where quantum number i ≡ {ν, n} indicates both the adiabatic electronic state of the molecule and the Fock states. 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 the basis for the hybrid system, because of the readily available adiabatic electronic states from the electronic structure calculations, as well as the dipole moments we need to construct the elements of Hamiltonian.