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 1.3 - published on 05 Jul 2017

doi:10.4231/D3RF5KH7G 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 quantumdynamics.wordpress.com 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 (2017), "Exciton Dynamics Lab for Light-Harvesting Complexes (GPU-HEOM)," https://nanohub.org/resources/gpuheompop. (DOI: 10.4231/D3RF5KH7G).

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