with the electronic Hamiltonian Ĥel and the mechanical nuclear kinetic energy operators. Note that we name the operator TN (R, t) mechanical kinetic energy operator in analogy with the mechanical momentum pν = mv ν = p ν -A ν in the presence of an electromagnetic field with p ν = -i ∇ ν being the canonical momentum operator that satisfies the commutation relations [p ν,i , R ν,j ] = iδ ij for i = x, y , z. TN is defined as