HYPERSPHERICAL ELLIPTIC COORDINATES FOR THE THEORY OF LIGHT ATOM-TRANSFER REACTIONS IN ATOM-DIATOM COLLISIONS

We formulate and demonstrate a new method for quantum 3D calculations of light atom transfer reactions in atom-diatom collisions. The method follows a general scheme of the hyperspherical method, in common with other hyperspherical formulations in the field. The main novelty cons ists in the hyperspherical elliptic coordinates (xi,eta) used to param etrize the hypersphere. These coordinates have been introduced recentl y for studying three-body Coulomb systems, and here we apply them to s tudy a system of three atoms. The coordinates are defined and their re lation with the Smith-Whitten and Delves coordinates is explored. On a ccount of a big difference between vibrational and rotational excitati on energies in molecules, the hyperspherical adiabatic Hamiltonian all ows adiabatic separation between xi and eta. This not only greatly fac ilitates solution of the hyperspherical adiabatic eigenvalue problem, but also provides an approximate classification of the states by a pai r of indices (n(xi),n(eta)) representing vibrational and rotational qu antum numbers simultaneously for a reagent and a product. Another nove l technology exploited here is the Slow/Smooth Variable Discretization (SVD) method. The SVD is used for treating nonadiabatic couplings bet ween the xi and eta motions, as well as between the motions with respe ct to the hyperradius and the hyperangular variables. The whole scheme is illustrated by calculations for the reaction O(P-3) + HCl-->OH+Cl for zero total angular momentum. It is shown to be very efficient, acc urate, and providing a framework of choice for elucidating light atom transfer reaction mechanisms. (C) 1998 American Institute of Physics. [S0021-9606(98)02319-8]