The role of resonant nuclear modes in vibrationally assisted energy transport: The LHCII complex

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

In this study, the site energy fluctuations, energy transfer dynamics, and some spectroscopic properties of the minor light-harvesting complex CP24 in a membrane environment were determined. For this purpose, a 3 μs-long classical molecular dynamics simulation was performed for the CP24 complex. Furthermore, using the density functional tight binding/molecular mechanics molecular dynamics (DFTB/MM MD) approach, we performed excited state calculations for the chlorophyll a and chlorophyll b molecules in the complex starting from five different positions of the MD trajectory. During the extended simulations, we observed variations in the site energies of the different sets as a result of the fluctuating protein environment. In particular, a water coordination to Chl-b 608 occurred only after about 1 μs in the simulations, demonstrating dynamic changes in the environment of this pigment. From the classical and the DFTB/MM MD simulations, spectral densities and the (time-dependent) Hamiltonian of the complex were determined. Based on these results, three independent strongly coupled chlorophyll clusters were revealed within the complex. In addition, absorption and fluorescence spectra were determined together with the exciton relaxation dynamics, which reasonably well agrees with experimental time scales.

Dyads with tunable near-infrared donor-acceptor excited-state energy gaps: molecular design and Förster analysis for ultrafast energy transfer

Bacteriochlorophylls, nature's near-infrared absorbers, play an essential role in energy transfer in photosynthetic antennas and reaction centers. To probe energy-transfer processes akin to those in photosynthetic systems, nine synthetic bacteriochlorin-bacteriochlorin dyads have been prepared wherein the constituent pigments are joined at the meso-positions by a phenylethyne linker. The phenylethyne linker is an unsymmetric auxochrome, which differentially shifts the excited-state energies of the phenyl- or ethynyl-attached bacteriochlorin constituents in the dyad. Molecular designs utilized known effects of macrocycle substituents to engineer bacteriochlorins with S₀ → S₁ (Q_y) transitions spanning 725-788 nm. The design-predicted donor-acceptor excited-state energy gaps in the dyads agree well with those obtained from time dependent density functional theory calculations and with the measured range of 197-1089 cm^-1. Similar trends with donor-acceptor excited-state energy gaps are found for (1) the measured ultrafast energy-transfer rates of (0.3-1.7 ps)^-1, (2) the spectral overlap integral (J) in Förster energy-transfer theory, and (3) donor-acceptor electronic mixing manifested in the natural transition orbitals for the S₀ → S₁ transition. Subtle outcomes include the near orthogonal orientation of the π-planes of the bacteriochlorin macrocycles, and the substituent-induced shift in transition-dipole moment from the typical coincidence with the NH-NH axis; the two features together afforded the Förster orientation term κ² ranging from 0.55-1.53 across the nine dyads, a value supportive of efficient excited-state energy transfer. The molecular design and collective insights on the dyads are valuable for studies relevant to artificial photosynthesis and other processes requiring ultrafast energy transfer.

A Comprehensive Approach to Exciton Delocalization and Energy Transfer

Electrostatic intermolecular interactions lie at the heart of both the Förster model for resonance energy transfer (RET) and the exciton model for energy delocalization. In the Förster theory of RET, the excitation energy incoherently flows from the energy donor to a weakly coupled energy acceptor. The exciton model describes instead the energy delocalization in aggregates of identical (or nearly so) molecules. Here, we introduce a model that brings together molecular aggregates and RET. We will consider a couple of molecules, each described in terms of two diabatic electronic states, coupled to an effective molecular vibration. Electrostatic intermolecular interactions drive energy fluxes between the molecules, that, depending on model parameters, can be described as RET or energy delocalization. At variance with the standard Förster model for RET and of the exciton model for aggregates, our approach applies both in the weak and in the strong coupling regimes and fully accounts for the quantum nature of molecular vibrations in a nonadiabatic approach. Coupling the system to a thermal bath, we follow RET and energy delocalization in real time and simulate time-resolved emission spectra.

