Role of potential structure in nonadiabatic collisions with applications to ${\mathrm{He}}^{+}$+Ne(2${\mathit{p}}^6$)→${\mathrm{He}}^{+}$+Ne(2${\mathit{p}}^5$3s) and Na+I→${\mathrm{Na}}^{+}$+${\mathrm{I}}^{\mathrm{-}}$

The first-order functional-sensitivity densities δ${\mathrm{\sigma }}_{12}$(E)/δ${\mathit{V}}_{\mathit{i}\mathit{j}}$(R) from close-coupling calculations are used for a quantitative probe of the role of structure in crossing diabatic curves used to model nonadiabatic collisions. Application to the excitation of Ne by ${\mathrm{He}}^{+}$ shows a region of significance for δ${\mathrm{\sigma }}_{12}$(E)/δ${\mathit{V}}_{12}$(R) as a prominent Gaussian-like profile around the crossing point (${\mathit{R}}^{\mathrm{*}}$) in accord with the δ(R-${\mathit{R}}^{\mathrm{*}}$) idealization of the Landau-Zener-Stueckelberg (LZS) theory. Similarly, the densities δ${\mathrm{\sigma }}_{12}$(E)/δ${\mathit{V}}_{11}$(R) and δ${\mathrm{\sigma }}_{12}$(E)/δ${\mathit{V}}_{22}$(R) mimic dδ(R-${\mathit{R}}^{\mathrm{*}}$)/dR-type behavior with one being the negative of the other in the neighborhood of ${\mathit{R}}^{\mathrm{*}}$, in qualitative agreement with the LZS theory. However, all three sensitivity profiles identify a much broader area of importance for the curves than the loosely defined avoided-crossing region. Also, although the sensitivities themselves decrease with increasing energy, the domain of importance of the curves increases. Examination of the functional-sensitivity densities δ${\mathrm{\sigma }}_{12}$(E)/δ${\mathit{V}}_{\mathit{i}\mathit{j}}$(R) for the chemi-ionization collision Na+I→${\mathrm{Na}}^{+}$+${\mathrm{I}}^{\mathrm{-}}$ reveals regions of potential-function importance very different from that predicted by the LZS theory.