The Gaussian wave-packet propagation (GWP) approach in the coherent state algebraic formalism has been applied to calculate the dynamics of a few model single-mode systems and a model two-mode system. To circumvent the problems arising in defining the initial conditions and the potential surface for such systems in this formalism, we have constructed a new Hamiltonian which is derived by mapping the original Hamiltonian on to a single electronic surface. Good agreement with exact results have been obtained.

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.

Recently, we had suggested that the motion along the promoter mode in the first part of the IRC of proton transfer reaction enhances the delocalization of $n_\sigma$ electrons on the acceptor atom into the $\sigma^\ast$ orbital of the donor-hydrogen covalent bond, and as a consequence weakens it. This leads to a reduction of the barrier to the proton transfer as well as the stretching frequency of donor-hydrogen bond. An extension of this to the concerted multiple proton transfer reactions implies that the kinetic isotope effect in such reaction depends exponentially on the number of protons that are being transferred. Computational evidence on three systems, (HF)₃, formic acid dimer, and (H₂O)$_n$ clusters is provided to support this assertion.

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.