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Exciton Dynamics Lab for Light-Harvesting Complexes (GPU-HEOM)

By Christoph Kreisbeck1, Tobias Kramer1

1. Harvard University

Non-Markovian calculation of absorption spectra, 2d echo-spectra, coherences and polulation dynamics for light-harvesting complexes.

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Version 1.1 - published on 03 Jun 2014

doi:10.4231/D3QB9V630 cite this

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Two-dimensional echo spectra



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For light-harvesting complexes (i.e. the Fenna-Matthews-Olson complex) or model systems with less than 8 sites, you can calculate absorption spectra, two-dimensional echo-spectra, and track the exciton populations and coherences.


This tool employs a variant of the reduced hierarchy equations of motion (HEOM) method 1 for generalized spectral densities and implemented on massively parallel graphics processing units (GPU-HEOM) 2,3.

GPU-HEOM handles non-Markovian effects and works well in the biologically relevant temperature range.


  • independent phonon baths attached to each site, the same shape of the spectral density J(omega) is taken for each independent bath
  • decomposition of the vibronic spectral density into a superposition of shifted Lorentzian peaks
  • high-temperature approximation
  • for two-dimensional spectra, the program computes up to six Feynman pathways 4, and constructs the manifolds for the two exciton states as described in 5


  • convergence must be verified by increasing the hierarchy depth (be careful, this quickly exhausts the available GPU memory) and by decreasing the time-step. We recommend to start from the examples provided.
  • at lower temperatures (for the FMO complex typically below 100 K), the high-temperature approximation becomes invalid
  • activation of excited-state absorption mode in two-dimensional spectroscopy requires longer computation times and consumes more memory. Use this option with caution.


The examples are a good starting point for own explorations. A short tutorial will be published soon, see also for additional background information and tutorials.


  1. Y. Tanimura and R. Kubo (1989): Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath, J. Phys. Soc. Jpn. vol. 58, p. 101
  2. C. Kreisbeck and T. Kramer (2012): Long-Lived Electronic Coherence in Dissipative Exciton-Dynamics of Light Harvesting Complexes, Journal of Physical Chemistry Letters, vol. 3, p. 2828
  3. C. Kreisbeck, T. Kramer, M. Rodríguez, B.Hein (2011): High-performance solution of hierarchical equations of motions for studying energy-transfer in light-harvesting complexes, Journal of Chemical Theory and Computation, vol. 7, p. 2166
  4. S. Mukamel, Principles of nonlinear optical spectroscopy
  5. B. Hein, C. Kreisbeck, T. Kramer, M. Rodríguez (2012): Modelling of Oscillations in Two-Dimensional Echo-Spectra of the Fenna-Matthews-Olson Complex, New Journal of Physics vol. 14, p. 023018

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We appreciate contributions by B. Hein for calculating absorption and two-dimensional echo-spectra and by M. Rodríguez.

Sponsored by

Emmy-Noether Programme of the Deutsche Forschungsgemeinschaft, grant KR 2889/2 German Academic Exchange Service (DAAD)

Cite this work

Researchers should cite this work as follows:

  • Christoph Kreisbeck; Tobias Kramer (2014), "Exciton Dynamics Lab for Light-Harvesting Complexes (GPU-HEOM)," (DOI: 10.4231/D3QB9V630).

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Tags, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.