Multicomponent Double-Hybrid Density Functional Theory

In this contribution we investigate how far multicomponent density functional theory (DFT) results can be improved by the admixture of Møller-Plesset (MP) perturbation theory electron-proton correlation energies. Three formulations are explored, based off the popular double-hybrid functionals B2PLYP, DSD-PBEP86 and PBEQIDH. Partial use of the PA23 proton binding affinities data set is made to parametrize the ratio in the DFT/MP2 correlation energies. The resulting models are evaluated on a separate set of titratable molecules. The combination of nuclear electronic orbital (NEO) DFT and MP2 electron-proton correlation leads up to a 2-fold reduction in the root-mean-square deviation (RMSD) compared to standard NEO-DFT, a trend that is confirmed in the independent test set. We apply the parametrized NEO-B2PLYP model to compute the energetics of protonated water hexamers as well as a challenging example for proton dynamics, a crown ether molecule. In the latter case we compare the energetics of localized vs shared proton configurations. Overall, a ratio of about 0.8:0.2 (DFT/MP2) in the electron-proton correlation delivers a robust improvement across the models, even with variations in the basis sets used and the type of chemical bonds investigated.