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