Calculating nonlinear response functions for multidimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion.

We present a methodology for simulating multidimensional electronic spectra of molecular aggregates with coupling of electronic excitation to a structured environment using the stochastic non-Markovian quantum state diffusion (NMQSD) method in combination with perturbation theory for the response functions. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise. We demonstrate that our approach shows fast convergence with respect to the number of stochastic trajectories, providing a promising technique for numerical calculation of two-dimensional electronic spectra of large molecular aggregates.

Simulation of absorption spectra of molecular aggregates: A hierarchy of stochastic pure state approach.

Simulation of spectroscopic observables for molecular aggregates with strong and structured coupling of electronic excitation to vibrational degrees of freedom is an important but challenging task. The Hierarchy of Pure States (HOPS) provides a formally exact solution based on local, stochastic trajectories. Exploiting the localization of HOPS for the simulation of absorption spectra in large aggregates requires a formulation in terms of normalized trajectories. Here, we provide a normalized dyadic equation where the ket- and bra-states are propagated in different electronic Hilbert spaces. This work opens the door to applying adaptive HOPS methods for the simulation of absorption spectra.

Molecular origins of induction and loss of photoinhibition-related energy dissipation qI.

Photosynthesis fuels life on Earth using sunlight as energy source. However, light has a simultaneous detrimental effect on the enzyme triggering photosynthesis and producing oxygen, photosystem II (PSII). Photoinhibition, the light-dependent decrease of PSII activity, results in a major limitation to aquatic and land photosynthesis and occurs upon all environmental stress conditions. In this work, we investigated the molecular origins of photoinhibition focusing on the paradoxical energy dissipation process of unknown nature coinciding with PSII damage. Integrating spectroscopic, biochemical, and computational approaches, we demonstrate that the site of this quenching process is the PSII reaction center. We propose that the formation of quenching and the closure of PSII stem from the same event. We lastly reveal the heterogeneity of PSII upon photoinhibition using structure-function modeling of excitation energy transfer. This work unravels the functional details of the damage-induced energy dissipation at the heart of photosynthesis.

Formally exact simulations of mesoscale exciton dynamics in molecular materials.

Excited state carriers, such as excitons, can diffuse on the 100 nm to micron length scale in molecular materials but only delocalize over short length scales due to coupling between electronic and vibrational degrees-of-freedom. Here, we leverage the locality of excitons to adaptively solve the hierarchy of pure states equations (HOPS). We demonstrate that our adaptive HOPS (adHOPS) methodology provides a formally exact and size-invariant (i.e., ) scaling algorithm for simulating mesoscale quantum dynamics. Finally, we provide proof-of-principle calculations for exciton diffusion on linear chains containing up to 1000 molecules.

Directed kinetic transition network model.

Molecular dynamics simulations contain detailed kinetic information related to the functional states of proteins and macromolecules, but this information is obscured by the high dimensionality of configurational space. Markov state models and transition network models are widely applied to extract kinetic descriptors from equilibrium molecular dynamics simulations. In this study, we developed the Directed Kinetic Transition Network (DKTN)-a graph representation of a master equation which is appropriate for describing nonequilibrium kinetics. DKTN models the transition rate matrix among different states under detailed balance. Adopting the mixing time from the Markov chain, we use the half mixing time as the criterion to identify critical state transition regarding the protein conformational change. The similarity between the master equation and the Kolmogorov equation suggests that the DKTN model can be reformulated into the continuous-time Markov chain model, which is a general case of the Markov chain without a specific lag time. We selected a photo-sensitive protein, vivid, as a model system to illustrate the usage of the DKTN model. Overall, the DKTN model provides a graph representation of the master equation based on chemical kinetics to model the protein conformational change without the underlying assumption of the Markovian property.

Models and mechanisms of the rapidly reversible regulation of photosynthetic light harvesting.

The rapid response of photosynthetic organisms to fluctuations in ambient light intensity is incompletely understood at both the molecular and membrane levels. In this review, we describe research from our group over a 10-year period aimed at identifying the photophysical mechanisms used by plants, algae and mosses to control the efficiency of light harvesting by photosystem II on the seconds-to-minutes time scale. To complement the spectroscopic data, we describe three models capable of describing the measured response at a quantitative level. The review attempts to provide an integrated view that has emerged from our work, and briefly looks forward to future experimental and modelling efforts that will refine and expand our understanding of a process that significantly influences crop yields.

