Explicitly correlated geminal-based perturbation theory

An explicitly correlated extension of a pair-function based perturbation theory is presented. The reference is obtained as the antisymmetrized product of strongly orthogonal geminals, termed SLG, which can capture static correlation at mean-field cost. Geminals entering SLG are spin unrestricted in general and are expanded in the one-electron basis of the natural orbitals of the unrestricted Hartree–Fock wavefunction. Dynamic correlation is accounted for by perturbation theory (PT) at second order via a Dyall-like Hamiltonian acting as the zero-order operator. An explicitly correlated (F12) correction is added to SLGPT2 to improve the description of dynamic correlation and enhance convergence with respect to the basis size. The resulting SLGPT2-F12 scheme inherits the fragmented structure of the SLGPT2 method, facilitating an efficient solution scheme. For numerical illustration, the SLGPT2-F12 approach is applied to singlet-triplet splittings in small biradical systems.