due to the fact that 1|0 = 0, even though that g(R)|∇ α |e(R) = 0. Thus, in the {|e, 0 , |g, 1 } subspace, the derivative coupling among these two states is 0, making them effectively "diabatic" even though |e and |g themselves are adiabatic states. Below, we give more detailed expressions of these gradient expressions in two specific subspaces. For clarity and concreteness, we will only consider two adiabatic electronic states |g and |e , which are the electronic ground and first excited states of the molecule, respectively. The eigenvalues corresponding to these two states |g and |e are E g and E e , respectively. The photon Fock basis considered here is from vacuum state |0 to some finite number which assures the convergence of the properties we calculate. Unless explicitly stated, we always assume that the photon number in the basis is in ascending order. For the state with the same photon number, the electronic states are also in ascending order. Under the above settings, the two simplest basis one can choose are {|e0 , |g1 } and {|g0 , |e0 , |g1 , |e1 } which are referenced hereafter as 2-state and 4-state basis, respectively.