A quantum-classical approach to the molecular dynamics of pyrazine with a realistic model Hamiltonian

Abstract

We investigate the molecular dynamics of pyrazine after excitation to the S2 electronic state by using the time-dependent discrete variable representation (TDDVR) method. The investigation has been carried out with a realistic 24-mode model Hamiltonian consisting of all the vibrational degrees of freedom of pyrazine molecule. First, we perform the simulation on a basic four-mode model, and then by including additional eight important modes and finally, by introducing 20 bath modes on the basic model. This sequential inclusion of bath modes demonstrates the effect of weak modes on the subsystem, where the calculations of energy and population transfer from basic model to the bath quantify the same effect. The spectral profile obtained by using TDDVR approach shows reasonably good agreement with the results calculated by quantum mechanical approach. It appears that the TDDVR approach for those large systems where quantum mechanical description is needed in a restricted region is a good compromise between accuracy and speed.

A “classical” trajectory driven nuclear dynamics by a parallelized quantum‐classical approach to a realistic model Hamiltonian of benzene radical cation

“…On the other hand, it has been pointed out in our previous articles [39][40][41] that the TDDVR approach has the clear scope to scale down the necessity of CPU time substantially through the parallelization of the major areas of the algorithm so that we can obtain the computational privilege.…”

“…Since the detailed formulations of the different versions of TDDVR approach were presented elsewhere [31][32][33][34][35][36][37][38][39][40] to bring the completeness of this article, we briefly demonstrate the relevant equations used for current perspective in the simplest but completely generalized way. The scheme propagates the DVR grid-points by utilizing the "classical" equation of motion with a time-independent width parameter in the primitive basis set.…”

“…Since the multi-surface multi-mode nuclear dynamics of any molecule is expected to be very efficiently determined by TDDVR approach [39][40][41][42][43], we want to demonstrate how the "classical" trajectories and corresponding energy functional for different modes on each surface can enlight the timedependent feature of nuclear density and its' nodal structure also to reproduce the MCTDH calculated population dynamics and the experimental photoabsorption spectra of benzene radical cation by using the parallelized version of TDDVR algorithm. As the intramolecular relaxation and the effects due to CI are post excitation phenomena, we assume a vertical excitation at the FC point (Q = 0) just before initiating the dynamics so that the wavefunction at t = 0 on the upper electronic state is same as that for neutral ground state.…”

“…It is precious to note that TDDVR with one grid-point corresponds to the classical limit known from Newtonian force. In our previous articles [31][32][33][34][35][36][37][38][39][40] different computational aspects of TDDVR method and other contemporary time-dependent techniques, namely, nested interaction representation (IR) [46,47] method, distributed approximating function (DAF) [48,49] approach as well as other time dependent DVR method [50] are described elaborately in a comparative manner.…”

Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation

“…A discretization error arises then; the involved projection is costly, as long as no fast Hermite transform is known. However, typical initial values in chemical applications are in terms of eigenfunctions of harmonic oscillators (see [11] and [13] for two examples among many). Hence, they are exactly such wavepackets or can be easily rewritten this way.…”