In this Letter is considered a reduced molecular manifold which is weakly c
oupled to several external states. It is shown, that if these couplings are
of the order of epsilon, 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 exten
t of O(epsilon (2)). (C) 2001 Elsevier Science B.V. All rights reserved.