Real-Time Path Integral Simulation of Exciton-Vibration Dynamics in Light-Harvesting Bacteriochlorophyll Aggregates

Abstract

The mechanism of excitation energy transfer in photoexcited bacteriochlorophyll (BChl) aggregates poses intriguing questions, which have important implications for the observed efficiency of photosynthesis. We investigate this process through fully quantum mechanical calculations of exciton-vibration dynamics in chains and rings of BChl a molecules, with parameters characterizing the B850 ring of the LH2 complex of photosynthetic bacteria. The calculations are performed using the modular path integral methodology, which allows the exact treatment of 50 intramolecular vibrations on each pigment using parameters obtained from spectroscopic Huang–Rhys factors with computational effort that scales linearly with aggregate length. Our results indicate that the interplay between electronic and vibrational time scales leads to the rapid suppression but not the overdamping of electronic coherence, which facilitates the spreading of excitation energy throughout the aggregate.

Dynamics of photosynthetic light harvesting systems interacting with N-photon Fock states

“…These show that ρ st is close to being diagonal in the energy eigenbasis, and that in the site basis, the off-diagonal coherence terms are generally smaller than the diagonal population terms. This behavior is consistent with the Frenkel character of excitons in LHCII, which show delocalization over a small number of sites (2)(3). Due to the random orientation of the dipoles and the smallness of the coherence between different sites, there is only a modest difference between collective and independent emission rates.…”

“…The site probabilities rise initially as the incoming pulse passes. These show oscillations over the following few hundreds of fs, due to the excitonic dipole-dipole couplings and to the interaction with phonons, as discussed in many recent studies [1,3]. At later times the system slowly approaches a quasi-steady state due to the dephasing interaction with phonons.…”

“…Exciton dynamics in natural photosynthetic systems have been studied extensively in recent years, using a range of theoretical techniques [1][2][3][4][5]. Most of such studies assume that an initial excitation is present or created at some initial time.…”

A tensor network representation of path integrals: Implementation and analysis

“…Figure 9 shows the spectral density obtained from the Huang-Rhys factors reported by Rätsep et al [66]. This vibrational bath has already been used to study the quantum dynamics of a bacteriochlorophyll (BChl) dimer using QCPI [67] and for longer BChl chains and rings [68] using modular path integral [69][70][71]. The dynamics of the same excitonic dimer system under this structured vibrational bath is shown in Fig.…”

Path-integral approximations to quantum dynamics

“…1 This review addresses the more recent extension of such methods to calculate the dynamical properties of atomic nuclei in systems which are too large to treat by wave-function methods. The aim is not to review all that has been done using pathintegral dynamics methods, since there are already several excellent reviews in the literature [8][9][10][11], nor is it to cover allied topics, such as real-time path-integral methods [12][13][14][15][16][17] or the application of static path-integral methods to infer dynamical properties (e.g., tunnelling splittings [18,19] or quantum instanton rates [20]). Instead, I hope to convince a perhaps sceptical reader that (imaginary-time) path-integral dynamics methods are approximations to the exact quantum dynamics, which are necessarily crude when compared with wavefunction methods, but are often good enough to capture at least the essential physics.…”