Second-order semiclassical calculations for diatomic molecules

Abstract The second-order WKB quantization condition is used to derive expressions for the second-order contributions to the vibrational energy levels and the rotational and centrifugal constants of a diatomic molecule. The second-order corrections to the RKR (Rydberg-Klein-Rees) turning points are also calculated. These second-order quantities are related to the quantities calculated from Kaiser's modified first-order quantization condition. Numerical calculations for the ground electronic state of carbon monoxide are compared with quantum-mechanical values obtained by numerical solution of the Schrodinger equation. In general, the second-order semiclassical values are in good agreement with the quantum-mechanical values, and can be computed by the present methods in a small fraction of the time.

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