A local grid method for modelling real-time quantum dynamical events is formulated. The formulation is straightforward for 1-D systems. For more than one dimension, appeal has to be made to mean-field approximation of the appropriate kind. The simplest mean-field model results in time-dependent Hartree-Fourier grid method. The relationship of the proposed method with some other methods available in the literature is examined. A few examples of numerical applications dealing with (i) the dynamics of dissociation and ionization processes in diatoms and atoms respectively and (ii) tunnelling dynamics in the intramolecular H-atom transfer phenomenon are presented.

Results from application of a new implementation of the time-dependent wave packet (TDWP) approach to the calculation of vibrational excitation cross-sections in resonant e-CO scattering are presented to examine its applicability in the treatment of e-molecule resonances. The results show that the SCF level local complex potential (LCP) in conjunction with the TDWP approach can reproduce experimental features quite satisfactorily.

We perform the nuclear dynamics simulation to calculate the broad band as well as better resolved (a) photodetachment spectra of nitrogen dioxide anion (NO$^-_2$), and (b) photoelectron spectra of benzene radical cation (C₆H$^+_6$) with degeneracy among the electronic states using our parallelized time dependent discrete variable representation approach. For this purpose, we first consider a theoretical model that describes the photodetachment spectrum originating due to the Franck-Condon (FC) transition from the anionic ground state to the conically intersecting $\widetilde{X}^2 A_1 - \widetilde{A}^2 B_2$ electronic manifold of the neutral NO₂, whereas two multi-state, multi-mode model Hamiltonians of C₆H$^+_6$ with degeneracy among the electronic states are explored for its’ photoelectron spectra. The dynamics of C₆H$^+_6$ has been carried out with two Hamiltonians: (a) one consists with four states and nine modes, and (b) the other is constituted with three states and seven modes. Since the electronic states of both the systems are interconnected by several conical intersections in the vicinity of the FC region, it would be challenging to persue the dynamical calculation due to the impact of non-adiabaticity among the electronic states. The spectral profiles obtained with the advent of TDDVR approach show reasonably good agreement with the results obtained by other theoretical methodologies and experimental measurements.

We have performed a nuclear dynamics simulation to calculate photoelectron spectra and population profiles of benzene radical cation (C₆H$^+_6$) employing the parallelized Time Dependent Discrete Variable Representation (TDDVR) approach. For this purpose, we have considered two multi-state multi-mode model Hamiltonians of C₆H$^+_6$ with degeneracy among the electronic states: (a) One consists of three states and eight modes, which in turn leads to a five state thirteen mode Hamiltonian ($X^2$E$_{1g}$-$B^2$E$_{2g}$-$C^2$A$_{2u}$) due to the degeneracy; and (b) The other is constituted of three states and thirteen modes which is basically a five state twenty mode Hamiltonian ($B^2$E$_{2g}$-$D^2$E$_{1u}$-$E^2$B$_{2u}$) for the same reason. Since these electronic states are interconnected by several conical intersections in the vicinity of the Franck Condon region, it will be challenging to pursue such large dynamical calculation in the presence of nonadiabaticity among the electronic states. The spectral as well as population profiles calculated with the advent of TDDVR approach show reasonably good agreement with the results obtained by the Multi Configuration Time Dependent Hartree (MCTDH) methodology.

Vibrational excitation cross-sections $\sigma_{v_f \leftarrow v_i}$(𝐸) in resonant e-F₂ and HCl scattering are calculated from transition matrix elements $T_{v_f \leftarrow v_i}$(𝐸) obtained using Fourier transform of the cross correlation function $\langle \phi_{v_f} (R) | \Phi_{v_i} (R, t) \rangle$. where $\Psi_{v_i} (R,t) \approx e^{i \hbar H_{AB^-}(R)t} \phi_{v_i} (R)$. Time evolution under the influence of the resonance anionic Hamiltonian H$_{AB^-}$ (AB=F₂/HCl) is effected using Lanczos reduction technique followed by fast Fourier transform and the target (AB) vibrational eigenfunctions $\phi_{ν_i}$ (𝑅) and $\phi_{v_f}$ (𝑅) are calculated using Fourier grid Hamiltonian method applied to potential energy (PE) curve of the neutral target. The resulting vibrational excitation cross-sections provide reasonable agreement with experimental and other theoretical results.