FULL NUMERICAL DIATOMIC MATRIX-ELEMENTS - SIMPLIFIED SHOOTING METHOD

The problem of diatomic matrix elements M(nn') = [PSI(n) Absolute valu e of Q PSI(n')] related to the anharmonic oscillator is considered for standard operators Q of the form x = r - r(e) (r is the radial variab le), powers of x, or exponentials, or combinations of such operators; the quantum numbers (n, n') may be equal or not. A ''full numerical'' method to determine M(nn') is presented for any type of the potential U, analytic like that of Morse or numerical like the RKR potential. Th is numerical method is a simplified version of the standard Cooley sho oting method (CSM). The present simplified shooting method (SSM): (1) shoots in one direction only (instead of two); (2) avoids starting pro blems and matching problems; (3) determines the ''end'' point automati cally (without prior guesses); and (4) reduces thus the number of grid points effectively needed. Examples for analytic (Morse) and RKR pote ntials are presented. The numerical application to a standard example used by Delgado-Barrio et al. [J. Comp. Chem., 7, 208 (1986) ] using t he CSM, and by Kobeissi et al. [J. Comp. Chem., 10, 358 (1989) using t he highly accurate ''Canonical Functions'' method, shows that when the SSM and CSM are used with the same integrator and the same mesh size the relative discrepancy DELTAM(nn')(between computed and exact M) is averaged for several (n, n') to 5.4 X 10(-4) for the CSM and to 8.5 x 10(-6) for the present SSM. This improvement in accuracy is supplement ed by a reduction in computer time consumption. (C) 1993 by John Wiley & Sons, Inc.