Probing the Effects of Electronic-Vibrational Resonance on the Rate of Excited-State Energy Transfer in Bacteriochlorin Dyads

The impact of vibrational-electronic resonances on the rate of excited-state energy transfer is examined in a set of bacteriochlorin dyads that employ the same phenylethyne linker. The donor/acceptor excited-state energy gap is tuned from ∼200 to ∼1100 cm^-1 using peripheral substituents on the donor and acceptor bacteriochlorin macrocycles. Ultrafast energy transfer is observed with rate constants of (0.3 ps)^-1 to (1.7 ps)^-1, which agree with those predicted by Förster theory to within a factor of 2. Furthermore, the measured rates follow a trend-line with only small deviations that do not correlate with the density of vibrations at the donor/acceptor excited-state energy gap. Thus, if vibrational-electronic resonances occur in any of these dyads, which seems likely, the impact on the rate of energy transfer is small.

2D electronic-vibrational spectroscopy with classical trajectories

Two-dimensional electronic-vibrational (2DEV) spectra have the capacity to probe electron–nuclear interactions in molecules by measuring correlations between initial electronic excitations and vibrational transitions at a later time. The trajectory-based semiclassical optimized mean trajectory approach is applied to compute 2DEV spectra for a system with excitonically coupled electronic excited states vibronically coupled to a chromophore vibration. The chromophore mode is in turn coupled to a bath, inducing redistribution of vibrational populations. The lineshapes and delay-time dynamics of the resulting spectra compare well with benchmark calculations, both at the level of the observable and with respect to contributions from distinct spectroscopic processes.

Vibronic resonance along effective modes mediates selective energy transfer in excitonically coupled aggregates

We recently proposed effective normal modes for excitonically coupled aggregates that exactly transform the energy transfer Hamiltonian into a sum of one-dimensional Hamiltonians along the effective normal modes. Identifying physically meaningful vibrational motions that maximally promote vibronic mixing suggested an interesting possibility of leveraging vibrational-electronic resonance for mediating selective energy transfer. Here, we expand on the effective mode approach, elucidating its iterative nature for successively larger aggregates, and extend the idea of mediated energy transfer to larger aggregates. We show that energy transfer between electronically uncoupled but vibronically resonant donor-acceptor sites does not depend on the intermediate site energy or the number of intermediate sites. The intermediate sites simply mediate electronic coupling such that vibronic coupling along specific promoter modes leads to direct donor-acceptor energy transfer, bypassing any intermediate uphill energy transfer steps. We show that the interplay between the electronic Hamiltonian and the effective mode transformation partitions the linear vibronic coupling along specific promoter modes to dictate the selectivity of mediated energy transfer with a vital role of interference between vibronic couplings and multi-particle basis states. Our results suggest a general design principle for enhancing energy transfer through synergistic effects of vibronic resonance and weak mediated electronic coupling, where both effects individually do not promote efficient energy transfer. The effective mode approach proposed here paves a facile route toward four-wavemixing spectroscopy simulations of larger aggregates without severely approximating resonant vibronic coupling.

Vibrational and vibronic coherences in the energy transfer process of light-harvesting complex II revealed by two-dimensional electronic spectroscopy

The presence of quantum coherence in light-harvesting complex II (LHCII) as a mechanism to understand the efficiency of the light-harvesting function in natural photosynthetic systems is still debated due to its structural complexity and weak-amplitude coherent oscillations. Here, we revisit the coherent dynamics and clarify different types of coherences in the energy transfer processes of LHCII using a joint method of the high-S/N transient grating and two-dimensional electronic spectroscopy. We find that the electronic coherence decays completely within 50 fs at room temperature. The vibrational coherences of chlorophyll a dominate over oscillations within 1 ps, whereas a low-frequency mode of 340 cm−1 with a vibronic mixing character may participate in vibrationally assisted energy transfer between chlorophylls a. Our results may suggest that vibronic mixing is relevant for rapid energy transfer processes among chlorophylls in LHCII.

Calculating Multidimensional Optical Spectra from Classical Trajectories

Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra.

Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Two-dimensional vibrational-electronic spectra with semiclassical mechanics

Two-dimensional vibrational-electronic (2DVE) spectra probe the effects on vibronic spectra of initial vibrational excitation in an electronic ground state. The optimized mean trajectory (OMT) approximation is a semiclassical method for computing nonlinear spectra from response functions. Ensembles of classical trajectories are subject to semiclassical quantization conditions, with the radiation-matter interaction inducing discontinuous transitions. This approach has been previously applied to two-dimensional infrared and electronic spectra and is extended here to 2DVE spectra. For a system including excitonic coupling, vibronic coupling, and interaction of a chromophore vibration with a resonant environment, the OMT method is shown to well approximate exact quantum dynamics.

