where quantum number i ≡ {α, n} indicates both the adiabatic electronic state of the molecule and the Fock state. We refer to |ψ i (R)⟩ as the adiabatic-Fock state in this work. Note that we have introduced a shorthand notation in Eq. 10, which will be used throughout the rest of this paper. This is one of the most straightforward choices of basis for the hybrid system because of the readily available adiabatic electronic information (e.g., wavefunctions, energies, and the dipole matrix) from electronic structure calculations.