
geometric change leads to a sign change of the adiabatic electronic wavefunction.
8
  Although we
can draw nice smooth lines, it is implicit that more complicated things are happening.  This
coupling of states about a conical intersection is highly quantum mechanical.  The coupling of
electronic surfaces at a conical intersection is facilitated by the interaction of the nuclei and
electrons.  This system is said to be non-adiabatic, and the breakdown of Born-Oppenheimer
approximation at the conical intersection makes describing conical intersections very difficult.
A Jahn-Teller (JT) effect is a special case of conical intersection.  The Jahn-Teller theorem
9
 states
that ?the nuclear configuration of non-linear polyatomic system in a degenerate electronic state is
unstable with respect to nuclear displacements that lower the symmetry and remove the
degeneracy?.  In other words, there is always at least one non-totally symmetric
Figure 1. (a) One-dimensional potential energy curves showing linear Jahn-Teller distortion.
(b) Renner-Teller (Type A) potential energy surface curves.  Both are adapted form
reference 6(b).
E
(a) (b)
E
Q
x
Q
x
7
normal coordinate for which the splitting results in two or more separate potential minima for
non-zero values of the normal coordinate.  It can be seen that for Q = 0 the two potential curves
cross at a non-zero angle as illustrated in Figure 1 (a).  This phenomenon is well known in
transition metal chemistry where an octahedral structure for an ion containing, for example, nine
d-electrons would have the electronically degenerate configuration te
gg2
63
.  Because of the Jahn-
Teller effect there will be a structure of lower symmetry which can be obtained by distorting the
regular octahedral structure along one of the normal coordinates.  When a molecule has a pseudo-
degenerate electronic state, provided only that the difference in their energies is lower than the
vibronic stabilization energy, a similar effect, called pseudo-Jahn-Teller effect, occurs.  The
pseudo-Jahn-Teller effect (PJT)
10
 is the distortion of a high symmetry non-degenerate species to a
lower symmetry geometry along a single non-totally symmetric vibrational coordinate.  An
energy stabilization occurs due to a mixing of the ground and excited states along this vibrational
coordinate and the excited state energy increases.  Geometries subject to the pseudo-Jahn-Teller
distortion are saddle points on the adiabatic potential energy surface.
A linear molecule with a degenerate electronic state is subject to a distinct distortion
termed the Renner-Teller effect.
11
  The degeneracy of such electronic states is two-fold, but along
the bending modes the degeneracy of electronic states is removed and the potential curve splits
into two curves as shown in Figure 1 (b).  However, in a Renner-Teller active molecule the
degeneracy of electronic states is not lifted to first order in nuclear displacements, and there is no
conical intersection.  Rather, there is a ?glancing? or ?touching? of the two surfaces.  Herzberg
suggested that Renner-Teller geometries should be referred to as ?glancing intersections?.
6(b),11(b)
Although a Renner-Teller geometry is not a conical intersection, it provides useful information
about the frequency analysis of the intersection space at a conical intersection.  Renner-Teller
species are stationary points so that they can be optimized and characterized using standard
analytical derivative techniques.  Five distinct types of Renner-Teller potential energy surfaces
8
classified by Schaefer
12
 are given below.
(A) The total energies of both electronic components of a degenerate state increase as the
molecule is bent, and the harmonic bending frequencies (no imaginary frequencies) for the
two states are different.
(B) Same as A except that the two bending frequencies are identical.  Thus larger displacement
from linearity is required to distinguish two curves than type A.
(C) One potential curve is attractive and the other is repulsive with respect to the bending
coordinate (one imaginary frequency).
(D) Both curves are attractive (2 imaginary frequencies), but there are two distinct harmonic
bending frequencies.
(E) Same as type D, but the two harmonic bending frequencies are identical.
1.4  Molecular Orbital (MO) Theory
Molecular orbital theory
13
 is another approximation in quantum mechanics which is
based on an independent-particle model for the molecular electronic wavefunction.  A form of
wavefunction can be chosen which would be appropriate if we could ignore the interelectronic
repulsion.  If this were the case then the electronic Schr?dinger equation for n electrons would be
separable into a set of n one-electron Schr?dinger equations which could be solved to obtain a set
of one electron functions which is often called spin orbitals ?
i
r(), where i=1,2,,?,n.
  
?(,) () () ()Rr r r r
nn
= ?? ?
11 2 2
L                                                                                                   (10)
Each spin orbital can be written as the product of a spatial function ?
ii
r(), which depends on the
coordinates r
i
 of electron i, and a spin function ? or ?, depending on whether the spin is up or
down.  This product is called a Hartree product.  Each spatial function can hold two electrons:
one with ?-spin and one with ?-spin.  Assuming a closed-shell system where all spatial functions
are doubly occupied, we can rewrite the electronic wavefunction ?(,)Rr  as
9
  
?(,) () () () ( ) ()
//
Rr r r r r r
nn nn
=
?
????? ?? ?? ?
11 1 2 2 3 2 1 2
L                                                        (11)
However, it is necessary to take into account the indistinguishability of the electrons by
recognizing that we can permute the electron labels among the orbitals.  At the same time we
have to ensure that the wave function satisfies the Pauli principle by being antisymmetric with
respect to the interchange of two electrons by taking the appropriate linear combination of all
permutations.  To satisfy both requirements, the electronic wavefunction (9) can be written in a
determinantal form called a Slater determinant.
  
?(,)
!
() () ( )
() () ()
() () ()
/
/
/
Rr
n
rr r
rr r
rr r
nn
n
nn nn
=
1
11 11 2
12 12 22
11 2
???? ? ?
???? ? ?
???? ? ?
L
L
MMMM
L
                                                                  (12)
An interchange of two electrons is equivalent to interchanging the labels for the electronic
coordinates r
i
 with r
j
 resulting in the swapping the rows corresponding to r
i
 and r
j
.  This results in
a change of sign, as required by the Pauli principle.  The Slater determinant is sometimes
represented by more compact notation
  
?=???????? ? ?? ?
112 2 2 2
L
nn//
.                                                                                        (13)
Spin orbitals spread throughout the molecule, and their exact form is determined by the
variational principle, which states that any approximate wave function has an energy above or
equal to the exact energy.  The variational theorem allows us to calculate an upper limit for the
system?s ground state energy.  Consequently, the better the wavefunction, the lower the energy
and the best wavefunction is obtained when the energy is lowest.
1.5  Hartree-Fock (HF) method
The Hartree-Fock approximation
4
 is equivalent to the MO approximation in quantum
chemistry.  It is based on a simple approximation of the true many-electron wave function which
is given by a single Slater determinant of spin orbitals.  In the HF model, the electronic
10
Hamiltonian operator is replaced with an effective one-electron operator called the Fock operator.
The HF molecular orbitals are eigenfunctions of the Fock operator, the eigenvalues being the
orbital energies.  The HF model takes into account electronic interactions only as an average
effect of repulsion (central field approximation) but not the explicit electron-electron interaction.
The HF model is the simplest method to use for chemical applications.  Although the HF method
is insufficient for accurate modeling due to the incomplete description of electron correlation, it
plays a central role in quantum chemistry.  The HF method provides a starting point for more
accurate approximations which include electron correlations.
For molecular calculations, numerical integration of the HF equations proves impossible,
and Roothaan introduced a linear combination of atomic orbital (LCAO) version of the self
consistent field (SCF) theory.
14
  The Roothaan-Hall equations are the Fock equations in the
atomic orbital basis, and all the equations may be collected in a matrix notation.
13
  The Roothaan-
Hall equations must be solved iteratively since the Fock matrix depends on its own solutions.
First, all one- and two-electron integrals are calculated and followed by generation of a suitable
starting guess for the MO coefficients.  Next, the initial density matrix is formed and then the
formations of the Fock matrix, the core intergrals and the density matrix times two-electron
integrals follow.  In the next step, the Fock matrix is diagonalized where the eigenvectors contain
the new MO coefficients.  Finally the new density matrix is formed and if it is sufficiently close
to the previous density matrix, then the self-consistency is achieved.  If not, a new Fock matrix is
formed and the same procedure is repeated until the density matrix converges.
The main deficiency of the HF model is its incomplete description of the correlation
among electrons.  Due to the neglect of electron correlation, even with a complete basis set, the
HF method cannot give an exact solution.  This is called the HF limit.  In order to include
electron correlation into HF calculations, post-HF methods for correction of electron correlations
are introduced.  Those methods will be discussed briefly in the electron correlation methods part.
11
1.6  Basis sets
A basis set
13,15
 is the set of mathematical functions from which the wave function is
constructed to describe the shape of the orbitals in an atom.  In the practical quantum mechanical
calculations, the molecular orbitals are expressed as linear combinations of a predefined set of
one-electron wave functions known as basis functions.
An individual molecular orbital can be written as:
  
??
?
?
?ii
N
c=
=
?
1
                                                                                                                              (14)
where the coefficients c
?i
 are known as the molecular orbital expansion coefficients.  These
coefficients provide the orbital description with some flexibility, and can be determined so that
the electronic energy calculated from the molecular orbital ?
i
 is minimized and is as close as
possible to the energy corresponding to the exact solution of the Schr?dinger equation by the
variational principle.  There are two types of basis functions commonly used in quantum
mechanics calculations: Slater-type orbitals (STO) and Gaussian-type orbitals (GTO).
13,15
  The
STOs have the functional form:
  
??? ??
?
?
,,, ,
(, , ) (, )
nlm lm
n r
rNYre=
? ?1
                                                                                        (15)
where N is a normalization constant and Y
l,m
 are the typical spherical harmonic functions.  The
parameter ? is the orbital exponent determining the size of the orbitals.  STOs provide reasonable
representations of atomic orbitals with standard ? values suggested by Slater.
16
  A major
deficiency of STOs is that they do not have radial nodes and hence are not mutually orthogonal.
Also, they are not appropriate for numerical computations of multi-centered integrals while
solving the Schr?dinger equation due to the high cost in computer time, and their practical use in
quantum-mechanical calculations is now limited.  Most quantum mechanics programs use GTOs
as basis functions, and the general form is:
12
???
?
?
,,,
(, , )
nlm
lmn r
rNxyze=
?
2
                                                                                                  (16)
where the sum of l, m, and n determines the type of orbital.  The dependence of r
2
 in the
exponential makes GTOs inferior to STOs in two aspects:  First, a GTO has zero slope at the
nucleus while a STO has a cusp.  The result is that GTOs have difficulty in describing the proper
behavior near the nucleus.  Secondly, GTOs fall off too rapidly far from the nucleus compared to
STOs, and the whole wave function is consequently represented poorly, which indicates that
more GTOs are required for achieving a certain accuracy compared to STOs.  Nevertheless,
GTOs have the important advantage over STOs that a GTO integral evaluation takes much less
computer time.  Therefore, GTOs are preferred and are generally used in computational
calculations.
Most semiempirical methods use a predefined basis set from STOs.  In ab initio and
density functional theory calculations, basis sets are used in the form of linear combinations of
GTOs.  Although it is possible to create a basis set from basis functions in an arbitrary way, most
calculations are done using existing basis sets which are already defined.  Choosing a basis set
significantly influences the accuracy of the calculation as much as the level of the theoretical
method.  The choice of a basis set also has a large effect on the computing cost.  Generally, the
cost of molecular calculations increases greatly with the number of functions in the basis set, N
4
for the integral computation and N
4
-N
7
 for the solution of the Schr?dinger equation where N is
the number of basis functions.
17
  Use of disk storage for HF calculations scales as N
4
 and the
amount of memory required scales as N
2
 for most program algorithms.
17
  There are a lot of well-
known basis sets available in the literature or built into computational programs.  These basis sets
are identified by one of a number of notation schemes.  Some of the commonly available basis
sets are introduced and described in the following section.
When a basis function is defined as a linear combination of Gaussians, it is referred as a
contracted basis function, and the individual Gaussians are called primitive Gaussians.  Thus, in a
13
basis set of contracted GTOs, each basis function is defined by the contraction coefficients and
exponents of each primitive.  The degree of contraction refers to the total number of primitives
used to make all of the contracted functions.  A contracted basis set is denoted with (primitives
functions)/[contracted functions].  For example, (6s3p/3s)/[2s1p/1s] denote that 3 each of 1s
primitives, 2s primitives and 2p primitives giving a total of 6s and 3p primitives are contracted to
create single 1s, 2s, and 2p sets so that the contracted functions are 2s1p for first row atoms while
for hydrogen 3s primitives are contracted to create a 1s function.
The smallest number of basis functions is called a minimal (or minimum) basis set,
13,15
which consists of one atomic basis function for each inner shell and valence shell atomic orbital
(AO) of each atom.  The most popular minimal basis set is called STO-3G which would be
(6s3p/3s)/[2s1p/1s] in contracted basis set notation.  Minimal basis sets are used for very large
molecules in order to obtain qualitative results.  Several methods exist so that the basis set can be
made larger than a minimal basis set in order to get better descriptions of energies and
geometries.  The Dunning-Huzinaga basis set is one popular basis set.  The double-zeta (DZ)
basis sets
13,15,18
 describe all molecular orbitals by using two sets of basis functions with different
orbital exponents (?) for each core and valence orbital.  A triple-zeta (TZ) basis set replaces each
basis function of a minimal basis set by three sets of basis functions, each with a different orbital
exponent.
Pople and co-workers
13,15,18
 designed split-valence (SV) basis sets which use two or more
basis functions for each valence shell AO and but only one basis function for each core shell AO.
Split-valence sets are called valence double-zeta (VDZ) and valence triple-zeta (VTZ) according
to the number of basis functions used for each valence AO.  For instance, 3-21G and 6-31G basis
sets have two sets of basis function for each valence AO, and a 6-311G basis set uses three sets of
basis functions for each valence AO.  In Pople-style basis sets, each basis function is expressed
as a linear combination of primitive Gaussians rather than represented by a single primitive
14
Gaussian.  For the 3-21G basis set, each core AO is represented by a basis function which is a
linear combination of three primitive Gaussians , while each valence AO use two sets of basis
functions, one of which is a contraction of two GTOs and the other of which is a single GTO that
is (6s3p/3s)/[3s2p/2s] for first row elements.  The 6-31G basis set uses six GTOs in each core
AO?s basis function and represent each valence AO by one basis function with three GTOs and
one basis function with one GTO, which is (10s4p/4s)/[3s2p/2s] for first row elements.  The
number of basis functions for 3-21G and 6-31G basis sets are the same, but the 6-31G basis set
has more GTOs than 3-21G.  Therefore, the 6-31G basis set describes molecular properties better
than the 3-21G basis set.
Split-valence basis sets allow orbitals to change size in the radial part, but not to change
the shape of orbitals.  Molecular orbitals are often distorted in shape and have their centers of
charge shifted depending on molecular formation.  By adding polarization functions such as d-
and f-type functions to SV basis sets, the shape of AOs can vary, thereby shifting charge density
away from the nuclei and into the bonding regions in the molecule.
13,15
  For example, the 6-
31G(d) basis set is a VDZ polarized basis set which adds six d-type functions to the 6-31G basis
set on each of the atoms other than hydrogen.  The 6-31G(d,p) basis set adds three p-type
functions to the 6-31G(d) basis set on each hydrogen.  The 6-31G(d) and 6-31G(d,p) basis sets
are often denoted as 6-31G* and 6-31G**, respectively.  These polarized basis sets are generally
used because they often result in more accurate computed geometries and vibrational
frequencies.
17,18
Anions, molecules having electron lone pairs, and hydrogen-bonded complexes have
significant electron density at large distances from the nuclei.  To improve the accuracy of
describing these problems, diffuse functions, s- and p-type functions with small orbital
exponents, can be added.
13,15
  The 6-31+G* basis set is formed from the 6-31G* basis set by
adding four diffuse functions (s, p
x
, p
y
, p
z
) on each non-hydrogen atom.  The 6-31++G* set also
15
includes one diffuse s-type function on each hydrogen atom.  However, diffuse functions on
hydrogen atoms do not usually increase the accuracy of a calculation.  Nowadays, larger basis
sets including multiple polarization and diffuse functions are practical for many systems due to
the increased speed of computers and program algorithms.  The largest Pople-style basis set is
6-311++G(3df,3pd) which is a triple split-valence with additional diffuse s- and p-type functions
and three sets of d-type functions and one set of f-type functions on heavy atoms and one diffuse
s-type function and three sets of p-type functions and one set of d-type functions on hydrogen
atoms.  Such basis sets are useful for describing interactions between electrons using methods
that include electron correlation.
The Pople and Dunning-Huzinaga basis sets are of the segmented-contraction type since
the primitives are partitioned into disjointed or almost disjointed sets.
19
  Modern contracted basis
sets aimed at producing very accurate wave functions often employ a general contraction scheme.
The atomic natural orbital (ANO) and correlation-consistent (cc) basis sets are of the general
contraction type.  ANO basis functions are obtained from the atomic natural orbitals obtained
from valence CISD calculations on the free atoms.  The natural orbitals are obtained as the
eigenvectors of the first-order density matrix and their associated eigenvalues are referred to as
the orbital occupation numbers.  The ANO contraction selects the important combinations of the
primitive GTOs from the magnitude of the occupation numbers.  A large primitive basis may
generate several different contracted basis sets by gradually lowering the selection threshold for
the occupation number.  The nice feature of the ANO contraction is that it automatically
generates balanced basis sets.  Furthermore, in such a sequence the smaller ANO basis sets are
true subsets of the larger, since the same primitive set of functions is used.  The primary
disadvantage of the ANO basis set is that there is a very large number of primitive GTOs.
Dunning?s correlation consistent (cc) basis set is smaller than the ANO basis set but yields results
comparable to those of the ANO basis sets.
18,19
  The name correlation consistent refers to the fact
16
that the basis sets are designed so that functions which contribute similar amounts of correlation
energy are included at the same stage, independently of the function type.  Several different sizes
of cc basis sets are available.  These are known by their acronyms: cc-pVDZ, cc-pVTZ, cc-
pVQZ, cc-pV5Z and cc-pV6Z (correlation-consistent polarized Valence Double/Triple/
Quadruple/Quintuple/Sextuple Zeta).
Basis set requirements for atoms beyond the third row of the periodic table are different
from the elements with lower atomic number.  For heavier metals, relativistic effects become
important and core electrons must be treated differently from valence electrons.  The effective
core potential (ECP)
20,21
 can be used to handle the core electrons of these heavier atoms
effectively.  The ECPs and associated basis sets of Hay-Wadt,
22
 Stevens and co-workers,
23
 and
Stuttgart-Dresden ECP
24
 are widely used and already implemented in many computational
chemistry packages.  The main advantage of using ECPs plus valence basis sets rather than all-
electron basis sets is that the former consider relativistic effects effectively and require less
computer time.
Commonly used basis sets for quantum mechanics program and literature references for
them are available on the web site of the EMSL Gaussian Basis Set Order Form
(http://www.emsl.pnl.gov/forms/basisform.html) at the Environmental Molecular Sciences
laboratory of the Pacific Northwest laboratory.
1.7  Electron correlation methods
Since the HF method does not include a full consideration of electron correlation, many
theoretical methods have been developed in order to consider electron correlation properly.
There are two kinds of electron correlations.  One is dynamic correlation which is mainly caused
by the instantaneous repulsion of the electrons.  In the HF scheme, electrons often get too close
to each other, because the electrostatic interaction is treated in only an average manner.  As a
17
consequence, the electron-electron repulsion term is too large resulting in higher energy.  It is
called dynamic electron correlation because it is related to the actual movements of the
individual electron and is known to be a short-range effect.  This dynamic correlation can be
treated by perturbation theory,
13,15
 coupled cluster (CC) theory,
13,15,25
 and density functional
theory (DFT).
26
  The other is non-dynamical or static correlation. It is related to the fact that in
certain circumstances a single Slater determinant is not a good approximation to the true ground
state, because there are other Slater determinants with comparable energies.  Two computational
methods are available to treat non-dynamical correlation.  Using a single Slater determinant, non-
dynamic correlation can be treated by increasing the order of electronic excitations incorporated
in dynamic correlation methods such as coupled cluster (CC) theory and configuration
interaction (CI).
13,15
  Non-dynamic correlation can be also corrected by the multi-configuration
self-consistent field (MCSCF) method
27
 via multi-configuration determinants.  Generally,
electron correlation methods are also referred as post-HF methods since the correlation
correction terms are added to the basic HF methods in them.
M?ller-Plesset (MP) perturbation theory is one of the most economical electron
correlation methods.
15
  MP methods treat the Hamiltonian operator as:
  
HH V=+
0
?                                                                                                                             (17)
where H
0
 is the HF Hamiltonian and ?V is a perturbation applied to H
0
.  The Rayleigh-
Schr?dinger perturbation theory
5
 provides a description of the perturbed system as:
  
HHV???=+ =(
0
? )E.                                                                                                      (18)
Here, wave function and energy obtained from eq. (18) can be expanded in powers of ?.
  
????
?
??=+ + +
() () ()0 1 1 2 2
L                                                                                               (19)
  
EEEE
?
??=+ + +
() () ()0 1 1 2 2
L                                                                                                  (20)
Practical MP methods may be formulated by truncating the series in eq. (19) and (20) to various
orders.  MP2 (truncation after 2nd-order), MP3, and MP4 are well known.  The MP energy
18
correct to first-order (MP1) is the HF energy.  MP2, MP3, and MP4 provide size extensive
energy correction systematically.  The simplest approximation to the electron correlation is the
MP2 method.  In practice, MP2 is the most popular among truncated MP methods due to the
reasonable computational cost with acceptable results.
17
  Higher orders of MP methods such as
MP3 and MP4 are available in case MP2 is inadequate.  However, MP4 is more often used
compared to MP3 because MP3 calculations are known to provide little improvement over MP2
results.
17,18
  
If a single Slater determinant contains substantial multi-reference character (i.e. biradical
species), MP methods often produce absurd results.  In order to correct this problem, the
multi-configuration self-consistent field (MCSCF) method
27
 can be applied.  MCSCF
calculations employ the molecular wave function as linear combinations of single Slater
determinants which is called configuration state function (CSF) and not only vary the expansion
coefficients but also optimize the forms of the molecular orbitals.  The major problem with
MCSCF methods is selecting the necessary configurations.  One of the most popular approaches
is the complete active space self-consistent field (CASSCF)
27
 method which is also called full
optimized reaction space (FORS).  The selection of configurations is done by partitioning the
MOs into active and inactive space.  The active MOs will typically be some of the highest
occupied and some of the lowest unoccupied MOs.  Within the active MOs a full CI is
performed.  A common notation is CASSCF(n,m), indicating that n electrons are distributed over
m orbitals.  CASSCF calculations provide a reasonable treatment of non-dynamic electron
correlation and some of dynamic correlation.  The more configurations are included, the more
dynamic correlations are included.  In general the number of singlet CSFs formed from the (n,m)
active space is determined by eq. (21).
28
N
mm
nn
m
n
m
n
=
+
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
?
?
?
?
?
?+
?
?
?
?
?
?
!( )!
!! ! !
1
22
1
22
1
                                                                                    (21)
19
Therefore a high computational cost is required to correct dynamic correlation fully by CASSCF
methods.  For example, in the case of (6,6) active space, there are only 175 CSFs.  If we consider
twice as many electrons and orbitals, (12,12) active space, then total number of CSFs would be
226512.  Indeed, CASSCF calculations having more than a million CSFs are extraordinarily
demanding of computing resources and are rarely performed.  Hence, application of CASPT2
method is a popular alternative, where the dynamic correlation is considered by MP2 method on
the CASSCF MOs.
The full configuration interaction (CI) is the most complete treatment of the molecular
system possible within the finite set of wave functions.
18
  A CI wave function is a multiple Slater
determinant.  Practical CI methods are limited by truncating the CI expansion at some level of
substitution because full CI is very expensive in terms of computer resources.  CI calculations are
classified by the number of excitations to make each determinant.  For example, the CI single
excitation (CIS) method adds single excitations to the single Slater determinant.  CIS calculations
provide a good estimate of the excited states and their properties.  A disadvantage of these limited
CI methods is in that they are not size-consistent.  The Quadratic CI (QCI) method was designed
to correct this problem.  The Quadratic CISD (QCISD) method
15,18
 is the most commonly used
among CI methods.  It is derived from CISD by including enough higher-order terms to make it
size-consistent.  Triple excitations are often included perturbatively into QCISD in order to
obtain greater accuracy, which is called QCISD(T),
15
 one of the most popular methods for
high-level treatment of electron correlation.
Coupled cluster (CC) methods
13,15,25
 treat electron correlation beyond MP4 with greater
accuracy.  CC methods include the effects of single and double excitation, effectively adding
higher order excitation than MP4.  CC calculations are similar to CI methods in that the CC
wavefunction is expressed as an exponential of excitations operating on a single Slater
determinant, which solves the size-consistency problem of CI methods.  The cluster operator is a
20
sum of excitations of singles and doubles, etc.  These excitations are commonly truncated at
double excitations to give Coupled Cluster Singles and Doubles (CCSD).
15
  The CCSD(T)
method includes the same perturbative correction from triples as in QCISD(T), and QCISD(T)
and CCSD(T) often gives similar quality in terms of accuracy of energies and geometries.
13,17
CC theory is also developed for treating excited states in a method called the equation-of-motion
(EOM) CCSD and gives very good estimates of vertical excitation energies.
13,18
Density functional theory (DFT) is based on the theorem by Hohenberg and Kohn
26
which states that the ground state molecular properties can be calculated from ground state
electron probability density ?.  The ground state energy E is a functional of ? and the total energy
can be expressed as:
  
