This question came to mind while writing another question here Extended Hybrid Methods, but I felt it was distinct enough to ask separately.
In double hybrids DFT methods, you essentially perform a hybrid DFT calculation (DFT plus Hartree-Fock exchange) and then perform an MP2 calculation using the orbitals from the hybrid calculation. The energies from both these calculations are weighted and combined to give a final energy.
I'm curious about this last step; beyond fitting, are there heuristics that can be used to set the correlation coefficient for a particular type of problem? Obviously there is no exact answer for picking how much correlation comes the DFT part and how much from MP2, but what sort of considerations go into that decision? I know for regular hybrids different ratios of exchange are chosen depending on the problem they hope to address with that functional. For example, the original PBE0 paper makes an argument based on perturbation theory that ~1/4 HF exchange should be the best for atomization energies. I was wondering if there were similar physical rationale for setting the correlation ratio for double hybrids.