Energy eigenvalues for Lennard-Jones potentials using the hypervirial perturbative method

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Abstract
The hypervirial perturbative method based on the use of the hypervirial and Hellmann-Feynman theorems to calculate the energy corrections is applied to the eigenvalue equation of Lennard-Jones (n, 6) potentials. The method is used to calculate high accuracy numerical energy eigenvalues and to derive analytic expressions which provide very good estimates for the eigenenergies. The results are compared with those from other procedures such as the shifted 1/N expansion method, the numerical integration of the eigenvalue equation and semiclassical WKBJ calculations.