A simple F12 geminal correction in multi-reference perturbation theory

We propose a simple F12 geminal correction in multi-reference perturbation theory. An explicitly correlated term is introduced in the external excitations of the first order wave function in an internally contracted manner. By the use of the s- and p-wave cusp conditions, the F12 correction is expressed as the expectation value of a two-body effective operator, which reduces to the MP2-F12/A∗(SP) energy in the single reference limit. The performance of the F12 multi-reference perturbation method is demonstrated for C, CH2, O2, and SiC3.