The TDDVR approach for molecular photoexcitation, molecule-surface and triatomic reactive scattering processes

The Time Dependent Discrete Variable Representation (TDDVR) method was initiated by Adhikari and Billing considering time dependent Gauss-Hermite basis functions, where all the parameters were assumed to be time dependent. Adhikari etal. had reformulated the TDDVR approach considering the width parameter as time independent, whereas the equation of motion for time dependent parameters (center of wave packet and its momentum) are derived from Dirac-Frenkel variational principle. Such a method is computationally efficient due to its inherent parallelizable nature to perform multistate (electronic) multidimensional (vibrational) quantum dynamics for well-converged results within reasonably fast computation time, where the complexity of the Hamiltonian is not a matter of concern. Its parallel version is computationally efficient as compared to other quantum dynamical method like the multiconfiguration time dependent Hartree (MCTDH). The parallelized version of this method has also been employed to different complex dynamical systems to calculate transition probabilities, tunnelling probabilities, inelastic surface scattering, bi-molecular reactive scattering and photoexcitation. We have also made use of TDDVR methodology successfully to different diatom (H-2/D-2)-metal surface (Cu/Ni) scattering processes and triatomic reaction dynamics by using 3D time dependent wave packet approach in hyperspherical coordinates to calculate state-to-state reaction probabilities of D+H-2 reaction for J = 0 case.