The validity of an effective harmonic oscillator approximation for anharmonic molecular vibrations is tested and compared with vibrational self consistent field and vibrational configurational interaction results. The effective harmonic oscillator is constructed variationally, by taking the trial wave function as a harmonic oscillator eigenfunction with the centroid and width parameter as variational paraeters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in these studies.

A comparative study is done on thermal average calculation by using the state specific vibrational self-consistent field method (ss-VSCF), the virtual vibrational self-consistent field (v-VSCF) method and the thermal self-consistent field (t-SCF) method. The different thermodynamic properties and expectation values are calculated using these three methods and the results are compared with full configuration interaction method (FVCI). We find that among these three independent particle model based methods, the ss-VSCF method provides most accurate results in the thermal averages followed by t-SCF and the v-VSCF is the least accurate. However, the ss-VSCF is found to be computationally very expensive for the large molecules. The t-SCF gives better accuracy compared to the v-VSCF counterpart especially at higher temperatures.