Example Configurations

Most of the provided examples are chosen to reproduce the figures shown in

[1] T. Kramer, M. Noack, A. Reinefeld, M. Rodríguez, Y. Zelinskyi, Efficient calculation of open quantum system dynamics and time-resolved spectroscopy with distributed memory HEOM (DM-HEOM), Journal of Computational Chemistry, vol. 39, pp. 1779-1794 (2018) and arXiv.

The choice of the hierarchy depth (typical ado_depth=3), the time-step (typical step_size=1.0e-15 seconds), and the number of Matsubara/Pade modes to include (typical matsubaras=2) is discussed in [1]. Depending on the desired level of accuracy, convergence should be tested by increasing the hierarchy depth.

The values of the FMO Hamiltonian (given in 1/cm) are discussed in [1], eq. (77) and are all offset by 11000 1/cm. For the examples we provide the FMO values from [R1]. The values of the dipole centers and directions are given in [1], Table 1.

Application	File	Description
app_population_dynamics	fmo_population_dynamics_77K.cfg	FMO population dynamics at 77K for 5 ps
note: this is the basic application to verify convergence before running more complex simulations		typical visualization: gnuplot>set key autotitle columnhead;plot "fmo_population_dynamics_77K_matrix_diagonal.dat" u 1:2 w l,"fmo_population_dynamics_77K_matrix_diagonal.dat" u 1:3 w l
app_thermal_state_search	fmo_thermal_state_77K.cfg	thermal state of the FMO population at 77K
	remarks: the thermal state search is not a physical population dynamics, but follows [R2]	typical visualization: gnuplot>set key autotitle columnhead;plot "fmo_thermal_state_77K_matrix_diagonal.dat" u 1:2 w l,"fmo_thermal_state_77K_matrix_diagonal.dat" u 1:3 w l
app_linear_absorption	fmo_linear_absorption_77K.cfg	FMO linear absorption spectra at 77K (time trace)
	remarks: the dipole directions are required, and to obtain rotationally averaged spectra set tensor_prefactors={1, 1, 1} and tensor_components={{0, 0}, {1, 1}, {2, 2}}	typical visualization to verify convergence and decay of the real and imaginary parts: gnuplot>set key autotitle columnhead;plot "fmo_linear_absorption_77K.dat" u 1:2 w l,"fmo_linear_absorption_77K.dat" u 1:3 w l further postprocessing to obtain the frequency spectra is done by FFT
app_static_fluorescence	fmo_static_fluorescence_77K.cfg	FMO static fluorescence spectra at 77K (time trace)
	remarks: in addition to the linear absorption case, the thermal state search parameters are required	typical visualization to verify convergence and decay of the real and imaginary parts: gnuplot>set key autotitle columnhead;plot "fmo_static_fluorescence_77K.dat" u 1:2 w l,"fmo_static_fluorescence_77K.dat" u 1:3 w l further postprocessing to obtain the frequency spectra is done by FFT
app_circular_dichroism	fmo_circular_dichroism_77K.cfg	FMO circular dichroism spectra at 77K (time trace)
	remarks: in addition to the linear absorption case, the dipole centers are required	typical visualization to verify convergence and decay of the real and imaginary parts: gnuplot>set key autotitle columnhead;plot "fmo_circular_dichroism_77K.dat" u 1:2 w l,"fmo_circular_dichroism_77K.dat" u 1:3 w l further postprocessing to obtain the frequency spectra is done by FFT
app_two_dimensional_spectra	fmo_2d_0000_010_nr.cfg	FMO 2d spectra at 100K (non-rephasing pathways, time traces)
note: depending on the polarization sequence, runtime can be long (up to 2h) for the example	remarks: rotational averaging and polarization sequences are explained in [1], Eq. (73). steps_t_delay specifies the t2-delay time in multiples of step_size pathways can be selected among {gbrp,serp,esarp,gbnr,senr,esanr}, where the first letters denote ground-state-bleaching (gb), stimulated emission (se), and excited state absorption (esa), the last letters differentiate between rephasing (rp) and non-rephasing (nr) contributions	typical visualization to verify convergence and decay of the real and imaginary parts: gnuplot>set key autotitle columnhead;plot "fmo_2d_0000_010_nr.dat" w image further postprocessing to obtain the frequency spectra is done by two FFTs with exponential sign depending on non/rephasing signal (see [1], Eq. (74f))

Further remarks: before performing the FFT, it is possible to zero-pad the result if the signals have decayed to negligible levels. This increases the frequency resolution. After the FFT, the upper half of the result corresponds to negative frequencies and before plotting might need to be shifted en bloc.

[R1] Adolphs, J., & Renger, T. (2006). How proteins trigger excitation energy transfer in the FMO complex of green sulfur bacteria. Biophysical journal, 91(8), 2778-2797

[R2] Zhang, H.-D., Qiao, Q., Xu, R.-X., Zheng, X., & Yan, Y. (2017) Efficient steady-state solver for hierarchical quantum master equations. The Journal of Chemical Physics, 147(4), 44105