E[ ]?? ?? ?=+ ++TV JE
s ext xc
[] [] [] [].                                                                                    (22)
Here T
s
[]?  is the kinetic energy of a set of n independent electrons, moving in an effective one-
electron potential which leads to the density ?(r), V
ext
[]?  is the potential energy in the field of
the nuclei plus any external perturbation, and J[]?  is the total Coulomb interaction.  E
xc
[]?  is
usually described as the exchange-correlation energy.  The one-electron Kohn-Sham operator is
the same as the Fock operator in the HF equation except that the Kohn-Sham operator has an
additional exchange-correlation term ( E
xc
).  This term represents the key problem in DFT, since
the exact expression of the E
xc
 is unknown, and approximations must be used.  Various
approximate functionals for E
xc
 are used in DFT calculations.  However, there is no systematic
way to improve electron correlation.
The simplest approach is the local spin density approximation (LDA), in which the
function for the uniform electron gas density ?
?
 is integrated over the whole space:
Erdr
xc
LDA
xc
unif
=
??
???
?
?
?
()()
/43
                                                                                              (23)
where ??
?xc
unif
() is the exchange-correlation energy distribution per unit volume, which depends
21
on the density only at the point where is evaluated.  While this approximation is responsible for
the early success of DFT, it often provides unsatisfactory results in chemical applications.
Several corrections for the non-uniformity of atomic and molecular densities have been
proposed.  In particular, those based on the gradient of the electron density (??
?
) have been
embraced due to their simplicity.  These corrections, collectively referred to as generalized
gradient approximation (GGA), are usually expressed in terms of an enhancement factor over the
exchange energy of the uniform electron gas, so that the total exchange energy takes the form:
EE F rdr
xc
GGA
xc
LDA
xc
GGA
=? ?
??
[, ]()
/
???
?
?
??
43
.                                                                    (24)
While ??
?xc
unif
() in equation (23) is uniquely defined, there is no unique function for F
xc
GGA
, and
a number of GGA exchange-correlation functionals have been proposed.  Roughly speaking, we
can consider two main classes: the first one is the functionals containing parameters, which are
fitted to some sets of experimental data, while the second class includes functionals which fulfill
a number of theoretical physical constraints.  Although most existing functionals combine both
approaches, recently attention has shifted to the first aspect even at the expense of a fitting
process to introduce a huge number of parameters and of overemphasizing the thermochemistry
of organic molecules.  In contrast with this tendency, functionals belonging to the second class
are particularly attractive to theoretical chemists, due to their strong theoretical background.  In
the line of this trend, the non-empirical GGA functional of Perdew, Burke and Ernzerhof
(PBE),
29,30
 can be considered as the most promising non-empirical functional.  In particular, it
was constructed to retain a number of physical features in the correlation and in the exchange
parts.
The difference between DFT methods lies in the choice of the functional for the
exchange-correlation term ( E
xc
).
26,31
  In practice, the functional for E
xc
 can be expressed as the
sum of an exchange functional ( E
x
) and a correlation functional ( E
c
) which only depend on the
22
electron density.  These gradient-corrected functionals give better results in terms of geometries
and relative energies than local density functionals.  Some commonly used gradient-corrected
exchange functionals are the PW86, B88, and PW91 functionals,
28,31 
and gradient-corrected
correlation functionals are the LYP and P86 functionals.  PBE, a relatively new GGA functional,
is gaining popularity.  Any exchange functional can be combined together with any correlation
functional.  For example, the PW91LYP functional is defined as the PW91 exchange functional
and the LYP correlation functional.
A further improvement can be achieved by hybridizing HF and DFT methods,
 31
 in which
a HF exchange term and DFT exchange functionals are mixed in conjunction with a correlation
functional.  One of the most successful approaches is Becke?s three-parameter model.  This
model rests on a linear combination of HF exchange with density functional exchange-
correlation contributions, equation (25).
EaE aEaEEaE
xc
hybrid
xxc
LDA
xx
HF
xx
GGA
c
LDA
cc
GGA
=+?+ ++
001
1() ??.                                         (25)
Three semiempirical parameters, a
x0
, a
x1
and a
c
, have been determined by fitting the heats of
formations of a standard set of molecules.  The most popular implementation is the B3LYP
method, which uses the Becke 88 exchange functional together with the Lee-Yang-Parr
correlation functional.
EaE aEaEEaE
xc
B LYP
xxc
LDA
xx
HF
xx
B
c
VWN
cc
LYP3
001
1=+?+++() ??                                            (26)
Another hybrid functional gaining popularity is PBE1PBE, which can be expressed as equation
(27).
EE E E
xc xc
GGA
x
HF
x
GGA
=+ ?
1
4
()?                                                                                                (27)
The PBE1PBE hybrid functional gives excellent nonbonding interaction energies and equilibrium
distances.  In addition, it also gives accurate results for a large number of molecular properties,
including EPR and NMR spectroscopic parameters, polarizabilities and vertical excitation
23
energies.
28,32
  The quest for a better pure GGA functional has led to a new generation of DFT
methods, called meta-GGA.  The ultimate goal is to construct a totally non-local density
functional, however the process is difficult.  A more practical way is to construct a functional
containing additional semi-local information.  This can be done by including the kinetic energy
density of the occupied Kohn-Sham (KS) orbitals:
??
??
() ()rr
i
i
occup
=?
?
1
2
2
                                                                                                           (28)
so that
EE F rdr
xc
m GGA
xc
LDA
xc
GGA?
=? ?
??
[, ,]()
/
????
?
?
??
43
.                                                             (29)
These new functionals are called meta-GGA (mGGA).
 33
Time-dependent density functional theory (TDDFT)
34
 has recently been introduced to
calculate excitation energies and oscillator strengths.  TDDFT is derived from the time-dependent
Hartree-Fock (TDHF) equation; it includes electron correlation which is not present in TDHF.
TDDFT is roughly comparable to CI single excitation (CIS).  Furthermore, excitation energies
computed by TDDFT are considerably improved as comparable to CIS.
DFT methods employ KS orbitals which allow the molecular ground state electron
density ? to be calculated.  The Kohn-Sham orbitals resemble HF MOs, and the KS orbitals can
be used in qualitative discussions of molecular properties and reactivities.  DFT has a
computational cost similar to the HF model, but is faster and more efficient than conventional
electron correlation methods such as MP2.  The advantage of DFT methods is that they include
electron correlation and take almost the same computer resources as HF calculations which
neglect electron correlation.  It is known that B3LYP results are at least equal to MP2 in terms of
geometries and relative energetics and often better.  However, DFT methods often fail to
reproduce excited state properties and non-bonded interactions such as hydrogen bonding and
London dispersion forces.
28,31
  However better exchange correlation functionals have been
24
constructed recently and expected to lead to more applications and better results.
1.8  Compound models
A calculation at a very accurate level of theory requires a high computational cost.  In an
effort to achieve high accuracy at less computational cost, several new models have been
suggested.  A series of calculations are run and their results are systematically combined to
predict a more accurate energy value for the molecule.  Even though multiple calculations are
run, their total computational cost is still significantly less than that of the single, high-level
calculation.
Gaussian theory was introduced by Pople and co-workers
35
 in order to compute
thermodynamic properties such as heats of formation and atomization energies with chemical
accuracy, meaning an error of less than 1-2 kcal/mol.  Gaussian theory is an empirically defined
energy correction scheme using several moderate size-correlated calculations to extrapolate to
high accuracy.  Three models, G1, G2 and G3, have been developed and the G3 model
32
 is the
most improved method.  The G3 calculation scheme will be briefly discussed.
(1) HF/6-31G(d) geometry optimization followed by frequency calculation to obtain zero-point
vibration energy which is scaled by 0.8929 to give a zero-point energy correction E(ZPE).
(2) MP2(full)/6-31G(d) geometry optimization.
(3) MP4/6-31G(d) single-point calculation on the MP2(full)/6-31G(d) geometry designated as
MP4/6-31G(d)//MP2(full)/6-31G(d).  This energy will be modified by the following series
of corrections.
i. Correction for diffuse functions:
?E(+) = E[MP4/6-31+G(d)]-E[MP4/6-31G(d)]                                                                  (22)
ii. Correction for polarization functions:
?E(2df,p) = E[MP4/6-31G(2df,p)]-E[MP4/6-31G(d)]                                                        (23)
25
iii. Correction for quadratic CI:
?E(QCI) = E[QCID(T)/6-31G(d)]-E[MP4/6-31G(d)]                                                        (24)
iv. Correction for larger basis set effects:
?E(G3large) = E[MP2(full)/G3large]-E[MP2/6-31G(2df,p)]
                        - E[MP2/6-31+G(d)] + E[MP2/6-31G(d)]                                                   (25)
where G3large basis set is 6-311+G with (2df,2p) for first row elements and hydrogen and
(3d2f) for second row elements.
(4) The MP4/6-31G(d) energy and the four corrections from the steps above are combined
along with a spin-orbit correction, ?E(SO), which is taken from experiments if available and
accurate calculations otherwise for atomic species only.
?E(combined) = E[MP4]/6-31G(d)] + ?E(+) + ?E(2df,p) +?E(QCI)
     + ?E(G3large) + ?E(SO)                                                                           (26)
(5) High level correction E(HLC) is added
E
e
(G3) = E(combined) + E(HLC)                                                                                        (27)
E(HLC ) is an empirical correction to take into account remaining deficiencies and is
defined by the number of ? and ? valence electrons.
(6) Total energy at 0K, E
0
(G3) is obtained by adding E(ZPE).
E
0
(G3) = E
e
(G3) + E(ZPE).                                                                                                 (28)
In order to test the accuracy of the G3 method, a reference set which is referred to as the G2/97
set was used.  It includes 148 enthalpies of formation, 88 ionization potentials, 58 electron
affinities, and 8 proton affinities.  The overall average absolute deviation of the G3 method with
experiment for this reference set is 1.02 kcal/mol.
36
There are some other compound methods which achieve even better accuracy.  The
complete basis set (CBS) method is aimed at extrapolating finite basis set calculations at various
levels of theory to obtain estimates of the CBS limit.
37
  Wiezmann-1 (W1) and Wiezmann-2 (W2)
26
theories are developed to reach a better accuracy, 0.2-0.3kcal/mol.
38
  This is very useful only
when the molecule under investigation is very small (up to 3-4 heavy atoms) and for benchmark
calculations.
27
1.9  References
1. Born, M; Oppenheimer, J. R. Ann. Phys. (Leipzig) 1927, 84, 457.
2. Hirst, D. M. Potential Energy Surfaces: molecular structure and reaction dynamics,
Talyer & Fransis: London, 1985.
3. (a) Lawley, K. P. Ed. Adv. Chem. Phys.: Potential Energy Surface; Wiley: New York,
1980. (b) Faraday Discussions of the Chemical Society, Chem. Soc.:London, 1977, 62 .
4. Hund, F. Z. Phys. 1927, 40, 742.
5. Neumann, J. v.; Wigner, E. P. Z. Phys. 1929, 30. 467.
6. For more comprehensive and theoretical discussion about conical intesections, please
refer to (a) Domcke, W.; Yarkony, D. R.; K?ppel, H. Ed. Adv. Ser. Phys. Chem.: Conical
Intersections: Electronic Stucture, Dynamics & Spectroscopy; World Scientific: New
Jersey, 2004. (b) Paterson, M. J.; Bearpark, M. J.; Robb, M. A.; Blancafort, L.; Worth, G.
A. Phys. Chem. Chem. Phys. 2005, 7, 2100.
7. Haas, Y.; Zilberg, S. ?Conical Intersections in Molecular Photochemistry: The Phase-
Change Approach? In Prigogine, I.; Rice, S. A. Ed. Adv. Chem. Phys.: The Role of
Degenerate States in Chemisry; Wiley: New York, 2002.
8. Longuet-Higgins, H. C. Proc. Roy. Soc. 1975, A344, 147.
9. Jahn, H. A.; Teller, E. Proc. Roy. Soc. Lond. Ser. A, 1937, 161, 220.
10. Bersuker, I. B.; Polinger, V. Z. Vibronic Interactions in Molecules and Crystals, Springer
Verlag: Heidelberg, 1989.
11. (a) Renner, R. Z. Phys. 1934, 92, 172.  (b) Herzberg, G. Molecular Spectra and
Molecular Structure III. Electronic Spectra and Electronic Structure of Polyatomic
Molecules; Van Nostrand: New York, 1967.
12. Lee, T. J.; Fox, D. J.; Schaefer, H. F.; Pitzer, R. M. J. Chem. Phys. 1984, 81, 356.
13. (a) Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry: Introduction to Advanced
28
Electronic Structure Theory; McGraw-Hill:New York, 1989. (b) Levine, I. N. Quantum
Chemistry, Fifth Ed., Prentice-Hall, Inc.: New Jersey, 2000.
14. Roothaan, C. C. J. Rev. Mod. Phys. 1951, 23, 69.
15. Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital
Theory, Wiley and Sons: New York, 1986.
16. Turner, A. G. Methods in Molecular Orbital Theory, Prentice-Hall, Inc.: New Jersey,
1974.
17. Foresman, J. B.; Frisch, A. Exploring Chemistry with Electronic Structure Methods, 2nd
Ed., Gaussian Inc.: Pittsburgh, 1996.
18. Jensen, F. Introduction to Computational Chemistry, Wiley: New York, 1999.
19. Feller, D.; Davidson, E. R. In Reviews in Computational Chemistry, Lipkowitz, K. B.;
Boyd, D. B. Ed. VCH: New York, 1990. pp 1-43.
20. Frenking, G.; Antes, I.; B?hme, M.; Dapprich, S.; Ehlers, A. W.; Jonas, V.; Neuhaus, A.;
Otto, M.; Stegmann, R.; Veldkamp, A.; Vyboishchikov, S. F. In Reviews in
Computational Chemistry Vol. 8; Lipkowitz, K. B.; Boyd, D. B. Ed. VCH: New York,
1996, pp 63-144.
21. Cundari, T. R.; Benson, M. T.; Lutz, M. L.; Sommerer, S. O. In Reviews in
Computational Chemistry Vol. 8; Lipkowitz, K. B.; Boyd, D. B. Ed., VCH:  New York,
1996, pp 145-202.
22. Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270.
23. Stevens, W. J.; Basch, H.; Krauss, M. J. Chem. Phys. 1984, 81, 6026.
24. Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. J. Chem. Phys. 1987, 86, 866.
25. Bartlett, R. J. J. Phys. Chem. 1989, 93, 1697.
26. Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules, Oxford Univ.
Press: Oxford, 1989.
29
27. Lawley, K. P. Ed. Adv. Chem. Phys.: Ab Initio Methods in Quantum Chemistry-II, Wiley:
New York, 1987.
28. Cramer, C. J. Essentials of Computational Chemistry: Theories and Models, Wiley: New
York, 2004.
29. Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1997, 78, 1396.
30. Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865
31. Koch, W.; Holthausen, M. C. A Chemist?s Guide to Density Functional Theory, Wiley-
VCH: Weinheim, 2000.
32. Xu, Xin; Goddard, W. A. III, J. Chem. Phys. 2004, 121, 4068.
33. Tao, J.; Perdew, J. P.; Scuseria, G. E.; Staroverov, V. N. Phys. Rev. Lett. 2003, 91,
146401.
34. Gross, E. K. U.; Kohn, W. Adv. Quantum Chem. 1990, 21, 255.
35. Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem.
Phys. 1989, 90, 5622.
36. Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. J. Chem. Phys.
1998, 109, 7764.
37. (a) Petersson, G. A.; Tensfeldt, T. G.; Montgomery, J. A. Jr. J. Chem. Phys. 1991, 94,
6091. (b) Montgomery, J. A. Jr.; Ochterski, J. W.; Petersson, G. A. J. Chem. Phys. 1994,
101, 5900.
38. Marin, J. M. L.; Oliveira, G. de, J. Chem. Phys. 1999, 111, 1843.
30
CHAPTER 2
AN INVESTIGATION OF THE BCP POTENTIAL ENERGY SURFACE
2.1  Introduction
The physical properties of nano-materials are affected by the nature of the constituting
elements, their composition, and their crystalline structure.  Great attention has been paid to
group 13, 14 and 15 elements because they have the same number of valence electrons as
materials that are already developed and widely used in industry.  Furthermore, there has been a
good deal of interest in materials composed of carbon, nitrogen and boron since they are expected
to have useful properties as semiconductors, batteries, etc.
1-6
  In addition, BCN compounds are
known to possess tunable band gaps by changing the elemental composition and by adapting
different synthetic methods which lead to different crystalline structures.  Even though a number
of theoretical studies of BCN are available,
7-10
 to our knowledge no experimental or theoretical
study of the BCP molecule, which is isoelectronic to C
3
 and BCN, has been reported.  Because of
similarity of the electronic structure, BCP can be expected to possess similar physical properties
to BCN, which piqued our interest.
BCP can be formed through the reaction of a diatomic with an atom such as BC + P, B + CP
and C + BP.  While both diatomic molecules BC and CP have been observed, boron carbide is
best known both theoretically and experimentally.
11-20
  By using mass spectrometry Drowart and
co-workers determined that BC has a bond dissociation energy of 105?10 kcal/mol.
11-12
  Kuoba
and ?hrn
13
 established the ground state for BC as 
4
?
-
 with the major configuration
31
1?
2
2?
2
3?
2
4?
2
5?1?
2
.  Fernando and co-workers obtained various spectroscopic parameters
including the equilibrium bond length r
e
 = 1.491 ? by studying gas phase emission spectra of
BC.
14
  Recently, Tzeli and Mavridis reported MRCI calculations using a complete basis limit
extrapolation and argued that their value for D
e
 (102.2?0.1 kcal/mol) was more accurate than the
experimental value (108?7 kcal/mol).
20
  Another interesting boron compound is boron phosphide,
BP, which is made into semiconducting thin films by chemical vapor deposition.
21
  The electronic
structure and band gaps of BP polymers have been studied,
22-24
 but investigations of monomeric
BP are rare.  Interest in carbon phosphide has been sparked by the discovery of CP in the inner
layers of the carbon star envelope IRC+10216.
25
  In addition, a serious deviation between the
calculated heat of formation of CP and the experimental values in the NIST webbook has been
discovered.
26-28
  Now, it is accepted that the recommended value for ?H
f
 (0K) of CP is about 124
kcal/mol rather than 106 kcal/mol.
We report herein a comprehensive study on the singlet and triplet potential energy surfaces of
the hypothetical BCP molecule using DFT, CASSCF and CASPT2 methods.  Various
spectroscopic and thermodynamic parameters are also calculated at each level.  For the linear
triatomic species which have degenerate electronic states (
3
?), Renner-Teller (RT) effects were
examined by harmonic vibrational frequency analysis.  This work has been published in the
Journal of the Physical Chemistry A  in 2004.
29
2.2  Computational details
The Gaussian98 program
30
 was used for density functional UB3LYP
31
 calculations, the
GAMESS program
32
 for Complete Active Space SCF (CASSCF)
33
 calculations and the
MOLCAS 5.4
34
 for CAS calculations with dynamic electron correlation introduced at the MP2
level (CASPT2).
35
  All calculations were carried out on a cluster of linux computers.  Geometry
32
optimizations for minima and transition states were carried out at the UB3LYP and full-valence
CASSCF(12,12) levels with the 6-311+G(2df) basis set.
36
  Further stability tests and wave
function optimizations were performed to find spin-broken symmetry solutions at the UB3LYP
level.  According to harmonic vibrational frequency analyses, each stationary structure was
characterized as a minimum (no imaginary frequencies) or as a transition state (one imaginary
frequency) at the UB3LYP/6-311+G(2df) level.  Zero-point vibrational energies and heat capacity
corrections were obtained from UB3LYP/6-311+G(2df) frequency calculations.  On the triplet
potential energy surface there were intruder state problems, which were solved by applying the
level shift (LS) technique.
37
  Transition vectors of transition states were visualized and animated
by the MOLDEN program
38
 to insure that the motions were as expected.
For triplet linear isomers vibrational frequencies at the CASSCF(12,12)/6-311+G(2df)
level were also calculated to investigate the Renner-Teller effect.
39
  Dynamic electron correlation
was considered by utilizing single-point full-valence CASPT2 calculations for every stationary
point calculated at the CASSCF(12,12)/6-311+G(2df) level with the ANO-L basis set
40
 which is a
[7s7p5d4f] contraction of the [17s12p5d4f] primitive set for the phosphorus atom and a
[7s7p4d3f] contraction of the [14s9p4d3f] primitive set for boron and carbon atoms.  Throughout
this paper, we will refer to UB3LYP/6-311+G(2df) as DFT, CASSCF(12,12)/6-311+G(2df) as
CAS, and CASPT2(12,12)/ANO-L//CASSCF(12,12)/6-311+G(2df) as CASPT2, respectively.  In
the GAMESS and MOLCAS calculations, the C
2v
 point group was adapted for linear isomers due
to limitations in handling high symmetry.  The geometry of the conical intersection was obtained
at the CASSCF(6,6)/6-311+G(2df) level by using Gaussian98, and then single-point calculations
for both electronic states (
3
A? and 
3
A?) were carried out at the CAS level with GAMESS and
CASPT2 level with MOLCAS.  The natural bonding orbital (NBO)
41
 program implemented in
Gaussian98 program was used for the Wiberg bond index (WBI)
42
 analysis.  Thermodynamic and
spectroscopic properties were calculated from the DFT and CASPT2 results as described in the
33
literature.
43
  For comparison, we also performed G3B3
44
 calculations to obtain the heat of
formation of S1 (Figure1).  We will use a notation scheme with a boldface ?S? for singlets and
?T? for triplets followed by one number for minima and two numbers for transition states.  Thus,
T12 is the triplet transition state between triplet T1 and triplet T2.
2.3  Results and Discussion
Important electronic configurations of diatomic fragments and minimum energy species
of BCP species are given in Table 1.  For the diatomic fragments only ground states are
considered.  The ground state electronic configurations of BC and CP are available from the
literature and we obtained the same configurations for the ground states of BC (
4
?
-
) and CP (
2
?
+
).
The ground state of BP is 
3
? with the electronic configuration [Core]5s
2
6s
2
2p
3
7s
1
, which is the
same as previously reported.
45
  This suggests that BP can be obtained by combining ground state
B and P atoms without change of electronic configuration.  This fact can help explain why BP
can easily polymerize to form a polymeric film (boronphosphide) since the diradical is expected
to be kinetically labile.
21
The ground state of the linear BCP (S1), the first excited linear triplet isomer (T1) and
other linear isomers have the electronic configurations:
[Core]6s
2
7s
2
8s
2
2p
4
9s
2
         S1 (
1
?
+
), S3 (
1
?
+
)
[Core]6s
2
7s
2
8s
2
2p
4
9s
1
3p
1    
 T1 (
3
?), T6 (
3
?), T34 (
3
?)
Triangular C
s
 symmetry isomers have electronic configurations:
[Core]7a?
2
8a?
2
9a?
2
10a?
2
2a?
2
11a?
2
S2 (
1
A?)
[Core]7a?
2
8a?
2
9a?
2
10a?
2
2a?
2
11a?
1
12a?
1
T2, T3 (
3
A?)
[Core]7a?
2
8a?
2
9a?
2
10a?
2
2a?
2
11a?
1
3a?
1
T4, T5 (
3
A?)
34
Table 1. Important electronic configurations of ground state diatomic fragments of BCP and
minimum energy isomers of BCP at the CASPT2 level
a
Species E-State Configurations C
i
2
3?
2 
4?
2 
5?
 
1?
x
 
1?
y
3?
2 
4?
  
5?
2 
1?
y
 
2?
x
BC
4
?
-
(
4
A
2
)
3?
2 
4?
  
5?
2 
1?
x
 
2?
y
0.89
0.02
0.02
CP
2
?
+
(
2
A
1
)
5?
2 
6?
2 
2?
4 
7?
5?
2 
6?
2 
2?
x
2 
7?
 
3?
y
2
5?
2 
6?
2 
2?
y
2 
7?
 
3?
x
2
5?
2 
6?
2 
2?
x
2 
1?
?
y
 
7?
 
3?
y
5?
2 
6?
2 
2?
?
x
 
1?
y
2 
7?
 
3?
x
 
0.85
0.02
0.02
0.01
0.01
BP
3
?
(
3
B
1
)
5?
2 
6?
2 
2?
x
 
2?
y
2 
7?
 
5?
2 
6?
2 
2?
x
 
7?
  
3?
y
2
0.90
0.02
S1
1
?
+
(
1
A
1
)
6?
2 
7?
2 
8?
2 
2?
4 
9?
2
6?
2 
7?
2 
8?
2 
2?
4 
3?
x
 
4?
?
x
6?
2 
7?
2 
8?
2 
2?
4 
3?
y
 
4?
?
y
6?
2 
7?
2 
8?
2 
2?
x
2 
9?
2 
3?
y
2
6?
2 
7?
2 
8?
2 
2?
y
2 
9?
2 
3?
x
2
6?
2 
7?
2 
8?
2 
2?
x
 
2?
y
 
9?
2 
3?
?
x
3?
?
y
0.82
0.01
0.01
0.01
0.01
0.01
S2
1
A?
7a?
2 
8a?
2 
9a?
2 
10a?
2 
2a?
2 
11a?
2
7a?
2
 8a?
2 
9a?
2 
10a?
2 
2a?
2 
12a?
2
7a?
2
 8a?
2 
9a?
2 
10a?
2 
11a?
2 
3a?
2
0.78
0.08
0.01
S3
1
?
+
(
1
A
1
)
6?
2 
7?
2 
8?
2 
2?
4 
9?
2
6?
2 
7?
2 
8?
2 
2?
y
2 
9?
2 
3?
x
2
6?
2 
7?
2 
8?
2 
2?
x
2 
9?
2 
3?
y
2
6?
2 
7?
2 
8?
2 
2?
x
2?
y
9?
2
3?
?
x
 
3?
?
y
6?
2 
7?
2 
8?
2 
2?
x
 
2?
?
y
 
9?
2 
3?
x
3?
?
y
6?
2 
7?
2 
8?
2 
2?
x
2  
2?
y
 
9?
2 
3?
?
y
 
6?
2 
7?
2 
8?
2 
2?
x
  
2?
y
2 
9?
2 
3?
?
x
 
0.73
0.05
0.05
0.03
0.02
0.01
0.01
T1
3
?
(
3
B
1
)
6?
2 
7?
2 
8?
2 
2?
4 
9?
 
3?
x
6?
2 
7?
2 
8?
2 
2?
x
2 
9?
 
3?
x
3?
y
2
0.85
0.02
T2
3
A?
7a?
2
 8a?
2 
9a?
2 
10a?
2 
2a?
2 
11a?
 
12a?
7a?
2
 8a?
2 
9a?
2 
10a?
2 
11a?
 
12a?
 
3a?
2
0.86
0.01
T3
3
A?
7a?
2
 8a?
2 
9a?
2 
10a?
2 
2a?
2 
11a?
 
12a?
7a?
2
 8a?
2 
9a?
2 
10a?
2 
11a?
 
12a?
 
3a?
2
0.79
0.01
T4
3
A?
7a?
2 
8a?
2 
9a?
2 
2a?
2 
10a?
2 
11a?
 
3a?
7a?
2 
8a?
2 
9a?
2 
2a?
 
10a?
2 
11a?
 
3a
?
?
 
4a?
0.80
0.01
T5
3
A?
7a?
2 
8a?
2 
9a?
2 
2a?
2 
10a?
2 
11a?
 
3a?
7a?
2 
8a?
2 
9a?
 
2a?
2 
10a?
2 
11a?
2 
3a?
0.80
0.01
T6
3
?
(
3
B
1
)
6?
2 
7?
2 
8?
2 
2?
4 
9?
 
3?
x
6?
2 
7?
2 
8?
2 
2?
x
2 
9?
 
3?
x
3?
y
2
6?
2 
7?
2 
8?
2 
2?
x
2 
2?
?
y
 
9?
 
3?
x
3?
y
6?
2 
7?
2 
8?
2 
2?
x
 
2?
?
y
 
9?
 
3?
x
2
3?
y
6?
2 
7?
2 
8?
2 
2?
x
2 
2?
y
 
9?
 
3?
x
3?
?
y
6?
2 
7?
2 
8?
2 
2?
x
2 
2?
y
 
9?
 
3?
?
x
3?
y
0.69
0.06
0.03
0.02
0.01
0.01
a 
Orbitals with a single ?-spin electron are indicated with a bar over the orbital designation.
Figure 
1
.
   Optimized geometric parameters of stationary points at 
the DFT level with the CAS level in parentheses. 
 Bond lengt
hs are in
                  
? and angles are in degrees.  The symbol (*) indicates the geometry was obtained at the DFT level using the 6
-311+G(df)
                  
basis set.  The brackets for 
S3
 indicate the values obtained with RDFT (i.e. 
S3?
).
35
B
C
P
B
P
C
P
B
C
P
B
C
P
C
B
C
B
P
1
.
515
(
1
.
563)
1
.
552
(
1
.
571)
S1  
1
????
+
S1
2  
1
A'
1.
45
9
(1
.4
6
4
)
1
.
590
(
1
.
625)
1.
421
(
1
.
427)
1.
8
6
9
(1
.
8
4
5
)
1.
676
(
1
.
698)
73.
7
(
71.
8)
S2  
1
A'
2.
183
(
2
.
030)
91
.
3
(
8
2.
0)
S3  
1
????
+
1.
4
4
7
[1
.
4
4
1
]
(1
.
4
6
9
)
1.
7
1
4
[1
.6
8
6
]
(1
.7
3
3
)
1.
3
9
3
(1
.
4
3
0
)
1
.
594
(
1
.
604)
T1  
3
????
T2
  
3
A'
1.
454
(
1
.
478)
1.
920
(
1
.
932)
1
.
691
(
1
.
718)
74.
8
(
73.
9
)
B
P
C
B
C
P
B
P
C
1.
764
(
1
.
770)
1
.
751
(
1
.
793)
12
0
.
5
(1
1
6
.
4
)
1.
76
5
(1
.7
9
1
)
1.
6
7
5
(1
.
6
7
8
)
147.
5
(
161.
9
)
T2
3  
3
A'
T3  
3
A'
1.
7
5
7
(1
.
7
9
0
)
1.
657
(
1
.
677)
T34
  
3
????
P
B
C
P
B
C
1.
771
(
1
.
793)
1.
693
(
1
.
697
)
110.
0
(
114.
5)
T4  
3
A"
1.
943
(
1
.
988)
1.
6
2
2
(1
.6
4
2
)
70.
1
(
70.
3)
T
45  
3
A"
B
P
C
1.
369
(
1
.
404)
1
.
990
(
2
.
127)
1.
796
(
1
.
788)
76
.
6
(
8
2.
7)
T5
  
3
A"
P
B
C
1.
82
2
(1
.8
9
1
)
1.
383
(
1
.
450)
103.
5
(
97.
2)
T
62  
3
A'
C
B
P
P
B
C
1.
38
3
(1
.4
1
0
)
126.
5
(
117.
1)
1.
737
(
1
.
750)
1.
396
(
1
.
424)
T6  
3
????
T56  
3
A"
B
C
P
S
13  
1
A"
1.
723
(
1
.
748)
1.
73
8
(1
.7
4
8
)
125.
3
(
117.
1)
1.
369
(
1
.
410)
C
P
B
1
.
832
(
1
.
839)
1.
932
(
1
.
939
)
1.
367
(
1
.
391)
72.
7
(
72.
3)
T15 
3
A"
*
P
C
B
1.
389
(
1
.
414
)
1.
665
(
1
.
691)
110.
4
(
108.
2
)
T12
  
3
A'
36
Excitation from singlet state to triplet state can be accomplished by exciting one electron from
the HOMO (9?) to LUMO (3?).  The other linear isomer on the singlet PES (CBP), S3, also has
the same configuration as S1, and two triplet linear species (CBP, BPC), T6 and T34, have the
same configuration as T1.  In our calculations for the triplet linear species, using the C
2v
 point
group, we only calculate one component of the degenerate triplet state; however, we give the
linear electronic state designation in Table 1.  Linear species have some multireference character
as judged by the square of coefficient of the dominant configuration to the wave function (C
i
2
)
which is between 0.69 and 0.85 (Table 1).  The low-lying ? orbitals (2?/3?/4?) play an important
role in this system where four to six electrons are distributed among the ? sets.
All possible linkage isomers of three atoms on singlet and triplet surfaces were
considered.  Optimized structures are as shown in Figure 1 and their relative energies are given
in Table 2.  Three singlet and six triplet minimum-energy structures are characterized from DFT
geometry optimizations and frequency calculations.  Among those isomers, singlet linear B-C-P,
S1 (
1
?
+
) proved to be the global minimum.  For most structures, geometries optimized at the
CAS level had slightly longer bonds lengths than those at the DFT level (Figure 1) due to the
population of antibonding orbitals.  The B-C bond lengths in S1 and T1 isomers showed larger
deviations between DFT and CAS, these may be attributed to the neglect of dynamic electron
correlations in the CASSCF method.  In S1 (BCP) the C-P bond is a triple bond (1.552 ?, DFT),
slightly shorter than the experimental
46
 bond length of CP (1.562 ?), while the B-C bond is a
single bond (1.515 ?, DFT), and slightly longer than experimental
14
 bond length in BC (1.491
?).  The C-P/B-C bond lengths (1.594/1.393 ?, DFT) in T1 (BCP) are longer and shorter than a
normal CP triple bond and a normal BC single bond, respectively.  These bond length changes
can be easily rationalized by drawing Lewis structures of S1 and T1.  As shown in Scheme 1, the
triplet T1 is formed from S1 by promoting an electron from the lone pair of boron into an empty
37
?
*
 orbital of phosphorus.  The CP bond in T1 becomes weaker while the BC bond becomes
stronger.  At the CASPT2 + ZPC level, T1 is 16.3 kcal/mol less stable than S1.
Three triangular planar structures, S2, T2, and T5 are found to be minima and their
electronic states are 
1
A?, 
3
A? and 
3
A?, respectively.  S2 and T2 have very similar geometries and
Scheme 1.  Lewis structures of S1 and T1
their energy difference is only 2.2 kcal/mol at the CASPT2 + ZPC level.  Therefore, it is possible
that vibrational excitation may lead to intersystem crossing.   The other triangular isomer, T5,
has a somewhat different structure from S2 and T2 with a much longer P-C bond (1.990 ?).  All
three isomers have relatively low energies despite high bond strain which may be attributed to
the large size of the phosphorus atom and the relatively weak repulsion among the electron pairs
around phosphorus.
Another pair of linear linkage isomers, S3/T6 (PBC), shows very similar properties to
S1/T1 (PCB) where the BC fragment is rotated by 180
o
.  The triplet (T6) can be formed from S3
by promoting a phosphorus lone pair electron to an empty carbon ?
*
-orbital which, in turn, can
form a partial B-C double bond.  Thus, the B-C bond is shorter in T6 than S3 but the P-B bond is
longer (B-C: 1.396/1.447 ? and P-B: 1.737/1.714 ?).
BCP
BC P
T1
S1
38
Table 2. Relative Energies (in kcal/mol) of species on the potential energy surface of BCP
a
Spin-squared values <S
2
>, zero-point corrections (kcal/mol), and heat capacity contributions
to enthalpy at 298K (kcal/mol) were calculated at the B3LYP/6-311+G(2df) level.
b
Reference weights, the fraction of electron correlation energy obtained within the active
space, were calculated at the CASPT2(12,12)/ANO-L//CASSCF(12,12)/6-311+G(2df) level.
c
For S1, the zero-point energy and heat capacity correction were computed with the RDFT
method which gives an energy 0.2 kcal/mol higher than the UDFT method.  The UDFT and
RDFT geometries are very similar.
d
The S3 species is determined by UDFT (broken-symmetry), while S3? is determined by
RDFT (closed-shell).  S3 is a minimum while S3? is a transition state.
e
DFT results were obtained by using B3LYP/6-311+G(df) geometry optimization with a
single-point calculation at the B3LYP/6-311+G(2df) level.
f
CASPT2 results were obtained by using the level shift method (see Table 3).
g
The geometry of the crossing point was obtained at the CASSCF(6,6)/6-311+G(2df) level.
The ZPC from T4 was used to compute the values under ??E + ZPC?.
?E ?E + ZPC
BCP State <S
2
>
a
Rw
b
ZPC
a
H
corr
a
DFT CAS CASPT2 DFT CAS CASPT2
S1
c 1
?
+
0.15 0.91 3.6 6.7 0.0 0.0 0.0 0.0 0.0 0.0
S2
1
A? 0.72 0.90 4.0 6.6 12.4 24.7 13.6 12.8 25.1 14.0
S3
d 1
?
+
0.56 0.90 3.4 6.5 35.6 42.4 35.6 35.4 42.2 35.4
S3?
d 1
?
+
0.00 3.3 5.5 37.2 36.9
S12
1
A? 0.29 0.90 3.0 5.4 19.8 29.7 19.4 19.2 29.1 18.8
S13
1
A
?
1.10 0.89 3.3 5.7 63.0 83.8 70.3 62.8 83.6 70.0
T1
3
? 2.02 0.90 4.3 7.0 11.2 19.7 15.6 11.9 20.4 16.3
T2
3
A? 2.01 0.88 4.0 6.5 15.1 28.3 15.8 15.5 28.7 16.2
T3
3
A? 2.06 0.89 2.5 5.5 93.5 97.6 91.2 92.5 96.6 90.2
T4
3
? 2.08 0.90 3.1 5.5 87.6 93.3 88.5 87.1 92.8 88.0
T5
3
A? 2.03 0.88 3.5 6.3 50.2 61.2 49.2 50.1 61.1 49.1
T6
3
A? 2.46 0.89 3.7 6.5 52.5 59.2 52.1 52.7 59.4 52.3
T12
3
A? 2.01 0.87 3.5 5.9 30.9 43.4 34.0 30.9 43.4 33.9
T23
3
A? 2.03 0.89 2.2 4.7 94.9 103.2 95.2 93.6 101.9 93.8
T34
3
? 2.05 0.89 2.5 4.6 93.9 97.7 91.0 92.8 96.6 89.9
T45
3
A? 2.38 0.90 2.0 4.6 99.1 102.1 99.8 97.6 100.5 98.3
T56
e3
A? 2.11 0.89 3.3 5.7 56.4 64.1 55.5 56.1 63.9 55.2
T15
f3
A
?
2.03 0.91 3.2 5.6 50.2 81.3 48.2 49.8 80.9 48.7
T26
f3
A
?
2.06 0.91 3.0 5.5 73.7 79.4 66.3 73.1 78.8 66.6
T
crs
g
3.1 5.5 96.1 91.4 95.7 91.0
Figure 2.
Schematic potential energy surface for the BCP system. Relative energies (kcal/mol) are obtained at the CASPT2
+ZPC level.  
More details of the PES within the brackets are given in Figure 4
.
39
S1
 
1
????
+
S2 
1
A'
T1
 
3
????
T2
 
3
A'
T6
 
3
????
T5
 
3
A"
S3 
1
????
+
0.0
14.0
16.
2
16.3
33.9
52.
3
49.1
55.2
18.8
In
t
e
r
m
e
d
iat
e
s
B(
2
P) + 
CP(
2
????
-
)
BC
(
4
????
-
) +
 
P(
4
S)
C (
3
P)
 +
 
B
P
(
3
????
)
P(
4
S)
 +
 
B
C
(
4
????
-
)
111
.7
128
.9
128.9
T1
2
3
A'
S1
2
1
A'
T6
2
3
A'66.6
T5
6
3
A"
35.4
70.0
S
13 
1
A"
T
15 
3
A"
48.7
P
B
C
BC
P
P
B
C
BP
C
PB
C
PB
C
R
e
ac
t
i
on
 C
o
o
r
d
i
n
a
t
e
146.2
[
T
23/T
3
/T
3
4
/
T
4/T
45,
 T
crs
]
S2 
1
A'
14
.
0
P
B
C
40
The remaining linkage isomer, B-P-C, was not found to be a minimum on either the
singlet or triplet potential energy surface.  Singlet linear B-P-C was found to be a high-energy
transition state between S2 configurations, while the triplet linear B-P-C (T34) is a degenerate
(
3
?) Renner-Teller state connecting the T3 (
3
A') and T4 (
3
A") minima (see below for further
discussion).
On the triplet surface there are intruder state problems with T15 and T62 at the CASPT2
level.  We observed a low reference weight (Rw); 0.15 for T15 and 0.34 for T62.  By applying
the level shift (LS) technique, we could remove the intrusion and obtained relative energies as
shown in Table 3.  When a 0.1 level shift parameter was applied, the problem was solved in T15
(Rw: 0.90), but T62 was still affected (Rw: 0.82).  With a 0.2 LS parameter all intruder state
problems disappeared.  The same shifted values were used to calculate both minima connected to
each transition state for comparison, and then zero-point energy corrections were applied to
obtain the energy differences relative to T2.  Finally, we note the strong structural similarity
between the diradical transition states S13 and T56 (
1
A? and 
3
A?) at the DFT and CAS levels.
The triplet T56 is 15.3 kcal/mol higher in energy than S13 (Figure 2) so intersystem crossing is
unlikely.
The singlet and triplet potential energy surfaces are constructed based on their relative
energies after zero-point energy corrections (Figure 2).  As mentioned above, S1 is the global
minimum.  On the singlet PES S1 and S2 are characterized as energy minima.  Between S1 and
S2, a first-order saddle point, S12, is located 18.8 kcal/mol higher than S1 and 4.8 kcal/mol
higher than S2.  An alternative mechanism for the S1?S2 rearrangement is over the S13
transition state (
1
A?) through S3, the linear P-B-C species.  At the UDFT level, S3 has a <S
2
>
value of 0.56 and no imaginary frequencies.  However, at the RDFT level, the optimized linear
structure (S3?) is only 1.5 kcal/mol higher in energy than the spin-broken symmetry UDFT
41
Table 3. Energies  relative to T2 (in kcal/mol) and reference weights (Rw) obtained by
using the level shift (LS) technique
a,b
T1 T15 T5 T2 T26 T6
LS
?E Rw ?E Rw ?E Rw ?E Rw ?E Rw ?E Rw
0.0 1.0 0.90 33.7 0.15 33.8 0.88 0.0 0.88 49.8 0.34 37.0 0.89
0.1 1.0 0.91 32.4 0.90 33.9 0.90 0.0 0.91 44.0 0.82 37.1 0.90
0.2 0.9 0.92 32.5 0.91 33.9 0.91 0.0 0.91 50.4 0.91 37.1 0.91
a
See Reference 37.
b
The reference weight is the fraction of the electron correlation obtained within the active
space.  A value significantly different from other species on the PES may indicate an
intruder state problem.
 
