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

Abstract

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 (C 6 H + 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 2 2 1 2 X A A B − electronic manifold of the neutral NO 2 , whereas two multi-state, multi-mode model Hamiltonians of C 6 H + 6 with degeneracy among the electronic states are explored for its' photoelectron spectra. The dynamics of C 6 H + 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.

A quantum-classical simulation of a multi-surface multi-mode nuclear dynamics on $ {\rm C_{6}H}_{6}^{+} $ incorporating degeneracy among electronic states

“…It is worthwhile to mention that the present TDDVR algorithm solves more than 14 × 10 7 number differential equations simultaneously at each time step and such computational effort is much demanding than all our previous studies. [16][17][18][19][20] The prime interest of this article is to theoretically calculate the photoelectron spectrum of C 6 H + 6 . The TDDVR method is used to propagate the nuclear wavefunction and thereby, to calculate the autocorrelation function [C(t)] where the Fourier transform of C(t) gives photoelectron spectra of C 6 H + 6 :…”

“…The TDDVR approach is a well established molecular dynamics simulation method for relatively large molecular systems. [17][18][19][20] At present, we have implemented the method for two multi-mode multi-surface model Hamiltonians of C 6 H + 6 to explore its' workability with respect to other contemporary methodologies, 21,22 where the formulation consists of 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. When this multi-dimensional multi-surface wavefunction matrix is substituted in the TDSE, the time dependence of the expansion coefficients brings the quantum dynamics and the 'classical' equation of motion for the central trajectory with its' momentum appears naturally.…”

“…Since we have already carried out the dynamics on C 6 H + 6 including five nondegenerate surfaces, 18 it will be interesting to explore the nuclear dynamics of the same cation, where the Hamiltonian 28,29 is constituted with strongly vibronically coupled doubly degenerate electronic states as well as DOFs. A preliminary investigation on the Hamiltonian was carried out in one 20 of our recent articles, where less computational effort was needed than this present work.…”