Multimode two-dimensional vibronic spectroscopy. II. Simulating and extracting vibronic coupling parameters from polarization-selective spectra

Experimental demonstrations of polarization-selection two-dimensional Vibrational-Electronic (2D VE) and 2D Electronic-Vibrational (2D EV) spectroscopies aim to map the magnitudes and spatial orientations of coupled electronic and vibrational coordinates in complex systems. The realization of that goal depends on our ability to connect spectroscopic observables with molecular structural parameters. In this paper, we use a model Hamiltonian consisting of two anharmonically coupled vibrational modes in electronic ground and excited states with linear and bilinear vibronic coupling terms to simulate polarization-selective 2D EV and 2D VE spectra. We discuss the relationships between the linear vibronic coupling and two-dimensional Huang-Rhys parameters and between the bilinear vibronic coupling term and Duschinsky mixing. We develop a description of the vibronic transition dipoles and explore how the Hamiltonian parameters and non-Condon effects impact their amplitudes and orientations. Using simulated polarization-selective 2D EV and 2D VE spectra, we show how 2D peak positions, amplitudes, and anisotropy can be used to measure parameters of the vibronic Hamiltonian and non-Condon effects. This paper, along with the first in the series, provides the reader with a detailed description of reading, simulating, and analyzing multimode, polarization-selective 2D EV and 2D VE spectra with an emphasis on extracting vibronic coupling parameters from complex spectra.

Multiscale QM/MM molecular dynamics simulations of the trimeric major light-harvesting complex II

Photosynthetic processes are driven by sunlight. Too little of it and the photosynthetic machinery cannot produce the reductive power to drive the anabolic pathways. Too much sunlight and the machinery can get damaged. In higher plants, the major Light-Harvesting Complex (LHCII) efficiently absorbs the light energy, but can also dissipate it when in excess (quenching). In order to study the dynamics related to the quenching process but also the exciton dynamics in general, one needs to accurately determine the so-called spectral density which describes the coupling between the relevant pigment modes and the environmental degrees of freedom. To this end, Born-Oppenheimer molecular dynamics simulations in a quantum mechanics/molecular mechanics (QM/MM) fashion utilizing the density functional based tight binding (DFTB) method have been performed for the ground state dynamics. Subsequently, the time-dependent extension of the long-range-corrected DFTB scheme has been employed for the excited state calculations of the individual chlorophyll-a molecules in the LHCII complex. The analysis of this data resulted in spectral densities showing an astonishing agreement with the experimental counterpart in this rather large system. This consistency with an experimental observable also supports the accuracy, robustness, and reliability of the present multi-scale scheme. To the best of our knowledge, this is the first theoretical attempt on this large complex system is ever made to accurately simulate the spectral density. In addition, the resulting spectral densities and site energies were used to determine the exciton transfer rate within a special pigment pair consisting of a chlorophyll-a and a carotenoid molecule which is assumed to play a role in the balance between the light harvesting and quenching modes.

Insights into Photosynthetic Energy Transfer Gained from Free-Energy Structure: Coherent Transport, Incoherent Hopping, and Vibrational Assistance Revisited

Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring the possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. In this work, we revisit the elementary aspects of environment-induced fluctuations in the involved electronic energies and present a simple way to understand energy flow with the intuitive picture of relaxation in a funnel-type free-energy landscape. The presented free-energy description of energy transfer reveals that typical photosynthetic systems operate in an almost barrierless regime. The approach also provides insights into the distinction between coherent and incoherent energy transfer and the criteria by which the necessity of the vibrational assistance is considered.

Quantum Ratcheted Photophysics in Energy Transport

In this paper, we explore the scope of vibrations as quantum ratchets that serve as nonthermal routes to achieving population transport in systems where excitation transport between molecules is otherwise energetically unfavorable. In addition to their role as channels of transport, we investigate the effect of resonance of the vibrations, which are described by Huang-Rhys mixing, with excitonic energy gaps, which leads to strongly mixed vibronic excitons. Finally, we explore the interplay of resonance and Huang-Rhys mixing with electronic coupling between the molecules, in the presence of a dissipative bath, in optimizing transport in such systems. We find that while resonance is desirable, a moderate electronic coupling has a stronger positive effect in contrast to a large electronic coupling, which results in delocalized excitations across molecules and hampers unidirectional transport. We also report a special resonance regime that is able to circumvent the transport problems arising from large electronic couplings.