P
P
P
P
P
P
P
P
S2 
1
A'
S1 
1
?
+
S12 
1
A'
S3 
1
?
+
S13 
1
A"
S13 
1
A"
S2 
1
A'
S12 
1
A'
BC
0.0
14.0 18.8
70.0
35.4
Figure 3. Schematic drawing for  revolution of the phosphorus atom around the B-C core
on the singlet PES.  The dashed lines represent the approximate B-C-P angle for
the stationary points with the energy (kcal/mol) relative to S1.  The outer circle
indicates the A? surface while the inner eclipse indicates the A? surface.  The A?
and A? surfaces are degenerate at S1 and S3.
42
solution and has two imaginary frequencies (S2?S3?(RDFT)?S2).   While we are not
confident that S3 is an intermediate on the PES, we do feel that the barrier to collapse to S2 must
be very small.  In addition, S2 should undergo rearrangement over a transition state very much
like S3 (i.e. S3?(RDFT)).  In these two scenarios, the P atom can ?orbit? the BC fragment
(Figure 3).  Movement around the C-end gives the global minimum S1, while movement around
the B-end gives the P-BC (S3) and then back to S2.
The triplet potential energy surface is somewhat more complicated than the singlet PES.
The triplet surface is composed of 
3
A?, 
3
A? and 
3
P states, and all are connected to one another.
From the lowest energy isomer T2, the reaction can proceed over a 17.7 kcal/mol barrier (T12)
to reach linear T1 by breaking the B-P bond, over a 50.4 kcal/mol barrier (T62) to reach linear
T6 by breaking the C-P bond, or over a 77.6 kcal/mol barrier (T23) to reach T3 by breaking the
B-C bond.  Breaking the C-P bond (T2?T6) occurs on the 
3
A? surface to give the linear P-B-C
isomer (T6) which can then proceed on the 
3
A? surface, since the 
3
A? and 
3
A? states are
degenerate in T6.  A small 2.9 kcal/mol barrier (T56) separates T6 from T5 on the 
3
A? surface.
From T5, the reaction proceeds without barrier (T15 is lower in energy than T5 at the
CASPT2+ZPC level).
A higher-energy pathway connecting T2 and T1 was calculated involving intermediate
species T3, T4, and a crossing point T
crs
.  While that pathway is not relevant on the T1/T2
pathway, it may be important in reactions between the fragments (BC + P, BP + C, CP + B).
As shown in Figure 4a, species T3 (
3
A?) is 0.3 kcal/mol higher in energy than T34 and
2.2 kcal/mol higher than T4 (T34, a transition state at the CAS level, is stabilized relative to T3
and T4 at the CASPT2 level).  Similar to the T62/T6/T56 pathway above, the reactant (T3)
starts on the 
3
A? surface and finishes on the 
3
A? surface (T4) while passing through T34 (
3
?).
Distortion along one of the two imaginary bending modes (?
x
 and ?
y
) of linear B-P-C (T34)
gives rise to the 
3
A? or 
3
A? electronic surface.
43
T3 
3
A'
T4 
3
A"
90.2
88.0
89.9
T34 
3
?
T
crs
(1.639)
(1.873)
(100.8)
98.3
93.8
88.0
16.2
91.0
CPB
C
B
P
CB
P
1.454
(1.478)
1.920
(1.932)
1.830
(1.718)
74.8
(73.9)
1.764
(1.770)
1.751
(1.793)
120.5
(116.4)
T23  
3
A'
P
B
C
1.943
(1.988)
1.622
(1.642)
70.1
(70.3)
T45  
3
A"
P
B
C
1.771
(1.793)
1.693
(1.697)
110.0
(114.5)
T4  
3
A"
T2  
3
A'
P
C
B
P
B
C
a)
b)
B C
P
Figure 4. (a) State crossing from the 
3
A? surface to 
3
A? surface via linear T34 (
3
?).
(b) State crossing through a conical intersection.  The geometry of T
crs
 is
optimized at the CASSCF(6,6)/6-311+G(2df) level, and single-point calculations
were performed for each state symmetry (
3
A? and 
3
A?) at the CASPT2 level.  The
relative energy of T
crs
 was obtained by averaging the two state energies. Energies
(kcal/mol) are relative to S1.
44
B C
P
B C
P
BC
B
P
C
11a'
12a'
4a"
11a'
3a"
3
A'
3
A"
B
P
C
13a'
P
BC
P
Figure 5. Orbital crossing diagram around the conical intersection (see Figure 4 for details of
the crossing).
Another interesting finding in this study is the occurrence of a conical intersection
between the 
3
A? and 
3
A? surfaces.  The location is between T2-T23 on the 
3
A? surface and T45-
T4 on the 
3
A? surface (Figure 4b).  The optimized structure of the crossing point (Figure 4b) is
3.0 kcal/mol higher in energy than T4.  As the B-P-C angle increases, the energy of the 
3
A?
surface rises, while the energy of the 
3
A? surface falls.  The orbital interactions that are
responsible for the crossing are given in Figure 5.  When the structure is triangular, the 3a?
orbital has a strong antibonding interaction between the p
z
 orbitals of boron and carbon which
decreases as the B-P-C angle increases.  At the same time, the bonding interaction in the 12a?
orbital becomes more antibonding as the angle increases.  The B-P-C angle at the crossing T
crs
(100.8
o
) is intermediate to the value in T2 (74.8
o
) and T4 (110.0
o
).
45
Calculated bond dissociation energies are shown in Table 4.  Our bond dissociation
energy (D
0
) of B-C (
4
?
-
) is 100.9 kcal/mol at the CASPT2 level and 101.7 kcal/mol at the DFT
level which is close to the experimental value
11,12
 (D
0
 = 106?7 kcal/mol) determined by mass
Table 4. Calculated bond dissociation energies (in kcal/mol)
a
Reference 20.
b
Theoretical values of 97.0 kcal/mol
16
 and 100.1 kcal/mol
19
 have been reported.
c
Reference 25.
d
Reference 45(b).
spectroscopy.  Tzeli and Marvridis
20
 reported MRCI/cc-pVnZ-CBS calculations including scalar
relativistic corrections (mass velocity + Darwin terms) and spin-orbit corrections and suggested a
value of 100.5?0.1 kcal/mol for the B-C bond dissociation energy (D
0
).  Martin and Taylor
19
used calculations at the CCSD(T) level to obtain a BDE of B-C as 98.3?1 kcal/mol.  Our
CASPT2 and DFT calculations of the BDE (100.9, 101.7 kcal/mol) are very similar to those
reported previously, while the G3B3 results give a slightly stronger B-C bond (102.7 kcal/mol).
For the bond dissociation energy of CP, our DFT results agree best with the reference D
e
value of 123.5 kcal/mol
46
 with CASPT2 about 4 kcal/mol lower and G3B3 about 3 kcal/mol
higher than the experimental D
e
 values.  The difference between the CASPT2 and G3B3
methods for the calculated D
e
 value of CP (as well as for the D
e
 values of BC and BP) are mainly
due to the higher level correction (HLC)
44(a)
 in which deficiencies in the basis set are empirically
D
e
D
0
Bond State Products
DFT CASPT2 G3B3 exptl DFT CASPT2 G3B3
B-C
4
?
- 2
P + 
3
P 103.4 102.6 104.3 102.2
a,b
101.7 100.9 102.7
C-P
2
?
 + 3
P + 
4
S 123.2 119.9 126.2 123.5
c
121.3 118.1 124.4
B-P
3
?
2
P + 
4
S 81.7 72.8 78.4 72.6
d
80.3 71.4 77.1
B-CP
1
?
 +2
P + 
2
?
+
117.4 113.4 118.0 115.7 111.7 116.3
BC-P
1
?
 +4
?
-
 + 
4
S 137.2 130.7 139.8 135.4 128.9 138.0
B-C-P
1
?
 + 2
P + 
3
P + 
4
S 240.6 233.3 244.2 237.1 229.7 240.7
46
corrected for based on the number of spin-paired electrons and unpaired electrons.
47
  Without
this higher-level correction, the CASPT2 results are very similar to the G3B3 results.
Table 5. Wiberg Bond Index calculated at the DFT level
B-C C-P B-P
S1 0.90 2.67 0.14
S2 1.76 1.74 1.16
S3 1.64 0.64 2.33
T1 1.40 2.06 0.16
T2 1.37 1.65 0.92
T3 0.19 2.02 1.53
T4 0.18 1.83 1.51
T5 2.02 0.70 1.34
T6 1.77 0.19 1.85
We report bond dissociation energies and atomization energy of BCP (S1) in Table 4.  It
is surprising that the bond energy (D
e
) of B-CP (113.4 kcal/mol, CASPT2) is larger than in BC
(102.6 kcal/mol, CASPT2), even though the DFT-based Wiberg Bond Index (WBI) of the B-C
bond is only 0.90 (Table 5).  Also, the bond dissociation energy (D
e
) of BC-P (130.7 kcal/mol,
CASPT2) is larger than that of the diatomic CP molecule (119.6 kcal/mol, Table 4).  These
unexpected results can be understood from the WBI and the NBO interaction energy analysis.
From the WBI analysis, there is a rather large 1,3-bonding interaction between the B and P atoms
(0.14) even though their atomic separation is 3.067 ? (DFT).  As shown in Table 6, the NBO
stabilization energy (?2e-stabilization?) between the C-P bonding ? orbitals and empty p orbitals
on boron is 28.5 kcal/mol.  In addition, the lone-pair electron donations from the B atom to the
C-P ?
*
 orbital and from the P atom to the B-C ?
*
 orbital is stabilizing by 14.3 kcal/mol and 16.5
kcal/mol, respectively.  Thus, breaking the B-C bond in BCP also breaks the B???P bonding
interaction.
47
Table 6. NBO stabilization energies associated with electron delocalization (kcal/mol) at
the DFT level
Donor Acceptor Energy
?
x
 (C-P) p
x
 (B) 13.9
?
y
 (C-P) p
y
 (B) 14.6
? (B) ?
*
 (C-P) 14.3
? (P) ?
*
 (B-C) 16.5
Calculated heats of formation are compared with experimental values in Table 7.  In the
JANAF table
48
 and NIST webbook,
49
 the heat of formation of BC at 0K is given as 196?10
kcal/mol based on the old bond dissociation of BC (105?10 kcal/mol) and heat of formation of
boron (132.6?2.9 kcal/mol).  Using the newer experimental bond dissociation energy of BC (D
e
= 102.2 kcal/mol)
20
 with a ZPC correction of 1.7 kcal/mol and a more recent heat of formation of
boron (136.2?0.2 kcal/mol),
43
 we obtained a heat of formation of BC at 0K as 206?1 kcal/mol,
which is in much better agreement with our best results (205.3 kcal/mol, CASPT2 level).  DFT
and G3B3 results are also in good agreement.
Previous studies have reported a disagreement between theory and experiment for the
heat of formation of CP.
26-28
  The calculated ?H
f
o
 (0K) for CP of 124.1 kcal/mol (DFT), 127.3
kcal/mol (CASPT2), and 121.0 kcal/mol (G3B3) are in good agreement with the best
computational heat of formation (124?2).  The variation between CASPT2 and G3B3 for the
heats of formation (0K) of CP (6.3 kcal/mol) and BP (5.7 kcal/mol) can be attributed largely to
the empirical higher-level correction (HLC) in the G3B3 method.
The heat of formation of S1 was calculated in two ways; directly from atoms (B +
C + P?BCP), and averaging the heats of formation calculated from reactions shown in Table 8
using reference heats of formation of reactants.  The two methods give similar results at the DFT
48
Table 7. Heats of formation (kcal/mol) of ground state diatomic fragments and S1
?H
f
o
 0K ?H
f
o
 298K
Species
DFT CASPT2 G3B3 exptl DFT CASPT2 G3B3
B 136.2?0.2
a
C 169.98?0.1
a
P 75.4?0.2
a
BC 204.5 205.3 203.5 206?1
b
206.1 206.8 205.0
CP 124.1 127.3 121.0 124?2
c
124.6 127.9 121.5
BP 131.3 140.2 134.5 131.9 140.7 135.0
BCP 144.5 151.9 140.9 145.8 153.1 142.1
BCP
d
145.3 150.5 143.6 146.9 152.2 145.2
a
Reference 43.
b
Revised based on Tzeli and Marvridis? D
e
 and heats of formation of boron and carbon from
Ref. 43.
c
References 26-28.
d
Averaged value.  See Table 8.
Table 8. Heats of formation (kcal/mol) of S1 at 0K and 298K by different reactions
?H
f
o
 0K ?H
f
o
 298K
reacction
DFT CASPT2 G3B3 DFT CASPT2 G3B3
B+C+P ? BCP 144.5 151.9 140.9 145.8 153.1 142.1
BC+P ? BCP 146.0 152.6 143.4 148.6 155.1 145.7
B+CP ?BCP 144.5 148.5 143.9 146.1 150.1 144.2
BC+CP ?BCP+C 146.0 149.2 146.4 147.0 150.3 148.6
Average
a
145.3?0.8 150.5?1.9 143.6?2.2 146.9?1.2 152.2?2.4 145.2?2.7
a
Error  is obtained at 95% confidence interval.
and CASPT2 levels, but the G3B3 results show more variation.  Our best estimate of ?H
f
o
 (0K)
of BCP (
1
?
+
) is 150.5?2 kcal/mol at the CASPT2 level.
We note that all three linear triplet species (T1, T6, and T34) have a degenerate
electronic state (
3
?), and so are Renner-Teller species.
38
  The vibrational frequencies of the linear
49
Table 9. Vibrational Frequencies (cm
-1
) and Renner-Teller Constants of Triplet Linear
Species
Isomer State Level ?
x
?
y
?
1
?
2
| ? |
a
DFT 314.5 225.9 859.6 1577.7 0.319
T1
3
?
(
3
B
1
)
CAS 326.3 231.3 826.1 1444.0 0.331
DFT 273.7 206.7 683.6 1455.4 0.274
T6
3
?
(
3
B
1
)
CAS 265.0 198.8 671.6 1379.2 0.280
DFT -82.1 -149.5 787.4 940.5 0.537
T34
3
?
(
3
B
1
)
CAS -54.8 -142.0 723.2 937.0 0.740
a
Calculated by using the equation ? = {(?
+
)
2
-(?
-
)
2
}/{(?
+
)
2
+(?
-
)
2
} in Ref. 51.
Table 10. Calculated Vibrational Frequencies (cm
-1
)  and IR intensities (km/mol) of S1, S2,
T1 and T2
a
a
IR intensities are given in parentheses.
triplet species were calculated at the DFT and CAS levels in order to determine the nature of the
? bending modes (Table 9).  While a more sophisticated study of the potential energy surface is
required for a full analysis of the Renner-Teller effect, we note that DFT and CAS give similar
results for the ? bending modes.  Both T1 and T6 are RT Type A (i.e. the ? modes are different
and real)
50
 with good agreement between DFT and CAS on the ? parameter (see Table 9).  The
S1 S2 T1 T2
DFT CAS DFT CAS DFT CAS DFT CAS
?
1
110.4
 (12.1)
180.7
 (3.5)
606.6
(21.7)
645.6
(75.2)
225.9
(5.9)
231.3
(3.5)
590.6
(19.8)
594.9
(15.2)
?
2
110.6
(12.0)
180.7
(3.5)
929.6
(21.7)
885.9
(40.0)
314.5
(16.1)
326.3
(11.2)
932.3
(8.8)
892.8
(7.3)
?
3
750.8
(129.2)
714.6
(122.7)
1308.4
(16.3)
1350.0
(16.4)
859.6
(0.3)
826.1
(0.6)
1243.8
(10.2)
1193.2
(7.5)
?
4
1558.6
(408.0)
1466.8
(341.6)
1577.7
(52.1)
1444.0
(15.2)
50
linear triplet T34 is an RT Type D (i.e. both ? modes are different and imaginary) with less
agreement on the ? value (0.54 DFT and 0.74 CAS).  At the CASPT2 level there is an indication
that T34 may actually be an RT Type C species (i.e. one ? real mode and one ? imaginary mode).
At the CAS level, T34 is a transition state between T3 (
3
A?) and T4 (
3
A?) while at the CASPT2
level, the energy order is T3, T34, T4 (i.e. T34 is intermediate in energy to T3 and T4).  Thus,
we expect that dynamic electron correlation may have an important effect around this part of the
PES.  To clarify this disagreement, we performed a series of CASPT2/ANO-L geometry
optimizations
52
 for the different electronic states (
3
A', 
3
A", and 
3
?) of T34 and found that a
slightly bent 
3
A' state is higher in energy than linear 
3
? state and a slightly bent 
3
A" state is lower
in energy than 
3
?; thereby confirming that T34 must be an RT Type C species.
We report the vibrational frequencies and IR intensities in Table 10 for S1, S2, T1 and
T2 calculated at the DFT and the CAS levels.  These are the lowest energy species on the BCP
potential energy surfaces and may be observable in a low-temperature matrix.  The most likely
species for observation is S1 with quite intense BC and CP IR stretching frequencies.
2.4  Conclusions
On the BCP PES, three singlet and six triplet minima were found.  The singlet linear BCP
(S1, 
1
?
+
) is the global minimum while both the triplet triangular T2 ( 
3
A?) and the triplet linear T1
are about 16 kcal/mol higher in energy.  Rearrangements of triplets on the 
3
A? and 
3
A? PES can
take place by two mechanisms, either by going through a linear species of 
3
? symmetry where
the 
3
A? and 
3
A? states are degenerate or by going through a conical intersection.  On the singlet
surface, the lowest energy pathways involve a B-C core with the phosphorus atom revolving
around on the A? surface S1?S2?S3 or on the A? surface S1?S3.
51
Calculation of thermodynamic data at the DFT, CASPT2, and G3B3 levels are in good
agreement with each other and with experimental values.  The B-C and C-P bond dissociation
energies (D
0
) in B-C-P are 111.7 and 128.9 kcal/mol by CASPT2, respectively, which are larger
that the BDE in the BC and CP diatomics, 100.9 and 118.1 kcal/mol, respectively.  The stronger
B-C and C-P bonds in BCP are due to stabilizing 1,3-interactions between the boron and
phosphorus atoms.  The calculated heat of formation (?H
f
o
) of BCP (
1
?
+
) is 150.5?2 kcal/mol at
the CASPT2 level.  The absence of other low-energy unimolecular reactions suggests that BCP
might be observed under appropriate conditions.  Three Renner-Teller species among BCP
isomers are discussed.  Two of them (T1 and T6) are classified as a Type A Renner-Teller
species and the other one (T34) is classified as a Type D or C Renner-Teller species.  In analogy
with the BCN monomer and BCN polymeric materials, we hope that this study of the BCP
monomer may contribute to its discovery or to the search for BCP polymer materials.  To this
end, studies are underway of polymers based upon the BCP monomer unit.
52
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Malmqvist, P.-?.; Nakajima, T.; Neogr?dy, P.; Olsen, J.; Roos, B. O.; Schimmelpfennig,
B.; Sch?tz, M.; Seijo, L.; Serrano-Andr?s, L.; Siegbahn, P. E. M.; St?lring, J.;
Thorsteinsson, T.; Veryazov, V.; Widmark, P.-O.; Lund University, Sweden, 2002.
(35) (a) Roos, B. O.; Andersson, K.; F?lscher, M. P.; Malmqvist, P.-?.; Serrano-Andr?s, L.;
Pierloot, K.; Merch?n, M. ?Multiconfigurational perturbation theory: Applications in
electronic spectroscopy? In: Prigogine, I; Rice, S. A., Ed. Advances in Chemical Physics:
New Methods in Computational Quantum Mechanics; John Wiley & Sons: New York,
1995.  (b) Andersson, K.; Malmqvist, P.-?.; Roos, B. O.; Sadlej, A. J.; Wolinski, K. J.
Phys. Chem. 1990, 94, 5483.  (c) Andersson, K.; Malmqvist, P.-?.; Roos, B. O. J. Phys.
Chem. 1992, 96, 1218.
(36) (a) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650.
(b) McLean, A. D.; Chandler, G. S.  J. Chem. Phys. 1980, 72, 5639.  (c) Clark, T.;
Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. J. Comp. Chem. 1983, 4, 294.
55
(37) (a) Roos, B. O.; Andersson, K. Chem. Phys. Lett. 1995, 245, 215.  (b) Roos, B. O.;
Andersson, K.; F?lscher, M. P.; Serrano-Andr?s, L.; Pierloot, K.; Merch?n, M.; Molina,
V. THEOCHEM 1996, 388, 257.
(38) MOLDEN, Schaftenaar, G.; Noordik, J. H. J. Comput.-Aided Mol. Design, 2000, 14, 123.
(38) (a) Renner, R. Z. Phys. 1934, 92, 172.  (b) Herzberg, G. Molecular Spectra and
Molecular Structure III. Electronic Spectra and Electronic Structure of Polyatomic
Molecules; Krieger: Malabara, FL, 1991.
(40) (a) Widmark, P. O.; Malmqvist, P.-?.; Roos, B. O. Theor. Chim. Acta 1990, 77, 291. (b)
Widmark, P. O.; Malmqvist, P.-?.; Roos, B. O. Theor. Chim. Acta 1991, 79, 419.
(41) Reed, A.; Curtiss, L.A.; Weinhold, F. Chem. Rev. 1988, 88, 899.
(42) Wiberg, K. B. Tetrahedron 1968, 24, 1083.
(43) (a) Ochterski, J. W. Gaussian White Paper ? Thermochemistry in Gaussian?
http://www.gaussian.com/g_whitepap/thermo.htm  (b) Curtiss, L. A.; Raghavachari, K;
Redfern, P. C.; Pople, J. A. J. Chem. Phys. 1997, 106, 1063.
(44) (a) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. J. Chem
Phys. 1998, 109, 7764.  (b) Baboul, A. G.; Curtiss, L. A.; Redfern, P. C.; Raghavachari,
K. J. Chem. Phys. 1999, 110, 7650.
(45) (a) Boldyrev, A. I.; Simons, J. J. Chem. Phys. 1993, 97, 6149. (b) Miguel, B.; Omar, S.;
Mori-S?nchez, P.; Garc?a de la Vega, J. M. Chem. Phys. Lett. 2003, 381, 720.
(46) Huber, K. P.; Herzberg, G. ?Molecular Spectra and Molecular Structure. IV. Constants of
Diatomic Molecules?, New York: Van Nostrand, 1979.
(47) We calculated ?E(HLC) as found in reference 43a.  The result ??E(HLC) for diatomic
fragments are as follow; BC: 3.6, CP:6.4, BP: 5.0 (kcal/mol).  These corrections increase
the bond dissociation energies computed by G3B3 method.  When this factor is taken into
account the CASPT2 and G3B3 methods give very similar bond dissociation energies.
56
(48) Chase, M. W., Jr.  NIST-JANAF Thermochemical Tables, 4th Ed.; J. Phys. Chem. Ref.
Data 1998, Monograph 9.
(49) NIST Chemistry Webbook Site http://webbook.nist.gov/chemistry .
(50) Lee, T. J.; Fox, D. J.; Schaefer, H. F.; Pitzer, R. M. J. Chem. Phys. 1984, 81, 356.
(51) Brown, S. T.; Yamaguchi, Y.; Schaefer, H. F. J. Phys. Chem. A 2000, 104, 3603.
(52) For a discussion of CASPT2 optimized geometries see: Page, C. S.; Olivucci, M. J.
Comp. Chem. 2003, 24, 298.
57
CHAPTER 3
AN EXPERIMENTAL AND THEORETICAL EVALUATION OF THE REACTIONS OF
SILVER HYPONITRITE WITH PHOSPHORUS HALIDES. IN SEARCH OF THE
ELUSIVE PHOSPHORUS-CONTAINING HYPONITRITES
3.1  Introduction
The existence of organic hyponitrites is well documented in the chemical literature.
These hyponitrites have been synthesized by reactions of appropriate organic halides and silver
hyponitrite.
1-3
  The hyponitrites are a source of alkoxy or aryloxy radicals.  The geometries of
alkyl hyponitrites are trans based on vibrational spectroscopy,
4,5
 dipole moment measurements,
6
and low temperature X-ray crystallography.
7
  Decomposition is thought to occur by homolytic
scission with loss of N
2
.
8-10
The presence of the N=N bond has been confirmed by ultraviolet spectrum.
11
  The trans
isomer has been found to be the product obtained by usual preparative methods as confirmed by
Raman
12-14
 and infrared
15-17
 spectroscopy.  Cis-hyponitrous acid has been postulated as an
unstable intermediate in the reaction of hydroxylamine and nitrous acid
18
 and in the reduction of
nitrous acid by europium(II).
19
A number of alkali metal, alkaline earth metal, mercury, silver, and lead hyponitrites
have been synthesized.  Mercury and silver hyponitrites are known to have a trans configuration,
4
while sodium hyponitrite has been synthesized in both the cis and trans geometries.
20,21
  Several
transition metal hyponitrites have been prepared including the very interesting [Ni(dppf)N
2
O
2
],
58
[Pd(dppe)N
2
O
2
], and [Pt(dppf)N
2
O
2
] hyponitrites, all of which have cis hyponitrite geometries
and decompose by unimolecular kinetics.
21,22
Beck et al.
13
 reported that the decomposition of triphenyltin hyponitrite, Ph
3
SnON=NOSnPh
3
,
yielded N
2
O and (Ph
3
Sn)
2
O.  On the other hand, Wiberg et al.
14
 prepared trimethylsilyl
hyponitrite, Me
3
SiON=NOSiMe
3
, and reported that thermolysis gave N
2
, trimethyl silanol, and
hexamethyl disiloxane.
Phosphorus-containing hyponitrites are conspicuous by their absence in the chemical
literature.  Furthermore, no attempts to synthesize these potentially interesting molecules have
been reported.  This is in spite of the potential use of such hyponitrites to generate extremely
interesting radicals (e.g., F
2
PO, F
2
PO
2
, F
2
P(S)O).  This work deals with the attempts to prepare
such hyponitrites by reaction with silver hyponitrite as shown in the equation below (eq 1):
 2R
2
P(Y)X + Ag
2
N
2
O
2
 ? 2AgX + R
2
P(Y)ON=NOP(Y)R
2
            (1)
 (R=CH
3
,F; Y=O,S; X=halide)
In the thermal decomposition of hyponitrites, the experimental evidence suggests that
trans hyponitrites decompose to N
2
 plus other products, while cis hyponitrites may decompose to
N
2
O plus other products.
23
  A related issue is whether the decomposition is concerted (eq 2a) or
stepwise (eq 2b).
 RON=NOR ? 2RO? + N
2
      (2a)
 RON=NOR ? RO? + ?N=NOR ? 2RO? + N
2
                     (2b)
 Neuman and Bussey determined the activation volume of the trans?di-t-butyl
hyponitrite decomposition and suggested the reaction follows the concerted pathway.
10
  For trans
59
hyponitrites, structural and mechanistic studies are well established.
20,24
  On the contrary,
mechanistic studies on cis hyponitrites are rare.
22
  
