Pengfei Huo

Iterative linearized density matrix propagation for modeling coherent excitation energy transfer in photosynthetic light harvesting

Rather than incoherent hopping between chromophores, experimental evidence suggests that the excitation energy transfer in some biological light harvesting systems initially occurs coherently, and involves coherent superposition states in which excitation spreads over multiple chromophores separated by several nanometers. Treating such delocalized coherent superposition states in the presence of decoherence and dissipation arising from coupling to an environment is a significant challenge for conventional theoretical tools that either use a perturbative approach or make the Markovian approximation. In this paper, we extend the recently developed iterative linearized density matrix (ILDM) propagation scheme [E. R. Dunkel et al., J. Chem. Phys. 129, 114106 (2008)] to study coherent excitation energy transfer in a model of the Fenna-Matthews-Olsen light harvesting complex from green sulfur bacteria. This approach is nonperturbative and uses a discrete path integral description employing a short time approximation to the density matrix propagator that accounts for interference between forward and backward paths of the quantum excitonic system while linearizing the phase in the difference between the forward and backward paths of the environmental degrees of freedom resulting in a classical-like treatment of these variables. The approach avoids making the Markovian approximation and we demonstrate that it successfully describes the coherent beating of the site populations on different chromophores and gives good agreement with other methods that have been developed recently for going beyond the usual approximations, thus providing a new reliable theoretical tool to study coherent exciton transfer in light harvesting systems. We conclude with a discussion of decoherence in independent bilinearly coupled harmonic chromophore baths. The ILDM propagation approach in principle can be applied to more general descriptions of the environment.

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation.

Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.

Communication: Predictive partial linearized path integral simulation of condensed phase electron transfer dynamics.

A partial linearized path integral approach is used to calculate the condensed phase electron transfer (ET) rate by directly evaluating the flux-flux/flux-side quantum time correlation functions. We demonstrate for a simple ET model that this approach can reliably capture the transition between non-adiabatic and adiabatic regimes as the electronic coupling is varied, while other commonly used semi-classical methods are less accurate over the broad range of electronic couplings considered. Further, we show that the approach reliably recovers the Marcus turnover as a function of thermodynamic driving force, giving highly accurate rates over four orders of magnitude from the normal to the inverted regimes. We also demonstrate that the approach yields accurate rate estimates over five orders of magnitude of inverse temperature. Finally, the approach outlined here accurately captures the electronic coherence in the flux-flux correlation function that is responsible for the decreased rate in the inverted regime.

Semi-classical path integral non-adiabatic dynamics: a partial linearized classical mapping Hamiltonian approach

A new partially linearized approximate approach to non-adiabatic quantum dynamics is derived based on linearizing the path difference for nuclear degrees of freedom (DOF) in the classical mapping Hamiltonian while keeping quantum interference effects inherent in the forward and backward propagators for the electronic DOF. With this new approach, the non-adiabatic force that acts on the nuclear DOF is a mean force rather than a state dependent force as found in some alternative approaches. Various benchmark examples are explored to test the accuracy of this new approach, and compare its performance with other approaches for a wide range of physical phenomena including: non-adiabatic scattering, excited state conical intersection dynamics, excited state photoisomerization, and excitation energy transfer in realistic condensed phase model systems. Results indicate that, even though the method is based on a “mean trajectory”-like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.

Semiclassical Path Integral Dynamics: Photosynthetic Energy Transfer with Realistic Environment Interactions

This article reviews recent progress in the theoretical modeling of excitation energy transfer (EET) processes in natural light harvesting complexes. The iterative partial linearized density matrix path-integral propagation approach, which involves both forward and backward propagation of electronic degrees of freedom together with a linearized, short-time approximation for the nuclear degrees of freedom, provides an accurate and efficient way to model the nonadiabatic quantum dynamics at the heart of these EET processes. Combined with a recently developed chromophore-protein interaction model that incorporates both accurate ab initio descriptions of intracomplex vibrations and chromophore-protein interactions treated with atomistic detail, these simulation tools are beginning to unravel the detailed EET pathways and relaxation dynamics in light harvesting complexes.

