Periodic local MP2 method employing orbital specific virtuals

We introduce orbital specific virtuals (OSVs) to represent the truncated pair-specific virtual space in periodic local Møller-Plesset perturbation theory of second order (LMP2). The OSVs are constructed by diagonalization of the LMP2 amplitude matrices which correspond to diagonal Wannier-function (WF) pairs. Only a subset of these OSVs is adopted for the subsequent OSV-LMP2 calculation, namely, those with largest contribution to the diagonal pair correlation energy and with the accumu- lated value of these contributions reaching a certain accuracy. The virtual space for a general (non diagonal) pair is spanned by the union of the two OSV sets related to the individual WFs of the pair. In the periodic LMP2 method, the diagonal LMP2 amplitude matrices needed for the construction of the OSVs are calculated in the basis of projected atomic orbitals (PAOs), employing very large PAO domains. It turns out that the OSVs are excellent to describe short range correlation, yet less appropriate for long range van der Waals correlation. In order to compensate for this bias towards short range correlation, we augment the virtual space spanned by the OSVs by the most di↵use PAOs of the corresponding minimal PAO domain. The Fock and overlap matrices in OSV basis are constructed in the reciprocal space. The 4-index electron repulsion integrals are calculated by local density fitting and, for distant pairs, via multipole approximation. New procedures for determining the fit-domains and the distant-pair lists, leading to higher eciency in the 4-index integral evaluation, have been implemented. Generally, and in contrast to our previous PAO based periodic LMP2 method, the OSV-LMP2 method does not require anymore great care in the specification of the individual domains (to get a balanced description when calculating energy di↵erences) and is in that sense a black box procedure. Discontinuities in potential energy surfaces, which may occur for PAO-based calculations if one is not careful, virtually disappear for OSV-LMP2. Moreover, due to much increased compactness of the pair-specific virtual spaces, the OSV-LMP2 calculations are faster and require much less memory than PAO-LMP2 calculations, despite the noticeable overhead of the initial OSV construction procedure.