Direct Calculation Of Time Delays And Eigenlifetimes For The Reaction He+H-2(+)Reversible-Arrow-Heh++H

The Parker and Pack method for calculating accurate three‐dimensional reactive scattering information uses adiabatically adjusting, principal axes hyperspherical (APH) coordinates to reduce the three‐dimensional Schrodinger equation to a set of coupled equations in the hyperradius ρ. Solution of these coupled equations in the usual manner produces the scattering S matrix for the three‐atom system of interest. To obtain these coupled equations it is necessary to solve a series of two‐dimensional Schrodinger equations on the surface of a hypersphere defined by the hyperspherical polar and azimuthal angles θ and χ, respectively. In this paper, the computational advantages of the direct method for obtaining the energy derivatives of the S matrix are further documented using both the discrete variable representation and the analytical basis method of Pack and Parker for obtaining surface functions. Detailed studies of the title reaction are used to explore various operational criteria to assure that the predicted scattering results such as state‐to‐state transition probabilities and time delays are converged to the extent desired. It is also shown that the Hermitian property of the Smith lifetime matrix Q, which is accurately produced with the direct energy derivative method, is often not preserved when numerical energy derivatives are employed.