Modeling irreversible molecular internal conversion using the time-dependent variational approach with sD₂ ansatz

Abstract

Effects of non-linear coupling between the system and the bath vibrational modes on the system internal conversion dynamics are investigated using the Dirac-Frenkel variational approach with the defined sD2 ansatz. It explicitly accounts for the entangled system electron-vibrational wavepacket states, while the bath quantum harmonic oscillator (QHO) states are expanded in a superposition of coherent states (CS). Using a non-adiabatically coupled three-level model, we show that quadratic system-bath coupling induces non-reversible internal conversion when the bath QHO wavepacket representation is highly non-Gaussian. The quadratic coupling results in a broadened and asymmetrically squeezed bath QHO wavepackets in the coordinate-momentum phase space. Additionally, we found that computational effort can be reduced using degenerate CSs to represent the initial bath wavepackets.

Temperature Controlled Open Quantum System Dynamics using Time-dependent Variational Method

“…The time-dependent variational approach with Davydov D 2 ansatz can be improved by considering more complex Davydov ansätze family members, e.g., multitude of D 1 ansatz (multi-D 1 ) and multi-D 2 [53,67,72,73] or its Born-Oppenheimer approximated variant [74], sD 2 . In either way, they all suffer from finite bath heating capacity, in most cases, even stronger than the D 2 ansatz, because of significantly increased computational effort needed to propagate numerous bath oscillators.…”

The hierarchy of Davydov's Ansätze and its applications

“…In the subsequent sections, we will use j D M 1,2 i to refer to the multiple Davydov Ansätze j Ψ M D 1,2 i. In Figure 1, occupying the top row are the two time-dependent, multiple Davydov Ansätze, namely, the multi-D 1 Ansatz and the multi-D 2 Ansatz, which have been successfully applied to a number of many-body quantum systems, [105][106][107] yielding numerically exact solutions.…”

“…The corresponding version for the multi‐ Ansatz is written as 27,104 In the subsequent sections, we will use to refer to the multiple Davydov Ansätze . In Figure 1, occupying the top row are the two time‐dependent, multiple Davydov Ansätze, namely, the multi‐D 1 Ansatz and the multi‐D 2 Ansatz, which have been successfully applied to a number of many‐body quantum systems, 105–107 yielding numerically exact solutions.…”

Modeling molecular J and H aggregates using multiple-Davydov D2 ansatz

“…The Davydov D 2 Ansatz, which was originally developed for the molecular chain soliton theory, 1,2 represents quantum states of molecular vibrational modes using Gaussian wavepackets, also known as coherent states (CS). It has been widely applied to study excitation relaxation processes in both isolated molecules and molecular aggregates, [3][4][5][6] as well as to compute their linear and nonlinear spectra. [7][8][9][10] While the TDVP method is based on propagating pure wavefunctions, its stochastic extension can be used to describe non-zero temperature by averaging over the initial equilibrium thermal state.…”

“…13 Accuracy can be greatly improved by considering a superposition of multiple copies of the D 2 Ansatz, termed the multi-Davydov D 2 Ansatz. The mD 2 Ansatz and, its more complex variant, mD 1 Ansatz 14 have been applied to study polaron dynamics in Holstein molecular crystals, 13 the spin-boson models 15 and for nonadiabatic dynamics of single molecules, 6,16 as well as to simulate nonlinear response function of molecular aggregates 7,13 and others. [17][18][19][20] A more in-depth overview of the various types of Davydov Ansatze and their applications can be found in a recent review article by Zhao et al 21 However, a well-defined strategy to determine the required number of multiples in mD 2 Ansatz (or the depth) needed to obtain the converged result is lacking.…”