Energy-dependent quenching adjusts the excitation diffusion length to regulate photosynthetic light harvesting.

An important determinant of crop yields is the regulation of photosystem II (PSII) light harvesting by energy-dependent quenching (qE). However, the molecular details of excitation quenching have not been quantitatively connected to the fraction of excitations converted to chemical energy by PSII reaction centers (PSII yield), which determines flux to downstream metabolism. Here, we incorporate excitation dissipation by qE into a pigment-scale model of excitation transfer and trapping for a 200 × 200-nm patch of the grana membrane. We show that excitation transport can be rigorously coarse grained to a 2D random walk with an excitation diffusion length determined by the extent of quenching. We present an alternative method for analyzing pulse amplitude-modulated chlorophyll fluorescence measurements that incorporates the effects of a variable excitation diffusion length during qE activation.

Photochemical Control of Exciton Superradiance in Light-Harvesting Nanotubes.

Photosynthetic antennae and organic electronic materials use topological, structural, and molecular control of delocalized excitons to enhance and direct energy transfer. Interactions between the transition dipoles of individual chromophore units allow for coherent delocalization across multiple molecular sites. This delocalization, for specific geometries, greatly enhances the transition dipole moment of the lowest energy excitonic state relative to the chromophore and increases its radiative rate, a phenomenon known as superradiance. In this study, we show that ordered, self-assembled light-harvesting nanotubes (LHNs) display excitation-induced photobrightening and photodarkening. These changes in quantum yield arise due to changes in energetic disorder, which in turn increases/decreases excitonic superradiance. Through a combination of experiment and modeling, we show that intense illumination induces different types of chemical change in LHNs that reproducibly alter absorption and fluorescence properties, indicating control over excitonic delocalization. We also show that changes in spectral width and shift can be sensitive measures of system dimensionality, illustrating the mixed 1-2D nature of LHN excitons. Our results demonstrate a path forward for mastery of energetic disorder in an excitonic antenna, with implications for fundamental studies of coherent energy transport.

Mechanistic Regimes of Vibronic Transport in a Heterodimer and the Design Principle of Incoherent Vibronic Transport in Phycobiliproteins.

Following the observation of coherent oscillations in nonlinear spectra of photosynthetic pigment protein complexes, in particular, phycobilliproteins such as PC645, coherent vibronic transport has been suggested as a design principle for novel light-harvesting materials. Vibronic transport between energetically remote pigments is coherent when the presence of a vibration resonant with the electronic energy gap supports transient delocalization between the electronic excited states. We establish the mechanism of vibronic transport for a model heterodimer across a wide range of molecular parameter values. The resulting mechanistic map demonstrates that the molecular parameters of phycobiliproteins in fact support incoherent vibronic transport. This result points to an important design principle: Incoherent vibronic transport is more efficient than a coherent mechanism when energetic disorder exceeds the coupling between the donor and vibrationally excited acceptor states. Finally, our results suggest that the role of coherent vibronic transport in pigment protein complexes should be reevaluated.

Local protein solvation drives direct down-conversion in phycobiliprotein PC645 via incoherent vibronic transport.

The mechanisms controlling excitation energy transport (EET) in light-harvesting complexes remain controversial. Following the observation of long-lived beats in 2D electronic spectroscopy of PC645, vibronic coherence, the delocalization of excited states between pigments supported by a resonant vibration, has been proposed to enable direct excitation transport from the highest-energy to the lowest-energy pigments, bypassing a collection of intermediate states. Here, we instead show that for phycobiliprotein PC645 an incoherent vibronic transport mechanism is at play. We quantify the solvation dynamics of individual pigments using ab initio quantum mechanics/molecular mechanics (QM/MM) nuclear dynamics. Our atomistic spectral densities reproduce experimental observations ranging from absorption and fluorescence spectra to the timescales and selectivity of down-conversion observed in transient absorption measurements. We construct a general model for vibronic dimers and establish the parameter regimes of coherent and incoherent vibronic transport. We demonstrate that direct down-conversion in PC645 proceeds incoherently, enhanced by large reorganization energies and a broad collection of high-frequency vibrations. We suggest that a similar incoherent mechanism is appropriate across phycobiliproteins and represents a potential design principle for nanoscale control of EET.