To understand the different chemical reactivities of trans and cis hyponitrites, theoretical
calculations were carried out.  No previous calculations have been reported on the structures,
stabilities, or decomposition reaction pathways of phosphorus-containing hyponitrites.  Hybrid
density functional theory, B3LYP, has been applied to study the decomposition pathways of
XON=NOY, X,Y=PF
2
,OPF
2
, to establish the probable reaction mechanisms leading to observed
final products. This work has been published in Journal of Physical Chemistry A in 2005.
25
3.2  Experimental
26
Standard vacuum line techniques were used to purify and transfer all volatile substances.
Non-volatile compounds were handled in a nitrogen-filled glove bag containing P
4
O
10
 as a
desiccant.
Infrared spectra were determined on a Perkin-Elmer 983 spectrophotometer.  Liquids
were examined as neat samples; solids were studied as Nujol and fluorolube mulls.  
31
P and 
1
H
nmr spectra were obtained at 162 and 400 MHz on a Bruker AM 400 spectrometer. 
31
P chemical
shifts were measured relative to H
3
PO
4
 (85%, external), and 
1
H relative to TMS (internal).  Mass
spectra were recorded on a Finnigan 3300 mass spectrometer equipped with a gas inlet system
and a solid probe.
Gaseous reactants were obtained from Matheson.  Toluene and benzene (dried over
sodium) and acetonitrile (purified by distillation over phosphorus pentoxide and collected over
molecular sieves) were obtained from Fisher.  Thiophosphoryl chloride was obtained from
Aldrich and distilled prior to use.  Bromopentafluorobenzene was obtained from Columbia
Organics and dried over 4A molecular sieves prior to use.  Phosphorus trichloride was obtained
from Matheson, Coleman & Bell and distilled prior to use.  Silver hyponitrite was prepared by the
60
literature method.
27
  (CH
3
)
2
P(S)Br,
28
 (CH
3
)
2
P(O)Cl,
29
 (C
6
F
5
)
2
PBr,
30
 F
2
P(O)Br,
31a
 and F
2
PBr
31b
were prepared by literature methods.
The reaction of dimethylthiophosphinic bromide with silver hyponitrite in 2:1 ratio
 (CH
3
)
2
P(S)Br (0.462 g, 2.67 mmol) was placed in a 100 mL three-necked flask
containing a magnetic stirring bar.  Toluene (30 mL) was added to the flask to dissolve the
bromide.  Silver hyponitrite (0.382 g, 1.38 mmol) was placed in a thumb-shaped solid addition
tube and added slowly over a period of 15 minutes at room temperature.  The system was
protected from light by wrapping the flask with aluminum foil.  The collected gas (1.33 mmol)
was shown to be N
2
O by its infrared and mass spectra.  The yellowish liquid was filtered off and
the solvent was removed in vacuo to give 0.269 g of solid, identified as (CH
3
)
2
P(S)OP(S)(CH
3
)
2
by its 
31
P nmr and infrared spectrum.
Several low-temperature reactions were carried out to see if any hyponitrite,
(CH
3
)
2
P(S)ON=NO(S)P(CH
3
)
2
, could be detected.  In one of those reactions, 0.219 g (1.27 mmol)
of dimethylthiophosphinic bromide was taken in a 100 mL flask as described in the previous
reaction, using 25 mL of toluene and 0.205 g (0.74 mmol) silver hyponitrite.  The reaction flask
was placed in a dry-ice acetone slush bath to keep the reaction mixture at -78
o
C.  The silver
hyponitrite was then added slowly over a 10-minute period.  After 20 minutes, no volatiles were
observed.  The reaction flask was then quickly transferred to a chlorobenzene-liquid nitrogen
slush bath (-45
o
C).  Again no gas was detected after 20 minutes.  The reaction flask was then
transferred to a carbon tetrachloride-liquid nitrogen slush bath (-23
o
C).  After 20 minutes, 2 torr
(V=396 mL) pressure was observed.  The color of the reaction mixture did not change.  The
reaction flask was then transferred to an ice bath.  After a while the pressure observed was 13 torr
(V=396 mL).  The reaction went to completion at this temperature.  In the second batch, the
reaction was monitored by 
31
P nmr on a Bruker AM 400 instrument at ?30
o
C, using 0.0981 g
61
(0.47 mmol) of the bromide.  From the previous low-temperature reaction, it was thought that the
reaction might have started well below ?23
o
C.  Therefore, the reactants were mixed at
bromobenzene-liquid nitrogen temperature (-30
o
C).  The amount of silver hyponitrite taken was
0.079 g (0.03 mmol).  After mixing the reactants for 20 minutes, a 2 mL portion of the solution
was transferred by a syringe into an nmr tube and the spectrum was recorded at ?30
o
C.  Two
peaks were found at 66.0 ppm and 91.3 ppm.  These peaks were assigned to
dimethylthiophosphinic bromide and (CH
3
)
2
P(S)OP(S)(CH
3
)
2
, respectively.
32
  The reaction was
allowed to go for six hours.  Again a 2 mL portion of the liquid from the flask was syringed out
and the 
31
P nmr spectrum was taken at -30
o
C.  Only one peak was observed at 91.3 ppm, which
corresponds to the phosphorus chemical shift in (CH
3
)
2
P(S)OP(S)(CH
3
)
2
.
The mass spectrum of the solid product showed the following peaks:
M
+
=[(CH
3
)
2
P(S)OP(S)(CH
3
)
2
+
] 202(44%); (M-CH
3
)
+
 187(3%); (M-HS)
+
 169(27%); (M-CH
3
-S)
+
155(3%); (CH
3
)
2
P(S)OH
+
 110(7%); (CH
3
)
2
PS
+
 93(100%); H
2
C=PS
+
 77(58%); PS
+
 63(45%); PO
+
47(77%); PCH
2
+
 45(51%); CH
3
+
 15(41%).  Mass spectrum of the gaseous product: N
2
O
+
44(100%); NO
+
 30(35%).
The infrared spectrum of the gaseous sample is given below (all values in cm
-1
) N
2
O:
2234(s), 2214(s), 1299(s), 1272(s).
Reaction of dimethylphosphinic chloride with silver hyponitrite in 2:1 ratio
Dimethylphosphinic chloride (0.331 g, 2.96 mmol) was dissolved in 20 mL toluene (Na
dried) in a 100 mL three-necked flask equipped with a magnetic stirring bar.  Silver hyponitrite
(0.440 g, 1.60 mmol) was placed in a thumb-shaped tube with ground joint and fitted to the flask.
The flask was then evacuated on the vacuum line.  The entire flask including the thumb-shaped
tube was wrapped with aluminum foil to protect the contents from light.  Silver hyponitrite was
then added to the solution over a period of 20 minutes.  The heterogeneous mixture was stirred
62
for two hours at room temperature.  The flask was then connected to the vacuum line and the
gaseous product was collected (1.46 mmol) at ?196
o
C.  The gas was shown to be N
2
O by infrared
and mass spectrometry.  The mixture in the three-necked flask was filtered and the solvent was
evaporated from the filtrate under high vacuum.  The solid recovered was 0.247 g (98% yield)
based on the amount of (CH
3
)
2
P(O)Cl reacted.  The 
31
P nmr of the solid run in toluene showed
only one signal at 49.6 ppm.  The mass spectrum of the compound (CH
3
)
2
P(O)OP(O)(CH
3
)
2 
was:
M
+
 peak not observed; (CH
3
)
2
PO
2
H
+
 94(41%); (CH
3
)
2
P(O)H
2
+
 79(100%); HPO
+
 48(4%); H
2
PO
+
49(7%); PO
2
+
 63(3%); (CH
3
)
2
P=O
+
 77(5%).  The mass spectrum and the infrared spectrum of the
gas collected at ?196
o
C is identical with that reported above.  The infrared of the solid in Nujol
showed the following peaks (all values in cm
-1
): 1305(s)(P=O), 972(vs)(P-O-P, asym.), 871(s)(P-
O-P, sym.), 723(m)(P-C).
Reaction of difluorophosphinic bromide with silver hyponitrite in 2:1 ratio
The reaction of difluorophosphinic bromide was performed in the absence of light.
F
2
P(O)Br (9.20 mmol) was condensed into a Fisher-Porter tube charged with silver hyponitrite
(1.701 g, 6.20 mmol).  The mixture was warmed to room temperature and left for two hours.  The
product was passed through four traps at ?78
o
C, -130
o
C, -160
o
C, and ?196
o
C.  The ?78
o
C and
?130
o
C traps each contained 4.40 mmol of gas with a liquid mixture of F
2
P(O)Br and
F
2
P(O)OP(O)F
2
33
 (as indicated by infrared).  There were no products in the ?160
o
C trap.  The
?196
o
C trap contained 4.0 mmol of a gas identified as N
2
O by its mass spectrum and infrared
spectrum.  The data are the same as that obtained for N
2
O in previous reactions.
The infrared spectrum of the samples from the ?78
o
C and ?130
o
C traps showed the
following absorptions (all values in cm
-1
): 1425(s)(P=O) F
2
P(O)OP(O)F
2
; 1375(ms) F
2
P(O)Br;
1325(s) F
2
P(O)Br; 1075(vs)(POP asym. stretch) F
2
P(O)OP(O)F
2
; 993(s)(POP sym. stretch)
63
F
2
P(O)OP(O)F
2
; 976(vs) F
2
P(O)OP(O)F
2
; 942(vs) F
2
P(O)Br; 899(s) F
2
P(O)OP(O)PF
2
; 885(vs)
F
2
P(O)Br; 560(vs) F
2
P(O)Br.
The mass spectra showed the following peaks for the gas in the  -130
o
C trap: F
2
P(O)Br
+
164(91%), 166(91%); FP(O)Br
+
 145(37%), 147(37%); F
3
PO
+
 104(91%); PF
3
+
 88(21%); F
2
PO
+
85(100%); PF
+
 50(35%); PO
+
 47(71%).
Reaction of bis(perfluorophenyl)bromophosphine and silver hyponitrite in 2:1 ratio
(C
6
F
5
)
2
PBr (1.171 g, 2.63 mmol) was dissolved in 25 mL benzene (Na dried) in a three-
necked flask.  The arrangement and precautions were the same as the previous reactions.  Silver
hyponitrite (0.376 g, 1.36 mmol) was added slowly over a period of 10 minutes and the mixture
was stirred for two hours at room temperature and then filtered.  The amount of product,
recovered from the filtrate by removing the solvent in vacuo, was 0.956 g.  The gas evolved (1.27
mmol) was N
2
O, identified by mass spectral and infrared data.  The 
31
P nmr spectrum run in
benzene showed a multiplet (apparent nonet) at +93.4 ppm assigned to (C
6
F
5
)
2
POP(C
6
F
5
)
2
.  The
mass spectrum of the white solid, (C
6
F
5
)
4
P
2
O, was: (C
6
F
5
)
4
P
2
O
+
 746(30%); C
24
F
19
P
2
O
+
 727(3%);
(C
6
F
5
)
3
P
2
O
+
 579(11%); (C
6
F
5
)
3
P
+
 532(25%); (C
6
F
5
)
2
PO
+
 381(92%); (C
6
F
5
)
2
P
+
 365(50%); C
12
F
8
+
296(100%); C
12
F
7
+
 277(11%); C
6
F
5
PF
+
 217(58%); C
6
F
5
P
+
 198(22%); C
6
F
4
P
+
 179(15%); C
6
F
4
+
148(20%); C
6
F
3
+
 129(95%); C
5
F
3
+
 117(35%); CF
3
+
 69(100%); PO
+
 47(8%).  The infrared
spectrum showed two intense peaks at 909 and 640 cm
-1
 (P-O-P asym. and sym.).  The absorption
at 1465(s) and 1102(s) cm
-1
 are P-C stretching modes, while the bands at 1377(s), 1303(s), and
1232(s) cm
-1
 are C-F stretching bands.  The N
2
O gas was identified as previously described.
Reaction of Bromodifluorophosphine and silver hyponitrite in 2:1 ratio
Silver hyponitrite (1.701 g, 6.2 mmol) was placed in a Fisher-Porter tube wrapped in
aluminum foil.  F
2
PBr gas (12.4 mmol) was condensed into the tube.  The mixture was warmed to
64
room temperature and kept for two hours.  The reactor contents were passed through ?90
o
C,
-130
o
C, -160
o
C, and ?196
o
C traps.  Nothing was collected in the ?90
o
C trap.  The ?130
o
C trap
contained 5.4 mmol of gas.  The infrared spectrum showed it to be a mixture of F
2
POPF
2
34
 and
F
2
PBr.  The ?160
o
C trap stopped 4.1 mmol of gas which was identified as N
2
O from its infrared
and mass spectrum.  The mass spectrum of the products collected in the -130
o
C trap was:
F
2
POPF
2
+
 154(60%); F
2
POPF
+
 135(23%); F
3
PO
+ 
104(13%); F
2
PO
+ 
85(33%); PF
2
+
 69(29%); PF
+
50(65%); PO
+ 
47(49%); P
+
 31(4%); F
2
PBr
+
 148(96%); F
2
PBr
+
 150(100%); FPBr
+
 129(29%);
FPBr
+
 131(23%).  The mass spectrum of the -160
o
C trap gas was: F
2
POPF
2
+
 154(37%); F
3
PO
+
104(33%); F
2
PO
+ 
85(41%); PF
2
+ 
69(100%); PF
+ 
50(31%); PO
+ 
47(46%); N
2
O
+ 
44(85%).
3.3  Computational methods
The decomposition of the three phosphorus-containing hyponitrite species listed in
Scheme 1 (A, B, C), where A and C were the synthetic targets of the experimental study, were
considered in our computational study (numbering system is given for C).  Hyponitrite B was
included to examine the effects of asymmetric oxygen substitution on phosphorus.  The
Gaussian03 program package
35
 running on a Beowolf cluster was used for all calculations.  The
hybrid B3LYP combination of exchange and correlation functions, which has been shown to
yield good results for a number of inorganic systems,
36
 was used throughout.  For geometry
optimization, the 6-31+G(d) basis set was used for F, N, O, and P atoms and the LANL2DZ
37
effective core potential (ECP) and basis set was used for the Ag
+
 ion.  For transition states with
strong biradical character we applied the unrestricted broken-symmetry UB3LYP method with
the same basis set.  At every optimized geometry, frequency calculations were made using the
same level of theory to characterize the stationary points as minima (0 imaginary frequencies) or
transition states (1 imaginary frequency).  The transition vector of every TS structure was
animated with the Molden program.
38
  If necessary, intrinsic reaction coordinates (IRC) were
65
calculated to connect a TS to the corresponding minima.  After the reaction profile was
constructed, single-point calculations were performed on stationary points with the larger
6-311+G(2df) basis set for F, N, O and P and the standard SDD
39
 effective core potential and
basis set for Ag.  For convenience, ?SBS? is used to indicate B3LYP/6-31+G(d)+LANL2DZ and
?LBS? to indicate B3LYP/6-311+G(2df)+SDD.  The natural population analysis (NPA) charges
were obtained by using the NBO
40
 program implemented in the Gaussian program.
The reactions of F
2
PBr and F
2
P(O)Br with AgON=NOAg were carried out in neat liquid.
In order to estimate the effect of medium, single-point energy calculations were carried out using
the conductor polarizable continuum model (CPCM)
41
 at the B3LYP/6-311+G(2df) level with the
dielectric constant of THF.  While the dielectric constants of F
2
PBr and F
2
P(O)Br are unknown,
the dielectric constant of Cl
3
PO is known to be 14.0 which is reasonably close to THF (7.58).
42
NN
OO PP
FF
F F
NN
OO PP
FF
F F
N
1
N
2
O
2
O
1
P
2
P
F
3
F
1
F
2
F
4
O
O O
A
B
C
Scheme 1
66
The structures and geometrical parameters of F
2
PON=NOPF
2
 (A), F
2
P(O)ON=NOPF
2
(B), and F
2
P(O)ON=NOP(O)F
2
 (C) species are given in Figure 1.  Relative energies, enthalpies,
and free energies (kcal/mol) at the B3LYP/LBS//B3LYP/SBS level of theory are given for A in
Table 1, for B in Table 2, and for C in Table 3.  A table of spin-squared values, absolute energies,
and free energies of solvation in THF is available as supporting information (Table S1) as well as
Cartesian coordinates of all structures in Tables 1-3 and 5 (Table S2).  Reaction profiles of free
energies (kcal/mol) at 298K at the B3LYP/LBS//B3LYP/SBS level of theory are provided for A
(Figure 2), B (Figure 3), and C (Figure 4).
3.4  Results and Discussion:
The reactions of silver hyponitrite with (CH
3
)
2
P(S)Br, (CH
3
)
2
P(O)Cl, F
2
P(O)Br and
F
2
PBr have been evaluated as potential synthetic paths to the hyponitrites R
2
P(Y)ON=NOP(Y)R
2
(Y=O,S; R=CH
3
,F) and R
2
PON=NOPR
2 
(R=C
6
F
5
,F).  In all cases the reactions were carried out in
the absence of moisture and light (because silver hyponitrite is light-sensitive).  The gaseous
products were identified by infrared and mass spectra; the solids were identified by nmr, mass
and infrared spectra.  The results obtained in this series of reactions may be expressed by the
following general equations (eq 3):
 2R
2
P(Y)X + AgON=NOAg ? 2AgX + N
2
O + R
2
P(Y)OP(Y)R
2
                     (3a)
 (R=CH
3
,F; Y=electron-pair,O,S; X=halide)
 2R
2
PX + AgON=NOAg ? 2AgX + N
2
O + R
2
POPR
2
                   (3b)
 (R=C
6
F
5
,F; X=Br)
Thus, no hyponitrites were isolated from the above synthetic pathway even when reactions were
carried out at low temperatures.  In all cases, ?-oxo phosphorus-containing species were obtained.
67
The change in substituents from electron-releasing methyl groups to the highly electronegative F
(eq 3a, R=CH
3
,F) or from tri-coordinate phosphorus to pentavalent phosphorus, P=O or P=S (eq
3a, Y=electron-pair,O,S) did not change the reaction pathway.  We had hoped that the postulated
hyponitrites formed in these reactions might have a stability comparable to t-butyl hyponitrite.
Since the stability of t-butyl hyponitrite has been attributed to its lack of an ?-hydrogen,
2
 we
reasoned that the proposed hyponitrites of phosphorus might have comparable stability to t-butyl
hyponitrite because they also lacked an ?-hydrogen.
Cis-hyponitrites are known to be less stable than trans-hyponitrites.
43,44
  Therefore, the
fact that we do not observe a phosphorus-containing hyponitrite might be due to an initially
formed cis-hyponitrite (which decomposes) or to the rearrangement of the trans-hyponitrite to
cis-hyponitrite under experimental conditions.  It is interesting to note that the electronegative
fluorine or less electronegative perfluorophenyl groups on the trivalent phosphorus did not result
in an identifiable hyponitrite.  To determine whether this might have a thermodynamic or kinetic
origin, we turned to theoretical calculations.
Optimized geometries for the hypothetical hyponitrites are shown in Figure 1 and
natural population analysis (NPA) charges are given in Table 4.  For all three molecules, the cis
isomer has slightly shorter N=N bond lengths (about 0.007 ?) and longer N-O bond lengths
which indicate less ? delocalization in the cis compared to the trans isomer (Figure 1, AC/AT,
BC/BT, CC/CT).  As the phosphinyl (F
2
P) groups in F
2
PON=NOPF
2
 are oxidized to phosphoryl
(F
2
P(O)) groups (AC?CC), the O-P bond lengths are shortened from 1.667 to 1.634 ?.  The
oxidation to phosphoryl groups makes these phosphorus atoms more positively charged (III?V)
and leads to a strong bonding interaction between P
1
 and O
1
 (See Scheme 1 for numbering).
Interestingly, in the unsymmetrical F
2
P(O)ON=NOPF
2
 (BC), the phosphoryl P
1
-O
1
 bond length is
much shorter than the phosphinyl O
2
-P
2
 bond length (1.623 and 1.680 ?, respectively), while the
68
F
F
P
N
O
O
N
P
F
F
F
F
P O
O P
N N
F F
F
F
NN
O
P
O
F
P
F
F
P
F
F
O
N
O
N
P
F
F
F
P
OOP
NN
F
F
2.423
1.429
1.220
1.667
2.473
1.223
1.682
1.427
2.529
2.542
1.380
1.221
1.729
1.464
1.428
2.139
1.961
1.274
1.145
2.127
1.151
1.764
1.588
2.718
1.228
1.418
1.667
1.590
1.769
1.159
1.315
1.441
1.671
AC
AC-TS1
AC-1
AC-TS2
AT-TS
AC-TS3
AT
ACT-TS
NNOP = 82.6
ONNO =  4.5
NNOP = 15.5
ONNO =  0.3
ONNO = 92.1
F
F
FP
O
NN
P
O
F
1.676
1.676
1.603
F
N N
P
O
F
F
F
O
P
F
F
P
O
N N
O
P
F
F
(A)
Figure 1. (A) Calculated geometries for species on the following PES F
2
PON=NOPF
2
 (A) at the
B3LYP/SBS level.
69
F
P
O
N
O
F
F
O
N
P
F
F
O
F
O
P
NN
O
P
F
F
F
P
O
F
NN
F
OP
F
O
F
O
P
O
N
F
F
N
O
P
F
F
O
F
P
P
O
N
O
N
F
F
O
F
P
F
N
O
N
F
O
P
F
O
F
P
F
P
F
N
O
N
O
F
F
O
P
O
N
P
N
O
F
F
F
F
NN
O
OP
O
F
F
P
F
F
F
NN
PO
OP
F
O
F
1.460
1.623
1.450 1.407
1.680
1.220
1.456
1.405
1.222
1.459
1.627
1.701
3.045
1.506
1.217
1.358
1.756
2.536
1.622
1.460
2.015
1.151
1.286
1.921
2.280
1.567
1.479
1.454
1.646
1.221
1.401
1.713
1.475
2.786
2.711
1.467
1.594
1.735
1.149
1.807
1.574
1.476
1.712
1.395
1.219
1.638
1.474
1.739
1.812
1.157
1.596
1.467
1.578
1.679
1.4561.227
1.430
1.626
1.459
1.888
1.864
1.292
1.156
1.978
1.484
1.675
BC
BC-TS1
BC-1
BC-TS2
BC-TS4
BC-2
BC-TS5
BC-TS3
BCT-TS
BT
BT-TS
2.412
1.321
1.422
1.684
1.450
1.630
1.460
ONNO = 91.9
ONNO =  0.5
NNOP = 15.4
ONNO =  4.5
NNOP = 79.8
ONNO =  4.5
PONN = 83.2
ONNO =  3.6
PONN = 61.2
O
F
P
P
F
O
O
F
N N
F
(B)
Figure 1. (B) Calculated geometries for species on the PES of F
2
P(O)ON=NOPF
2
 (B) at the
B3LYP/SBS level.
70
Figure 1. (C) Calculated geometries for species on the PES of F
2
P(O)ON=NOP(O)F
2
 (C) at the
B3LYP/SBS level.
F
F
O
P
N
O
O
N
P
O
F
F
F
O
P
O
F
NN
F
O
P
O
F
O
P
F
O
F
N
F
N
O
P
F
O
F
F
O
P
N
O
N
F
O
P O
F
N
O
N
F
O
F
P
F
P
O
F
O
F
NN
OO
P
O
F
F
P
F
O
F F
O O
P
O O
P
N N
F F
1.220
1.426
1.634
1.458
2.402
1.220
1.417
1.664
1.470
1.445
1.474
1.651
2.999
1.220
1.421
1.663
1.470
1.436
1.656
2.860
1.474
1.146
1.879
1.283
2.047
2.030
1.588
1.465
1.469
1.142
1.801
1.593
1.469
2.758
1.569
1.572
1.227
1.634
1.415
1.458
1.568
1.570
1.150
1.801
1.596
1.469
1.458
1.640
1.430
1.328
ONNO = 91.7
CC
CC-TS1
CC-1
CC-TS2
CT
CCT-TS
CT-TS
CC-TS3
ONNO =  4.0
NNOP = 78.8
ONNO =  3.4
NNOP = 68.1
FF
OO
P
OO
P
NN
FF
(C)
71
Table 1. Relative Enthalpies and Free Energies (kcal/mol) on the Potential Energy Surface
of F
2
PON=NOPF
2
 at the B3LYP/LBS//B3LYP/SBS Level
a) Including solvation free energy calculated by CPCM method in THF.
Table 2. Relative Enthalpies and Free Energies (kcal/mol) on the Potential Energy Surface
of F
2
P(O)ON=NOPF
2
 at the B3LYP/LBS//B3LYP/SBS Level
?E
e
?H
0K
?H
298K
?G
298K
?G
THF
a
BC 0.0 0.0 0.0 0.0 0.0
BC-1 6.1 5.8 5.8 6.0 6.6
BC-2
b
8.5 8.2 8.3 8.3 7.5
BT 2.2 2.2 2.2 2.2 2.2
BC-TS1 7.4 7.1 6.6 7.4 7.9
BC-TS2 9.6 8.5 8.6 8.8 7.7
BC-TS3 14.5 11.9 12.5 10.5 10.9
BC-TS4
b
8.3 8.0 7.5 8.8 7.8
BC-TS5 30.4 29.5 29.2 30.8 28.9
BT-TS 19.2 16.5 17.1 15.3 15.7
BCT-TS 54.0 51.5 51.5 51.2 49.9
N
2
+OPF
2
+O
2
PF
2
-26.3 -30.4 -29.4 -51.7 -47.4
N
2
O+F
2
POP(O)F
2
-49.5 -50.2 -49.8 -60.9 -58.6
a) Including solvation free energy calculated by CPCM method in THF.
b) Geometry optimized at the B3LYP/cc-pVDZ level.
?E
e
?H
0K
?H
298K
?G
298K
?G
THF
a
AC 0.0 0.0 0.0 0.0 0.0
AC-1 6.0 5.7 5.8 5.7 6.0
AT 1.9 1.9 1.9 1.9 2.2
AC-TS1 6.8 6.6 6.1 7.0 7.5
AC-TS2 14.4 13.3 13.4 13.2 13.9
AC-TS3 11.5 9.1 9.7 7.8 9.3
AT-TS 15.5 13.1 13.9 12.1 13.1
ACT-TS 53.3 50.7 50.7 50.5 51.2
N
2
+2OPF
2
-44.3 -47.3 -46.5 -69.2 -66.2
N
2
O+F
2
POPF
2
-47.4 -48.2 -47.7 -58.3 -55.8
72
Table 3. Relative Enthalpies and Free Energies (kcal/mol) on the Potential Energy Surface
of F
2
(O)PON=NOP(O)F
2
 at the B3LYP/LBS//B3LYP/SBS Level
a) Including solvation free energy calculated by CPCM method in THF.   
b) Geometry optimized at the B3LYP/cc-pVDZ level.
O
1
-N
1
 and N
2
-O
2
 bond lengths change in the opposite direction (1.450 and 1.407 ?, respectively)
which suggests a resonance contribution from P
1
=O
1
?N
1
=N
2
=O
2
?P
2
.
The elimination of N
2
O can occur after the phosphorus-containing group (F
2
P or (F
2
P(O))
has rotated around the N-O bond.  This allows interaction between a phosphorus center and a
remote oxygen center (i.e. P
2
 with O
1
 in AC-1, BC-1, CC-1 or P
1
 with O
2
 in BC-2).  In AC-1 and
BC-1, the interacting phosphorus center is a ?OPF
2
 group which is more electrophilic than a
?OP(O)F
2
 group.  As a consequence, the non-bonded P
2
?O
1
 interactions in AC-1 and BC-1
cause the O
2
-P
2
 bond lengths to increase relative to AC and BC (1.667?1.729 and 1.680?1.756
? for AC?AC-1 and BC?BC-1, respectively).  In turn, the free energy of activation for
elimination of N
2
O is small for AC-1?AC-TS2 and BC-1?BC-TS2 (7.9, 1.1 kcal/mol,
respectively).  On the other hand, in BC-2 and CC-1, the ?OP(O)F
2
 group is the electrophile
which causes a much smaller increase in the P-O bond length relative to BC and CC
(1.623?1.646 and 1.634?1.656 ? for BC?BC-2 and CC?CC-1, respectively) and leads to a
?E
e
?H
0K
?H
298K
?G
298K
?G
THF
a
CC 0.0 0.0 0.0 0.0 0.0
CC-1
b
10.0 9.5 9.6 8.5 8.2
CT 2.0 1.9 2.0 1.9 2.1
CC-TS1
b
9.7 9.1 8.7 9.4 9.3
CC-TS2 29.9 28.9 28.8 29.3 25.8
CC-TS3 19.5 16.5 17.2 15.1 15.3
CT-TS 24.7 21.5 22.2 19.9 16.3
CCT-TS 54.3 51.8 51.9 51.5 52.3
N
2
+2O
2
PF
2
-9.7 -15.0 -13.9 -36.7 -30.7
N
2
O+F
2
P(O)OP(O)F
2
-49.8 -50.5 -50.0 -61.7 -59.2
AC
AT
AT-
T
S
0.
0
2.
2
13
.
1
AC
-
1
6.
0
7.
5
9.
3
13.
9
51
.
2
AC
-TS
3
-5
5
.
8
PF
2
-O
-PF
2
  
+ N
2
O
N
2
 + 
2
O
PF
2
-6
6
.
2
AC
-TS
2
AC
T
-
TS
AC
-TS
1
F
F
P
O
O
P
N
N
F
F
F
F
F
P
O
N
N
P
O
F
F
P
F
F
O
N
O
N
P
F
F
F
N
N
O
P
O
F
P
F
F
F
P
O
O
P
N
N
F
F
F
N
N
P
O
F
F
F
O
P F
F
P
N
O
O
N
P
F
F
F
F
P
O
N
N
O
P
F
F
N
N
F
O
P
F
N
N
O
F
F
P
O
P
F
F
 Figure 2.
Reaction profiles of free energies for the reaction of 
A
 in THF solution at the B3LYP/LBS//B3LYP/SBS level.
73
Figure 
3
.
Reaction profiles of free energies for the reaction of 
B
 in THF solution at
 the B3LYP/LBS//B3LYP/SBS level.
74
BT
0.0
2.2
15.7
BC
-1
6.6
7.9
10.9
7.7
52.5
BC
-
T
S
1
-5
8
.
6
F
2
P
(
O
)-O
-P
F
2
  +
 N
2
O
-
47.4
BC
28.9
BC
-TS
5
7.8
7.5
BT
-T
S
B
C
T-
TS
BC
-T
S3
BC
-
T
S
2
BC
-
T
S
4
BC
-
2
N
2
 + 
O
P
F
2
 + O
2
PF
2
O
F
P
P
F
O
O
F
N
N
F
F
N
N
O
O
P
O
F
F
P
F
F
O P
O
N
P
N
O
F
F
F
F
O
P
O
N
F
F
N
O
P
F
F
O
F
P
P
O
N
O
N
F
F
F
P
O
F
N
N
F
O
P
FO
O
F
P
F
P
F
N
O
N
O
F
O
F
P
F
N
O
N
F
O
P
F
FO
F
O
P
N
N
O
P
F
F
F
P
O
N
O
F
F
O
N
PF
F
F
N
N
P
O
O
P
F
O
F
N
N
N
N
O
F
O
P
F
O
F
F
P
O
F
PO F
F
O
P
F
Figure 
4
.
Reaction profiles of free energies for the reaction of 
C
 in THF solution at the B3LYP/LBS//B3LYP/SBS level
75
CT
0.
0
2.
1
16.
3
15.
3
25.
8
-
59.
2
F
2
P(
O
)
-
O
-P
(
O
)
F
2
 
