Determination of vibrational level spacings of van der waals molecules from the Lennard-Jones potential

An approximate expression for the eigenvalues for van der Waals molecules by use of the Lennard-Jones (12-6) potential in the WKB approximation is presented. The expression is applied to the rare gas molecules. Ar₂, Kr₂, and Xe₂ by fitting the potential function to the observed potential parameters. Calculated results of vibrational energy spacings for these molecules agree well with the experiment and other calculations which are based on numerical integration of the Schrödinger equation. For Xe₂, the energy spacing expression is used to determine the thermodynamic functions of the van der Waals bond.