Combining strongly orthogonal geminals with explicitly correlated corrections

Recent accounts of the good performance of the pair coupled cluster doubles (pCCD) method extended by an explicitly correlated (F12) model in describing essential correlation effects motivated us to further explore pair-function based methodologies in conjunction with the explicitly correlated framework. While pCCD can be reformulated as the antisymmetrized product of interacting two-electron fragments (geminals), driven by the special structure of the resulting reference function, we opt for employing strongly orthogonal geminals in the Ansatz. In this work, the antisymmetrized product of strongly orthogonal geminals wavefunction (SLG), which is capable of capturing static correlation in a computationally efficient manner, is corrected by an F12 addition via perturbation theory. The explicitly correlated terms of the wavefunction are internally contracted and are entirely responsible for describing the dynamic correlation missing from SLG, by virtue of incorporating all possible double excitations from the reference. A Slater-type function is used as a correlation factor, while amplitudes obtained from the variational optimization of the Hylleraas-functional as well as those fixed according to the s- and p-wave cusp conditions (SP-Ansatz) are explored. The presented SLG-F12 model is applied in order to investigate the splitting of the lowest singlet and triplet states in small biradicals and in other multireference systems.