Efficient calculation of open quantum system dynamics and time‐resolved spectroscopy with distributed memory HEOM (DM‐HEOM)

Abstract

Time- and frequency-resolved optical signals provide insights into the properties of light-harvesting molecular complexes, including excitation energies, dipole strengths and orientations, as well as in the exciton energy flow through the complex. The hierarchical equations of motion (HEOM) provide a unifying theory, which allows one to study the combined effects of system-environment dissipation and non-Markovian memory without making restrictive assumptions about weak or strong couplings or separability of vibrational and electronic degrees of freedom. With increasing system size the exact solution of the open quantum system dynamics requires memory and compute resources beyond a single compute node. To overcome this barrier, we developed a scalable variant of HEOM. Our distributed memory HEOM, DM-HEOM, is a universal tool for open quantum system dynamics. It is used to accurately compute all experimentally accessible time- and frequency-resolved processes in light-harvesting molecular complexes with arbitrary system-environment couplings for a wide range of temperatures and complex sizes. © 2018 Wiley Periodicals, Inc.

Energy flow in the Photosystem I supercomplex: Comparison of approximative theories with DM-HEOM

“…The HEOM method [3] has been used as reference method for studying energy transfer processes, since it accurately covers a wide parameter range of couplings and temperatures [7]. HEOM is expressed as a system of coupled differential equations for the time evolution of N matrices auxiliary density matrices σ u of dimensions N × N (for PSI I: N = 96).…”

“…Therefore, we base all computations on the numerically exact hierarchical equations of motion (HEOM) method [3,4,5], which captures the system-environment dissipation and decoherence, while retaining coherences and non-Markovian effects in a non-perturbative manner. For computing the dynamics and spectra of PS I an efficient parallelization of the HEOM method is required, which is provided by the Distributed Memory DM-HEOM software package [6,7].…”

Machine learning of two-dimensional spectroscopic data

“…Lacking conclusive results from challenging first principle calculations it is a general consensus in the field to assign the dipole orientations of the BChls to the N B − N D axis, although deviations of up to 6 • have been pointed out by several authors [38,39,40]. We use the distributed DM-HEOM [27,28] to efficiently generate the 2DES data. A complete expression of the 2D spectra in terms of the dipole moment operators can be found in [28], Eqs.…”

“…We use the distributed DM-HEOM [27,28] to efficiently generate the 2DES data. A complete expression of the 2D spectra in terms of the dipole moment operators can be found in [28], Eqs. (64-69).…”

Effect of disorder and polarization sequences on two-dimensional spectra of light-harvesting complexes

“…The hierarchical equation of motion (HEOM) method introduced by Tanimura and Kubo (1989) solves the Frenkel exciton-model dynamics in an exact way and does not rely on small parameter assumption (Ishizaki and Fleming 2009;Kreisbeck et al 2011). A comprehensive comparison of Redfield and HEOM spectra for the Fenna-Matthews-Olson (FMO) complex is given by Hein et al (2012); Kramer et al (2018b), for the Photosystem I supercomplex and Foerster theory by Kramer et al (2018a), and for combined Foerster-Redfield theory applied to the light har- (k, l, m, n) C klmn 0 • , 0 • , 0 • , 0 • (1, 1, 2, 2), (1, 1, 3, 3), (1, 2, 1, 2), (1, 2, 2, 1), (1, 3, 1, 3), (1, 3, 3, 1) + 1…”