Ab initio description of the quantum mechanics in light-harvesting complexes of purple bacteria

• Applicant: Professor Dr. Ulrich Kleinekathöfer
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: from 2005 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 18592143

• Final Report Year: 2011

Final Report Abstract

In this project light-harvesting (LH) complexes have been investigated starting from full atomistic models to excitation transfer and optical properties. Subsequent to molecular dynamics simulations, quantum chemistry calculations of the optically active pigments were performed along the classical trajectories which describe the thermal motions of the nuclear positions within the respective LH complex. In this way energy gap fluctuations between the ground and first excited state were obtained. Due to the large number of up to 60.000 quantum chemistry calculations per pigment in a LH complex, we have chosen the semi-empirical ZINDO/S method for calculating the electronic energie. This procedure has been applied to the LH-2 complexes of the purple bacteria Rhodospirillum molischianum and Rhodopseudomonas acidophila as well as to the Fenna-Matthews-Olson (FMO) complex. Such long trajectories combining classical and quantum approaches have so far not been performed for systems of this kind. Besides the energy gaps which serve as site energies in a tight-binding description also the time dependence of the coupling between single bacteriochlorophylls have been extracted. Different methods for obtaining the latter quantity have been compared. Once the time-dependent site energies and couplings were determined, a time-dependent Hamiltonian was constructed. This served as input for wave-packet calculations in order to calculate the time dependence of the excitonic energy levels as well a the linear absorption spectra in the LH2 complex. A few years ago experiments on the FMO complex were reported that showed strong but surprising evidence that excitonic coherence is protected by the protein environment. The surprising feature of the quantum coherent energy transfer is that coherence survives for several hundreds of femtoseconds in a complex biological system. Spatial correlations were discussed to be very important for this long-lived coherence effect. Our simulations at room temperatures were the first of this kind that rather clearly ruled out this reasoning. They showed that there is only weak correlation in the movements of the pigments and none between the site energies. This clarifies that the often applied uncorrelated-bath approximation is actually valid. Furthermore, the excitonic properties of the FMO system were analyzed using the time-dependent Hamiltonian formalism. Besides the distributions of site energies and couplings, the excitation energy transfer as well as optical properties were calculated. The linear absorption spectra is well reproduced in line shape and peak position. The calculated two-dimensional correlation spectroscopy spectra show no apparent features similar to the experimental counterparts. In the time-dependent Hamiltonian formalism ensemble averages lead to dissipative effect. Alternatively, in the density matrix approaches the dissipation is described via the spectral density while a time-averaged Hamiltonian is employed. To get insight into the different approximations involved, a comparison has been performed. Rather long trajectories of the energy gap fluctuations are required to obtain reliable spectral densities. In addition to these atomic level investigations, the influence of the shape of the spectral density as well as of static disorder on the shape of the linear absorption spectra of the LH2 systems was demonstrated. To this end, different time-dependent and time-independent methods based on perturbation theory have been used. Moreover, a time-dependent modified Redfield theory was developed and compared to the previous methods for the linear absorption of the LH2 system. The methods were likewise tested for spectral densities based on atomic-level calculations. Finally, the spectral density was used to describe the dissipation during the time evolution of a reduced density matrix based on a hierarchical set of equations of motion. Meanwhile using this approach has become rather popular in the context of calculation transfer properties in light-harvesting systems.

Publications

• Calculation of absorption spectra for light-harvesting systems using non-Markovian approaches as well as modified Redfield theory, J. Chem. Phys. 124, 084 903–1–14 (2006)
  M. Schröder, U. Kleinekathöfer & M. Schreiber
  
• Reduced dynamics of coupled harmonic and anharmonic oscillators using higher-order perturbation theory, J. Chem. Phys. 126, 114 102–1–10 (2007)
  M. Schröder, M. Schreiber & U. Kleinekathöfer
  
• Time-local quantum master equations and their applications to dissipative dynamics and molecular wires, in Energy flow dynamics in biomaterial systems, edited by I. Burghard, V. May, D. A. Micha, and E. Bittner, Vol. 93 of Springer Series in Chemical Physics (Springer, New York, 2009)
  U. Kleinekathöfer
  
• Time-dependent atomistic view on the electronic relaxation in light-harvesting system II, J. Phys. Chem. B 114, 12 427–12 437 (2010)
  C. Olbrich & U. Kleinekathöfer
  
• Modeling of light-harvesting in purple bacteria using a time-dependent Hamiltonian approach, phys. stat. sol. (b) 248, 393–398 (2011)
  C. Olbrich, J. Liebers & U. Kleinekathöfer
  
• Quest for spatially correlated fluctuations in the FMO light-harvesting complex, J. Phys. Chem. B 115, 758–764 (2011)
  C. Olbrich, J. Strümpfer, K. Schulten & U. Kleinekathöfer