Various quantum-classical approaches to the simulation of processes taking place in real molecular systems have been shown to provide quantitatively correct results in a number of scenarios. However, it is not immediately clear how strongly the approximations related to the classical treatment of the system’s environment compromise the accuracy of these methods. In this work, we present the analysis of the accuracy of the forward–backward trajectory solution (FBTS) of the quantum-classical Liouville equation. To this end, we simulate the excitation dynamics in a molecular dimer using the FBTS and the exact hierarchical equations of motion approach. To facilitate the understanding of the possible benefits of the FBTS, the simulations are also performed using a closely related quantum-classical Poisson Bracket Mapping Equation (PBME) method, as well as the well-known Förster and Redfield theories. We conclude that the FBTS is considerably more accurate than the PBME and the perturbative approaches for most realistic parameter sets and is, therefore, more versatile. We investigate the impact each parameter has on the accuracy of the FBTS. Our results can be used to predict whether the FBTS may be expected to yield satisfactory results when calculating system dynamics for the given system parameters.

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Non-photochemical quenching (NPQ) is responsible for the protection of the photosynthetic apparatus of plants from photodamage at high-light conditions. It is commonly agreed that NPQ takes place in the major light-harvesting complexes (LHCII), however, its exact mechanisms are still under debate. Valuable information about its molecular nature can be provided by measuring time-resolved fluorescence (TRF) spectra of LHCII complexes and their aggregates. Previously [Chmeliov et al., Nat. Plants 2, 16045 (2016)], we analysed the corresponding TRF spectra using the multivariate curve resolution method and proposed a three-state model to describe the spectroscopic data. Usually, such data is described in terms of global analysis resulting in decay or evolution-associated spectra. In this work, we apply such analysis to the TRF data of LHCII aggregates and show that, although mathematically feasible, it cannot be directly related to the physical kinetic model. Nevertheless, a careful examination supplemented with additional spectroscopic information still results in the same three-state model proposed before.

Absorption and fluorescence spectroscopy techniques provide a wealth of information on molecular systems. The simulations of such experiments remain challenging, however, despite the efforts put into developing the underlying theory. An attractive method of simulating the behavior of molecular systems is provided by the quantum–classical theory—it enables one to keep track of the state of the bath explicitly, which is needed for accurate calculations of fluorescence spectra. Unfortunately, until now there have been relatively few works that apply quantum–classical methods for modeling spectroscopic data. In this work, we seek to provide a framework for the calculations of absorption and fluorescence lineshapes of molecular systems using the methods based on the quantum–classical Liouville equation, namely, the forward–backward trajectory solution (FBTS) and the non-Hamiltonian variant of the Poisson bracket mapping equation (PBME-nH). We perform calculations on a molecular dimer and the photosynthetic Fenna–Matthews–Olson complex. We find that in the case of absorption, the FBTS outperforms PBME-nH, consistently yielding highly accurate results. We next demonstrate that for fluorescence calculations, the method of choice is a hybrid approach, which we call PBME-nH-Jeff, that utilizes the effective coupling theory [ Gelzinis A. Gelzinis A. 051103 32035455 J. Chem. Phys. 2020 152 ] to estimate the excited state equilibrium density operator. Thus, we find that FBTS and PBME-nH-Jeff are excellent candidates for simulating, respectively, absorption and fluorescence spectra of real molecular systems.