with Te (x i ) denoting the electronic kinetic energy operator for electron i, VeN (x i ; X A ) the (attractive) coulomb operator for electron i and nucleus A, Vee (x i , x j ) the (repulsive) coulomb operator for electrons i and j, and V NN is the total (repulsive) coulomb potential between all of the nuclei. Within the Born-Oppenheimer approximation, V NN is a constant, the nuclear kinetic energy is neglected, and the electron-nuclear attraction depends parametrically on the fixed nuclear coordinates. The photonic contribution is captured by the complex energy