Long-range energy transport in photosystem II.

We simulate the long-range inter-complex electronic energy transfer in photosystem II-from the antenna complex, via a core complex, to the reaction center-using a non-Markovian (ZOFE) quantum master equation description that allows the electronic coherence involved in the energy transfer to be explicitly included at all length scales. This allows us to identify all locations where coherence is manifested and to further identify the pathways of the energy transfer in the full network of coupled chromophores using a description based on excitation probability currents. We investigate how the energy transfer depends on the initial excitation-localized, coherent initial excitation versus delocalized, incoherent initial excitation-and find that the overall energy transfer is remarkably robust with respect to such strong variations of the initial condition. To explore the importance of vibrationally enhanced transfer and to address the question of optimization in the system parameters, we systematically vary the strength of the coupling between the electronic and the vibrational degrees of freedom. We find that the natural parameters lie in a (broad) region that enables optimal transfer efficiency and that the overall long-range energy transfer on a ns time scale appears to be very robust with respect to variations in the vibronic coupling of up to an order of magnitude. Nevertheless, vibrationally enhanced transfer appears to be crucial to obtain a high transfer efficiency, with the latter falling sharply for couplings outside the optimal range. Comparison of our full quantum simulations to results obtained with a "classical" rate equation based on a modified-Redfield/generalized-Förster description previously used to simulate energy transfer dynamics in the entire photosystem II complex shows good agreement for the overall time scales of excitation energy transport.

Multiscale model of light harvesting by photosystem II in plants.

The first step of photosynthesis in plants is the absorption of sunlight by pigments in the antenna complexes of photosystem II (PSII), followed by transfer of the nascent excitation energy to the reaction centers, where long-term storage as chemical energy is initiated. Quantum mechanical mechanisms must be invoked to explain the transport of excitation within individual antenna. However, it is unclear how these mechanisms influence transfer across assemblies of antenna and thus the photochemical yield at reaction centers in the functional thylakoid membrane. Here, we model light harvesting at the several-hundred-nanometer scale of the PSII membrane, while preserving the dominant quantum effects previously observed in individual complexes. We show that excitation moves diffusively through the antenna with a diffusion length of 50 nm until it reaches a reaction center, where charge separation serves as an energetic trap. The diffusion length is a single parameter that incorporates the enhancing effect of excited state delocalization on individual rates of energy transfer as well as the complex kinetics that arise due to energy transfer and loss by decay to the ground state. The diffusion length determines PSII's high quantum efficiency in ideal conditions, as well as how it is altered by the membrane morphology and the closure of reaction centers. We anticipate that the model will be useful in resolving the nonphotochemical quenching mechanisms that PSII employs in conditions of high light stress.

A structure-based model of energy transfer reveals the principles of light harvesting in photosystem II supercomplexes.

Photosystem II (PSII) initiates photosynthesis in plants through the absorption of light and subsequent conversion of excitation energy to chemical energy via charge separation. The pigment binding proteins associated with PSII assemble in the grana membrane into PSII supercomplexes and surrounding light harvesting complex II trimers. To understand the high efficiency of light harvesting in PSII requires quantitative insight into energy transfer and charge separation in PSII supercomplexes. We have constructed the first structure-based model of energy transfer in PSII supercomplexes. This model shows that the kinetics of light harvesting cannot be simplified to a single rate limiting step. Instead, substantial contributions arise from both excitation diffusion through the antenna pigments and transfer from the antenna to the reaction center (RC), where charge separation occurs. Because of the lack of a rate-limiting step, fitting kinetic models to fluorescence lifetime data cannot be used to derive mechanistic insight on light harvesting in PSII. This model will clarify the interpretation of chlorophyll fluorescence data from PSII supercomplexes, grana membranes, and leaves.

