A quantum-classical approach to the photoabsorption spectrum of pyrazine

Abstract

We have used the time-dependent discrete variable representation (TDDVR) method to simulate the photoabsorption spectrum of pyrazine. The time-dependent molecular dynamics of pyrazine after excitation to the S2 electronic state is considered as a benchmark to investigate the S2 absorption spectrum. We have carried out the dynamics on a basic four-mode model of pyrazine with the inclusion of five major modes as well as the rest of the vibrational modes as bath modes. Investigations reveal the effect of bath modes such as energy and population transfer from the subsystem to the bath. Calculated results demonstrate excellent agreement with traditional quantum-mechanical findings during the entire propagation and converge to the exact quantum results when enough gridpoints are used. It appears that TDDVR, as a numerical quantum dynamics methodology, 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 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.…”

A quantum-classical simulation of the nuclear dynamics in NO 2 − and C6H 6 + with realistic model Hamiltonian

“…Since the detailed formulations of the different versions of TDDVR approach were presented elsewhere, [28][29][30][31][32][33][34][35][36][37][38][39] in order 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.…”

“…When this multidimensional multi-surface wavefunction matrix is substituted in the TDSE, we find that the timedependence of the expansion coefficients measure the quantum dynamics where the classical equation of motion for the central trajectory and its' momentum appear naturally; (b) time evolution of the amplitudes on the grid points comes through quantum dynamics and movement of the grid points is obtained from classical mechanics where grid points are associated with a distribution of 'classical' momenta; (c) the formulation has enough scope to incorporate the details associated with the respective surface through TDDVR basis set as well as timedependent coefficients while moving from one surface to another; (d) each TDDVR basis function is originated due to multiplication of the corresponding DVR basis with a plane wave which differs from one surface to another by its' parameter; (e) the eigenfunctions of harmonic oscillator constructs the DVR basis set; (f) the plane wave is defined by a classical trajectory and its' momentum. In this regard, it is worthy to mention that the formulation is based on time-independent width parameter [28][29][30][31][32][33][34] to bypass the inaccuracy 26 in the quantum equation of motion as well as the stiffness in the classical equation of motion due to time-dependent width parameter. When enough trajectories are included, the method is numerically exact, whereas with one grid point, one can recover the classical molecular dynamics approach.…”

“…The time dependent discrete variable representation (TDDVR) method [26][27][28][29][30][31][32][33][34][35][36][37][38][39] takes the advantages of both DVR and time-dependent basis. TDDVR is a very convenient formulation with the following attributes: (a) a very few number of optimized set of asymmetrically dense grid-points are used which are generated from the Hermite polynomial associated with the eigenfunction of a harmonic oscillator defined around the center of an initial wave packet, GWP; (b) the classical dynamics of the timedependent parameters of GWP dictates the movement of these unevenly spaced grid-points; (c) though the evaluation of KE matrices is needed once for the entire propagation, the diagonal potential energy (PE) matrix by which the electronic states are coupled has to be calculated at each time-step; (d) the independent contributions of different modes on a time-dependent amplitude motivate us to parallelize the algorithm which reduces the computational time remarkably.…”