13.1.2 Perturbative Corrections

The SSG description of molecular electronic structure can be improved by perturbative description of missing inter-geminal correlation effects. We have implemented Epstein-Nesbet form of perturbation theory ³²⁸ Epstein P. S.
Phys. Rev.
(1926), 28, pp. 695. Link ^{, 883} Nesbet R. K.
Proc. Roy. Soc. Ser. A
(1955), 230, pp. 312. Link that permits a balanced description of one- and two-electron contributions to excited states’ energies in SSG model. This form of perturbation theory is especially accurate for calculation of weak intermolecular forces. Also, two-electron $[i\overline{j},j\overline{i}]$ integrals are included in the reference Hamiltonian in addition to intra-geminal $[i\overline{j},i\overline{j}]$ integrals that are needed for reference wave function to be an eigenfunction of the reference Hamiltonian. ¹⁰⁴⁰ Rassolov V. A., Xu F., Garaschchuk S.
J. Chem. Phys.
(2004), 120, pp. 10385. Link

All perturbative contributions to the SSG(EN2) energy (second-order Epstein-Nesbet perturbation theory of SSG wave function) are analyzed in terms of largest numerators, smallest denominators, and total energy contributions by the type of excitation. All excited states are subdivided into dispersion-like with correlated excitation within one geminal coupled to the excitation within another geminal, single, and double electron charge transfer. This analysis permits careful assessment of the quality of SSG reference wave function. Formally, the SSG(EN2) correction can be applied both to RSSG and USSG wave functions. Experience shows that molecules with broken or nearly broken bonds may have divergent RSSG(EN2) corrections. USSG(EN2) theory is balanced, with largest perturbative corrections to the wave function rarely exceeding 0.1 in magnitude.