Scalable High-Performance Algorithm for the Simulation of Exciton Dynamics. Application to the Light-Harvesting Complex II in the Presence of Resonant Vibrational Modes

Abstract

The accurate simulation of excitonic energy transfer in molecular complexes with coupled electronic and vibrational degrees of freedom is essential for comparing excitonic systemparameters obtained from ab-initio methods with measured time-resolved spectra. Several exact methods for computing the exciton dynamics within a density-matrix formalism are known, * To whom correspondence should be addressed † Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany ‡ Mads Clausen Institute, University of Southern Denmark, Alsion 2, 6400 Sønderborg, Denmark ¶ Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford St, Cambridge, Massachusetts 02138, USA 1 but are restricted to small systems with less than ten sites due to their computational complexity. To study the excitonic energy transfer in larger systems, we adapt and extend the exact hierarchical equation of motion (HEOM) method to various high-performance many-core platforms using the Open Compute Language (OpenCL). For the light-harvesting complex II (LHC II) found in spinach, the HEOM results deviate from predictions of approximate theories and clarify the time-scale of the transfer-process. We investigate the impact of resonantly coupled vibrations on the relaxation and show that the transfer does not rely on a fine-tuning of specific modes.

Two-dimensional electronic spectra of the photosynthetic apparatus of green sulfur bacteria

“…The resulting signal is proportional to the third order optical response function , where the excitation frequency is denoted by ω 1 and the emission frequency by ω 3 . The frequency resolved 2DES are computed from a time propagation of the density matrix using the numerically exact hierarchical equation of motion (HEOM) method on massively parallel graphic processing units113638. In contrast to perturbative treatments using Redfield or Förster theory, HEOM accounts for the different reorganization process of the FMO complex compared to the chlorosome antenna.…”

The Role of Resonant Vibrations in Electronic Energy Transfer

“…Gradually, the consensus has been reached that the oscillation longevity and frequencies must be explained by mixing of electronic and vibrational coherences . In particular, vibrational modes with frequencies resonant with electronic energy gaps were suggested to be important for both spectroscopic signals and energy‐transfer dynamics …”

Electronic energy transfer in biomacromolecules

“…The real equilibrium populations, however, will reflect the mixing with nuclear degrees of freedom, which effectively renormalizes the eigenstates of the full Hamiltonian . Förster and GF theory describe qualitatively well the EET rates even when the electronic couplings are not very small, and predict qualitatively correct populations at equilibrium …”