Sensitivity analysis in molecular dynamics and inverse scattering

Abstract

The computational techniques of sensitivity analysis in molecular scattering and inverse scattering problems are discussed. Emphasis is placed on the computation of functional sensitivity densities (functional derivatives) of the dynamical observables with respect to an arbitrary variation in the interaction potential. In the case of quantum mechanics, these sensitivity densities are completely determined by the scattering wave functions. Thus, it is shown that scattering wave functions may be used not only to yield the traditional dynamical observables but also the sensitivity of these observables to detailed features in the interaction potential. In the case of classical dynamical calculations, functional sensitivity analysis requires a solution of an additional set of sensitivity differential equations. These equations may require special treatment due to the singular nature of the trajectory functional sensitivities as well as the high sensitivity associated with long-lived trajectories. The functional sensitivity densities provide a means to extract maximal information from dynamical calculations. Furthermore, the sensitivity densities may be employed to establish an iterative procedure for reconstruction of the fundamental underlying interaction potential from experimentally measured dynamical observables.