Towards the formulation of a new multi–determinant electron propagator for open–shell molecular systems
Type of DegreePhD Dissertation
Chemistry and Biochemistry
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The efforts of this thesis are focused on extending the capabilities of the current single determinant electron propagator formalism to a formulation in which multiple determinants can be employed, enabling the formulation of a new electron propagator approximation that allows the calculation of ionization energies of open-shell molecules in which spin-contamination represents a challenge in the calculation of correct and accurate ionization energies. This new electron propagator method overcomes the spin–contamination problem by using determinants that are more general than those generated in restricted Hartree–Fock theory. For this new electron propagator formulation, generalized matrix elements of the superoperator Hamiltonian that accommodates non–integer occupation numbers associated with general, orthogonal spin orbitals were obtained for the first time. For the definition of the self–energy matrix of this new propagator, the partitioning scheme for the primary and secondary blocks of the superoperator Hamiltonian was redefined. In this new formulation, the ionization–operator spaces will contain sets of operators that change the quantum number Ms by ±1/2. These sets include electron removal plus spin-flip processes. This new method not only has the advantage of conserving correct spin quantum number (<S^2>) values but also takes advantage of point-group symmetry. It also has an O2V3 arithmetic scaling factor, where O and V are, respectively, the numbers of occupied and virtual spin-orbitals.