where g n (R) = ∂En(R) ∂R is the gradient of adiabatic state |n⟩. In deriving the Eq. 12d, the derivative of nonadiabatic coupling vector d nm (R) was tactically removed by utilizing the chain rule. By recognizing ∆P = F n,m x n p m d nm (R) ≡ f (x, p, R) and using V eff to represent the electronic part of our Hamiltonian, we obtain Ṗkin = Ṗ + ∂∆P ∂t