where the sum includes both the nuclear and electronic DOFs, r j and p j are the position and momentum of the charged particle j, with the charge q j and mass m j . Further, A ⊥ (r), E ⊥ (r) and B ⊥ (r) are the transverse vector potential, electric field, and magnetic field, respectively. The energy associated with E ∥ (r) (the second term in Eqn. 35) is given by