 + N
2
O
CC
N
2
 + 2
O
2
PF
2
52.
3
-
30.
7
CC-
T
S
1
9.
3
8.
2
CT
-T
S
CC-T
S
3
CC-T
S
2
CCT
-T
S
CC-
1
F
F
O
P
N
O
N
F
O
P
O
F
F
F
O
O
P
O
O
P
N
N
F
F
F
F
O
O
P
O
O
P
N
N
F
F
O
P
F
O
F
N
F
N
O
P
FO
F
N
N
O
O
P
O
F
F
P
F
O
F
F
O
P
N
O
O
N
P
O
F
F
F
O
P
O
F
N
N
F
O
P
O
F
N
O
N
F
O
F
P
F
P
O
F
O
N
N
N
N
O
F
O
P
F
O
F
F
F
O
P
P
O
O
F
76
Table 4. Natural Population Analysis (NPA) Charges for Stationary Points at the
B3LYP/SBS level
a
P
1
P
2
N
1
N
2
O
1
O
2
O=P
1
O=P
2
Ag
AC 1.73 1.73 0.13 0.13 -0.70 -0.70
AC-1 1.75 1.71 0.11 0.18 -0.78 -0.71
AT 1.73 1.73 0.11 0.11 -0.68 -0.68
AC-TS1 1.74 1.70 0.14 0.14 -0.72 -0.69
AC-TS2 1.72 1.76 0.17 0.31 -1.12 -0.48
AC-TS3 1.80 1.80 0.13 0.13 -0.78 -0.78
BC 2.64 1.74 0.12 0.15 -0.70 -0.68 -1.02
BC-1 2.65 1.73 0.11 0.20 -0.79 -0.63 -1.02
BC-2 2.60 1.75 0.16 0.16 -0.70 -0.69 -1.02
BT 2.53 1.66 0.10 0.13 -0.64 -0.64 -0.97
BC-TS1 2.64 1.71 0.13 0.16 -0.72 -0.67 -1.01
BC-TS2 2.65 1.79 0.19 0.30 -1.07 -0.50 -1.05
BC-TS3 2.62 1.85 0.13 0.13 -0.72 -0.78 -0.99
BC-TS4 2.60 1.74 0.14 0.16 -0.71 -0.67 -1.02
BC-TS5 2.56 1.79 0.29 0.20 -0.49 -1.03 -1.04
CC 2.63 2.63 0.14 0.14 -0.67 -0.67 -1.01 -0.67
CC-1 2.62 2.60 0.15 0.17 -0.68 -0.69 -0.99 -1.11
CT 2.63 2.63 0.11 0.11 -0.65 -0.65 -1.01 -1.01
CS-TS1 2.62 2.60 0.15 0.16 -0.67 -0.69 -0.99 -1.02
CS-TS2 2.66 2.56 0.23 0.31 -1.07 -0.48 -1.02 -1.00
CS-TS3 2.61 2.61 0.14 0.14 -0.69 -0.69 -0.96 -0.96
AgCC
+
2.70 2.69 0.18 0.22 -0.72 -0.70 -1.11 -1.14 0.96
AgCC-TS2
+
2.69 2.65 0.33 0.37 -1.19 -0.48 -1.20 -1.03 0.95
AgCC-TS3
+
2.67 2.67 0.20 0.20 -0.80 -0.68 -1.04 -1.09 0.95
a) See Scheme 1 for numbering.
larger free energy of activation for N
2
O elimination (21.4, 17.6 kcal/mol for BC-2?BC-TS5,
CC-1?CC-TS2, respectively).
The transition states for rotation around the N=N bond, which interconverts cis- and
trans-hyponitrites (XCT-TS, X=A,B,C), were located.  The transition states, which have strong
biradical character (<S
2
>=1.01-1.02), are reached after about 92
o
 rotation around the N-N bond
which breaks the N=N ? bond and causes the N-N bond to elongate by about 0.1 ?.  The
77
activation enthalpies (298K) for the cis?trans rearrangement are very similar for AC, BC, and
CC (50.7-51.9 kcal/mol, Tables 1-3).
In all three cases the cis isomers are found to be global minima and trans isomers are
about 2 kcal/mol higher in free energy.  Their potential energy surfaces are very similar along the
free energy reaction coordinates (Figures 2-4).  Rotation about the N-O bond in the cis isomer
leads to a transition state (XC-TS1, X=A,B,C) and then an intermediate (XC-1,
X=A,B,C) followed by another barrier (XC-TS2, X=A,B,C) to yield N
2
O plus product.
The cis isomer is predicted not to form the trans isomer due to the high free energy
barriers for breaking the N=N bond ((XCT-TS, X=A,B,C), 51.2-52.5 kcal/mol).  We would like
to emphasize that these predictions are for unimolecular rearrangement of the cis isomer.  It is
possible that the coordination of an electrophile to the cis isomer could lower the barrier for cis
? trans isomerization.  For example, coordination of Ag
+
 to nitrogen could lower the barrier for
cis ? trans isomerization by stabilizing the transition state (Figure 5).
N N
O
O
P
F
P
F
F
Ag
+
N N O
O
P
F
F
P
F
F
Ag
+
N N
O
O
P
F
F
P
F
F
Ag
+
[Ag
+
 Catalyzed]
Figure 5. Illustration of possible catalytic effect of Ag
+
 on the cis?trans isomerization of
F
2
PON=NOPF
2
.
78
The trans isomers are predicted to undergo concerted synchronous fragmentation (XT-
TS, X=A,B,C) of both N-O bonds to form N
2
 plus two radicals.  Thus, if a trans isomer is
initially formed, it can only fragment to produce N
2
 because rearrangement to the cis isomer is
blocked by a high barrier (unassisted
reaction).  On the other hand, the cis isomer
can fragment to form either N
2
 (with radicals
formed) or N
2
O (with no radicals formed)
with competitive activation free energies
(Figures 2-4).  For A and C, the pathway for
N
2
 production is 4.6 and 10.5 kcal/mol lower
than the pathway for N
2
O production, while
for B, the N
2
O production pathway is lower
than the N
2
 production by 3.0 kcal/mol.  The
N
2
O production pathway for C is much
higher than for A or B because only the
?OP(O)F
2
 group (not the ?OPF
2
 group) can
attack the remote oxygen atom.
Since only N
2
O is observed with no
radical products for A and C, the N
2
O
production pathway must be the preferred
pathway under our experimental conditions.
If the phosphorus-containing hyponitrite (A,
B, or C) is an intermediate in the reaction,
this suggests: (1) the cis-hyponitrite is formed
in the reaction and (2) the cis-isomer
2.3362.366
1.475
1.624
1.435
1.216
1.453
1.613
1.477
2.195
2.590
1.507
1.460
2.271
2.692
1.518
1.794
1.273
1.123
2.339
2.307
1.497
1.580
1.865
1.145
1.723
1.602
1.487
AgCC-TS2
+
AgCC-TS3
+
OAgO = 139.5
ONNO =  12.1
NNOP =  96.5
OAgO = 105.9
ONNO =   5.4
NNOP =  68.2
OAgO = 95.9
ONNO =  1.8
NNOP =  1.3
F
O
Ag
P
O
O
O
N N
F
P
F
F
F
F
F
P
O
N
O
N
P
O
O
F
Ag
F
O
NN
O
P
F
P
O
Ag
O
F
F
AgCC
+
Figure 6. Optimized geometries of
F
2
P(O)ON=NOP(O)F
2
 with
Ag(I) at the B3LYP/SBS
level.
79
decomposes via the N
2
O production pathway.  While the two pathways (N
2
-production and N
2
O-
production) have very similar free energies of activations for A, the calculations clearly predict
N
2
 production for C, in conflict with experiment.  Thus, the reaction profile of C constructed by
considering all the thermodynamic corrections and solvation free energies fails to explain the
reaction mechanism.  The question is why.
The possibility that silver cation might have a catalytic effect on the decomposition of
the cis-isomer of C was considered.  Optimized geometries of silver cation complexes with C are
given in Figure 6.  The most stable Ag(I)-C complex is not with CC (the global minimum) but
rather with CC-1 due to the much stronger Ag(I) interactions with the P=O oxygens (2.366 and
2.336 ?, Figure 6). Structural parameters of AgCC
+
 show slightly longer bond lengths for O
1
-N
1
and N
2
-O
2
 than those of CC-1 but shorter P
1
-O
1
 and O
2
-P
2
 bond lengths.  Interestingly, O=P
1
,
O=P
2
 and N
1
-N
2
 bond lengths remain essentially the same.
The effect of Ag(I) on the PES of C is shown in Figure 7 and Table 5.  The binding
enthalpy (298K) of Ag
+
 to both P=O oxygen atoms of the bidentate ligand is 37.8 kcal/mol (Table
5) relative to the lowest conformation (CC) of the ligand and 47.4 kcal/mol relative to the less
stable CC-1 conformation.  In comparison, the experimental gas-phase binding enthalpy
45
 (298K)
of the first two waters to Ag
+
 is 58.7 (33.3+25.4) kcal/mol.  Calculated Ag
+
 binding enthalpies to
Table 5. Binding Energies, Enthalpies, and Free Energies (kcal/mol) of Ag(I) with
F
2
P(O)ON=NOP(O)F
2
a
?E
e
?H
0K
?H
298K
?G
298K
?G
THF
b
AgCC
+
37.9 37.6 37.8 30.1 6.0
AgCC-TS2
+
55.3 54.7 54.4 48.4 23.8
AgCC-TS3
+
41.8 41.0 41.3 33.2 7.7
a) Calculated at B3LYP/LBS+CPCM//B3LYP/SBS level.
b) Including solvation free energy calculated by CPCM method in THF.
Figure 7.
Comparison of the free energy reaction profiles for 
C
 in THF with 
C
 catalyzed by Ag(I) in THF.
80
15
.
3
25
.
8
8.
0
13.
6
CC
0.
0
Ag
+
 a
s
s
i
s
t
ed
 m
ech
a
n
i
s
m
U
n
im
o
l
ecu
la
r m
e
cha
n
is
m
CC-
T
S
C
CC-
T
S
B
Ag
CC-
T
S
3
+
6.
0
 F
2
P(
O)
OP
(O
)F
2
 
  
   +
  N
2
O
CC + 
Ag
+
Ag
CC-
T
S
2
+
Ag
CC
+
2
 + 
2
O
2
PF
2
-3
0.
7
-5
9.
2
N
2
 + 2
O
2
PF
2 
+ Ag
+
 F
2
P
(
O)
OP
(
O
)F
2
 
  
 +
 N
2
O +
 
A
g
+
-
24.
7
-5
3.
2
0.
0
FO
Ag
P
O
O
O
N
N
F
P
F
F
F
F
F
P
O
N
O
N
P
O
O
F
Ag
F
O
N
N
O
P
F
P
O
Ag
O
F
F
81
oxygen range from 32-38 kcal/mol (water, methanol, ethanol, diethyl ether, and acetone).
46
  In
THF (which models the F
2
P(O)Br neat reaction environment), the Ag
+
 cation is predicted to be
bound relative to Ag
+
 + CC by 6.0 kcal/mol in free energy (Figure 7).  The bound Ag
+
 has a
dramatic effect on the free energies of the two reaction pathways, N
2
-producing and N
2
O-
producing.  The bound Ag(I) reduces the free energy barrier of the N
2
O-producing pathway from
25.8 to 8.0 kcal/mol.  On the other hand, the bound Ag(I) reduces the free energy barrier of the
N
2
-producing pathway by only 1.7 kcal/mol (15.3?13.6 kcal/mol, Figure 7).  Thus, the Ag(I)
reverses the relative free energies of the two pathway compared to the Ag(I)-free reaction and
may explain why the N
2
O-producing pathway is observed experimentally.
The relative stabilities of possible radical products including PF
2
, OPF
2
 and O
2
PF
2
 were
also examined (Table 6).  The PF
2
 radical has been observed and computed
47
 but the OPF
2
 and
O
2
PF
2
 radicals have not yet been reported.  Some experimental evidence for the existence of
O
2
PF
2
 has been given.
48
  From the first four reaction enthalpies (298K) in Table 6, it can be seen
that the O-P bond enthalpies vary from 70.8 to 96.8 kcal/mol.  This variation can be understood
from differences in radical stabilization energies (RSE), i.e. the fact that the unpaired electron
density reorganizes from the nascent radical fragment to the final radical product.  From a
comparison of the spin densities and NPA charges (Table 7), it is clear that almost all of the
Table 6. Reaction Enthalpies and Free Energies (kcal/mol) for Radical Recombinations
Bond Energy ?E
e
?H
0K
?H
298K
?G
298K
?G
THF
b
PF
2
+OPF
2
 ? F
2
P-OPF
2
-72.2 -70.6 -70.8 -58.4 -58.8
OPF
2
+OPF
2
 ? F
2
PO-P(O)F
2
-83.0 -80.7 -81.0 -68.7 -67.7
PF
2
+O
2
PF
2
 ? F
2
PO-P(O)F
2
-92.3 -89.5 -89.8 -78.4 -80.5
OPF
2
+O
2
PF
2
 ? F
2
P(O)-OP(O)F
2
-100.0 -96.5 -96.8 -84.5 -84.8
OPF
2
+OPF
2
 ? F
2
P(O)-P(O)F
2
-63.5 -60.8 -61.1 -47.9 -46.0
OPF
2
+OPF
2
 ? F
2
PO-OPF
2
7.2 8.0 8.0 20.6 21.2
a) Calculated at B3LYP/LBS//B3LYP/SBS level.
b) Including solvation free energy calculated by CPCM method in THF.
82
unpaired spin density is on phosphorus in PF
2
 and OPF
2
 while it is distributed between the two
oxygen atoms in O
2
PF
2
.  Thus, the initial radical formed by breaking the N-O bond in N-OPF
2
will undergo significant RSE to form a radical with spin on the phosphorus center, while the
initial radical formed by breaking the O-P or N-O bond in O-PF
2
 or N-OP(O)F
2
 will undergo little
RSE.
Radical stabilization energies (RSE) are defined in this work as the enthalpy change of
the isodesmic reaction eq 4
HO-H + XO     ?    XO-H + OH                                                                                    (4)
X=PF
2
,OPF
2
where RSE=?H
rxn
=?H
products
-?H
reactants
.  From this isodesmic reaction, the RSE of OPF
2
 was
determined to be 24.2 kcal/mol, which is much larger than the value for O
2
PF
2
 (4.2 kcal/mol at
the B3LYP/LBS//B3LYP/SBS level including ZPC and C
p
 corrections to 298K).
Table 7. Atomic Mulliken Spin Densities and NPA Charges of Radical Species Calculated
at the B3LYP/SBS Level
PF
2
OPF
2
O
2
PF
2
Radical
Atom
Spin
Density
NPA
Charge
Spin
Density
NPA
Charge
Spin
density
NPA
Charge
P 1.02 1.17 0.77 2.03 -0.09 2.57
F -0.01 -0.58 -0.01 -0.55 0.01 -0.54
O 0.25 -0.93 0.53 -0.74
The much larger RSE of OPF
2
 compared to O
2
PF
2
 explains the large change in reaction
exothermicities in the N
2
-producing pathways of AC, BC, and CC (Tables 2-4; -46.5, -29.4, and
?13.9 kcal/mol, respectively).  The N
2
-producing pathway of AC breaks two N-OPF
2
 bonds
compared to one N-OPF
2
 bond for the BC reaction and none for the CC reaction.  The difference
83
in reaction exothermicities (??H
rxn
) is 17.1 kcal/mol for the BC/AC reactions and 15.1 kcal/mol
for the CC/BC reactions which approximately equals the difference between the RSE of OPF
2
and O
2
PF
2
 (20.0 kcal/mol).
Table 8. Kinetic and Thermodynamic Data (kcal/mol) for the Concerted N
2
-Producing
Pathway
a
trans-XN=NX
X=
?H
a
(298K)
N
2
-Producing
?H
rxn
(298K)
RSE
b
OPF
2
12.0 -48.4 2?24.2=48.4
O
2
PF
2
20.2 -15.9 2?4.2=8.4
OR 25-30
c
-6.3
d
~0
e
a) Calculated with respect to the trans hyponitrite isomer.  See Tables 1-3.
b) From eq 4.
c) See ref. 49 where R=CH
3
, CH
3
CH
2
, (CH
3
)
2
CH, and (CH
3
)
3
C.
d) See ref. 49 where R=(CH
3
)
3
C.
e) The RSE for the alkoxy radical (OR) is assumed to be near zero.
The variation in the activation enthalpies for the N
2
-procducing pathway for
XN=NX?2X+N
2
, X=OPF
2
,OP(O)F
2
 can also be understood in terms of the RSE of the radicals
produced; ?OPF
2
 and ?OP(O)F
2
 (Table 8).  When two OPF
2
 radicals are formed by the N
2
-
procducing pathway, the activation barrier is smaller than when two O
2
PF
2
 radicals are produced
(12.0 compared to 20.2 kcal/mol, Table 8) due to the much larger RSE of the OPF
2
 radicals.
Support for this interpretation comes from the experimental activation enthalpies of organic
hyponitrites RON=NOR, R=CH
3
,CH
3
CH
2
,(CH
3
)
2
CH,(CH
3
)
3
C which are known to produce N
2
upon decomposition
47
 with experimental barriers of 25 to 30 kcal/mol.
49
  It is reasonable to expect
the RSE?s of the RO radicals (R=CH
3
,CH
3
CH
2
,(CH
3
)
2
CH,(CH
3
)
3
C) to be small since little spin
reorganization is expected upon decomposition.  Therefore, it is expected (and found) that their
84
N
2
-producing barriers (25-30 kcal/mol) are larger than for either F
2
PON=NOPF
2
 or
F
2
P(O)ON=NOP(O)F
2
.
3.5  Conclusion
The reaction of neat F
2
PBr and F
2
P(O)Br with silver hyponitrite (AgON=NOAg) did not
produce the expected phosphorus-containing hyponitrites, F
2
PON=NOPF
2
 and
F
2
P(O)ON=NOP(O)F
2
, but rather N
2
O and ?-oxo phosphorus species.  A computational study of
XON=NOY, X,Y=PF
2
,P(O)F
2
 using density functional theory was carried out to explain the
absence of any phosphorus-containing hyponitrites.  Single-point energies (B3LYP/6-
311+G(2df)//B3LYP/6-31+G(d)) using the CPCM method with the dielectric constant of THF
were used to simulate the experimental environment of neat F
2
PBr or F
2
P(O)Br.  Two
dissociation pathways, N
2
-producing and N
2
O-producing, were considered.  For
F
2
P(O)ON=NOPF
2
, the N
2
O-producing pathway was lower in free energy while the two
pathways were of similar free energy in F
2
PON=NOPF
2
.  For F
2
P(O)ON=NOP(O)F
2
, the N
2
-
producing pathway was 10.5 kcal/mol lower in free energy which is in conflict with experiment
(only N
2
O is produced).  The disagreement is removed when the catalytic effect of Ag
+
 (present
from the silver hyponitrite reactant) is considered.  The Ag
+
 is predicted to lower the free energy
barrier of the N
2
O-producing pathway much more than the N
2
-producing pathway.
85
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88
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Rodriquez, C. F.; Hopkinson, A. C.; Siu, K. W. M. J. Phys. Chem. A 2002, 106, 2908.
(47) (a) Howe, J. D.; Ashfold, M. N. R.; Hudgens, J. W.; Johnson, III, R. D. J. Chem. Phys.
1994, 101, 3549.  (b) Burdet, J. K.; Hodges, L; Dunning, V.; Current, J. H. J. Phys.
Chem. 1970, 74, 4053.  (c) Nelson, W.; Jackel, G.; Gordy, W. J. Chem. Phys. 1970, 52,
4572.  (d) Wei, M. S.; Current, J. H.; Gendell, J. J. Chem. Phys. 1970, 52, 1592.  (e)
Hinchliffe, A.; Bounds, D. G. J. Mol. Struct. 1979, 54, 231.
(48) Eisenberg, M.; Desmarteau, D. D. Inorg. Chem. 1972, 11, 1901.
(49) Chen, H.-T. E.; Mendenhall, G. D. J. Am. Chem. Soc. 1984, 106, 6375.
89
CHAPTER 4
COMPUTATIONAL STUDY OF THE ?STABLE? BIS(AMINO)SILYLENE REACTION
WITH HALOMETHANES.  A RADICAL OR CONCERTED MECHANISM?
4.1  Introduction
The first report of the isolation of a stable silylene, N,N?-di-t-butyl-1,3-diaza-2-
silacyclopent-4-en-2-ylidene, 1, in 1994
1
 resulted in a flurry of publications investigating its
chemical and physical properties.  At the forefront of the research was the origin of its stability.
Both theoretical
2-10
 and experimental
8-12
 studies have concurred that ?-electron donation from the
?-substituent to the formally empty silicon p orbital and possible aromaticity of the 6-? electron
ring are the main factors causing the divalent silicon species to be stabilized.
Si
N
N
R
R
Si
N
N
R
R
Si
SiMe
3
Me
3
Si
Me
3
Si
SiMe
3
Si
N
N
R
R
Scheme 1
1  : R = t-Bu
A : R = H
2
90
In addition, there has been an active interest in the reactivity of 1 and related
silylenes.
12-18
  A divalent silylene, like the isolelectronic divalent carbene,
19
 can be a Lewis acid
or a Lewis base by virtue of its low-lying vacant p orbital (Lewis acid) and its nonbonding
electron pair (Lewis base).  It is now well established that acyclic silylenes and cyclic alkyl
silylenes behave as Lewis acids.
7a,12
  On the other hand, cyclic bis(amino)silylenes can act as
Lewis bases by donating the nonbonding electron pair on the silicon atom as in silylene-metal
complexes,
14-18
 or in Arduengo carbenes (1,3-diimidazol-2-ylidene).
19
As shown in Scheme 1, ? conjugation increases the electron population of the empty p
orbital on the Si atom which leads to lower acidity and higher basicity.  This can account for the
different reactivities of the two types of silylenes, dialkylsilylenes (Lewis acids) and
bis(amino)silylenes (Lewis bases).
A number of reactions utilize the electron donicity of 1, and are well understood.
13-17
However, few examples can be found for the reaction of 1 with Lewis bases.  Recently, reactions
of silylenes with halocarbons were reported.
18,20-22
  The reactions of dialkylsilylene, 2,2,5,5-
tetrakis(trimethylsilyl)silacyclopentane-1,1-diyl, 2, with halomethanes were studied by Ishida et
al.
20
  The reactions of 2 with CCl
4
 and CHCl
3
 gave dichlorosilane by a radical mechanism.
Methyl iodide also reacts with 2 to give a single insertion product.  However, the reaction with
CH
2
Cl
2
 gave double insertion products in which two Si atoms are bonded to a carbon atom.  The
authors
20
 suggested that the activation of the C-Cl bond by silylene complexation would facilitate
the nucleophilic attack of another silylene and proposed a Lewis acid-Lewis base reaction
mechanism via an acid-base complex.  Similarly, the reactions of 1 with halomethanes (Scheme
2) were reported by West and co-workers.
18,21,22
  The reaction between 1 and ICH
3
 was reported
to give a 1:1 adduct as exclusive product, while  chlorocarbons, except for t-BuCl, reacted with 1
to give a 2:1 adduct.  Interestingly, reaction with bromobenzene gave mixed products of the 1:1
and 2:1 adducts (Scheme 2).  Further investigation showed that the proportion of product yields,
91
1:1 and/or 2:1 adducts, changed depending upon the ratio of the reactants.  Also, increasing the
bromobenzene ratio led to a higher proportion of 1:1 adduct with exclusively 1:1 adduct after four
equivalents of bromobenzene.  From these observations, a radical mechanism was suggested
Si
N
N
R'
R'
R' =  t-Bu
R"X
+
Si
N
N
R'
R'
Si
N
N
R'
R'
Si
N
N
R'
R'
X
R"
X
R"
X = Cl;
R" = CH
2
Cl, 
          CHCl
2
, 
          CCl
3
, 
          CH
2
Ph
X = I; R" = CH
3
X = Cl; R"= t-Bu
X = Br; 
R" = Ph
Scheme 2
for the formation of the 1:1 adducts with ICH
3
, but a 1,2-shift mechanism with bromobenzene
and t-BuCl via a 1:1 intermediate complex.  For chlorocarbons, a halophilic mechanism via a 1,3-
shift from a 2:1 intermediate complex was proposed.  Both silylenes, 1 and 2, show similar trends
92
of reactivities towards halomethanes, even though they have completely different chemical
properties.
Recently theoretical studies on the mechanism of halophilic reactions of silylene A
(Scheme 1) with ClCH
3
, CHCl
3
 and CHBr
3
 were reported at the B3LYP/6-31G* level.
23
  The
author suggested that the reactions follow the general pathway: insertion of silylene into a
halogen-carbon bond followed by dimerization with another silylene to form the final 2:1 reaction
product.  However, the reported results cannot completely account for the experimental
observations.  If the disilane product (2:1 adduct) were formed via initial insertion into Si-X bond
of the 1:1 product, the 1:1 product should be observed in the reaction of silylene 1 with a 100-fold
excess of CHCl
3
 as is the case in the reaction with bromobenzene.
22
  Furthermore, the possibility
of radical involvement was excluded in the study, since only restricted DFT calculations were
performed.
23
  Therefore, we felt that it is necessary to reinvestigate the reaction of
bis(amino)silylene (A) with halomethanes to consider the radical mechanism.  This work has
been published in Journal of Physical Chemistry A in 2005.
24
4.2  Computational Details
Possible reactions of silylene A with XCH
3
 (X=Cl, Br, I) were examined by using density
functional theory
25
 implemented in the Gaussian03 program.
26
  The hybrid B3LYP combination
of exchange and correlation functionals
25b
 was utilized throughout this study.  Geometry
optimizations of all stationary points were performed with a 6-31+G(d) basis set for H, C, N, Si,
Cl and Br and with a standard LanL2DZ
27
 effective core potential (ECP) and basis set for I
(Figure 1).  At each stationary point, vibrational frequencies were calculated to confirm whether it
was a minimum (no imaginary frequencies) or transition state (one imaginary frequency).  At
every transition state, the transition vector was animated with the Molden program,
28
 and if
necessary, the intrinsic reaction coordinate (IRC)
29
 was computed to connect the corresponding
93
minima.  To obtain a better energetic description of the reaction profile, single-point calculations
were performed with a larger 6-311++G(2df,p) basis set for all atoms except for I, for which the
SDD
30
 ECP and basis set were used.  Thermodynamic corrections to 298K, zero-point vibrational
energy corrections (ZPC), heat capacity corrections (C
p
), and entropy corrections (?S) obtained at
the B3LYP/6-31+G(d)+LanL2DZ level were applied to single-point energies at the B3LYP/6-
311++G(2df,p)+SDD level.  The reaction profiles were constructed based on relative free
energies at 298K (Figure 2-4).  For convenience, ?SBS? will be used to denote the 6-
31+G(d)+LanL2DZ basis set and ?LBS? to denote the 6-311++G(2df,p)+SDD basis set.  The
transition states on the singlet PES were tested to determine whether a spin broken-symmetry
solution was lower in energy.  If so, the transition state was reoptimized with the spin broken-
symmetry method.  These structures are tabulated in Table 1 (Cl-TS3, Br-TS2, Br-TS3, I-TS2)
with the <S
2
> expectation value.  A notation scheme is used in the text, Figures, and Tables for
the various structures where ?X? is the halogen (Cl, Br, or I), ?A? is the cyclic
bis(amino)silylene, ?D? stands for two cyclic silylene units bonded with a Si-Si bond, and ?P?
stands for a product.
Natural population analysis (NPA) was carried out on the important radical intermediates
at the UB3LYP/SBS level by utilizing the NBO program
31
 implemented in Gaussian to explain
the different reactivity of silylene toward halomethanes.  In addition, Si-CH
3
 and Si-X bond
enthalpies were determined in X-P1 (Figure 1; X=Cl, Br, I) and compared with X-CH
3
 bond
enthalpies.
4.3  Results and Discussion
Bond lengths and bond angles of A optimized at the B3LYP/6-31+G(d) level are in good
agreement with those at the MP2/6-311G(d) level
2b
 and also agree with those determined by gas-
phase electron-diffraction
1
 and solid state X-ray diffraction
32
 of the t-Bu derivative, 1 (Figure 1a).
94
Table 1. Calculated Electronic Energies (hartrees), Zero-Point Energies, Heat Capacity
Corrections to 298K (kcal/mol), Entropy (cal/mol?K) and Spin-Squared Values
(<S
2
>) are Calculated at the B3LYP/SBS Level
ZPC C
p corr
S<S
2
> B3LYP/SBS B3LYP/LBS
A 41.9 3.4 67.6 -477.64745 -477.73632
AT
a
40.6 3.9 74.6 2.01 -477.55314 -477.63895
CH
3
18.8 2.5 46.5 0.75 -39.84264 -39.85653
Me-A 64.1 5.0 82.9 0.76 -517.53588 -517.63997
Me-D 106.3 9.0 118.1 0.76 -995.19985 -995.39464
Me-TS 61.2 6.0 95.6 0.75 -517.49031 -517.59302
MeD-TS 106.3 8.7 122.3 0.76 -995.18501 -995.37706
ClCH
3
23.9 2.5 56.0 -500.11152 -500.15697
Cl-A 42.2 4.6 82.1 0.76 -937.86658 -937.98978
Cl-D 84.6 8.5 115.6 0.76 -1415.53326 -1415.74792
Cl-P1 65.9 6.0 90.0 -977.83386 -977.97601
Cl-P2 107.8 10.0 125.4 -1455.48668 -1455.71920
Cl-TS1 65.0 6.0 93.8 -977.67677 -977.81091
Cl-TS2 64.3 6.3 97.2 -977.67376 -977.81063
Cl-TS3 62.7 6.7 100.6 0.69 -977.70646 -977.84346
ClD-TS 84.6 8.2 115.8 0.76 -1415.51770 -1415.72991
ClA-TS 65.2 7.5 109.9 0.76 -1437.95702 -1438.13061
ClMeA-TS 87.3 7.9 112.3 0.76 -1017.63345 -1017.78579
ClMeD-TS 129.2 11.9 147.0 0.76 -1495.29462 -1495.53768
ClDCl-TS 107.5 11.4 143.3 0.76 -1915.62568 -1915.88940
BrCH
3
23.5 2.5 58.8 -2611.63240 -2614.07317
Br-A 42.1 4.7 85.0 0.76 -3049.39289 -3051.90445
Br-D 84.5 8.7 118.9 0.76 -3527.06051 -3529.66078
Br-P1 65.7 6.1 92.5 -3089.35807 -3091.88715
Br-P2 107.6 10.2 127.9 -3567.01446 -3569.63195
Br-TS1 64.8 6.1 95.7 -3089.20762 -3091.73264
Br-TS2 62.7 6.7 103.6 0.71 -3089.21634 -3091.74032
Br-TS3 61.2 7.5 111.8 1.00 -3089.23614 -3091.76072
BrD-TS 84.5 8.2 116.8 0.76 -3527.04677 -3529.64438
BrA-TS 64.7 7.6 114.5 0.76 -5661.02212 -5665.96792
BrMeA-TS 87.3 7.8 113.2 0.76 -3129.17238 -3131.71068
BrMeD-TS 129.1 12.0 148.4 0.76 -3606.83581 -3609.46322
ICH
3
23.2 2.6 60.8 -51.29691 -51.34492
I-A 42.1 4.8 87.6 0.76 -489.04402 -489.17480
I-D 84.5 8.7 120.9 0.76 -966.70179 -966.92838
I-P1 65.6 6.2 95.0 -529.00236 -529.15297
I-P2 107.7 10.2 129.5 -1006.65409 -1006.89921
I-TS1 64.6 6.2 98.4 -528.86767 -528.99464
I-TS2 62.4 6.9 107.3 0.82 -528.87552 -529.00960
ID-TS 84.3 8.4 121.3 0.76 -966.69006 -966.91470
IA-TS 63.9 8.0 120.9 0.78 -540.32671 -540.51151
IMeA-TS 86.9 8.0 116.1 0.77 -568.82684 -568.98773
-continue-
95
-continued-
ZPC C
p
 
corr
S<S
2
> B3LYP/SBS B3LYP/LBS
IMeD-TS 128.9 12.0 148.8 0.77 -1046.48418 -1046.74062
CH
2
Cl
2
18.6 2.8 64.6 -959.70053 -959.77776
CHCl
3
12.5 3.4 70.7 -1419.28431 -1419.39407
CCl
4
5.8 4.1 74.2 -1878.85980 -1879.00285
Cl2-TS 58.3 7.0 108.1 0.60 -1437.30515 -1437.47319
Cl3-TS 53.1 7.5 114.0 0.49 -1896.89944 -1897.09927
Cl4-TS 47.1 8.2 118.6 0.35 -2356.48627 -2356.71888
SiM 76.9 5.4 83.4 -556.26415 -556.26415
SiM-TS 97.6 8.9 119.5 0.67 -1056.32575 -1056.48006
SiM-Cl2TS 93.2 9.2 125.4 0.59 -1515.92477 -1516.11026
a) Triplet silylene A.
The slightly longer Si-N bond lengths in A than in 1 can be rationalized by greater electron
donation from the t-Bu group in 1.  The possible radical intermediates, X-A (X=Cl, Br, I) and
Me-A, show interesting characteristics.  Since the 4n+2 ?-electron system is interrupted by the
addition of a halogen radical in X-A or a methyl radical in Me-A, the Si-N bonds lengthen
(0.047-0.053 ? in X-A and 0.028 ? in Me-A).  In addition, the C-C bonds become longer and the
C-N bonds shorter indicating a greater degree of localization in the (-NHCH)
2
 unit.  When the
methyl radical is added (Me-A), the C-C and C-N bond lengths show very little change, while the
Si-CH
3
 bond is long (1.923 ?) compared to other Si-C bonds.  Electron donation from the methyl
group strengthens the Si-N bonds and increases delocalization over the (?NHCH)
2
 unit.  On the
other hand, the halogen atom withdraws electron density from the silicon atom and weakens (and
lengthens) the Si-N bonds.  The atomic NPA charges and spin densities of X-A and Me-A
support this interpretation (Table 2).  When a Cl or Br atom is attached to A (Cl-A or Br-A), the
spin density is delocalized over the ring with very little spin density on the halogen atom, while,
in contrast, the iodine atom has significant spin density in I-A.  In Me-A, most of the spin density
resides on silicon (0.62 e
-
) due to 2c-2e Si-C bond formation and the prerequisite electron
promotion.
96
Figure 1. Geometries optimized at
B3LYP/6-31+G(d) level where bond lengths are in ?, angles are in degrees, and Sch?nflies symbols are given in parentheses.
             (a) Geometrical parameters
for stationary points in the reaction of 
A
 with ClCH
3
.
The geometry of 
A
 is
compared with MP2/6- 311G(d)
2b
 underlined; with
1
 by gas phase electron
diffraction
1
 in parentheses;
and with 
1
 by X-ray
diffraction
32
 
