Electronic non-adiabatic transitions: the line integral and approximations

In this Letter is considered a reduced molecular manifold which is weakly coupled to several external states. It is shown, that if these couplings are of the order of ε, the adiabatic-to-diabatic transformation matrix A(s), as obtained by solving the line integral within the reduced manifold, as well as the corresponding diabatic potentials are perturbed to the extent of O(ε2).