A critical test of the diagonal variation-perturbation technique for the partition function of anharmonic oscillators

The diagonal variation-perturbation technique to fourth order is applied to the partition function of asymmetric anharmonic oscillators. Their constants are taken from spectroscopic constants of diatomic molecules. In contrast to thermodynamic perturbation theory the series does not diverge for very low and high temperatures over a wide range of anharmonicities, but it oscillates slightly around the second order result. The approximation is excellent, differing only 10−3 to 10−4 from the exact numerical results. This technique can be extended to systems of coupled anharmonic oscillators with polynomial anharmonicity and interactions.