Beyond the Born-Oppenheimer approximation with quantum Monte Carlo methods

In this work we develop tools that enable the study of nonadiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave-function ansatz for electron-ion systems that can involve a combination of both clamped ions and quantum nuclei. We explicitly calculate the ground-state energies of ${\mathrm{H}}_{2}$, LiH, ${\mathrm{H}}_{2}\mathrm{O}$, and ${\mathrm{FHF}}^{\ensuremath{-}}$ using fixed-node quantum Monte Carlo with wave-function nodes that explicitly depend on the ion positions. The obtained energies implicitly include the effects arising from quantum nuclei and electron-nucleus coupling. We compare our results to the best theoretical and experimental results available and find excellent agreement.