Emission lineshapes of the B850 band of light-harvesting 2 (LH2) complex in purple bacteria: A second order time-nonlocal quantum master equation approach

Stark absorption and Stark fluorescence spectroscopies: Theory and simulations

Stark spectroscopy experiments are widely used to study the properties of molecular systems, particularly those containing charge-transfer (CT) states. However, due to the small transition dipole moments and large static dipole moments of the CT states, the standard interpretation of the Stark absorption and Stark fluorescence spectra in terms of the Liptay model may be inadequate. In this work, we provide a theoretical framework for calculations of Stark absorption and Stark fluorescence spectra and propose new methods of simulations that are based on the quantum-classical theory. In particular, we use the forward-backward trajectory solution and a variant of the Poisson bracket mapping equation, which have been recently adapted for the calculation of conventional (field-free) absorption and fluorescence spectra. For comparison, we also apply the recently proposed complex time-dependent Redfield theory, while exact results are obtained using the hierarchical equations of motion approach. We show that the quantum-classical methods produce accurate results for a wide range of systems, including those containing CT states. The CT states contribute significantly to the Stark spectra, and the standard Liptay formalism is shown to be inapplicable for the analysis of spectroscopic data in those cases. We demonstrate that states with large static dipole moments may cause a pronounced change in the total fluorescence yield of the system in the presence of an external electric field. This effect is correctly captured by the quantum-classical methods, which should therefore prove useful for further studies of Stark spectra of real molecular systems. As an example, we calculate the Stark spectra for the Fenna-Matthews-Olson complex of green sulfur bacteria.

Computational elucidations on the role of vibrations in energy transfer processes of photosynthetic complexes

Coupling between pigment excitations and nuclear movements in photosynthetic complexes is known to modulate the excitation energy transfer (EET) efficiencies. Toward providing microscopic information, researchers often apply simulation techniques and investigate how vibrations are involved in EET processes. Here, reports on such roles of nuclear movements are discussed from a theory perspective. While vibrations naturally present random thermal fluctuations that can affect energy transferring characteristics, they can also be intertwined with exciton structures and create more specific non-adiabatic energy transfer pathways. For reliable simulations, a bath model that accurately mimics a given molecular system is required. Methods for obtaining such a model in combination with quantum chemical electronic structure calculations and molecular dynamics trajectory simulations are discussed. Various quantum dynamics simulation tools that can handle pigment-to-pigment energy transfers together with their vibrational characters are also touched on. Behaviors of molecular vibrations often deviate from ideality, especially when all-atom details are included, which practically forces us to treat them classically. We conclude this perspective by considering some recent reports that suggest that classical descriptions of bath effects with all-atom details may still produce valuable information for analyzing sophisticated contributions by vibrations to EET processes.

Quantum-Classical Approach for Calculations of Absorption and Fluorescence: Principles and Applications

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.; J. Chem. Phys. 2020, 152, 051103] 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.

Analytical derivation of equilibrium state for open quantum system

Calculation of the equilibrium state of an open quantum system interacting with a bath remains a challenge to this day, mostly due to a huge number of bath degrees of freedom. Here, we present an analytical expression for the reduced density operator in terms of an effective Hamiltonian for a high temperature case. Comparing with numerically exact results, we show that our theory is accurate for slow baths and up to intermediate system-bath coupling strengths. Our results demonstrate that the equilibrium state does not depend on the shape of spectral density in the slow bath regime. The key quantity in our theory is the effective coupling between the states, which depends exponentially on the ratio of the reorganization energy to temperature and, thus, has opposite temperature dependence than could be expected from the small polaron transformation.

Computational Modeling of Exciton-Bath Hamiltonians for Light Harvesting 2 and Light Harvesting 3 Complexes of Purple Photosynthetic Bacteria at Room Temperature

Light harvesting 2 (LH2) complex is the primary component of the photosynthetic unit of purple bacteria that is responsible for harvesting and relaying excitons. The electronic absorption line shape of LH2 contains two major bands at 800 and 850 nm wavelength regions. Under low light conditions, some species of purple bacteria replace LH2 with light harvesting 3 (LH3), a variant form with almost the same structure as the former but with distinctively different spectral features. The major difference between the absorption line shapes of LH2 and LH3 is the shift of the 850 nm band of the former to a new 820 nm region. The microscopic origin of this difference has been the subject of some theoretical/computational investigations. However, the genuine molecular level source of such a difference is not clearly understood yet. This work reports a comprehensive computational study of LH2 and LH3 complexes so as to clarify different molecular level features of LH2 and LH3 complexes and to construct simple exciton-bath models with a common form. All-atomistic molecular dynamics simulations of both LH2 and LH3 complexes provide detailed molecular level structural differences of bacteriochlorophylls (BChls) in the two complexes, in particular, in their patterns of hydrogen bonding (HB) and torsional angles of the acetyl group. Time-dependent density functional theory calculation of the excitation energies of BChls for structures sampled from the MD simulations suggests that the observed differences in the HB and torsional angles cannot fully account for the experimentally observed spectral shift of LH3. Potential sources that can explain the actual spectral shift of LH3 are discussed, and their magnitudes are assessed through fitting of experimental line shapes. These results demonstrate the feasibility of developing simple exciton-bath models for both LH2 and LH3, which can be employed for large-scale exciton quantum dynamics in their aggregates.

Generalized master equation with non-Markovian multichromophoric Förster resonance energy transfer for modular exciton densities

A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations of small length scales into dynamics over large length scales, and also provides a non-Markovian generalization and rigorous derivation of the Pauli master equation employing multichromophoric Förster resonance energy transfer rates. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over coupled chromophores can be accurately described by transitions between subgroups (modules) of delocalized excitons. Application of the GME-MED to the exciton dynamics between a pair of light harvesting complexes in purple bacteria demonstrates its promise as a computationally efficient tool to investigate large scale exciton dynamics in complex environments.