Abstract :
For a given vibrational level ν 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 en = (φ0Rφn−1)−∑m=0n−1 em(φ0φn−m). Once the vibrational energy e0 = Eν is known the determination of en requires successively that of φ0, e1, φ1, e2, φ2, …, en−1, φn−1. The rotational functions φn are the successive solutions of the rotational inhomogeneous Schrödinger 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 rƒ ≈ ∞, 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.
