Nuclear quantum e↵ects (NQEs) play an important role in quantum chemistry, becoming particularly significant in scenarios such as conical intersections, molecular vibrations, and lowtemperature atomic coherence and exchange effects. This is especially true for light nuclei like hydrogen, where even at room temperature NQEs cannot be overlooked. Traditional quantum chemical calculations often rely on the Born-Oppenheimer (BO) approximation to separate electronic and nuclear degrees of freedom. While this allows for classical propagation of nuclei on the electronic potential energy surface or the use of approximations to extract dynamic nuclear information, it fails to capture the substantial coupling between nuclear and electronic wave functions that directly influence chemical phenomena.