The sensitivity approach to the analysis of parameter dependencies in reactive collision theory

Abstract

New working expressions are given for the first derivatives or elementary sensitivity coefficients of reactive and non-reactive scattering matrices with respect to an arbitrary input parameter. The expressions, as in an earlier paper, are constructed for collinear reaction but within now a less restricted representation of the electronic-vibrational degrees of freedom. Application is made to two simple test problems. The first deals with the collision energy dependence of transmission and reflection on a one dimensional potential curve. We examine the relative convergence behavior of values and energy derivatives of the scattering elements with the steplength in our procedure for integrating the dynamical equations, and find that errors in the sensitivity coefficients are sometimes larger and sometimes smaller than those in the corresponding scattering elements. The second test problem adds on a closed potential curve which is non-adiabatically coupled to the potential curve of the first (test problem). We examine the effectiveness of sensitivity and non-sensitivity calculations in describing how the scattering elements behave through the space of a parameter which centers the non-adiabatic coupling envelope. Our findings are drawn into the following concluding statement (of the application section) that: for the single parameter variation, sensitivity and half-spaced non-sensitivity calculations using a common steplength, yield essentially equal quality descriptions of the parameter dependence. When this conclusion is projected into a multi-parametric context and we roughly estimate the relative work involved in the two approaches, a minimum order for the parameter space, i.e. 2, is identified such that the sensitivity approach may be expected to be the more efficient.