Multicomponent Orbital-Optimized Perturbation Theory Methods: Approaching Coupled Cluster Accuracy at Lower Cost.

Multicomponent quantum chemistry methods such as the nuclear-electronic orbital (NEO) method allow the consistent quantum mechanical treatment of electrons and nuclei. The development of computationally practical, accurate, and robust multicomponent wave function methods is challenging because of the importance of orbital relaxation effects. Herein the variational orbital-optimized coupled cluster with doubles (NEO-OOCCD) method and the orbital-optimized second-order Møller-Plesset perturbation theory (NEO-OOMP2) method with scaled-opposite-spin (SOS) versions are developed and applied to molecular systems in which a proton and all electrons are treated quantum mechanically. The results highlight the importance of orbital relaxation in multicomponent wave function methods. The NEO-SOS'-OOMP2 method, which scales the electron-proton correlation energy as well as the opposite-spin and same-spin components of the electronic correlation energy, is found to achieve nearly the same level of accuracy as the NEO-OOCCD method for proton densities, proton affinities, and optimized geometries. An advantage of the NEO-SOS'-OOMP2 method is that it can be implemented with N4 scaling, where N is a measure of the system size. This method will enable future multicomponent wave function calculations of structures, energies, reaction paths, and dynamics for substantially larger chemical systems.