italicized.
The geometry of 
Cl-P2
 is
compared with X-ray diffraction
22
 where the 
t
-
Bu groups have replaced the hydrogens on nitrogen.
N
C
C
Si
N
Cl
C
Cl
N
C
C
N
Si
C
C
Si
N
N
N
C
C
Si
N
Cl
C
Cl
N
C
Si
N
C
C
N
C
Si
N
C
A (
C
2v
)
1.
7
7
9
1
.
7
6
5
1.
7
5
1
(1.
7
53)
1
.
391
1
.
3
8
4
1
.
383
(
1
.
400)
1.
360
1
.
3
6
4
1.
341
1.
347
)
84.
9
8
5
.
0
88.
2
(90.
5)
1
12.
0
1
1
1
.
6
1
09.
5
(
1
14.
1
)
N
CC
Si
N
Cl
-
T
S2
Cl
-
T
S
1
2.
4
7
2
2.
5
6
8 2.
9
6
9
1.
777
1.
80
7
1.
3
7
3
1.
37
2
1.
37
9
N
Si
C
C
N
C
Cl
2.
458
2.
700
2.
582
1.
771
1.
39
3
1.
3
9
6
1.
3
5
8
1.
77
2
1
.
372
Cl
-
T
S
3
1.
801
1.
37
7
2.
2
5
9
2.
602
C
l
-A
(C
s
)
1.
83
2
1.
3
6
4
1.
382
2.
16
8
N
C
Si
C
Cl
N
Cl
D-
TS
Cl
-
P
1(
C
s
)
1.
418
2.
123
1.
868
1.
73
9
1.
3
4
8
2.
1
8
6
3.
27
8
1.
77
2
1
.
778
1.
8
1
1
1.
82
4
1.
36
9
1.
37
8
1.
36
9
1.
393
1
.
362
1.
387
N
C
Si
C
C
Cl
C
N
N
N
Si
N
C
C
Si
C
N
Cl
3.
01
3
Cl
-
P
2
2.
16
4
2.
10
3
2.
371
2.
423
1.
883
1.
937
1.
7
5
5
1.
7
3
7
1.
75
7
1.
74
2
1.
74
9
1.
72
5
1.
7
5
5
1.
7
3
5
1
.
413
1.
41
7
1.
349
1.
4
1
9
1.
348
1.
41
8
Cl
-
D
2.
1
5
9
2.
4
0
8
1.
38
0
1.
81
0
1.
7
4
7
1.
74
6
1.
412
1.
4
1
2
1.
3
7
8
1.
3
6
9
1.
350
1.
81
0
Figure 1. (b)
Geometrical parameters of stationary points in the reaction of 
A
 with BrCH
3
.
N
C
Si
C
N
C
Br
N
C
C
Si
C
N
Br
N
C
Si
C
N
Br
C
N
C
Si
N
Br
C
Br
-TS
1
2.
6
2
1
3.
09
7
2.
57
1
1.
78
1
1
.
811
1.
3
7
8
1.
372
1.
3
7
3
Br
-TS
3
3.
750
2.
33
7
1.
8
2
5
1.
36
6
1.
38
0
B
r
-T
S
2
(C
s
)
2.
649
3.
53
7
2.
5
6
8
1.
81
2
1.
371
.3
7
7
N
Si
C
C
N
Br
C
Br
-A
(C
s
)
2.
3
3
9
1.
83
0
1.
382
1.
3
6
4
Br
-P
1(C
s
)
1.
868
2.
28
8
1.
7
4
0
1.
41
8
1
.
348
Br
-P
2
Br
D-TS
3.
1
5
3
1.
77
1
1.
77
9
2.
3
6
2
1.
819
1.
80
5
1.
3
7
0
1.
370
1.
377
1.
3
9
1
1.
38
5
1.
362
2.
9
0
8
2.
334
2.
368
1.
744
1.
7
5
6
1.
74
9
1.
416
1.
3
4
9
1.
413
1.
882
1.
4
1
7
1.
34
8
1.
419
1.
75
3
N
C
C
Si
N
C
N
C
Si
N
Br
Br
N
C
C
N
Si
C
C
Si
N
N
C
Br
-
D
2.
408
2.
331
1.
80
8
1.
8
1
0
1.
3
7
7
1.
370
1.
380
1.
746
1.
748
1.
412
1.
4
1
1
1.
35
0
N
C
Br
C
C
N
Si
C
N
N
Si
Me
-
T
S
3.
755
1.
7
8
0
1.
391
1
.
360
N
C
Si
C
N
C
97
N
N
Si
C
C
Si
C
N
C
N
C
I
N
C
N
C
Si
C
C
N
Si
N
C
N
I
C
C
N
C
Si
C
N
N
Si
C
C
N
N
Si
C
N
Si
C
I
N
N
C
C
Si
C
N
I
N
C
Si
C
N
I
N
C
Si
C
C
N
I-
T
S
1
I-
T
S
2
(
C
s
)
3.
487
2
.
899
2.
602
1.
81
0
1
.
789
1
.
376
1.
3
7
5
1
.
370
3.
047
3.
7
7
6
1
.
810
1.
368
2.
9
0
2
1
.
379
Si
N
C
I
C
N
C
I-
P1
(
C
s
)
2.
566
1.
870
1.
740
1.
416
1.
349
ID
-
T
S
1.
3771.
3
6
9
1
.
3701.
81
6
1.
801
3.
1
5
3
2
.
688
3.
357
1.
7
7
2
1.
363
1.
391
1.
7
7
9
1.
386
I-
P2
2.
3
8
0
2.
655
1.
8
8
0
1.
754
1.
751
1.
417
1
.
349
1
.
419
1.
74
5
1
.
750
1.
4
1
3
1.
410
1.
351
M
e
-A
(C
s
)
1.
807
1.
386
1.
365
1.
9
2
3
Me
D
-
T
S
1.
921
3.
5
1
7
1.
80
0
1.
386
1.
8
0
1
1.
3
8
7
1.
365
1.
779
1.
777
1.
390
1.
3
6
0
1.
392
C
N
C
N
Si
N
C
Si
C
C
N
Me
-
D
1
.
893
2.
4
5
8
1.
771
1.
808
1.
388
1
.
364
1.
38
5
1.
4
1
1
1.
3
5
2
1
.
411
1.
8
1
4
1.
769
N
C
Si
C
C
N
I
I-
A
(
C
s
)
2.
673
1.
8
2
6
1.
363
1.
383
I-
D
1.
749
1.
747
2.
65
6
2.
422
1.
409
1.
410
1.
351
1
.
375
1
.
378
1.
372
1.
8
0
8
1.
810
Figure 1. (c) 
Geometrical parameters of stationary points in the reaction of 
A
 with ICH
3
.
98
C
Br
N
N
C
C
Si
C
C
Si
N
N
C
C
Cl
C
N
N
C
C
Si
Si
N
C
N
C
2.
6
1
7
2
.
107
2.
403
2.
207
2.
4
0
0
2.
7
3
6
C
I
C
N
N
C
C
Si
Si
N
C
N
C
2.
51
1
2.
9
2
4
2.
402
I
M
e
D
-T
S
  (8.
4
)
Br
M
e
D
-
TS
  
(
11.
4)
ClM
e
D-T
S
  
(1
6
.
6
)
C
N
C
Si
Cl
C
N
C
2.
6
2
2
2.
049
N
C
C
Br
Si
C
C
N
2.
7
7
6
2.
1
4
3
ClM
e
A-T
S
  (
1
4
.
6
)
BrMeA
-
TS  
(
1
0
.
0)
C
N
C
I
Si
C
C
N
2.
9
5
8
2.
404
I
M
e
A
-
T
S  
(6
.4
)
Figure 1. (d) 
Geometrical parameters of transition states in the reaction of 
Me-A
 with XCH
3
 (
XMeA-TS
) and in the reaction of 
Me-D
with XCH
3
 (
XMeD-TS
).  Free energies in kcal/mol are given in parentheses with respect to reactants.
99
100
C
C
N
Cl
C
Si
N
Cl
C
C
N
Br
C
Si
N
Br
C
C
N
I
C
Si
N
I
2.726
2.575
2.585
2.207
2.488 2.080
ClA-TS  (18.0)
BrA-TS  (14.4)
IA-TS  (12.6)
Cl
N
CN
Si
C
C
Si
N
N
C
Cl
C
2.111
2.549
ClDCl-TS  (17.5)
The products from concerted oxidative addition of XCH
3
, X-P1, (X=Cl, Br, I) show very
similar ring geometries.  All have a localized C-C double bond (1.348-1.349 ?) and C-N single
bonds (1.416-1.418 ?).  The Si-N bond lengths in the series A ? Cl-A ? Cl-P1 vary irregularly,
1.779 ? 1.832 ? 1.739 ?.  In A, the Si-N bonds are short due to ? conjugation from nitrogen
lone pairs into the empty silicon orbital, while in Cl-P1 the Si-N bonds are short due to the
stronger Si-N single bonds (more s character).
Relative electronic energies (?E), enthalpies at 0K (?H
0K
), enthalpies at 298K (?H
298K
),
and free energies at 298K (?G
298K
) of all stationary points relevant to the reaction pathways are
tabulated in Tables 3-5.  Bond enthalpies of X-C in XCH
3
 and X-Si bond enthalpies in X-A and
Figure 1. (e) Geometrical parameters of transition states in the reaction of X-A with XCH
3
(XA-TS) and in the reaction of Cl-D with ClCH
3
 (ClDCl-TS).  Free energies in
kcal/mol are given in parentheses with respect to reactants.
101
Table 2. Natural Atomic Charges (NPA) and Mulliken Spin Densities (MSD) of X-
Si(NHCH)
2
, (X=ep
a
, CH
3
, Cl, Br, I) Radicals Calculated at the B3LYP/SBS Level
Si X NH CH (NHCH)
2
d
NPA MSD NPA MSD NPA MSD NPA MSD NPA
A 0.94 0.00 -0.60 0.00 0.13 0.00 -0.94
Me-A 1.26 0.62 -0.42
b
-0.01
c
-0.56 0.13 0.14 0.07 -0.84
Cl-A 1.11 0.33 -0.45 0.04 -0.51 0.20 0.18 0.14 -0.65
Br-A 1.04 0.29 -0.39 0.08 -0.51 0.19 0.18 0.14 -0.65
I-A 0.96 0.12 -0.32 0.24 -0.51 0.20 0.19 0.14 -0.65
a) Electron pair, designating A.
b) Methyl group charge; atomic charges on methyl hydrogens are summed with charge on
carbon.
c) Spin density on methyl carbon.
d) Ring -(NHCH)
2
 group.
Table 3. Relative Energies, Enthalpies, and Free Energies (kcal/mol) in the Reaction Profile
for the Reaction of A with ClCH
3
Label
Species ?Ee ?H0K ?H298K ?G298K
a1 3A+2ClCH
3
0.0 0.0 0.0 0.0
ats1 Cl-TS3+2A+ClCH
3
31.3 28.2 29.0 35.9
a2 Cl-A+CH
3
+2A+ClCH
3
29.5 24.7 26.0 24.5
ats2 Me-TS+A+ClCH
3
+Cl-A 29.4 25.1 26.5 30.5
a3 Me-A+A+ClCH
3
+Cl-A -0.1
a
-1.4 -1.0 6.9
ats3 ClMeA-TS+A+Cl-A 6.9 4.8 5.7 21.4
a4 Cl-P1+CH
3
+A+Cl-A -22.4 -27.1 -25.7 -17.1
ats4 MeD-TS+ClCH
3
+Cl-A -0.6
a
-1.7 -0.8 15.4
a5 Me-D+ClCH
3
+Cl-A -11.6 -12.8 -11.6 5.9
ats5 ClMeD-TS+Cl-A -2.9 -4.9 -3.4 22.2
a6 Cl-P2+CH
3
+Cl-A -26.7 -31.5 -29.3 -11.2
a) Since the transition state is lower in energy than the reactant (a3?ats4), there must be an
intervening intermediate.  At the ?E
e
 level, the Me-A/A complex is 2.7 kcal/mol more
stable than a3.
102
Table 4. Relative Energies, Enthalpies, and Free Energies (kcal/mol) in the Reaction Profile
for the Reaction of A with BrCH
3
Label
 Species  ?Ee  ?H0K  ?H298K  ?G298K
b1 3A+2BrCH
3
0.0 0.0 0.0 0.0
bts1 Br-TS3+2A+BrCH
3
30.6 26.4 28.0 32.3
b2 Br-A+CH
3
+2A+BrCH
3
30.4 25.8 27.2 25.7
bts2 Me-TS+A+BrCH
3
+Br-A 30.3 26.3 27.7 31.7
b3 Me-A+A+BrCH
3
+Br-A 0.9
a
-0.3 0.3 8.0
bts3 BrMeA-TS+A+Br-A 2.4 1.0 1.7 18.0
b4 Br-P1+CH
3
+A+Br-A -18.3 -22.6 -21.1 -12.5
bts4 MeD-TS+BrCH
3
+Br-A 0.4
a
-0.5 0.4 16.6
b5 Me-D+BrCH
3
+Br-A -10.6 -11.6 -10.4 7.0
bts5 BrMeD-TS+Br-A -7.8 -9.3 -7.8 18.1
b6 Br-P2+CH
3
+Br-A -23.6 -27.9 -25.7 -7.5
a) Since the transition state is lower in energy than the reactant (b3?bts4), there must be an
intervening intermediate.  At the ?E
e
 level, the Me-A/A complex is 2.7 kcal/mol more
stable than b3.
Table 5. Relative Energies, Enthalpies, and Free Energies (kcal/mol) in the Reaction Profile
for the Reaction of A with ICH
3
Label
 Species  ?Ee  ?H0K  ?H298K  ?G298K
c1 3A+2ICH
3
0.0 0.0 0.0 0.0
c2 I-A+CH
3
+2A+ICH
3
31.3 27.0 28.4 26.7
cts2 Me-TS+A+ICH
3
+I-A 31.2 27.4 28.9 32.7
c3 Me-A+A+ICH
3
+I-A 1.8
a
0.9 1.5 9.1
cts3 IMeA-TS+A+I-A 0.0
a
-1.3 -0.3 15.5
c4 I-P1+CH
3
+A+I-A -13.7 -17.5 -15.9 -7.6
cts4 MeD-TS+ICH
3
+I-A 1.3
a
0.7 1.6 17.6
c5 Me-D+ICH
3
+I-A -9.8
a
-10.4 -9.2 8.1
cts5 IMeD-TS+I-A -10.4
a
-11.6 -10.0 16.2
c6 I-P2+CH
3
+I-A -19.9 -23.5 -21.3 -3.1
a) Since the transition state is lower in energy than the reactant (c3?cts3, c3?cts4, and
c5?cts5), there must be an intervening intermediate. At the ?E
e
 level, the Me-A/ICH
3
complex is 1.8 kcal/mol more stable than c3; the Me-A/A complex is 2.7 kcal/mol more
stable than c3; the Me-D/ICH
3
 complex is 2.2 kcal/mol more stable than c5.
103
X-P1 (X=Cl, Br, I) are given in Table 6.  The X-C bond enthalpies of methyl halides are in good
agreement with well-known experimental values.
33
Bond formation in X-A can be viewed as somewhere between two extremes.  At one end
of the spectrum, 2c-2e bond formation takes place after electron promotion, while at the other
end, 2c-3e bond formation takes place without electron promotion.  The preferred mode depends
on the required promotion energy versus the strength of the 2c-2e bond.  The promotion energy in
A can be estimated from the singlet-triplet energy gap (?H
s-t
) which was calculated to be 60.3
kcal/mol (?H
s-t
298
).  Thus, the new 2c-2e bond energy must be greater than 60.3 kcal/mol;
otherwise 2c-3e bonding will be favored.  The Si-X bond strength in X-P1 should be a good
estimate of full intrinsic Si-X bond strength since no promotion energy is required.  As shown in
Table 6, the BDE
298
 of Si-Cl, Si-Br, and Si-CH
3
 in X-P1 is larger than ?H
s-t
298
 but the BDE
298
 of
Si-I is only slightly larger.  Therefore, in A, where a promotion of 60.3 kcal/mol is required, the
2c-2e bond enthalpy of 65 kcal/mol is barely enough to form a 2c-2e bond in I-A.  Indeed, the Si-
I bond strength in X-A is only 20.1 kcal/mol and is characterized by a much longer Si-I bond than
found in I-P1 and a much higher spin density on iodine (Table 2).  Both properties indicate that
the Si-I bond in I-A may have significant 2c-3e character.
In the series X=Cl, Br, I, the Si-X bond enthalpies in X-A (52.5 > 37.8 > 20.1 kcal/mol)
and X-P1 (103.1 > 86.3 > 65.9 kcal/mol) follow similar trends.  The former bond enthalpies (X-
A) are 50.6, 48.5, and 45.8 kcal/mol smaller than the latter (X-P1) for X=Cl, Br, I, respectively,
due to the required promotion energy in A (estimated from the singlet-triplet splitting as 60.3
kcal/mol) which must take place before a 2c-2e Si-X bond can form.  On the other hand, the 2c-
2e Si-X bond in X-P1 can form without any additional promotion energy.
In the currently proposed mechanism,
23
 the first step in the reaction of XCH
3
 with A is the
concerted oxidative addition of XCH
3
 (eq 1a).  The monomer product, X-P1 would follow
immediately when X=I.  The dimer product, X-P2, follows from the insertion of A into the X-Si
104
bond of X-P1 (eq 1b).  An alternative mechanism involving a dimer of A cannot occur because
the dimer is not stable.
6
The calculations below support a radical mechanism (eq 2-5).  Free energy profiles in
kcal/mol at 298K are given in Figure 2-4 for X=Cl, Br, and I.  The profile is divided into three
sections, the initiation step (eq 2), the common propagation step (eq 3), and the competition
between the two propagation steps (eq 4 and 5) which lead to X-P1 and X-P2, respectively.
N
N
Si
H
H
+
XCH
3
N
N
Si
H
H
X
CH
3
N
N
Si
H
H
N
N
Si
H
H
X
CH
3
+
N
N
Si
H
H
X
N
N
Si
H
H
CH
3
(1a)
(1b)
The concerted oxidative-addition barriers are compared with the lower-energy halogen-
abstraction barriers in Table 7.  The concerted transition states (X-TS1 and X-TS2) have
significantly higher free energies of activation than the halogen abstraction (X-TS3) free energy
barrier.  The latter barriers are 22.9, 16.0, and 22.8 kcal/mol lower in free energy than the
concerted processes for X=Cl, Br, and I, respectively.  In the case of iodine, a transition state for
iodine abstraction could not be found.  When X=Cl, Br, the activation free energy for halogen
abstraction decreases (Table 8) while the reaction free energy increases.  For X=I, the two trends
meet, which explains why there is no transition state.
105
From the NBO analysis, there are three important donor-acceptor interactions in X-TS1
and X-TS2 (Table 9 and Figure 5).  These are labeled 1, 2, and 3 and correspond to  electron
donation from the silicon lone pair (LP
Si
) to the antibonding X-C orbital (?
*
X-C
), to electron
N
N
Si
H
H
+
XCH
3
N
N
Si
H
H
X
+
CH
3
+CH
3
N
N
Si
H
H
N
N
Si
H
H
CH
3
N
N
Si
H
H
CH
3
XCH
3
+
N
N
Si
H
H
X
CH
3
+
CH
3
N
N
Si
H
H
CH
3
+
N
N
Si
H
H
N
N
Si
H
H
N
N
Si
H
H
CH
3
N
N
Si
H
H
N
N
Si
H
H
CH
3
XCH
3
+
N
N
Si
H
H
N
N
Si
H
H
CH
3
X
CH
3
+
(2)
(3)
(4)
(5a)
(5b)
N
C
Si
C
Cl
N
35
.
9
24
.5
a5
a1
a2
at
s
1
0.0
15
.
4
30.5
6.9
-1
1.2
Free E
n
erg
y
kca
l/m
o
l
N
N
Si
C
C
Si
C
N
C
N
C
C
N
C
N
Si
N
C
Si
C
C
N
Cl
N
C
Si
N
C
C
N
C
Si
N
C
N
C
C
Si
N
Cl
C
N
CC
Si
N
at
s
2
a3
N
C
Si
C
C
N
+ CH
3
5.
9
N
C
Si
C
N
C
21.4
+ CH
3
N
CC
Si
N
24.
5
6.9 a3
6.
9
a3
N
CC
Si
N
+
I
n
it
ia
t
i
o
n
 1
P
r
op
agat
i
o
n
 2
P
r
op
a
g
ati
o
n
 3b
P
r
o
p
agati
o
n
 3a
+ ClC
H
3
ClC
H
3
 +
a4
-17.1
+ CH
3
+ CH
3
C
N
C
Si
Cl
C
N
C
22.2
C
Cl
C
N
N
C
C
Si
Si
N
C
N
C
N
C
Cl
C
Si
N
C
+
Cl
C
H
3
ats
3
at
s
4
ats
5
a6
a2
106
Figure 2.  Schematic reaction free
energy profile is presented for the reaction of 
A
 with
ClCH
3
 at the
B3LYP/LBS//B3LYP/SBS level.  The figure is divided into an initiation step (1), a common propagation step (2), and two competing propagation steps (3a and 3b).  The initiation step produces a CH
3
 radical
which, in turn, adds to another bis
(amino)silylene.
The free energy of 
Cl-A
 +
CH
3
 and CH
3
 + 
Me-A
 are
shown at the same free energy so that free energies over the entire reaction can be compared.  The entire list of species represented by the label (e.g. 
a2
) is
given in Table 3.
           