Ring Polymer Surface Hopping: Incorporating Nuclear Quantum Effects into Nonadiabatic Molecular Dynamics Simulations

We apply a recently proposed ring polymer surface hopping (RPSH) approach to investigate the real-time nonadiabatic dynamics with explicit nuclear quantum effects. The nonadibatic electronic transitions are described through Tullys fewest-switches surface hopping algorithm and the motion of the nuclei are quantized through the ring polymer Hamiltonian in the extended phase space. Applying the RPSH method to simulate Tullys avoided crossing models, we demonstrate the critical role of the nuclear tunneling effect and zero-point energy for accurately describing the transmission and reflection probabilities with low initial momenta. In addition, in Tullys extended coupling model, we show that the ring polymer quantization effectively captures decoherence, yielding more accurate reflection probabilities. These promising results demonstrate the potential of using RPSH as an accurate and efficient method to incorporate nuclear quantum effects into nonadiabatic dynamics simulations.

Enhancing Singlet Fission Dynamics by Suppressing Destructive Interference between Charge-Transfer Pathways

We apply a real-time path-integral approach to investigate the charge-transfer (CT)-mediated singlet fission quantum dynamics in a model pentacene dimer. Our path-integral method gives reliable fission dynamics across various reaction regimes as well as a broad range of reorganization energies and temperatures. With this method, we investigated the destructive interference between the two CT-mediated fission pathways and discovered two mechanisms that can suppress this deleterious effect. First, increasing the energy gap between the two CT states effectively shuts down the high-lying CT pathway, leaving a better functioning low-lying CT pathway with a minimum amount of destructive interference. Second, intermolecular vibrations induce electronic coupling fluctuations, such that the destructive cancellations due to the different signs in static electronic couplings are suppressed. Our numerical results suggest that these two effects can enhance the fission rate up to three times. These findings reveal promising design principles for more efficient singlet fission materials.

Coherent state mapping ring polymer molecular dynamics for non-adiabatic quantum propagations

We introduce the coherent-state mapping ring polymer molecular dynamics (CS-RPMD), a new method that accurately describes electronic non-adiabatic dynamics with explicit nuclear quantization. This new approach is derived by using coherent-state mapping representation for the electronic degrees of freedom (DOF) and the ring-polymer path-integral representation for the nuclear DOF. The CS-RPMD Hamiltonian does not contain any inter-bead coupling term in the state-dependent potential and correctly describes electronic Rabi oscillations. A classical equation of motion is used to sample initial configurations and propagate the trajectories from the CS-RPMD Hamiltonian. At the time equivalent to zero, the quantum Boltzmann distribution (QBD) is recovered by reweighting the sampled distribution with an additional phase factor. In a special limit that there is one bead for mapping variables and multiple beads for nuclei, CS-RPMD satisfies detailed balance and preserves an approximate QBD. Numerical tests of this method with a two-state model system show very good agreement with exact quantum results over a broad range of electronic couplings.

Quasi-Diabatic Representation for Nonadiabatic Dynamics Propagation

We develop a nonadiabatic dynamics propagation scheme that allows interfacing diabatic quantum dynamics methods with commonly used adiabatic electronic structure calculations. This scheme uses adiabatic states as the quasi-diabatic (QD) states during a short-time quantum dynamics propagation. At every dynamical propagation step, these QD states are updated based on a new set of adiabatic basis. Using the partial linearized density matrix (PLDM) path-integral method as one specific example for diabatic dynamics approaches, we demonstrate the accuracy of the QD scheme with a wide range of model nonadiabatic systems as well as the on-the-fly propagations with density functional tight-binding (DFTB) calculations. This study opens the possibility to combine accurate diabatic quantum dynamics methods with adiabatic electronic structure calculations for nonadiabatic dynamics propagations.