On the inclusion of post-MP2 contributions to double-hybrid density functionals

In this study, we explore the effect of supplementing the DuT spin-component-scaled double-hybrid density functional method with post-second-order Møller-Plesset-type theory (MP2) correlation terms. We find that the inclusion of additional MP3 correlation energies has almost no effect on the performance. Further addition of correlation effects from MP4 generally leads to a small improvement in the performance. However, we find that the inclusion of the higher-order perturbative correlation effects does not rectify some major shortcomings of DuT for more challenging systems, and the use of MP4, in fact, leads to a significant deterioration in the performance in some cases. We also find that the use of correlation energies from CCSD(T) instead of those from MP3 and MP4 does not lead to a substantial improvement over the MP4-based method, both in general and in some difficult cases that we have examined. An additional observation is that, for large systems that are dominated by noncovalent interactions, DuT and the two MPn-based post-MP2 double-hybrid density functional theory (DFT) procedures all benefit from the inclusion of dispersion corrections. Overall, our investigation suggests that the current generation of MP2-based double-hybrid DFT methods may already be providing close to the optimal performance that can be achieved with the double-hybrid methodology paired with spin-component-scaling. Development of even better double hybrids is an active research field, and we hope that our study provides valuable insights. We recommend the continuing use of existing MP2-based double-hybrid methods as a bridging level between hybrid density functional procedures and high-level wave-function-based procedures.