Unconventional semiclassical method for calculating the energetic values of diatomic molecules

Abstract

In previous papers we proved that the geometrical elements of the wave described by the Schrödinger equation, namely the wave surfaces and their normals, denoted by C curves, are solutions of the Hamilton–Jacobi equations, written for the same system, in the case of stationary systems. The C curves correspond to the same constants of motion as the eigenvalues of the Schrödinger equation. In two recent papers we presented a central field method for the calculation of the C curves, and of the corresponding energetic values. The method was verified for the atoms He, Li, Be, B, C, N and O. In this paper we extend this method, using the symmetry properties of the systems, in the case of the diatomic molecules, with exemplification for Li₂, Be₂, B₂, C₂, LiH, BeH, BH and CH. The accuracy of the method is, as in the case of the atoms, comparable to the accuracy of the Hartree–Fock method, for the same system. This could be a potential useful result, because our approach predicts also basic properties of the molecules in discussion.

Keywords:

• diatomic molecules
• energetic values
• unconventional semiclassical method

Acknowledgements

This work was done in the frame of the basic research program of the National Institute for Laser, Plasma and Radiation Physics, entitled ‘Nucleus Program’.