32.
3
25.
7
b6
b1
b2
bts
1
0.
0
16.
6
31
.
7
8.
0
-7
.
5
F
ree
En
ergy
k
c
al/m
ol
N
N
Si
C
C
Si
C
N
C
N
C
C
N
C
N
Si
N
C
Si
C
C
N
N
CC
Si
N
bts
2
b3
N
C
Si
C
C
N
+ C
H
3
7.
0
N
C
Si
C
N
C
18.
0
+ C
H
3
N
CC
Si
N
25
.
7
8.
0
b3
8.
0
b3
N
CC
Si
N
+
I
n
it
iat
i
on 1
P
r
op
agat
i
o
n 2
P
r
opagat
ion 3b
P
r
op
agat
i
o
n 3a
+ B
r
C
H
3
BrC
H
3
+
b4
-1
2
.
5
+ C
H
3
+ C
H
3
18
.
1
N
C
Br
C
Si
N
C
N
C
C
Br
Si
C
C
N
C
Br
N
N
C
C
Si
C
C
Si
N
N
C
Br
N
C
C
N
Si
C
C
Si
N
N
C
N
Si
C
C
N
Br
C
N
C
Si
C
N
Br
b2
+
BrC
H
3
bt
s
3
bt
s
4
bt
s
5
b5
Figure 3.
Schematic reaction free energy profile is presented for the reaction of 
A
 with BrCH
3
 at the B3LYP/LBS//B3LYP/SBS level.
107
26
.
7
c6
c1
c2
0.
0
17
.
6
32
.
7
9.
1
-3
.1
Fre
e
En
er
gy
kc
a
l
/
m
o
l
N
N
Si
C
C
Si
C
N
C
N
C
C
N
C
N
Si
N
C
Si
C
C
N
N
CC
Si
N
ct
s
2
c3
N
C
Si
C
C
N
+ C
H
3
8.
1
N
C
Si
C
N
C
15
.
5
+ C
H
3
N
CC
Si
N
26
.
7
9.
1
c3
9.
1
c4
N
CC
Si
N
+
Ini
t
i
a
t
i
o
n
 1
P
r
op
ag
at
io
n
 2
P
r
op
a
gat
io
n
 3
b
P
r
op
ag
at
i
o
n
 3
a
+ IC
H
3
IC
H
3
+
c3
-7
.6
+ C
H
3
+ C
H
3
16.
2
c2
+
IC
H
3
N
C
I
C
Si
N
C
C
N
C
I
Si
C
C
N
C
I
C
N
N
C
C
Si
Si
N
C
N
C
N
C
Si
C
N
I
I
N
C
N
C
Si
C
C
N
Si
N
C
c5
ct
s
3
ct
s
4
ct
s
5
Figure 4.
Schematic reaction free energy profile is presented for the reaction of 
A
 with ICH
3
 at the B3LYP/LBS//B3LYP/SBS level.
The initiation step of 
A
 + ICH
3
 does not have a transition state.
108
109
Table 6. Bond Dissociation Energies (BDE), Bond Dissociation Enthalpies at 0K (BDE
0
)
and at 298K (BDE
298
) Calculated at the B3LYP/LBS//B3LYP/SBS Level
(kcal/mol)
Bond BDE BDE
0
BDE
298
Ref.
c
Cl-CH
3
82.0 76.9 78.5 84.1
d
Br-CH
3
68.2 63.5 65.0 70.0
d
I?CH
3
51.5 47.1 48.5 56.6
d
H
3
C-Si
a
29.6 26.1 26.9
Cl-Si
a
52.6 52.3 52.5
Br-Si
a
37.8 37.7 37.8
I-Si
a
20.2 20.1 20.1
Si-Cl
b
104.4 102.6 103.1 117.1?2
e
, 98.9
f
Si-Br
b
87.4 85.8 86.3 101.6?2
e
, 82.1
f
Si-I
b
67.0 65.5 65.9 82.2?2
e
, 62.7
f
ClSi-CH
3
b
81.4 76.4 77.6
BrSi-CH
3
b
79.2 74.3 75.5
ISi-CH
3
b
76.3 71.5 72.7
94.2?1
e
, 70.5
f
a) From Me-A and X-A (X=Cl, Br, I) radical species.
b) From X-P1 (X=Cl, Br, I).
c) Literature values for BDE
298
.
d) Reference 33.
e) BDE of Me
3
Si-X (X=CH
3
, Cl, Br, I), from reference 34.
f) Bond energy terms of Si-X (X=C, Cl, Br, I) derived from least squares method.  Reference
35.
Table 7. Comparison of Free Energies of Activation (kcal/mol) for Concerted Oxidative
Addition with Halogen Abstraction Reaction for A + XCH
3
X=Cl X=Br X=I
X-TS1
a
60.0 57.0 63.1
X-TS2
a
58.8 48.3 49.5
X-TS3
b
35.9 32.3 26.7
c
a) Oxidative addition.
b) Halogen abstraction.
c) There is no transition state for halogen atom abstraction by A from ICH
3
.  The free
energy of I-A plus CH
3
 is 26.7 kcal/mol.
110
Table 8. Predicted Differences in Free Energies of Activation (??G
298
, kcal/mol) for
Formation of CH
3
 and I-Si Radical from ClCH
3
 and BrCH
3
 at
B3LYP/LBS//B3LYP/SBS Level
Si
R
2
N
R
2
N
CH
3
X
?
X-C
LP
*
Si
Si
R
2
N
R
2
N CH
3
X
?
X-C
LP
Si
LP
*
Si
LP
X
LP
X
X-TS1 X-TS2
?
?
X-C
?
?
X-C
LP
Si
1
2
3
1
2
3
Figure 5. Orbital interactions are depicted that are analyzed by NBO in Table 9.
Table 9. Orbital Interaction Energies (kcal/mol) from Second Order Perturbation Theory
Analysis in NBO Analysis at the HF/LBS Level
Orbital Interaction
Donor Acceptor Cl-TS1 Cl-TS2 Br-TS1 Br-TS2 I-TS1 I-TS2
1
a
LP
Si
?
*
X-C
b
42.4 58.1 31.6 13.0 25.1 40.1
2
a
LP
X
LP
*
Si
0.4 62.6 0.4 43.1 0.3 21.1
3
a
?
X-C
b
LP
*
Si
10.3 22.4 12.3 51.8 14.9 35.4
a) For depiction of orbital interactions see Figure 5.
b) The ? and ?* X-CH
3
 bonds were defined by using CHOOSE and DEL keywords within
the NBO analysis program.
X X=Cl X=Br X=I
X-TS3 35.9 32.3 ---
CH
3
 + X-A 24.5 25.7 26.7
?(?G
298
) 11.4 6.6 ~0.0
111
donation from the lone pair orbital on X (LP
X
) to the empty orbital on silicon (LP
*
si
), and to
electron donation from the X-C bonding orbital (?
X-C
) to the empty orbital on silicon (LP
*
si
),
respectively (Table 9).  In X-TS1, the stable bis(amino)silylene is acting as the Lewis base, where
interaction 1 is larger than 2+3.  The decrease of interaction 1 in X-TS1 as X is changed from Cl
to I (Cl 42.4 kcal/mol; Br 31.6 kcal/mol; I 25.1 kcal/mol) can be attributed to the destabilization
of the X-C ?
*
 orbital which reduces its acceptor ability.  On the other hand, the stable
bis(amino)silylene is acting as a Lewis acid in X-TS2 as shown by the combined interactions of 2
and 3 in which the acceptor orbital is LP
*
si
.  The largest interaction (2+3) occurs for X=Br (94.9
kcal/mol), followed by X=Cl (85.0 kcal/mol) and X=I (56.9 kcal/mol).  Indeed, the lowest
concerted free energy barrier for oxidative addition of XCH
3
 to A occurs via Br-TS2.  There has
been extensive discussion in the literature about the increased Lewis basicity of A relative to
dialkylsilylenes.  However, in the concerted oxidative addition of XCH
3
 to the stable
bisaminosilylene A, it appears that the silylene is still acting as the Lewis acid.  It is interesting
that the Lewis acid-Lewis base character of A can be captured by the two concerted transition
states X-TS1 and X-TS2.  For X=Cl, the two transition states are separated by only 1.2 kcal/mol
in free energy.  This difference increases to 8.7 kcal/mol for X=Br and 13.6 kcal/mol for X=I.
The increased separation between the two transition states (X-TS1 and X-TS2) for X=I is likely
due to the soft-soft acid-base character between iodine (soft base) and A (soft acid) in I-TS2.  It
must be emphasized that, while interesting from a pedagogical point of view, the concerted
oxidative transition states, X-TS1 and X-TS2, do not play a role in the reaction mechanism.  For
all three reactions, X=Cl, Br, and I, the halogen abstraction reaction, X-TS3 is lower in free
energy than the concerted oxidative addition (Table 7).
It has been reported that bis(amino)silylenes are electronically similar to trivalent
phosphorus compounds (eq 6,7),
17,37
 because of strong ?-conjugation.  We suggest that a better
analogy might be disilenes, R
2
Si=SiR
2
 (Scheme 3).  Kira has characterized the reaction of
112
X
3
P Y
Si
N
N
R
R
Y
X
3
PY
Si
N
N
R
R
Y
+
( 7 )+
( 6 )
N
N
Si
H
H
Si Si
R
R
R
R
?*
?
Si
empty
Si
lone pair
Scheme 3
R
2
Si=SiR
2
 with R?X as proceeding through a ?bimolecular abstraction mechanism?.
13
 In fact, in
the reaction of (i-Pr
3
Si)
2
Si=Si(i-Pr
3
Si)
2
 with t-BuCl, the radical product is stable and has been
identified by ESR.
38
More supportive evidence for the analogue between bis(amino)silyene and disilene can
be found from the nature of the transition state for halogen atom abstraction by both compounds.
By comparing rate constants and exothermicities for the reactions of disilene with a series of
chlorine- and bromine-containing molecules, it was concluded
13,38
 that the transition states are
?late? (silicon-halogen bond formation and halogen-carbon bond cleavage are well-advanced).  In
the reaction of bis(amino)silyene with halomethanes, the transition states (X-TS3) are also ?late?
as judged by short forming Si-X and long breaking X-C bonds (Figure 1d,e).  In contrast to the
reactions of A (bis(amino)silyene) with XCH
3
 which are ?late?, the reactions of Me-A with XCH
3
113
are ?early? as judged by the long forming Si-X bonds and the short breaking X-C bonds in the
transition states XMeA-TS (Figure 1d).  Thus, the addition of the methyl substituent to A (A +
CH
3
 ? Me-A) makes the halogen abstraction reactions much more exothermic and changes the
transition states from ?late? to ?early?.
The free energy barrier for halogen abstraction (forming two radical products) is clearly
lower than the concerted oxidative addition barriers as illustrated in Table 7 for the three
halomethanes considered, ClCH
3
, BrCH
3
, and ICH
3
.  In Figures 2-4, we present the free energies
for the radical mechanism to X-P1 and X-P2, X=Cl, Br, I.
In the initiation step, a halogen atom is abstracted by bis(amino)silylene (A), leaving
behind a methyl radical.  The methyl radical can react with another methyl radical to form ethane
(chain terminating), react with the solvent (hexane or benzene) to form side products, react with
XCH
3
 in a degenerate reaction (CH
3
 + X-CH
3
 ? CH
3
-X + CH
3
), or (much more likely) react with
A.  Reaction with A (labeled ?Propagation 2?), a common step for all halomethanes, has a free
energy barrier of 6.0 kcal/mol.  The product, Me-A, can react with X-CH
3
 (?Propagation 3a?) or
with another A (?Propagation 3b?).  The competition between 3a and 3b will determine which
products are formed.  In the reaction of ClCH
3
 with A, the two relevant free energies are ?ats3?
and ?ats5?, 21.4 and 22.2 kcal/mol.  The calculation would predict a mixture of Cl-P1 and Cl-P2
since the free energy barriers are very similar.
In the chain mechanism, we depict the Me-D radical reacting with ClCH
3
 to form Cl-P2
plus CH
3
 (Propagation 3b).  In reality, there is the possibility that Me-D can react with another A
to form Me-T (?T? for trimer).  The free energy barrier for the Me-D + A ? Me-T reaction is
lower than for the Me-D + ClCH
3
 ? Cl-P2 reaction (9.6 versus 16.3 kcal/mol), but the reaction
is nonspontaneous by 5.9 kcal/mol.
39
  When we consider that the experiments involve 1 with
bulky t-butyl groups on nitrogen rather than A, the possibility for forming the trimer adduct is
even less likely.
114
This prediction agrees with the experimental result where reaction of 1 with CCl
4
afforded a mixture of products.
14b
  However, the only reported product of the reaction of 1 (not A)
with CH
2
Cl
2
 or CHCl
3
 (not ClCH
3
) is the disilane product (Cl-P2).  It should be noted that
solvation effects in hexane or benzene (which have not been included in the present study) are
expected to be small but could be large enough to affect the outcome of the reaction.  Of course,
the reaction can be ?pushed? toward one product or the other by changing the initial ClCH
3
:A
ratio.
In the BrCH
3
-containing pathway 3a (Figure 3, Me-A + BrCH
3
), the transition state has a
free energy of 18.0 kcal/mol, very similar to the free energy from pathway 3b (18.1 kcal/mol).
The two pathways are expected (and found) to be competitive.  In the ICH
3
-containing pathway
3a (Figure 4, Me-A + ICH
3
), the transition state has a smaller free energy than the pathway to
disilane products (I-P2), 15.5 versus 17.6 kcal/mol.  In addition, nonstatistical behavior (see
below) may lead to the formation of I-P1 by the capture of the CH
3
 radical released in the
initiation step.
It is very reasonable that the two barriers for addition of XCH
3
 to Me-A or Me-D should
be similar.  In both transition states, the halogen atom is abstracted by a silicon atom in a similar
chemical environment.  For Me-A + XCH
3
, the substituent on the trivalent silicon is methyl while
in Me-D + XCH
3
, the substituent is methyl-bis(amino)silylene.  We also explored the fate of X-A
which should lead to minor products, perhaps below the detection limit in the experimental
studies.  The reaction of X-A with A has free energy barriers of 8.3, 9.0, and8.4 kcal/mol for
X=Cl, Br, and I (for structures see: XD-TS, Figure 1).  In analogy with Me-D, the most likely
reaction of Cl-D is with ClCH
3
 to give the dichloro version of the disilane product.  The free
energy barrier for this reaction is 17.5 kcal/mol (Figure 1e).  The alternative reactions of X-A are
with XCH
3
 which have free energy barriers of 18.0, 14.4, and 12.6 kcal/mol for X=Cl, Br, and I,
respectively, to form the dihalogen version of X-P1 (Figure 1e).  Thus, there may be dihalogen
115
C
N
Si
C
C
N
Cl
C
C
Cl
C
N
C
Si
C
N
Cl
C
C
N
C
Si
C
N
Cl
Cl
C
Cl
Cl
N
C
Si
C
N
Cl
C
Cl
Cl
N
C
Si
C
N
Cl
C
Cl
C
N
C
C
Si
N
C
Cl
C
Cl
1.792
1.088
Cl
C
Cl
Cl
1.788
1.086
Cl
Cl
C
Cl
Cl
1.793
1.727
2.516
2.297
1.799
1.376
1.372
1.739
1.739
2.429
2.321
1.376
1.794
1.794
1.377
1.372
1.759
1.759
2.358
2.325
1.786
1.379
1.370
1.781
1.459
1.387
1.361
2.567
2.298
1.815
1.366
1.378
1.457
2.490
2.332
1.730
1.813
1.366
1.378
1.457
CH
2
Cl
2 
(C
2v
)
CHCl
3 
(C
3v
) CCl
4 
(T
d
)
Cl2-TS (C
s
)
Cl3-TS Cl4-TS (C
s
)
SiM (C
2v
) SiM-ClTS (C
s
)
SiM-Cl2TS (C
s
)
Figure 6. Geometries (B3LYP/6-31+G(d)) of reactants CH
2
Cl
2
, CHCl
3
, and CCl
4
 and the
transition states for the initiation steps (chlorine atom abstraction by A) Cl2-TS,
Cl3-TS, and Cl4-TS, and geometries of reactant SiM and the transition states for
the initiation steps of chlorine atom abstraction by SiM, (SiM-ClTS and SiM-
Cl2TS).
116
products produced (i.e. two halogens on X-P1 and X-P2) in the reaction of XCH
3
 + A, but the
concentrations may be low since X-A is only generated in the initiation step.
One shortcoming of our model is that the free energy barriers for the initiation steps are
still too high to explain the experimental observation where the reactions proceed at room
temperature.  This can be explained by the fact that our model system is not the same as the
observed reaction.  Most of the reported reactions are those of stable silylene 1 with CH
2
Cl
2
,
CHCl
3
, and CCl
4
.  Therefore, the effect of additional halogen atoms on the entering methyl
carbon was examined in the reaction of A with CH
2
Cl
2
, CHCl
3
, and CCl
4
, as well as the effect of
additional methyl groups on the ring nitrogen atoms in the silylene (i.e. N,N?-dimethyl derivative,
SiM) in the reaction with ClCH
3
.  In addition, to confirm the additivity of these effects, an
investigation of the reaction of SiM with CH
2
Cl
2
 was also carried out.  Optimized geometries of
the reactants and transition states are given in Figure 6, while the calculated activation barriers are
tabulated in Table 10.  The additional halogens on the methyl group lower the activation free
energy barrier by about 5 kcal/mol per chlorine (CH
4-n
Cl
n
: n=1,2,3,4; ?G
?
298K
= 35.9, 31.5, 26.2,
19.9 kcal/mol, respectively).  The lowering of the free energy barriers can be attributed to the
stabilizing effect of the chlorine on the forming methyl radical.
Two methyl substituents on the ring nitrogen atoms cause the activation free energy
barrier to be lower by about 2 kcal/mol.  The electron donation from the methyl groups to the
bis(amino)silylene ring enhances the electron delocalization over the five-membered ring system
and stabilizes the transition state.  The two effects (methyl groups on nitrogen and additional
chlorine atoms on carbon) are additive, and the activation free energy barrier for the reaction of
SiM with CH
2
Cl
2
 (?G
?
298K
= 29.6 kcal/mol) is 6.3 kcal/mol lower than that of the model reaction.
Thus, if we consider the stable silylene 1 reacting with CH
2
Cl
2
, CHCl
3
, or CCl
4
, the initiation free
energy barriers might be reasonable for a reaction that occurs at room temperature.
117
Table 10. Comparison of Activation Energies, Enthalpies, and Free Energies (kcal/mol) in
the Initiation Steps for the Reaction of A with ClCH
3
, CH
2
Cl
2
, CHCl
3
 or CCl
4
 and
for the Reaction of SiM with ClCH
3
 and CH
2
Cl
2
N
C
C
Si
N
Cl
C
N
Si
C
C
N
Br
C
Cl-TS3
231i  cm
-1
Br-TS3
49i  cm
-1
Figure 7. Transition vectors of the two transition states (Cl-TS3 and Br-TS3) which indicate
the ejection of a methyl radical during halogen abstraction.  A transition state does
not exist in the abstraction of iodine from ICH
3
 by A.
One experimental peculiarity of the RCl + A reaction is that R=t-Bu and R=CHCl
2
 lead to
different products.  While CHCl
3
 leads to Cl-P2 (with a CHCl
2
 substituent rather than CH
3
),
t-BuCl leads to the corresponding Cl-P1 product, the same product observed with ICH
3
.  We
?E
e
?H
0K
?H
298K
?G
298K
Cl-TS3 31.3 28.2 29.0 35.9
Cl2-TS 25.7 23.5 24.3 31.5
Cl3-TS 19.5 18.2 19.0 26.2
Cl4-TS 12.7 12.1 12.8 19.8
SiM-ClTS 30.0 26.8 27.9 33.8
SiM-Cl2TS 24.1 21.8 22.8 29.6
118
think the answer to this riddle may come from nonstatistical kinetic models.
40
  In the transition
state for the initiation step, the transition vector (231i cm
-1
) is a Cl-CH
3
 bond stretch (Figure 7).
The radical products are 3.0 kcal/mol lower in enthalpy (Table 1) than the transition state and the
excess energy will become kinetic energies of two separating species such that the methyl radical
will leave the vicinity of the Cl-A radical.  If the reaction of t-BuCl follows a similar path, the 3.0
kcal/mol of enthalpy may be absorbed by vibrations of the t-Bu group such that the t-Bu group
may not depart the vicinity of Cl-A and be captured to form the corresponding Cl-P1 product.
Another reason why R=t-Bu leads to the monomer is due to steric congestion in the
transition state for formation of the dimer.  In the case of t-BuCl reacting with 1, there are five t-
Bu groups in the transition state (MeD-TS) with significant crowding between the two units.  In
this case, there is an advantage of propagation step 3a over 3b.
4.4  Conclusion
The present calculations on the reaction of bis(amino)silylene with halomethane indicate
a radical reaction mechanism rather than a concerted oxidative addition of the halomethane.  The
free energies of activation for the radical mechanism are 16 to 23 kcal/mol lower than for the
concerted pathway.  The chain pathway includes the initiation step, which produces a halogen-
addition product and a methyl radical and propagation steps which consume one methyl radical
and produce one methyl radical.  The monomer and dimer products from the halomethane
addition arise from the competition between two propagation steps.  In one pathway, the
halomethane adds to the methyl-bis(amino)silylene radical (Me-A), while in the competing
pathway, the methyl-bis(amino)silylene radical first reacts with another bis(amino)silylene which,
in turns, reacts with halomethane to abstract a halogen atom.  Since the competing pathways are
within a few kcal/mol of each other, secondary effects (such as solvation) may have decisive roles
in determining the outcome of the reaction.
119
The observation that CHCl
3
 and t-BuCl lead to different products can be explained within
the present mechanism if nonstatisical effects are important.  The large manifold of vibrational
modes in the t-Bu radical may couple efficiently with the transition vector allowing the t-Bu
radical to be ?captured? in a single reaction step.  A complete understanding of the reaction
mechanism may require trajectory studies of branching propagation steps.  However, these
studies are beyond the scope of the present work.
120
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Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi,
M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.;
Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.;
Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.;
Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.;
Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.;
Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas,
O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui,
Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.;
Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng,
C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong,
M. W.; Gonzalez, C.; Pople, J. A. Gaussian, Inc., Pittsburgh PA, 2003.
(27) (a) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270.  (b) Wadt, W. R.; Hay, P. J. J.
Chem. Phys. 1985, 82, 284.  (c) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299.
123
(28) MOLDEN, Schaftenaar, G.; Noordik, J. H. J. Comput.-Aided Mol. Design 2000, 14, 123.
(29) (a) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (b) Gonzalez, C.;
Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523.
(30) Dolg, M.; Stoll, H.; Preuss, H.; Pitzer, R. M. J. Phys. Chem. 1993, 97, 5852.
(31) Reed, A.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899.
(32) Becker, J. S.; Staples, R. J.; Gordon, R. G. Cryst. Res. Technol. 2004, 39, 85.
(33) James, A.; Lord, M. VNR Index of Chemical and Physical Data; Van Nostrand Reinhold:
New York, 1992, 485.
(34) Becerra, R.; Walsh, R. In Rappoport, Z., Apeloig, Y., Eds. The Chemistry of Organic
Silicon Compounds; Wiley: New York, 1998; Vol. 2. Part 1, p 153.
(35) Leroy, G.; Temsamani, D. R.; Wilante, C. THEOCHEM 1994, 306, 21.
(36) Metrangolo, P.; Resnati, G. In Atwood, J. L.; Steed, J. W., Eds. Encyclopedia of
Supramolecular Chemistry; Marcel Dekker: New York 2004, 628.
(37) Tumanskii, B.; Pine, P.; Apeloig, Y.; Hill, N. J.; West, R. J. Am. Chem. Soc. 2002, 124,
7786.
(38) Kira, M.; Ishima, T.; Iwamoto, T.; Ichinohe, M. J. Am. Chem. Soc. 2001, 123, 1676.
(39) The free energy barrier for Me-D + A ? Me-T is lower than the free energy barrier for
Me-D + BrCH
3
 ? Br-P2  (9.6 versus 11.1 kcal/mol) but the free energy of reaction is
less spontaneous (5.9 versus ?14.5 kcal/mol).  The free energy barrier for Me-D + A ?
Me-T is higher than the free energy barrier for Me-D + ICH
3
 ? I-P2  (9.6 versus 8.1
kcal/mol) and the free energy of reaction is less spontaneous (5.9 versus ?11.2 kcal/mol).
(40) (a) Carpenter, B. K. In Moss, R. A.; Platz, M. S.; Jones, M., Jr. Eds. Reactive ntermediate
Chemistry; Wiley-Interscience: New York, 2004, p 925. (b) Carpenter, B. K. Angew.
Chem. Int. Ed. 1998, 37, 3340. (c) Nummela, J. A.; Carpenter, B. K. J. Am. Chem. Soc.
124
2002, 124, 8512. (d) Carpenter, B. K. J. Am. Chem. Soc. 1995, 117, 6336. (e) Carpenter,
B. K. Acc. Chem. Res. 1992, 25, 520.
125
CHAPTER 5
COMPUTATIONAL STUDY OF CARBON ATOM (
3
P and 
1
D) REACTION WITH CH
2
O;
THEORETICAL EVALUATION OF 
1
B
1
 METHYLENE PRODUCTION BY C (
1
D)
5.1  Introduction
The chemistry of atomic carbon is central to the mechanistic and quantitative
understanding of organic chemistry in that it is the ultimate case of a low-valent carbon-centered
reactive intermediate that exhibits a thermodynamic drive to form a tetravalent carbon.  However
it is very difficult to achieve a complete understanding of C atom reactions because the reaction
of C atom produces other reactive intermediates, such as carbenes, which can react to form more
stable products.  Hence, the experimental studies of the mechanisms of C atom reactions has
been often limited, and complementary computational studies have been utilized successfully.
1
Most reactions of C atoms are usually highly exothermic because of the extremely high
heat of formation of the C atom.  The ground state atomic carbon is triplet (
3
P) with a heat of
formation of ?H
f
o
=171 kcal/mol.  The first and second excited states are singlet states, 
1
D with
?H
f
o
=201 kcal/mol and 
1
S with ?H
f
o
=233 kcal/mol, respectively.
1,2
  Many of the C atom
reactions involve the 
1
D state, and this species brings an additional 30 kcal/mol of energy to its
reaction.  Therefore the products from C atom reactions contain a great deal of excess energy.
When the initial product of a C atom reaction is another reactive intermediate such as a carbene,
then very interesting reactivity can be observed due to the high exothermicity.
1,3
 When C atoms react with unsaturated hydrocarbons, abstraction of hydrogen, insertion
126
into a C-H bond, or ? addition occurs.
1,4-8
  In analogy with carbenes,
9
 atomic carbon reacts with
alkenes by double-bond addition to give cyclopropylidenes which undergo the ring opening to
allenes.  In the case of carbonyl compounds, the singlet 
1
D state C atom can react in a similar
fashion: carbon atom addition to the C=O double bond followed by ring opening to give a
      (1)
ketene as shown in eq. (1).  There is also possibility of end-on attack via a lone pair of electrons
on oxygen forming a ylide-like species ( R
2
C-O-C).  However no compelling evidence for the
end-on intermediate has been reported.
10
  Although a ketene is the global minimum on the
potential energy surfaces
,
 no ketene has been isolated.  However, the existence of an intermediate
ketene was confirmed by the formation of pentanoic acid by the reaction with H
2
O in the process
of the reaction of arc-generated carbon with butanal.
10
  All observed products of the reaction of
arc-generated carbon with carbonyl compounds came from the carbenes which formed from
deoxygenation of the carbonyl compounds.  Although C=C double bond cleavage in ketene is
highly endothermic, this reaction is still feasible because of the high exothermicity of the initial
reaction.
Now, it is well established that the deoxygenation occurs in the reaction of C (
1
D) atoms
with ketones and aldehydes.
1,10-16
  Furthermore, it has been suggested that singlet excited-state
(
1
B
1
) carbenes form in the C (
1
D) atom deoxygenation of formaldehyde
13
 and cyclopentanone.
16
The C atom deoxygenation of formaldehyde was reported in 1983 by Shevlin, where the
generated carbene was allowed to react with  (Z)-2-butene.  By assessing the stereochemistry of
the product mixture, the formation of CH
2
 (
1
B
1
) was suggested.
13
  However, the excited singlet
carbene in this deoxygenation process was not observed, and it is still not clear how they can
form in this process.
O
R
R'
+   C
O
C
R
R'
C O
R
R'
R
C
R'
+   CO
127
Numerous studies on electronic states, photodissociation paths, and oxirene
rearrangement of CH
2
CO have been reported.
 17-23
  However, comprehensive studies of the
potential energy surface are rare.  Hereupon, we report the computational study of ground state
(
3
P) and first excited state (
1
D) of the C atom reaction with formaldehyde.  Both the triplet and
singlet potential energy surfaces are constructed at the MCQDPT2//CASSCF level.  The carbene-
producing channels are discussed.
5.2  Computational Details
The Gaussian03 program
24
 was used for the hybrid density functional PBE1PBE
25
calculations, while the GAMESS program
26
 was used for Complete Active Space SCF
(CASSCF),
27
 and MCQDPT2
28
 calculations.  Geometry optimizations for minima and transition
states were carried out at the (U)PBE1PBE/6-311++G(3df,p) (DFT) and
CASSCF(14,13)/6-311+G(2d,p) (CAS)  levels.  At the DFT level, harmonic vibrational analysis
was performed and the minima and transition states were characterized.  Thermodynamic
correction terms, zero-point vibrational energies (ZPC), heat capacity corrections and entropies
were obtained at the DFT level.  Transition vectors of transition states were visualized and
animated by the MOLDEN program
29
 and if necessary, IRC calculations were carried out to
connect the transition state to the corresponding minima.
For CASSCF geometry optimization, a (14,13) active space (14 electrons in 13 orbitals)
was chosen from the full (16,14) valence active space of CH
2
CO.  To maintain a consistent active
space we included all valence electrons except for an oxygen lone pair that lies lowest in energy.
For the product fragments we considered the same orbitals so that the total active space was
maintained as in CH
2
CO.  For example, a (6,6) active space was used for CH
2
 and a (8,7) active
space was used for CO.
At each stationary point at the CAS level, single-point energy calculations were carried
128
out at the MCQDPT2/6-311+G(2d,p) (MCPT) level.  Since the (14,13) active space calculations
at the MCPT level are very challenging in terms of computing resources and computing cost, a
(12,11) active space was used, where one low-lying C-H bonding orbital and its antibonding
orbital were excluded.  The active space of product fragments was chosen in the same way as at
the CAS level (a (4,4) active space for CH
2
 and a (8,7) active space for CO).   The potential
energy surfaces were constructed at the MCPT level with zero-point energy correction, heat
capacity correction and free energy correction calculated at the DFT level.  The singlet and triplet
surfaces are considered separately and possible singlet-triplet crossings are not considered in this
study.  Further wavefunction analysis was carried out with CASSCF wavefunctions to examine
correlations between the reaction intermediates and the products.  We will use a notation scheme
with a boldface "S" for singlets and "T" for triplets followed by one number for minima and two
numbers or one number and a character for transition states.  Thus, S12 is the singlet transition
state between S1 and S2 and T5p is the transition state between T5 and products.
5.3  Result and Discussion
The structural isomers of CH
2
CO in the singlet and triplet states at the DFT and CAS
level are given in Figures 1 and 2.  The calculated electronic energies and thermodynamic
correction terms and spin-squared values are listed in Table 1.  Numerous theoretical calculations
on electronic states and photodissociation paths of CH
2
CO have been reported.
17-23
  The obtained
geometric parameters in this study are in good agreement with those available in the literature
17-23
which are not given in the Figures 1 and 2 for the clarification.  The optimized geometries of S2
(
1
A
1
), S4 (
1
A
1
), T2 (
3
A"), and T2p (
3
A") optimized at DFT and CAS levels show good agreement
with previous studies by East,
19(b)
 Schaefer
18(b),23(a)
 and Nemes.
19(c)
  The C-C bond of S2 is shorter
than a normal single-bond distance due to the electron delocalization over the C-C-O ? bonding
system.  On the triplet surface, T2 is the lowest-energy structure with a normal C-C single bond
129
Table 1. Calculated electronic energies (a.u.) at DFT, CAS and MCPT level along with ZPC
(kcal/mol), H
corr
 (kcal/mol), entropy (S) (cal?K
-1
mol
-1
), spin squared value (<S
2
>),
reference weight of dominant configuration (c
i
2
), and electronic states.
 ZPC H
corr
S<S
2
>c
i
2
State DFT CAS MCPT
C (
3
P) 0.0 1.5 35.6 2.00
3
P -37.80321 -37.70299 -37.76948
C (
1
D) 0.0 1.5 33.4 1.01
1
D -37.78825 -37.64525 -37.71821
C (
1
S) 0.0 1.5 33.4 0.00
1
S -37.73128 -37.60755 -37.67319
CO 3.2 5.3 47.2 0.00
1
? -113.22500 -112.90363 -113.09712
CH
2
O 16.8 19.2 52.2 0.00
1
A
1
-114.41299 -114.03723 -114.25908
CH
2
 (
3
B
1
) 10.9 13.3 46.6 2.01 0.97
3
B
1
-39.11334 -38.96922 -39.04985
CH
2
 (
1
A
1
) 10.5 12.8 45.2 0.00 0.92
1
A
1
-39.08598 -38.95214 -39.02520
CH
2
 (
1
B
1
) 10.8 13.2 45.0 0.79 0.48
1
B
1
-39.09191 -38.90222 -38.99299
CH
2
 (c
1
A
1
)
a
10.6 13.0 42.0 0.49
1
A
1
-38.85490 -38.95163
CH 4.1 6.2 42.3 0.75 0.49
2
? -38.43636 -38.31836 -38.38820
HCO 8.3 10.6 53.6 0.75 0.94
2
A' -113.76579 -113.40462 -113.62390
S1 20.4 22.9 58.3 0.00 0.90
1
A' -152.37894 -151.86774 -152.15813
S2 19.9 22.7 57.7 0.00 0.90
1
A' -152.48037 -151.96541 -152.26748
S2? 19.6 22.3 59.5 1.02 0.40
1
A" -152.39395 -151.86882 -152.17944
S3 17.6 20.9 63.4 0.66 0.86
1
A -152.35063 -151.83978 -152.13372
S4 18.7 21.6 59.5 0.00 0.88
1
A
1
-152.35261 -151.82673 -152.14154
S5 20.1 23.1 59.0 0.00 0.90
1
A' -152.42108 -151.90656 -152.21047
S6
b
18.6 21.6 60.9 0.00
1
A' -152.31492
S7
c
17.5 20.4 60.1 1.01 0.46
1
A" -152.29307 -151.78186 -152.06890
S12 17.5 20.3 60.7 0.55 0.12
1
A' -152.34339 -151.83313 -152.13225
S13 16.8 19.3 58.6 0.00 0.88
1
A -152.29228 -151.76894 -152.07458
S15 15.8 18.4 58.8 0.00 0.89
1
A -152.26001 -151.74954 -152.03200
S2?2? 18.0 20.6 57.1 1.02 0.31
1
A
2
-152.36022 -151.83125 -152.14786
S23 17.2 20.0 59.8 0.64 0.89
1
A' -152.35024 -151.83890 -152.13009
S25 16.0 19.1 60.6 0.00 0.83
1
A' -152.32577 -151.79756 -152.12003
S34 18.4 21.0 59.2 0.00 0.84
1
A -152.35046 -151.84396 -152.13308
S66 18.4 21.2 57.9 0.00 0.87
1
A
1
-152.31127 -151.79402 -152.09282
S6p
b
17.5 20.6 61.4 0.00
1
A' -152.31396
S7p
c
15.9 19.2 64.0 1.00 0.41
1
A' -152.27168 -151.73690 -152.05775
Sr7
c
17.2 20.2 59.7 1.01 0.37
1
A
2
-152.26256 -151.73876 -152.03349
S
ci
d
19.6 22.3 59.5 -151.84950 -152.16824
T1 20.1 22.7 60.6 2.01 0.91
3
A" -152.29621 -151.76542 -152.08428
T2 19.1 21.9 62.2 2.01 0.16
3
A" -152.39793 -151.87873 -152.18798
T3 19.6 22.2 59.2 2.01 0.91
3
B -152.32432 -151.78806 -152.10321
T4 19.0 21.7 61.9 2.03 0.90
3
A" -152.36686 -151.85794 -152.15574
T5 17.9 21.0 63.5 2.01 0.06
3
A" -152.29754 -151.79195 -152.07875
T6 17.1 20.1 63.5 2.01 0.90
3
A" -152.24274 -151.74531 -152.02303
T7 19.0 21.8 62.0 2.01 0.84
3
A" -152.31178 -151.77501 -152.10270
T12 19.6 22.0 60.5 2.13 0.03
3
A" -152.26744 -151.73773 -152.06021
T13 16.3 18.9 60.8 2.01 0.89
3
A -152.24172 -151.70055 -152.02343
T15 17.1 20.1 65.2 2.01 0.80
3
A" -152.25769 -151.75622 -152.04323
T22 18.0 20.7 61.7 2.01 0.91
3
A' -152.38049 -151.86024 -152.17257
T24 15.4 18.2 61.7 2.02 0.87
3
A -152.30075 -151.77008 -152.08981
T27 15.0 17.7 61.4 2.02 0.51
3
A" -152.23731 -151.71033 -152.02596
T2p 15.0 18.9 72.0 2.01 0.84
3
A" -152.33779 -151.84749 -152.14815
-continue-
130
 (a) Thermodynamic correction data are obtained at the CAS level, because at the DFT level
we could not locate the excited c
1
A
1
 minimum.
(b) At the CAS level, stationary points could not be found, and at the DFT level, after the
zero-point energy correction, the relative energy order of the minimum (S6) and the
transition state (S6p) becomes reversed. Therefore, S6 will follow the dissociation path
without barrier.
(c) These three structures have an imaginary frequency that corresponds to out-of-plane
distortion.  We located a minimum or transition states with C
1
 symmetry at the DFT level.
However their distortion from planarity is very small and after the zero-point energy
correction the structures with C
s
 symmetry are lower than C
1
 structures.  Hence, at the
CAS level geometry optimization we used C
s
 symmetry.
(d) Single point energy calculations at the CAS and MCPT levels are performed for both 
1
A?
and 
1
A? state on the geometry obtained from conical intersection optimization at the
CAS(6,6)/6-311+G(2d,p) level.  The energies reported are averaged for both states.
Thermodynamic corrections of S2? are used for the enthalpies and free energy the
correction.
-continued-
 ZPC H
corr
S<S
2
>c
i
2
State DFT CAS MCPT
T34 17.6 20.2 61.2 2.01 0.74
3
A -152.28006 -151.75141 -152.07125
T56 15.0 17.7 61.5 2.02 0.84
3
A" -152.22171 -151.69994 -152.02092
T5p 15.5 18.9 66.4 2.02 0.64
3
A" -152.28497 -151.77296 -152.08015
T22? 18.0 20.7 59.2 2.01 0.91
3
A
2
-152.36096 -151.82249 -152.14431
T55 17.3 20.2 61.3 2.02 0.64
3
A
2
-152.26537 -151.71934 -152.03924
131
O
CC
C O
C
C
C O
C O CC
O C
C C
O
C C
O
C C
O
O
CC
O
C
C
O
C
C
1.278
1.296
1.495
1.496
1.457
1.522
51.3
50.8
1.084
1.095
C C O
1.307
1.330
1.312
1.156
1.167
1.160
121.1
121.9
121.8
1.478
1.519
1.491
1.259
1.280
1.276
1.072
1.084
1.075
S4
S2
S1
1.063
1.074
1.197
1.211
1.300
1.329
0.963
0.969
110.4
107.4
S5
1.576
1.727
1.196
1.164
88.7
104.7
1.958
2.314
1.086
1.095
S12
C
C O
1.571
1.643
1.354
1.375
1.349
1.372
1.296
1.309
1.404
1.441
1.082
1.069
S13
C
O
C
1.428
1.428
1.105
1.119
1.415
1.444
1.149
1.144
1.777
1.851
1.340
1.373
79.8
81.8
S15
80.0
95.9
1.072
1.076
1.082
1.079
1.331
1.268
1.683
1.969
1.287
1.383
S34
CC
O
1.092
1.094
1.423
1.468
1.215
1.217
1.116
1.143
122.4
131.2
S23
S25
1.064
1.077
1.228
1.260
1.187
1.166
1.275
1.302
69.9
73.8
1.413
1.485
1.881
2.025
1.335
1.362
1.171
1.180
1.073
1.083
14.8
14.0
S66
1.409
1.460
1.226
1.233
1.104
1.116
OCCH = 63.8
82.6
1.089
1.091
S3
1.081
1.091
1.076
50.4
49.9
50.6
S7
1.375
1.416
1.078
1.088
1.080
1.066
1.276
1.294
122.0
118.7
1.279
1.283
1.318
1.374
1.085
1.077
124.8
128.3
Sr7
1.737
1.812
1.079
1.093
1.081
1.093
1.184
1.196121.5
118.5
134.8
134.6
S7p
OCCH = 96.6
99.4
2.151
2.092
C
O
C
119.8
120.4
1.090
1.073
1.426
1.454
1.190
1.208
129.6
129.3
1.082
1.093
S2"
C C O
1.374
1.405
1.196
1.212
114.8
114.9
1.101
1.112
S2"2"
C
O
C
S
ci
1.623
1.073
1.075
1.139
118.4
120.5
Figure 1.  Optimized geometries of singlet species at the DFT and CAS (in italic) level.
Literature values (underlined) for S2 are from reference 19(b) and for S4 are from
23(a).  S
ci
 geometry obtained at the CASSCF(6,6)/6-311+G(2d,p) level.  Bond
lengths are in ? and angles are in degrees.
132
C
O
C
C
C O
C O
C
COC
C C O
C O
C
C
O
C
O
C
C
OC
C
OC
C
T1
1.331
1.370
1.433
1.525
1.507
1.452
1.088
1.100
C C
O
1.432
1.432
1.466
1.188
1.198
1.193
1.090
1.100
1.086
1.082
1.070
1.080
128.8
127.9
127.7
T2
T6
T5
CC
O 62.0
61.9
1.427
1.453
1.087
1.089
1.386
1.414
T3
1.275
1.275
1.374
1.420
1.082
1.091
1.078
1.065
122.2
119.3
1.112
1.096
1.336
1.327
1.303
1.381
1.089
1.095
121.8
116.3
T15
T12
T55
O
C
C
1.089
1.075
1.372
1.417
1.296
1.321
0.977
0.983
120.3
123.4
125.0
119.5
110.7
109.7
T7
97.9
101.1
1.318
1.352
1.374
1.392
1.099
1.111
1.091
1.103
1.319
1.330
1.428
1.481
1.673
1.777
1.404
1.417
1.211
1.204
OCCH=145.2
156.7
T13
2.284
2.363
1.307
1.331
1.381
1.409
1.082
1.072
116.4
119.2
1.086
1.067
1.308
1.352
1.285
1.285
124.4
126.8
CC
O
1.097
1.081
1.371
1.416
1.202
1.363
1.429
1.471
HCCO=102.1
129.9
T24
C
O
C
T34
1.726
1.807
1.323
1.323
1.393
1.442
1.082
1.077
79.4
81.5
1.104
1.099
T22
1.493
1.541
1.176
1.189
123.3
123.4
1.085
1.081
T22'
114.4
117.2
1.101
1.079
1.370
1.411
1.196
1.216
C C
O
1.080
1.071
1.081
1.096
2.511
2.081
1.127
1.149113.2
117.5
T2p
C
O
C
1.085
1.095
1.421
1.463
1.324
1.325
1.457
1.478
1.220
1.276
90.3
91.6
T27
O
C
C
1.095
1.204
1.399
1.448
1.284
1.299
1.311
1.343
1.534
1.537
91.7
92.0
99.4
98.4
T56
C
OC
T4
1.413
1.458
1.227
1.231
1.085
1.073
1.103
1.115
120.2
121.8
130.8
129.2
T5p
1.193
1.220
1.664
1.631
1.082
1.094
1.080
1.092
121.3
118.5
1.080
130.1
Figure 2.  Optimized geometries of triplet species at DFT and CAS (in italic) level.
Literature values (underlined) for T2 from reference 18(b).  Bond lengths are in ?
and angles are in degrees.
133
distance of (1.432 ?) and C-C-O angle of 127.9?.  The C-O bond length of T2 is about 0.03 ?
longer than in S2.   However, the C-H distances are very similar in S2 and T2.  T22? (
3
A
2
) has the
same atomic arrangement as S1 and its C-O and C-C bond lengths are longer than those of S1
(0.049 and 0.081 ? longer, respectively).  The C atom end-on attack structures, S66 (
1
A
1
), Sr7
(
1
A
2
) and T55 (
3
A
2
), are found to be transition states with one imaginary frequency.  All of them
display distinct structural characteristics.  S66 has the shortest C-O bond length (1.180 ?) and
longest C-C bond (1.362 ?).  The structures of Sr7 and T55 are rather similar to each other.  The
C-O bond lengths are almost the same (1.283 and 1.285 ?) and the C-C distances are only 0.022
? different.  Sr7 and S7p have two imaginary frequencies and S7 has one imaginary frequency.
Distortion along the smaller imaginary frequency, which is out-of-plane bending, leads to real
transition states or minimum with lower-symmetry at the DFT level.  However, the stationary
points are close to the higher-symmetry species and, after zero-point correction, the higher-
symmetry species are lower in energy.  We consider the Sr7, S7 and S7p as stationary points and
we used the higher-symmetry structure for geometry optimization at the CAS level.  The singlet
and triplet carbene (S3 and T4) intermediates are also characterized.  Structurally both are similar
except that S3 has an OCCH dihedral angle of 82.6? but T4 is planar.  On the singlet surface,
several carbenes similar to S3 are identified at the DFT level; among them we chose one with
lowest free energy and closest structure to the CAS level geometry for thermodynamic correction.
We optimized the four lowest energy states of methylene structures (
3
B
1
, 
1
A
1
,
1
B
1
 and c
1
A
1
); the
structures obtained in this study are shown in Figure 3, and they are close to those reported in the
literature.
31
The calculated relative energies are given in Table 2 and 3 for triplet and singlet species,
respectively and the schematic potential energy surfaces for each state are given in Figure 4 and
5.  In the discussion, we will use ?G
298
 which is the MCPT electronic energy with ZPC, heat
capacity (C
p
)
 
