Accuracy of approximate methods for the calculation of absorption-type linear spectra with a complex system–bath coupling

Abstract

The accuracy of approximate methods for calculating linear optical spectra depends on many variables. In this study, we fix most of these parameters to typical values found in photosynthetic light-harvesting complexes of plants and determine the accuracy of approximate spectra with respect to exact calculation as a function of the energy gap and interpigment coupling in a pigment dimer. We use a spectral density with the first eight intramolecular modes of chlorophyll a and include inhomogeneous disorder for the calculation of spectra. We compare the accuracy of absorption, linear dichroism, and circular dichroism spectra calculated using the Full Cumulant Expansion (FCE), coherent time-dependent Redfield (ctR), and time-independent Redfield and modified Redfield methods. As a reference we use spectra calculated with the Exact Stochastic Path Integral Evaluation method. We find the FCE method to be the most accurate for the calculation of all spectra. The ctR method performs well for the qualitative calculation of absorption and linear dichroism spectra when pigments are moderately coupled (∼15 cm-1), but ctR spectra may differ significantly from exact spectra when strong interpigment coupling (>100 cm-1) is present. The dependence of the quality of Redfield and modified Redfield spectra on molecular parameters is similar, and these methods almost always perform worse than ctR, especially when the interpigment coupling is strong or the excitonic energy gap is small (for a given coupling). The accuracy of approximate spectra is not affected by resonance with intramolecular modes for typical system-bath coupling and disorder values found in plant light-harvesting complexes.

Protein Effects on the Excitation Energies and Exciton Dynamics of the CP24 Antenna Complex

“…In the present study, we employ the FCE formalism to calculate the absorption spectra as given by eq in the study Cupellini et al In addition, we use a Redfield-like formalism because we want to calculate the absorption as well as the fluorescence spectrum with the same approach. However, it is known that Redfield-like theories certainly have their limitations and have been shown to be problematic for some LH complexes. ,, The excitation energies and the respective transition dipole moments determine the energetic positions and intensities of the spectroscopic features. The broadening of these lines, i.e., the line shapes, of these contributions to the spectra are determined by the spectral densities in a way detailed below.…”

Electric Field Susceptibility of Chlorophyll c and its Effect on the Excitation Energy Ladder in the Major Light-Harvesting Complex of Diatoms

“…Recently, Cao and co-workers have developed the full second-order cummulant expansion (FCE) to calculate the linear absorption, an approach that neither includes the Markovian nor the secular approximation 39,40 . The FCE method has been found to overcome several shortcomings of Redfield-like methods 37,41 . Here, we have employed a code provided by Cupellini and Lipparini to determine the absorption spectra based on the FCE method 42 .…”

Excitation dynamics in photosynthetic light-harvesting complex B850: exact solution versus Redfield and Förster limits

“…In the mR approach the lineshapes are calculated with explicit inclusion of the diagonal exciton-phonon coupling, 27 whereas off-diagonal coupling is accounted for by a phenomenological Markovian term determined by the inverse lifetime of the exciton states (the thus defined term is real and describes a relaxation-induced broadening). 34,35 Besides, more versatile theories of absorption lineshapes have been developed, [36][37][38][39][40][41][42][43] containing non-Markovian generalizations of the modified Redfield lineshapes. Comparison of the absorption spectra calculated with the mR, complex time-dependent Redfield (ctR) theory, 40,42 and nonperturbative hierarchical equation of motion (HEOM) approach 44,45 has been done for model systems 40 and for real antenna complexes from higher plants, i.e.…”

“…34,35 Besides, more versatile theories of absorption lineshapes have been developed, [36][37][38][39][40][41][42][43] containing non-Markovian generalizations of the modified Redfield lineshapes. Comparison of the absorption spectra calculated with the mR, complex time-dependent Redfield (ctR) theory, 40,42 and nonperturbative hierarchical equation of motion (HEOM) approach 44,45 has been done for model systems 40 and for real antenna complexes from higher plants, i.e. LHCII, 46 Lhca4, 47 and Lhca1.…”