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

Abstract

We are investigating the molecular dynamics of the butatriene cation after excitation from the ground state (X(2)B(2g)) to the first excited electronic state (A(2)B(2u)) by using the time-dependent discrete variable representation (TDDVR) method. The investigation is being carried out with a realistic 18-mode model Hamiltonian consisting of all the vibrational degrees of freedom of the butatriene molecule. First, we perform the simulation on a basic five mode model, and then by including additional thirteen modes as bath on the basic model. This sequential inclusion of bath modes demonstrates the effect of so called weak modes on the subsystem, where the calculations of energy and population transfer from the basic model to the bath quantify the same effect. The spectral profile obtained by using the TDDVR approach shows reasonably good agreement with the results calculated by the quantum mechanical approach/experimental measurement. 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.…”

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.…”

“…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.…”

“…The movements of the grid-points in the TDDVR are dictated by the so called 'classical' mechanics and help to avoid the wastage of many grid-points to represent empty space. In our previous articles,33,35,36 we mentioned that TDDVR approach has the clear scope to scale down the present necessity of CPU time substantially, because it has the possibility to parallelize the major areas of the algorithm. The contributions of different modes on a time-dependent amplitude 1 2 .... ,…”

The multistate multimode vibronically coupled nuclear dynamics of monofluorobenzene radical cation using a parallelized TDDVR approach

“…The TDDVR approach is a well established molecular dynamics simulation method for relatively large molecular systems [19][20][21][22][23]. At present, we have implemented the method on a multimode multisurface model Hamiltonian for monofluorobenzene radical cation to explore its' workability with respect to other contemporary methodologies [24,25], where the formulation consists the following assumptions on the form of the molecular wavefunction: (a) the total wavefunction is expressed as a linear combination of the product type TDDVR basis functions of different modes with time dependent coefficients; (b) the TDDVR basis set is obtained by multiplying the DVR basis with a plane wave; (c) the DVR basis functions are constructed by using the eigenfunctions of harmonic oscillator as the primitive one; (d) the plane wave is defined by a 'classical' trajectory and its' momentum.…”