and entropy (?S) corrections at the DFT level.  On the triplet potential energy
134
C
1.113
1.127
1.107
101.6
100.9
102.4
C
138.5
134.4
139.3
1.079
1.092
1.086
C
CH
2
(
3
B
1
)
1.080
1.092
1.075
134.8
131.3
133.9
C
CH
2
(
1
B
1
)
CH
2
(
1
A
1
)CH
2
(c
1
A
1
)
1.077
1.068
169.1
171.3
Figure 3.  Optimized geometries of the four lowest energy states of methylenes at the DFT
and CAS (in italic) level.  Literature values (underlined) are from reference 31.
Bond lengths are in ? and angles are in degrees.
surface (Figure 4), T2 is the lowest-energy species, -91.1 kcal/mol relative to CH
2
O + C (
3
P).
The addition of a C atom to the C-O ? bond initially forms a triplet oxiranylidene T1 without
barrier.  T1 can undergo H
2
C-O bond breaking, C-C bond breaking or hydrogen transfer to
oxygen or carbon.  All four pathways were examined, but no transition state for hydrogen transfer
to oxygen was found.  The lowest-energy pathway leads to T2 on the triplet surface, with a free
energy barrier of 14.5 kcal/mol and a reaction free energy of -66.3 kcal/mol.  There must be a
valley-ridge inflection (VRI) points or a bifurcation along the H
2
C-O bond breaking (T1?T2),
33
because a C-O stretching mode cannot directly connect two minima and a rotation or bending
mode is also necessary.  At a VRI point along the angle CCO opening coordinate, C-O stretching
vector becomes zero and a rotational mode around C-C bond becomes negative.  Therefore, there
are two saddle points connected along the C
s
 symmetry coordinate. T12 is one with C-O
stretching vector and T22? is the other with bending mode as transition vector.  T2 can undergo
two interconversions: a rotation around the C-C bond (8.5 kcal/mol free energy barrier)
135
Table 2.  Relative enthalpies (kcal/mol) of C
2
H
2
O triplet isomers at 0K (?H
0
), 298K (?H
298
)
and free energies at 298K (?G
298
) calculated at the MCPT level with
thermodynamic corrections at the DFT level.
?H
298
 ?H
0
Calc. Exp.
a
?G
298
CH
2
O+C (
3
P) 0.0 0.0 0.0 0.0
CH
2
O+C (
1
D) 32.2 32.2 29.1
b
32.8
CH
2
O+C (
1
S) 60.4 60.4 61.9
b
61.1
CO+CH
2
 (
3
B
1
) -77.0 -76.4 -76.7
c
-78.2
CO+CH
2
 (
1
A
1
) -61.9 -61.3 -67.7
c
-62.7
CO+CH
2
 (
1
B
1
) -41.4 -41.4 -43.8
c
-42.3
CO+CH
2
 (c
1
A
1
) -18.8 -17.4 -16.6
c
-15.8
CH+HCO 5.9 6.5 8.2
d
4.1
T1 -31.6 -32.9 -24.8
T2 -97.7 -98.7 -91.1
T3 -44.0 -45.3 -36.8
T4 -77.5 -78.7 -71.0
T5 -30.4 -31.2 -23.9
T6 5.3 4.5 11.8
T7 -44.3 -45.4 -37.7
T12 -17.0 -18.5 -10.2
T13 2.8 1.4 9.5
T15 -8.9 -9.7 -3.0
T22 -89.1 -90.3 -82.6
T24 -39.8 -40.9 -33.1
T27 -0.1 -1.3 6.5
T2p -76.8 -76.8 -72.1
T34 -25.9 -27.2 -19.3
T56 3.1 1.9 9.7
T5p -33.6 -34.1 -27.7
T22? -71.4 -72.6 -64.1
T55 -5.5 -6.5 0.8
a. ?H
298
 values relative to CH
2
O + C (
3
P).
b. For C (
3
P), 171.3 kcal/mol and for CH
2
O, -27.7 kcal/mol, are used as ?H
298
. Relative
energies are calculated by using the data from ref. 2.
c. 93.3 kcal/mol was used as ?H
298
 of methylene from ref. 32. The energy separations 
3
B
1
-
1
A
1
: 9.0 kcal/mol (ref. 31(c)), 
3
B
1
-
1
B
1
: 32.9 kcal/mol (ref. 31(d)) and 
3
B
1
-c
1
A
1
: 60.1
kcal/mol (ref. 31(b)) were used.
d. As ?H
298
 of CHO, 10.0 kcal/mol was used from ref. 32.
C
C
O
C
O
C
O=C
H
2
 +C
(
3
P)
T1
(
3
A")
0.
0
-24
.
8
-3
.
0
-
10.
3
-9
1.
1
0.
8
-33
.
1
-2
3.
9
-72
.
1
-71.
0
4.
1
-78
.
2
-78
.
2
T2
O
C
C
C
C
O
T2
2'
-64.
1
C
O
C
T5
p
-2
7.
7
T2
p
C
C
O
C
O
C
C
C
O
C
O
C
9.
5
-36
.
8
C
C
O
-
19.
3
T12
T3
T1
3
T34
T4
T24
T1
5
T5
5
T5
T5
T2
2
-8
2.
6
-91.
1
T2
(
3
A")
CO
 +
CH
2
 (
3
B
1
)
CO
 +
CH
2
  
(
3
B
1
)
HC
O +
CH
C
O
C
O
C
C
C
C
O
O
C
C
C
O
C
-
23.
9
-8
4.8
-1
00.
1
1
A"
1
A'
C
O
C
Figure 4.
Triplet potential energy surface constructed from 
?
G
298
 at the MCPT level.  Relative energies are given in kcal/mol.
136
137
and an inversion via a linear C-C-O structure (T22? 37.0 kcal/mol barrier).  It is also possible to
transfer a hydrogen atom to the other carbon to form a triplet carbene (T4), though the free
energy barrier is quite unfavorable (58.0 kcal/mol).  The fate of this carbene is not clear.
Breaking the C-C bond to yield CH and HCO is very unfavorable (75.1 kcal/mol free energy
barrier).  Therefore, T4 most likely will undergo reactions with reactants (i.e. CH
2
O).  The
pathway we are most interested in for T2 is breaking the C-C bond to form carbon monoxide and
triplet state methylene (CH
2
 
3
B
1
) with a 19.0 kcal/mol free energy barrier (reverse barrier: 6.1
kcal/mol).  This result is in good agreement with those of Allen.
18b
  The C-C bond dissociation
energy (?H
0
=20.7 kcal/mol, Table 2) is also close to calculated value (18.6 kcal/mol) and
proposed value 22.3 kcal/mol.
18b
  The enthalpy barrier (forward: 20.9 kcal/mol, reverse: 0.2
kcal/mol) is somewhat lower than their estimation (forward: 25-27 kcal/mol, reverse: 3-4
kcal/mol), and therefore, the reaction of triplet state methylene with CO to form T2 has a very
low barrier.
In T1, hydrogen transfer to another carbon is not likely to occur due to a 34.3 kcal/mol
free energy barrier.  If C atoms have large amount of kinetic energy, then this barrier can be
overcome.  This will lead to formation of triplet oxirene, T3 which can transform into a carbene
T4.  If C-C bond cleavage occurs in T1, the bent H
2
C-O-C (T5) isomer will form. However, T5
will dissociate into CO and CH
2
 (
3
B
1
) without a free energy barrier.  T5p was located as a
transition state at both the DFT and CAS levels, but at the MCPT level the energy is lower than
T5.   Clearly, dynamic electron correlation is important and may be underestimated at the DFT
and CAS levels.  A transition state T55 was located along the interconversion of T5.  It can also
form from direct attack of a C (
3
P) atom on oxygen, which is slightly uphill from reactants.
It is known experimentally that the triplet C atom abstracts hydrogen from organic
compounds.
1
  On this PES no evidence of the hydrogen abstraction was found.  We investigated
direct hydrogen abstraction pathways, but no transition state was located.  The hydrogen
138
abstraction from formaldehyde by C (
3
P) is endothermic (4.1 kcal/mol free energy) and proceeds
without reverse barrier.  The hydrogen abstractions from formaldehyde by halogen atoms have
been studied theoretically; these studies revealed that this reaction is almost barrierless (at the
CCSD(T)//B3LYP/6-311++G(d,p))
34(a)
 or has a very low barrier (for F, 8.5 kcal/mol and for Cl,
4.4 kcal/mol at the MP2/aug-cc-PVDZ level).
34(b)
  Therefore, the C-H bond in formaldehyde is
weak and can be abstracted easily by radicals.  In this context, the hydrogen abstraction from
formaldehyde by C (
3
P) proceeds without reverse barrier.  In addition, as shown in equation (2),
no electron rearrangement is necessary to produce two ground state products in this reaction.
Therefore, this reaction occurs without reverse barrier.
(2)
On the singlet PES (Figure 5), the most probable reaction between C (
1
D) with
formaldehyde is also ? addition to form S1.  This reaction is 103.0 kcal/mol exothermic, and S1
will have enough energy to undergo interconversion.  The lowest energy reaction path is to form
ground state S2 (
1
A
1
) via S12 over a 12.9 kcal/mol barrier by breaking the H
2
C-O bond.  Another
possible path is hydrogen transfer to either carbon or oxygen.  Although hydrogen transfer to
carbon has a high barrier (48.7 kcal/mol), the system has enough energy to overcome it to yield
singlet carbene S3.  The singlet carbene, S3 can easily covert into S2 (2.5 kcal/mol barrier).  It
can also make a C-O bond to form a oxirene, S4.  A number of studies has been performed on the
singlet oxirene rearrangement mechanism (Wolff rearrangement),
23
  and  we found that this result
agrees previous results very well.  S3 is lower in energy at the CAS level than S4 but their energy
order is reversed at the MCPT level.  Similar disagreement has been shown at the MP2 level,
O
H H
C
O
H
H
C
+
+
1
A
1
3
P
2
A'
2
?
139
where the singlet carbene (S3) is not a minimum.
23b,e
  The truncation after second-order term in
perturbation theory is responsible for poor description of the singlet carbene, S3.  In S1, hydrogen
Table 3.  Relative enthalpies (kcal/mol) of C
2
H
2
O singlet isomers at 0K (?H
0
), 298K (?H
298
)
and free energies at 298K (?G
298
) calculated at the MCPT level with
thermodynamic corrections at the DFT level.
?H
298
 ?H
0
Calc. Exp.
a
?G
298
CH
2
O+C (
3
P) 0.0 0.0 0.0 0.0
CH
2
O+C (
1
D) 32.2 32.2 29.1 32.8
CH
2
O+C (
1
S) 60.4 60.4 61.9 61.1
CO+CH
2
 (
3
B
1
) -77.0 -76.4 -76.7 -78.2
CO+CH
2
 (
1
A
1
) -61.9 -61.3 -67.7 -62.7
CO+CH
2
 (
1
B
1
) -41.4 -41.4 -43.8 -42.3
CO+CH
2
 (c
1
A
1
) -18.8 -17.4 -16.6 -15.8
CH (
2
?)+HCO (
2
A') 5.9 6.5 8.2 4.1
S1 -77.7 -79.0 -70.2
S2 -146.8 -147.9 -155.0
b
-138.9
S2? -91.9 -93.0 -84.6
S3 -65.1 -65.7 -58.5
S4 -69.0 -69.9 -61.5
S5 -110.8 -111.7 -103.1
S7 -25.7 -26.8 -18.5
S12 -64.4 -65.4 -57.3
S13 -28.9 -30.2 -21.5
S15 -3.1 -4.4 4.2
S23 -63.2 -64.4 -56.0
S25 -58.2 -58.9 -50.8
S34 -64.0 -65.2 -56.7
S66 -38.7 -39.8 -30.8
S7p -19.1 -19.7 -12.6
Sr7 -2.7 -3.5 4.9
S
ci
-84.8 -86.0 -77.5
a. ?H
298
 values relative to CH
2
O + C (
3
P).  For the detailed explanation see Table 2.
b. 11.4 kcal/mol from ref. 32 was used for ?H
298
 of ground state ketene (S2) to calculate
relative enthalpy.
C
C
O
C
C
O
O=
C
H
2
 +C(
1
D)
32.8
-
138.
9
-
70.2
-
30.
8
S
66 (
1
A
1
)
O
C
C
C
C
O
-
21.5
-
61.5
4.
2
-
103.1
C
C
O
O
C
C
C
O
C
-5
8
.
5
-5
6
.
0
-
56.7
-
57.3
S1
(
1
A')
S2
 (
1
A
1
)
-
18.5
-1
2
.
6
S1
2
S2
3
S3
S4
S5
(
1
A'
)
S1
5
S2
5
-5
0
.
8
4.9
CO
 +
C
H
2
 (
1
A
1
)
-
62.7
-4
2
.
3
S7
p
Sr
7
 (
1
A
2
)
CO
 +CH
2
 (
1
B
1
)
S7
 (
1
A"
)
-
15.8
CO
 +
CH
2
 (c
1
A
1
)
0.0
O=
C
H
2
 +C(
3
P)
C
O
C
C
O
C
O
C
C
C
O
C
S3
4
S2
3
O
C
C
C
C
O
CO
 +
CH
2
 (
1
A
1
)
-6
2
.
7
CO
 +
CH
2
 (
1
B
1
)
-4
2
.
3
S2
"
(
1
A"
)
-
84.6
Sc
i
-
77.
5
C
C
O
O
C
C
     Figure 5.
Singlet potential energy surface constructed from 
?
G
298
 at MCPT level.  Relative energies are given in kcal/mol.
140
141
transfer to oxygen to form S5 has a high barrier (66.0 kcal/mol).  S5 has a co-linear H-C-C-O
arrangement and it is the second lowest species on the potential energy surface.  A transition state
between S5 and S2 has been located.  Surprisingly, a hydrogen atom jumps from oxygen to the
other end carbon directly to go from S5 to S2.  Thermodynamic advantage of making a C-O
double bond might be the driving force of this process.
In S1, the C-C bond breaking process is complicated.  Opening the C-C bond will lead to
S66 (
1
A
1
) which has an out-of-plane bending mode of two hydrogen atoms as a transition vector.
At the DFT level, a minimum and a transition state were located, but after the zero-point energy
correction, the transition state has a lower energy than the minimum.  At the CAS level, no
minimum was located and distortion along the transition vector led directly to dissociation of
ketene to CO + CH
2
 (
1
A
1
).  Another way to form S66 is direct addition of the C atom to oxygen.
This pathway has no barrier and will lead to the 
1
A
1
 carbene only.
On the singlet PES, two pathways which lead to formation of the 
1
B
1
 carbene were found.
One starts from direct attack of C (
1
D) on oxygen to form Sr7 (
1
A
2
) which is a transition state of
interconversion of S7 (
1
A").  S7 dissociates via a 5.9 kcal/mol free energy barrier to give CO and
singlet excited carbene (
1
B
1
).  These three are biradical species on the 
1
A" surface.  In Figure 6
two singly occupied orbitals of S7p transition state are shown.  The a" orbital is located on the
CH
2
 carbon and the other a' orbital is the H
2
C-O antibonding orbital and directly correlates with
(a)  a? orbital
(b) a? orbital
Figure 6. Two singly occupied orbitals of S7p.  (a) a? orbital, (b) a? orbital.
142
the excited singlet carbene (
1
B
1
) plus CO.  Now, the question is if it is possible for 
1
B
1
 methylene
to form on the 
1
A" surface.  The 
1
D state has five microstates which will split into 2A
1
 + A
2
 + B
1
+ B
2
 in C
2v
 symmetry, and into 3A? + 2A? in C
s
 symmetry.  When the 
1
D carbon attacks the
formaldehyde oxygen atom, the microstates will split into 3
1
A? and 2
1
A" states and the ratio
between a? and a? will be 3 to 2.  Therefore, it is possible to form the 
1
A? state.  Next question to
consider is if this deoxygenation process is faster than intersystem crossing (ISC).  The
quantitative answer to this question is not possible from this study, but it can be answered
qualitatively.  The dissociation will proceed very quickly, since it has only a 5.9 kcal/mol barrier,
and the system will have about 50 kcal/mol extra energy at S7.  The ISC occurs along the seam of
two potential energy surfaces if the spin-orbit coupling is large enough and geometries are similar
to each other.
35-39
  Generally speaking, the spin-orbit coupling is large in heavier elements, but in
the first-row elements the spin-orbit coupling is very small.
36,38
   However, triplet-singlet
intersystem crossing rate was derived as 4?10
12
 s
-1
.
40
  In  fact, the energy gap between 
1
A? surface
and 
3
A? surface is small (S7-T5: 5.4 kca/mol) and so, the excited singlet species can undergo ISC
to the lower 
3
A? surface.  Therefore, the formation of 
1
B
1
 state methylene via 
1
A? surface (Sr7-
S7-S7p) may not be significant.
The other pathway involves low lying 
1
A? surface. 
 
The transition state, S12 is
highly multireferential (reference weight of the dominant configuration is 0.12) and biradical. The
H
2
C-O stretching mode will lead to global minimum S2, while rotation around C-C bond will
lead to form 
1
A? state S2?.  The S2? is lowest in free energy on the 
1
A? surface and will lead to
form 
1
B
1
 methylene.  However, at CAS level the analytical hessian calculation is too demanding
and it is not certain that if the S12 is a first order or second order saddle point.  If it is a first order
saddle point as at the DFT level, then there must be an VRI or conical intersection between S12
and S2?.  The existence of a conical intersection was reported by Yoshimine.
22(a)
  Therefore we
tried to locate the conical intersection around this part of PES at the CAS(6,6)/6-311+G(2d,p)
CC
O
H H
CC
O
H H
a
1
b
1
b
2
b
1
CO CO
CC
O
H H
????
?
C
H
H
C
H
H
b
1
a
1
CC
O
H H
a
1
b
1
b
2
b
1
CO CO
C
H
H
C
H
H
b
1
a
1
????
?
a
1
b
1
b
2
b
1
CO
CO
????
?
C
H
H
C
H
H
b
1
a
1
S2
 (
1
A
1
)
CH
2 
(
1
A
1
)
+ C
O
 
(
1
????
++++
))))
CH
2 
(
1
B
1
)
+ C
O
 (
1
????
++++
))))
CH
2
 (c 
1
A
1
)
+ C
O
 (
1
????
++++
))))
S2 (
1
A
1
)
S2
 (
1
A
1
)
E
CO
C
H H
CO
C
H H
CC
H H
a
1
b
1
b
2
b
1
CO
CO
C
H
H
C
H
H
CO
C
H H
b
1
a
1
????
?
S66 (
1
A
1
)
CH
2 
(
1
A
1
) +
 CO (
1
????
++++
))))
a
1
b
1
b
2
b
1
CO
CO
b
1
a
1
????
?
CH
2
 (c 
1
A
1
)
 
+ C
O
 
(
1
????
++++
))))
C
H
H
C
H
H
S66
 (
1
A
1
)
a
1
b
1
b
2
b
1
CO
CO
C
H
H
C
H
H
b
1
a
1
????
?
S66 (
1
A
1
)
CH
2 
(
1
B
1
) +
 CO (
1
????
++++
))))
O
E
CH
2 
(
1
A
1
)
+ C
O
 
(
1
????
++++
))))
CH
2 
(
1
B
1
)
+ C
O
 
(
1
????
++++
))))
CH
2
 (c 
1
A
1
)
+ C
O
 (
1
????
++++
))))
(a
)
(b
)
(d
)
(f)
(e
)
(c
)
Figure 7.
Orbital crossing diagram for the 
singlet methylene producing reactions from 
S2
 and 
S66
.
(a) 
S2
 
?
 CO + CH
2
 (
1
A
1
), (b) 
S66
 
?
 CO + CH
2
 (
1
A
1
), (c) 
S2
 
?
 CO + CH
2
 (
1
B
1
),
(d) 
S66
 
?
 CO + CH
2
 (
1
B
1
), (e) 
S2
 
?
 CO + CH
2
 (c
1
A
1
), (f) 
S66
 
?
 CO + CH
2
 (c
1
A
1
)
143
144
level, but we could not obtain desirable results.  Depending upon the active space size, the PES
shape is very different.   That is why we cannot locate the right conical intersection.  The second
possibility that S12 might be a second order saddle point was also examined by optimizing the
geometry at the CAS(12,11)/6-311+G(2d,p) level and by numerical vibrational analysis.  The
transition state, S12 found to be second order saddle point with two distinct imaginary
frequencies (a?: 319.8i, a?: 163.7i) at this level.  Therefore, at S12 the PES will split into 
1
A? and
1
A? surfaces.  The S2? can dissociate to give 
1
B
1
 methylene plus CO by breaking the C-C bond
without reverse barrier.  Along the C-C bond breaking pathway a conical intersection S
ci
 between
1
A? and 
1
A? surface was found.  The conical intersection is lower in free energy by 14.8 kcal/mol
than the CH
2
 (
1
A
1
) plus CO.  This conical intersection can be a radiationless decay channel of 
1
A?
state ketene, S2? or excitation of S2 to S2?.  If the bond breaking process of S2? is fast enough to
pass the conical intersection, then it is possible to form CH
2
 (
1
B
1
) plus CO in accordance with
Carpenter?s non-statistical dynamic effect.
41
It is still not clear if the observed products could form from other lower-energy
intermediates on the singlet PES.  Thus, we examined orbital correlations between ketene with
C
2v
 symmetry (S2 and S66) and carbene products (Figure 7) and their valence electron
configurations are given in Table 4.  Interestingly, neither S2 nor S66 directly correlate to the
lowest 
1
A
1
 state methylene plus CO, but both correlate to the third excited c
1
A
1
 state methylene
plus CO.  As the C-C (C-O) distance becomes longer in S2 (S66), the C-C antibonding orbital (a
1
)
will be stabilized but the occupied b
1
 orbital will be destabilized due to the loss of ? bonding
interaction.  As shown in Figure 6, to correlate the 
1
A
1
 state ketene (S1 or S66) with the 
1
A
1
 state
methylene plus CO, the orbital crossing between b
1
 and a
1
 orbitals is unavoidable.  The
correlation diagram between the 
1
A
1
 state ketene with the 
1
B
1
 state methylene plus CO (Figure 6
(c) and (d)) also shows a crossing, but the energies of two orbitals (a
1
 and b
1
) are so close each
other as to be pseudo-degenerate.  The 
1
A
1
 state ketene isomers, S2 and S66, correlate with the
145
Table 4. Important valence electron configurations of four lowest electronic state methylene
and four singlet species obtained at CAS level
Configuration
a
|ci |
b
CH
2
 (
3
B
1
) abab
1
2
2
2
11
0.98
CH
2
 (
1
A
1
)
aba
1
2
2
2
1
2
abb
1
2
2
2
1
2
0.97
0.18
CH
2
 (
1
B
1
)
abab
1
2
2
2
11
abab
1
2
2
2
11
0.70
0.70
CH
2
 (c
1
A
1
)
abb
1
2
2
2
1
2
aba
1
2
2
2
1
2
0.73
0.67
S2  (
1
A
1
)
aabaabbb
1
2
1
2
2
2
1
2
1
2
1
2
2
2
1
2
aabaabbb
1
2
1
2
2
2
1
2
1
2
1
2
1
2
2
2
aabaabbb
1
2
1
2
2
2
1
2
1
2
1
2
2
2
1
2
0.95
0.12
0.10
S2? (
1
A?)
aaaaaa aaa'''''"'"'
22222 22
aaaaaa aaa'''''"'"'
22222 22
aaaaaa aaa'''''"''"
22222 22
aaaaaa aaa'''''"''"
22222 22
0.63
0.63
0.17
0.17
S66 (
1
A
1
)
aabababb
1
2
1
2
2
2
1
2
1
2
1
2
2
2
1
2
aabababb
1
2
1
2
2
2
1
2
1
2
1
2
2
2
2
2
0.93
0.15
Sr7 (
1
A
2
)
aaabbabbb
1
2
1
2
1
2
2
2
1
2
1
2
2
2
12
aaabbabbb
1
2
1
2
1
2
2
2
1
2
1
2
2
2
12
aaabbabbb
1
2
1
2
1
2
2
2
1
2
1
2
2
2
12
aaabbabbb
1
2
1
2
1
2
2
2
1
2
1
2
2
2
12
0.61
0.61
0.29
0.29
S7p (
1
A?)
aaaa aaaaa'''"''''"
222 2222
aaaa aaaaa'''"''''"
222 2222
aaaa aaaaa'''"''''"
222 2222
aaaa aaaaa'''"''''"
222 2222
0.64
0.64
0.17
0.17
a. For clarification core electron configurations are omitted. Singly occupied ? orbitals are
designated with bar over the orbital designation.
b. Absolute value of coefficient of each configuration.
excited c
1
A
1
 methylene state plus CO without orbital crossing (Figure 6 (e) and (f)).  In this case,
there must be a transition state in the dissociation pathway of ketene along the C-C bond
elongation.
Finally, the reaction enthalpies and free energies of oxygen abstraction reactions by
146
C atom obtained in this study are summarized in Table 5.  Our results are in very good agreement
with experimental results.  The reaction, C + CH
2
O ? CO + CH
2
 is highly exothermic and the
reaction free energy of excited singlet 
1
B
1
 carbene producing reaction is calculated to be ?75.1
kcal/mol.
Table 5. Reaction enthalpies at 0K (?H
0
) and 298K (?H
298
) and free energies at 298K (?G
298
)
at MCPT level (in kcal/mol)
a. ?H
298
 values are given. For detailed information about the experimental values, see Table
2.
b. T2 energies are calculated from S2 (
1
A
1
) - T2 (
3
A?) separation 54.8 kcal/mol (T
0
)
reported by Schaefer in ref. 20 with heat capacity correction obtained in this study.
5.4  Conclusion
 The reactions of triplet (
3
P) and singlet (
1
D) atomic carbon with formaldehyde were
studied computationally.  S2 (
1
A
1
) is the global minimum on the entire ketene (CH
2
CO) potential
energy surface.  On the triplet PES, a C atom adds to the C-O double bond to form cyclic T1
which undergoes intramolecular rearrangement. The bent H
2
C-C-O linkage isomer (T2) is lowest
on the triplet PES, and it dissociates to give CO and the ground state methylene (CH
2
 
3
B
1
).  On
?H
0
?H
298
?G
298
Reactants Products
Calc. Calc. Exp.
a
Calc.
C (
3
P) + CH
2
O T2  (
3
A?) -97.7 -98.7 -101.2
b
-91.1
C (
1
D) + CH
2
O S2  (
1
A
1
) -179.0 -180.1 -184.1 -171.7
T2 (
3
A?) CO + CH
2
 (
3
B
1
) 20.7 22.3 24.5
b
12.9
S2 (
1
A
1
) CO + CH
2
 (
1
A
1
) 84.9 86.6 87.3 76.2
S2 (
1
A
1
) CO + CH
2
 (
1
B
1
) 105.4 107.1 112.2 97.0
S2 (
1
A
1
) CO + CH
2
 (c
1
A
1
) 128.0 130.5 138.4 123.1
C (
3
P) + CH
2
O CO + CH
2
 (
3
B
1
) -77.0 -76.4 -76.7 -78.2
C (
1
D) + CH
2
O CO + CH
2
 (
1
A
1
) -94.1 -93.5 -96.8 -95.5
C (
1
D) + CH
2
O CO + CH
2
 (
1
B
1
) -73.6 -73.0 -72.9 -75.1
C (
1
D) + CH
2
O CO + CH
2
 (c
1
A
1
) -51.1 -49.6 -45.7 -48.6
147
the triplet surface, linear C-C-O or C-O-C isomers (T22? and T55) were found to be transition
states for the interconversion of corresponding bent isomers (T2 and T5).  Hydrogen abstraction
from formaldehyde by C (
3
P) is nonspontaneous (4.1 kcal/mol) and can proceed without a reverse
free energy barrier.  On the singlet surface, the C (
1
D) addition to the C-O double bond also
occurs without barrier to form S1 with a free energy change of -103.0 kcal/mol.  S1 can also
undergo various isomerization reactions to form the global minimum S2, or S5 which is the
second lowest species on both potential energy surfaces.  On both surface intermediate carbenes
are identified (T4 and S3). The triplet carbene (T4) may survive long enough to react with
another reagents in the reaction mixture but singlet carbene (S3) probably will not.
The possible pathways to form excited singlet methylene (
1
B
1
) were found.  One is along
the reaction path Sr7 (
1
A
2
)-S7 (
1
A")-S7p (
1
A") which leads to the 
1
B
1
 carbene directly.  The other
possible pathway is by way of S2? which is lowest on the 
1
A? surface, if the C-C bond
dissociation in S2? occurs very fast.  Interestingly the ground state S2 (
1
A
1
) correlates better with
the third excited singlet state methylene (c
1
A
1
) than the first excited singlet methylene (
1
A
1
).
However, this level of theory is not enough to explain the dynamic behavior of molecule, and we
are preparing ab initio molecular dynamics calculations on the basis of our constructed potential
energy surfaces.
148
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