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The Journal of Chemical Physics

Efficient quantum dynamics simulations of complex molecular systems: A unified treatment of dynamic and static disorder

Maxim F. Gelin, Amalia Velardo, Raffaele Borrelli

Published Oct 1, 2021• 32 citations
Publisher

Abstract

We present a unified and highly numerically efficient formalism for the simulation of quantum dynamics of complex molecular systems, which takes into account both temperature effects and static disorder. The methodology is based on the thermo-field dynamics formalism, and Gaussian static disorder is included into simulations via auxiliary bosonic operators. This approach, combined with the tensor-train/matrix-product state representation of the thermalized stochastic wave function, is applied to study the effect of dynamic and static disorders in charge-transfer processes in model organic semiconductor chains employing the Su-Schrieffer-Heeger (Holstein-Peierls) model Hamiltonian.

DOI
10.1063/5.0065896

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We present a unified and highly numerically efficient formalism for the simulation of quantum dynamics of complex molecular systems, which takes into account both temperature effects and static disorder. The methodology is based on the thermo-field dynamics formalism, and Gaussian static disorder is included into simulations via auxiliary bosonic operators. This approach, combined with the tensor-train/matrix-product state representation of the thermalized stochastic wave function, is applied to study the effect of dynamic and static disorders in charge-transfer processes in model organic semiconductor chains employing the Su-Schrieffer-Heeger (Holstein-Peierls) model Hamiltonian.
Abstract This review provides the fundamental theoretical tools for the development of a complete wave‐function formalism for the study of time‐evolution of chemico‐physical systems at finite temperature. The methodology is based on the non‐equilibrium thermo‐field dynamics (NE‐TFD) representation of quantum mechanics, which is alternative to the commonly used density matrix representation. TFD concepts are extended and integrated with the tensor‐train (TT) numerical tools leading to a novel and powerful theoretical and computational framework for the study of complex quantum dynamical problems. In addition, NE‐TFD techniques are extended to enable the study of dissipative open systems via a new formulation of the hierarchical equations of motion (HEOM) fully integrated with TT methodologies. We demonstrate that the combination of the TFD machinery with computational advantages of TTs results in a powerful theoretical and computational framework for scrutinizing dynamics of complex multidimensional electron‐vibrational systems. We illustrate the validity and the computational advantages of the developed methodologies by applying them to the study of quantum coherence effects in the energy‐transfer processes in antenna systems, to the analysis of fingerprints of vibrational modes in electron‐transfer and charge‐transfer processes in various model and realistic multidimensional molecular systems, as well as to simulation of other fundamental models of physical chemistry. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Theoretical and Physical Chemistry > Statistical Mechanics
Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.
The non-equilibrium thermo-field dynamics formulation of the hierarchical equations of motion combined with the tensor-train representation of the density matrix is discussed, and a new numerical integration scheme is introduced. The numerical methodology is based on an adaptive low-rank Galerkin reduction scheme and can preserve linear invariants (such as the trace of the density matrix). The method is applied to the study of the charge transfer dynamics in model pentacene molecular aggregates. The combined effect of a discrete set of molecular vibrational modes and a thermal bath is investigated, paying special attention to the coherent-incoherent transition of the charge transport. The new computational framework is shown to be a very promising methodology for the study of the quantum dynamics of complex molecular systems in the condensed phase.
We present a streamlined implementation of a computational framework for constructing and analyzing reduced dynamical maps for complex system--bath models at finite temperature. The methodology is based on three established ingredients of quantum dynamics: the Choi--Jamiołkowski isomorphism for the representation of quantum channels, thermofield (TFD) purification of thermal environments, and tensor-train (TT) propagation of the resulting enlarged pure state. The reduced map is obtained from a single unitary propagation in a thermofield-doubled Hilbert space and represented in matrix form through the Choi--Jamiołkowski isomorphism. The TFD evolution is implemented in the TT representation, enabling efficient propagation of high-dimensional purified thermal states. We illustrate the methodology for exciton transfer in the Fenna--Matthews--Olson complex with site-dependent structured spectral densities represented by discretized bosonic environments. The resulting maps are used to analyze decoherence, relaxation, and finite-memory effects, and to assess the crossover to an effectively time-local description. The proposed approach provides a route to compute reduced propagators and to post-process them into memory kernels, transfer tensors, and effective kinetic rate descriptions for complex molecular systems.
Static disorder plays a crucial role in the electronic dynamics and spectroscopy of complex molecular systems. Traditionally, obtaining observables averaged over static disorder requires thousands of realizations via direct sampling of the disorder distribution, leading to high computational costs. In this work, we extend the auxiliary degree-of-freedom based matrix product state (MPS) method to handle system-bath correlated thermal equilibrium initial states, which can capture static disorder effects using a one-shot quantum dynamical simulation. We validate the effectiveness of the extended method by computing the dipole–dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates. Our results show that the one-shot method is very accurate with only a moderate increase in MPS bond dimension, thereby significantly reducing computational cost. Moreover, it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost, thus reducing statistical errors. This method provides a broadly useful tool for calculating equilibrium time correlation functions in system-bath coupled models with static disorder.
Photosynthesis is a fundamental process that converts solar energy into chemical energy. Understanding the microscopic mechanisms of energy transfer in photosynthetic systems is crucial for the development of novel optoelectronic materials. Simulating these processes poses significant challenges due to the intricate interactions between electrons and phonons, compounded by static disorder. In this work, we present a numerically nearly exact study using the time-dependent density matrix renormalization group (TD-DMRG) method to simulate the quantum dynamics of the Fenna-Matthews-Olson (FMO) complex considering an eight-site model with both thermal and static disorders. We employ the thermo-field dynamics formalism for temperature effects. We merge all electronic interactions into one large matrix product state (MPS) site, boosting accuracy efficiently without increasing complexity. Previous combined experimental and computational studies indicated that the static disorders range from 30 to 90 cm –1 for different FMO sites. We employ a Gaussian distribution and the auxiliary bosonic operator approach to consider the static disorder in our TD-DMRG algorithm. We investigate the impact of different initial excitation sites, temperatures, and degrees of static disorder on the exciton dynamics and temporal coherence. It is found that under the influence of the experimentally determined static disorder strength, the exciton population evolution shows a non-negligible difference at zero temperature, while it is hardly affected at room temperature.