"Nonintegral" expressions for the diatomic centrifugal distortion constants

Abstract

The problem of the centrifugal distortion constants (CDC), Dν, Hν, … for a diatomic molecule is considered. It is shown that a new formulation of the standard Rayleigh–Schrödinger perturbation theory can give simple and compact analytical expressions of the CDC (up to any order). Thus, the constants e1 = Bν, e2 = −Dν, e3 = Hν,…, en,… are all of the form en = lim σn(r)/σ0(r) as r → ∞. σ0 is the particular solution of the nonhomogeneous equation y″ + k(Eν – U)y = s, with s = ψν, where (Eν, ψν) is the eigenvector corresponding to the rotationless potential U(r) and to the vibrational level ν; and where σ0(0) = σ′0(0) = 0. σn is the particular solution of the above equation, where s is known for each order of n. The numerical application to the standard Lennard–Jones model potential shows that good results are obtained for Dν, Hν, Lν,…,Oν, Pν, for ν = 0 to 22, which is only at 2 × 10−4 of the well depth. The program uses one routine (the integration of the equation y″ + fy = s) repeated for different s; it is quite simple and gives no difficulties at the boundaries and there is no need to use any mathematical or numerical artifices.