Construction of classical functional sensitivity maps for rotationally inelastic collisions of H₂ with HD

Classical functional sensitivity analysis has been used to probe the detailed physics of how the dynamics in coplanar rotationally inelastic collisions of H₂ and HD draws on the underlying potential energy surface. A new expression for the full sensitivity map is derived, and maps are calculated as a function of angle for the three observables of interest at two values of the initial relative kinetic energy. These full sensitivity maps were compared with full sensitivity maps generated from a truncated Fourier sum. This comparison showed that a Fourier sum of radial sensitivity coefficients (δO/δυ_m1,m2) through _m1,m2 = ±6 was sufficient to generate full sensitivity maps. The effect of varying the initial relative kinetic energy was found to have a profound effect on both the radial sensitivity coefficients and the full sensitivity maps and indicates that a localized perturbation of the potential will affect observables differently at different values of the initial relative kinetic energy.