Role of potential structure in nonadiabatic collisions

The role of structure in crossing potential-energy curves upon nonadiabatic collisions is probed by means of functional sensitivity analysis. The inelastic transition [He++Ne(3p6)]2 2[He++Ne(3p54s)] modeled by a crossing of the corresponding diabatic potential-energy curves (V11 and V22) is used as an illustration. The functional derivatives 12(E)/ V11(R), 12(E)/V22(R), and 12(E)/V12(R) of the corresponding nonadiabatic collision cross section 12 are calculated using the exponential distorted-wave approximation. These functional derivatives offer a quantitative measure of the importance of different regions of the potential [V11(R) and V22(R)] and coupling [V12(R)] functions to the nonadiabatic collision cross section 12. The prominent Gaussian-like feature of the 12(E)/V12(R) curve in the crossing point region (R R*) is found to be in qualitative accord with the (R-R*) function idealization of the Landau-Zener-Stueckelberg (LZS) theory. Similarly, the most prominent feature of the 12(E)/V11(R) and 12(E)/V22(R) curves occurs in the vicinity of the crossing point region where they mimic the d (R-R*)/dR behavior predicted by the LZS theory. The breadths of all three functional derivative curves identify a much broader region of potential function importance than the loosely defined avoided-crossing region. The region of significance is also found to increase with an increase in the total energy. This considerable sensitivity away from the crossing point along with the quantum interference structure of the functional sensitivity curves and the dynamical dependence of these sensitivities offer new insights and bring out the limitations of the intuitive pictures rooted in the LZS theory of curve crossing.