The coupled nuclear and electronic equations of motion (eqs. 4 and 5) describe the dynamical interaction between electrons and nuclei beyond the adiabatic regime. This interaction is mediated by the time-dependent vector potential (TDVP) A ν (R, t), the time-dependent potential energy surface (TDPES) ϵ(R, t), and the electron-nuclear coupling operator Ûen [ϕ, χ]. These quantities are defined as: