  Based on quantum reactive-scattering theory, we propose a method for studying
the electronic nonadiabaticity in collision processes involving electron-ion
rearrangements. We investigate the state-to-state transition probability for
electron-ion rearrangements with two comparable approaches. In the first
approach the information of the electron is only contained in the ground-state
Born-Oppenheimer potential-energy surface, which is the starting point of
common reactive-scattering calculations. In the second approach, the electron
is explicitly taken into account and included in the calculations at the same
level as the ions. Hence, the deviation in the results between the two
approaches directly reflects the electronic nonadiabaticity during the
collision process. To illustrate the method, we apply it to the well-known
proton-transfer model of Shin and Metiu (one electron and three ions),
generalized by us in order to allow for reactive scattering channels. It is
shown that our explicit electron approach is able to capture electronic
nonadiabaticity and the renormalization of the reaction barrier near the
classical turning points of the potential in nuclear configuration space. In
contrast, system properties near the equilibrium geometry of the asymptotic
scattering channels are hardly affected by electronic nonadiabatic effects. We
also present an analytical expression for the transition amplitude of the
asymmetric proton-transfer model based on the direct evaluation of integrals
over the involved Airy functions.
