On the diatomic vibration–rotation eigenvalue equation: Highly accurate results for high levels

Accurate vibration–rotation eigenvalues E vJ are sought for very high levels (up to dissociation) of a diatomic potential. The method used is the recent “eigenvalue equation” method [Kobeissi et al., J. Comput. Chem. , 4 , 218 (1983)] which dissociates the determination of the eigenvalue from that of the eigenfunction. A new mathematical formulation for any numerical potential is presented, which reduces the problem to the use of a single recurrent formula. A numerical application to the model potential used by Cashion [ J. Chem. Phys. , 39 , 1872 (1963)], up to v = 23, gives results equal to the exact eigenvalues to approximately 10 −14 cm −1 . Another application to the model potential used by Johnson [ J. Chem. Phys. , 67 , 4086 (1977)], up to v = 60, gives similar results.