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This study implements the full multicomponent third-order (MP3) andfourth-order (MP4) many-body perturbation theory methods for the first time.Previous multicomponent studies have only implemented a subset of the fullcontributions and the present implementation is the first multicomponentmany-body method to include any connected triples contribution to theelectron-proton correlation energy. The multicomponent MP3 method is shown tobe comparable in accuracy to the multicomponent coupled-cluster doubles methodfor the calculation of proton affinities, while the multicomponent MP4 methodis of similar accuracy as the multicomponent coupled-cluster singles anddoubles (CCSD) method. From the results in this study, it is hypothesized thatthe relative accuracy of multicomponent methods is more similar to theirsingle-component counterparts than previously assumed and that the previousexplanation for the better performance of multicomponent CCSD compared to otherab initio multicomponent methods may be incorrect. It is demonstrated that formulticomponent MP4, the fourth-order triple-excitation contributions can besplit into electron-electron and electron-proton contributions and theelectron-electron contributions ignored with very little loss of accuracy ofprotonic properties.

Multicomponent MP4 and the Inclusion of Triple Excitations in Multicomponent Many-Body Methods