# Why are single excitations ignored in the MP2 component of double hybrid functional calculations?

In the original paper by Grimme introducing double hybrid functionals (also summarized in just 3 paragraphs here), it says:

"[As] opposed to nonempirical versions of KS-PT2 [19], the single excitations contribution is neglected, i.e., we implicitly assume for all Fock matrix elements $$f_{ia}=0$$."

What is the reason for neglecting these single-excitations?
Please accept my apologies if this question is too trivial, since my knowledge of how double-hybrid (or single hybrid!) functionals work, began and ends with my browsing of the original paper to write the above-mentioned 3 paragraph summary, fewer than 2 months ago.

• My guess is: the first implementation was either in Gaussian (via iops) or using Turbomole. In both, you basically just run a MP2 calculation with a slightly different input and scale down the result (I've done that long time ago). Later, someone somewhere probably tried including the singles, but did not get significantly better results. – TAR86 Jul 25 '20 at 6:38
• My gut reaction is that it is because in the formulation of MP2 where one uses a shifted Fock operator, the first-order correction is equal to zero. If one does not use the shifted Fock operator, the first-order correction reclaims the HF energy. So, either way, one sort of knows what the first-order correction is without any calculation. This is appealing for a functional in the sense that one can choose complete exact exchange and complete MP2 correlation and recover the MP2 energy exactly. I'm not a DFT expert though, so this is just speculation. – jheindel Aug 3 '20 at 17:56
• @jheindel but I would assume that only holds if you have a HF reference. DFT orbitals / the DFT density is not a HF solution so it has non-vanishing singles..? – Susi Lehtola Oct 8 '20 at 22:28
• @ShoubhikRMaiti Are you saying that the singles contribution to the energy will be 0? The first half of the quoted sentence implies that it's not true for "non-empirical versions of KS-PT2". – Nike Dattani Apr 10 at 20:44