Inclusion of dynamic ?-? polarization in ?-electronab initio calculations

Abstract

A method is presented, whereby dynamic σ-π polarization, i.e. the correlation effect expressed by simultaneous (σ-σ*, π-π*) excitations, can be approximately included in a multi-reference configuration interaction (MRCI) or multi-configurational self-consistent field (MC-SCF) calculation, without need to explicitly correlate the sigma orbitals. The method, which we call the capacitance matrix method, is based on the use of conventional one-electron integrals, from which a σ polarization potential (SPP) contribution is computed and added to the one- and two-electron Hamiltonian. In the present form, the method requires one parameter for each type of atom, and one for each type of bond. These parameters were adjusted to reproduce the dynamic σ-π polarization energy, computed by restricted multi-reference CI calculations, of a number of states of different hydrocarbons, and the agreement was within a few percent. Using the same parameters in CAS (Complete Active Space) SCF calculations of various states of benzene gives excitation energies, when SPP is included, which is comparable to those obtained by much more elaborate MRCI calculations.