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.

We propose a perturbative approximation to the vibrational coupled cluster method in bosonic representation to reduce the cost of calculating the cluster matrix elements by considering only the first order of S and r for the construction of the effective Hamiltonian e^se^-SHe^Se^s. With the systematic analysis of theresults of two molecules, H2O and 1,1-difluoroethylene, we find that the accuracy of the transition energies with such low order approximation is comparable to the fully converged VCCM