Gerhard Ritschel

An efficient method to calculate excitation energy transfer in light-harvesting systems: application to the Fenna-Matthews-Olson complex

A master equation derived from non-Markovian quantum state diffusion is used to calculate the excitation energy transfer in the photosynthetic Fenna–Matthews–Olson pigment–protein complex at various temperatures. This approach allows us to treat spectral densities that explicitly contain the coupling to internal vibrational modes of the chromophores. Moreover, the method is very efficient and as a result the transfer dynamics can be calculated within about 1 min on a standard PC, making systematic investigations w.r.t. parameter variations tractable. After demonstrating that our approach is able to reproduce the results of the numerically exact hierarchical equations of motion approach, we show how the inclusion of vibrational modes influences the transfer.

Non-Markovian Quantum State Diffusion for temperature-dependent linear spectra of light harvesting aggregates.

Non-Markovian Quantum State Diffusion (NMQSD) has turned out to be an efficient method to calculate excitonic properties of aggregates composed of organic chromophores, taking into account the coupling of electronic transitions to vibrational modes of the chromophores. NMQSD is an open quantum system approach that incorporates environmental degrees of freedom (the vibrations in our case) in a stochastic way. We show in this paper that for linear optical spectra (absorption, circular dichroism), no stochastics is needed, even for finite temperatures. Thus, the spectra can be obtained by propagating a single trajectory. To this end, we map a finite temperature environment to the zero temperature case using the so-called thermofield method. The resulting equations can then be solved efficiently by standard integrators.

Analytic representations of bath correlation functions for ohmic and superohmic spectral densities using simple poles.

We present a scheme to express a bath correlation function (BCF) corresponding to a given spectral density (SD) as a sum of damped harmonic oscillations. Such a representation is needed, for example, in many open quantum system approaches. To this end we introduce a class of fit functions that enables us to model ohmic as well as superohmic behavior. We show that these functions allow for an analytic calculation of the BCF using pole expansions of the temperature dependent hyperbolic cotangent. We demonstrate how to use these functions to fit spectral densities exemplarily for cases encountered in the description of photosynthetic light harvesting complexes. Finally, we compare absorption spectra obtained for different fits with exact spectra and show that it is crucial to take properly into account the behavior at small frequencies when fitting a given SD.

Open quantum system parameters for light harvesting complexes from molecular dynamics

We extract the site energies and spectral densities of the Fenna-Matthews-Olson (FMO) pigment protein complex of green sulphur bacteria from simulations of molecular dynamics combined with energy gap calculations. Comparing four different combinations of methods, we investigate the origin of quantitative differences regarding site energies and spectral densities obtained previously in the literature. We find that different forcefields for molecular dynamics and varying local energy minima found by the structure relaxation yield significantly different results. Nevertheless, a picture averaged over these variations is in good agreement with experiments and some other theory results. Throughout, we discuss how vibrations-external or internal to the pigment molecules-enter the extracted quantities differently and can be distinguished. Our results offer some guidance to set up computationally more intensive calculations for a precise determination of spectral densities in the future. These are required to determine absorption spectra as well as transport properties of light harvesting complexes.

Closures of the functional expansion hierarchy in the non-Markovian quantum state diffusion approach

To find a practical scheme to numerically solve the non-Markovian Quantum State Diffusion equation (NMQSD), one often uses a functional expansion of the functional derivative that appears in the general NMQSD equation. This expansion leads to a hierarchy of coupled operators. It turned out that if one takes only the zeroth order term into account, one has a very efficient method that agrees remarkably well with the exact results for many cases of interest. We denote this approach as zeroth order functional expansion (ZOFE). In the present work, we investigate two extensions of ZOFE. Firstly, we investigate how the hierarchy converges when taking higher orders into account (which, however, leads to a fast increase in numerical size). Secondly, we demonstrate that by using a terminator that approximates the higher order contributions, one can obtain significant improvement, at hardly any additional computational cost. We carry out our investigations for the case of absorption spectra of molecular aggregates.