The nonequilibrium Fermi's golden rule (NE-FGR) describes the time-dependent rate coefficient for electronic transitions, when the nuclear degrees of freedom start out in a nonequilibrium state. In this paper, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer (CT) rates in the carotenoidporphyrin-C 60 molecular triad dissolved in explicit tetrahydrofuran. The initial nonequilibrium state corresponds to impulsive photoexcitation from the equilibrated ground-state to the ππ * state, and the porphyrin-to-C 60 and the carotenoid-to-C 60 CT rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C 60 CT process. We also derive an instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcuslike expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.

Charge transfer rate constants were calculated for the carotenoid-porphyrin-C60 (CPC60) molecular triad dissolved in explicit tetrahydrofuran. The calculation was based on mapping the all-atom anharmonic Hamiltonian of this system onto the spin-boson Hamiltonian. The mapping was based on discretizing the spectral density from the time correlation function of the donor–acceptor potential energy gap, as obtained from all-atom molecular dynamics simulations. Different spin-boson Hamiltonians were constructed for each of the possible transitions between the three excited electronic states in two different triad conformations. The rate constants of three possible transitions were calculated via the quantum-mechanically exact Fermi’s golden rule (FGR), as well as a progression of more approximate expressions that lead to the classical Marcus expression. The advantage of the spin-boson approach is that once the mapping is established, the quantum-mechanically exact FGR and the hierarchy of approximations are known in closed form. The classical Marcus charge transfer rate constants obtained with the spin-boson Hamiltonians were found to reproduce those obtained from all-atom simulations with the linearized semiclassical approximation, thereby confirming the equivalence of the two approaches for this system. Within the spin-boson Hamiltonian, we also found that the quantum-mechanically exact FGR rate constants were significantly enhanced compared to the classical Marcus theory rate constants for two out of three transitions in one of the two conformations under consideration. The results confirm that mapping to the spin-boson model can yield accurate predictions for charge transfer rate constants in a system as complex as CPC60 dissolved in tetrahydrofuran.

The nonequilibrium Fermi’s golden rule (NE-FGR) describes the time-dependent rate coefficient for electronic transitions, when the nuclear degrees of freedom start out in a <i>nonequilibrium</i> state. In this letter, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer rates in the carotenoid-porphyrin-C₆₀ molecular triad dissolved in explicit tetrahydrofuran. The initial nonequilibrium state corresponds to impulsive photoexcitation from the equilibrated ground-state to the ππ* state, and the porphyrin-to-C₆₀ and the carotenoid-to-C₆₀ charge transfer rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C₆₀ CT process. We also derive the instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcus-like expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.

To gain better insight into how the fluctuating protein environment influences the site energy ordering of the chromophores in PE545 light-harvesting antenna system, we carried out quantum mechanics/molecular mechanics (QM/MM) calculations along the molecular dynamics (MD) trajectory. The Polarized Protein-Specific Charge (PPC) scheme was adopted in both the MD simulation and the QM/MM calculations for a more realistic description of the protein environment. The deduced site energy ladder calculated using ZINDO/S-CIS agrees well with the best model extracted from experiments by a simultaneous fit of the steady-state spectra and transient absorption spectra. Three combinations of charge schemes were compared to elucidate how the protein environment modulates the site energy of chromophores. The result indicates that the multiroles that the protein environment is playing, for instance, by fine-tuning of the conformation of chromophores or by specific pigment−protein interactions, are both crucial for site energy arrangement. Furthermore, we investigated the effects of individual environments and found that the polar residues and water molecules contribute most to the energy shifts.

The structural basis for the spectral differences between the Fenna–Matthews–Olson (FMO) proteins from Chlorobaculum tepidum (C. tepidum) and Prosthecochloris aestuarii 2K (P. aestuarii) is yet to be fully understood. Mutation-induced perturbation to the exciton structure and the optical spectra of the complex provide a suitable means to investigate the critical role played by the protein scaffold. In this work, we have performed quantum-mechanics/molecular-mechanics calculations over the molecular dynamics simulation trajectories with the polarized protein-specific charge scheme for both wild-type FMOs and two mutants. Our result reveals that a single-point mutation in the vicinity of BChl 6, namely, W183F of C. tepidum, significantly affects the absorption spectrum, resulting in a switch of the absorption spectrum from type 2, for which the 806 nm band is more pronounced than the 815 nm band, to type 1, for which the 815 nm band is pronounced. Our observations agree with the single-point mutation experiments reported by Saer et al. (Biochim. Biophys. Acta, Bioenerg. 2017, 1858, 288–296) and Khmelnitskiy et al. (J. Phys. Chem. Lett. 2018, 9, 3378–3386). In contrast, the absorption spectrum of the P. aestuarii experiences the opposite transition (from type 1 to type 2) upon the same mutation. Furthermore, by comparing the contributions of individual pigments to the spectra in the wild type and its mutant, we find that a single-point mutation near BChl 6 not only induces changes in excitation energy of BChl 6 per se but also affects the excitonic structures of the neighboring BChls 5 and 7 through strong interpigment electronic couplings, resulting in a significant change in the absorption spectra.