An operator approach to functional sensitivity analysis in reactive molecular scattering

The effect of infinitesimal functional variations in a scattering potential on reactive transition amplitudes is studied. A formalism is derived for the functional sensitivity coefficients, i.e., the functional derivatives of the reactive transition amplitudes with respect to the variation of a potential. The resultant coefficients provide a means to access the significance of any region of the potential surface upon the scattering cross section. The formal theory is presented for reactive scattering with variations allowed in the internal Hamiltonian as well as the scattering potential. Both local and nonlocal Hamiltonians are treated. A clear relationship is shown to exist between the structure of the scattering wave function and the regions of significance in the Hamiltonian. The application of the formalism to one-dimensional barrier penetration and reactive scattering of collinear H+H₂ shows that the most important region of the potential for the tunneling is the classical turning point region while the most responsible region for the resonance scattering in H+H₂ is the saddle point region. In addition broad regions of significant potential sensitivity are also found adjacent to these specific locations.