which is the gauge-dependent contribution. In Eqs. (10) to (15), the symbol • r stands for an integration over electronic positions, and we thus removed any dependence on r of the arguments within the integral operation to show that this variable is integrated out. The electronic evolution equation is i ∂ Φ(r,t; q, R) ∂t = ĤBO (r, R) + VP (q)+ ĤPM (r, q, R)