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. = R n-I (cko qb._ 1) -~m=O em (dpoqb.-m). Once the vibrational energy e0 = E. is known the determination of e. requires successively that of ~bo, el, ~bl, e2, ~bz ..... en-l, q~.-1. The rotational functions ~b. are the successive solutions of the rotational inhomogeneous Schr6dinger 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 r0 ~ 0 toward rf ~ cx~, 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.