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Hybrid DFT methods, where the functional is supplemented with Hartree-Fock exchange, have become increasingly popular due to their low cost and decent accuracy. Double hybrids, which mix in an MP2 contribution, have also been developed as a way to improve the accuracy.

Has this idea been extended to other Post-SCF methods? For example, one could consider doing coupled cluster or configuration interaction calculations where a DFT wavefunction is used as the primary configuration. If not, is there a major hurdle, technical or theoretical, that prevents this from being done?

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    $\begingroup$ @NikeDattani I had initially thought of asking about a "reverse hybrid", but after reading a bit more on double hybrids, apparently there isn't much of a distinction. Double hybrid DFT methods actually perform an MP2 calculation with the DFT wavefunction, so its not necessarily a clear distinction whether you are improving DFT with MP2/Post-SCF or the other way around. $\endgroup$
    – Tyberius ♦
    May 16, 2020 at 17:19
  • $\begingroup$ I once asked about mixing in coupled cluster. The main reluctance to mix in CC is probably that the cost would become $N^6$ for CCSD, which might defeat the purpose of DFT (some people might say that the purpose of DFT is to provide a low-cost method). The nice thing about DFT+MP2 is that the accuracy tends to be better than standard MP2, and gets quite close to CCSD(T) accuracy with roughly MP2 cost. But let me ask Stefan Grimme for a better answer! $\endgroup$
    – Nike Dattani
    May 30, 2020 at 4:45

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As far as I am aware, double hybrids were first proposed by Truhlar and coworkers in J. Phys. Chem. A 2004, 108, 21, 4786–4791. If you look at the paper, in addition to MP2 they also proposed a double hybrid based on QCISD, i.e. the quadratic configuration interaction method which can be viewed as an approximate coupled-cluster method.

There's no reason a priori why more elaborate post-HF methods than MP2 couldn't be employed in a double hybrid DFT functional. However, the reason why this isn't usually done is probably due to cost and accuracy: going to higher-order methods introduces much steeper scaling with system size (already MP2 is quite expensive!), while the improvements in accuracy are probably quite low and still dominated by the DFT part: at some point it's just better to discard DFT altogether and just use the post-HF method!

Note also that in addition to MP2, some double hybrids employ the random phase approximation, see e.g. Phys. Chem. Chem. Phys. 18, 20926 (2016)

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