A one directional shooting method for the computation of diatomic centrifugal distortion constants

For a given vibrational level v the problem of the centrifugal distortion constants (CDC) for a given electronic state of a diatomic molecule is considered. Within the perturbation theory approach, a CDC of order n is given by e(n) = [phi(0)R phi(n-1)] - Sigma(m=0)(n-1) e(m)[phi(0)phi(n-m)]. Once the vibrational energy e(0) = E-v is known the determination of e(n) requires successively that of phi(0), e(1), phi(1), e(2), phi(2), ..., e(n-1), phi(n-1). The rotational functions phi(n) are the successive solutions of the rotational inhomogeneous Schrodinger equations integrated by a new one-directional shooting method inspired from the conventional Cooly-Hutson one. The present method shoots in one sense starting at r(0) approximate to 0 toward r(f) approximate to infinity, it stops automatically according to a convenient criterion and saves unnecessary grid points, and it avoids conventional matching problems and normalization calculations. The application to the model. Lennard-Jones potential shows that the one directional shooting method allows an accuracy higher than that of the conventional one when the integrator and the same mesh-size are used. The consumption in computer time is reduced by a factor of three when the new shooting method replaces the conventional one. (C) 1999 Elsevier Science B.V. All rights reserved.