Mapping the spatial overlap of excitons in a photosynthetic complex via coherent nonlinear frequency generation.

We experimentally demonstrate a nonlinear spectroscopic method that is sensitive to exciton-exciton interactions in a Frenkel exciton system. Spatial overlap of one-exciton wavefunctions leads to coupling between them, resulting in two-exciton eigenstates that have the character of many single-exciton pairs. The mixed character of the two-exciton wavefunctions gives rise to a four-wave-mixing nonlinear frequency generation signal. When only part of the linear excitation spectrum of the complex is excited with three spectrally tailored pulses with separate spatial directions, a frequency-shifted third-order nonlinear signal emerges in the phase-matched direction. We employ the nonlinear response function formalism to show that the emergence of the signal is mediated by and carries information about the two-exciton eigenstates of the system. We report experimental results for nonlinear frequency generation in the Fenna-Matthews-Olson (FMO) photosynthetic pigment-protein complex. Our theoretical analysis of the signal from FMO confirms that the emergence of the frequency-shifted signal is due to the interaction of spatially overlapped excitons. In this method, the signal intensity is directly measured in the frequency domain and does not require scanning of pulse delays or signal phase retrieval. The wavefunctions of the two-exciton states contain information about the spatial overlap of excitons and can be helpful in identifying coupling strengths and relaxation pathways. We propose this method as a facile experimental means of studying exciton correlations in systems with complicated electronic structures.

Experimental and theoretical study of rotationally inelastic collisions of CN(A2pi) with N2.

Optical-optical double resonance was employed to study rotational energy transfer in collisions of selected rotational/fine-structure levels of CN(A2pi, v = 3) with N2. The CN radical was generated by 193 nm photolysis of BrCN in a slow flow of N2 at total pressures of 0.2-1.4 Torr. Specific fine-structure lambda-doublet levels of CN(A2pi, v = 3) were prepared by pulsed dye laser excitation on isolated lines in the CN A-X (3,0) band, while the initially excited and collisionally populated levels were observed after a short delay by laser-induced fluorescence in the B-A (3,3) band. Total removal rate constants for specified rotational/fine-structure levels involving total angular momentum J from 4.5 to 12.5 were determined. These rate constants decrease with increasing J, with no obvious dependence on the fine-structure/lambda-doublet label. State-to-state relative rate constants were determined for several initial levels and show a strikingly strong collisional propensity to conserve the fine-structure/lambda-doublet label. Comparison is made with the results of quantum scattering calculations based on potential energy surfaces averaged over the orientation of the N2 molecule. Reasonable agreement is found with experimentally determined total removal rate constants. However, the computed state-to-state rate constants show a stronger propensity for fine-structure and lambda-doublet changing transitions. These differences between experiment and theory could be due to the neglect of the N2 orientation and the correlation of the CN and N2 angular motions.

Comparing electronic structure predictions for the ground state dissociation of vinoxy radicals.

This paper reports a series of electronic structure calculations performed on the dissociation pathways of the vinoxy radical (CH(2)CHO). We use coupled-cluster with single, double, and perturbative triple excitations (CCSD(T)), complete active space self-consistent field (CASSCF), multireference configuration interaction (MRCI), and MRCI with the Davidson correction (MRCI+Q) to calculate the barrier heights of the two unimolecular dissociation pathways of this radical. The effect of state averaging on the barrier heights is investigated at the CASSCF, MRCI, and MRCI+Q levels. The change in mixing angle along the reaction path is calculated as a measure of derivative coupling and found to be insufficient to suggest nonadiabatic recrossing. We also present a new analysis of previous experimental data on the unimolecular dissociation of ground state vinoxy. In particular, an error in the internal energy distribution of vinoxy radicals reported in a previous paper is corrected and a new analysis of the experimental sensitivity to the onset energy (barrier height) for the isomerization reaction is given. Combining these studies, a final "worst case" analysis of the product branching ratio is given and a statistical model using each of the calculated transition states is found to be unable to correctly reproduce the experimental data.

Photodissociation of propargyl chloride at 193 nm.

The photodissociation of propargyl chloride (C3H3Cl) has been studied at 193 nm. Ion imaging experiments with state-selective detection of the Cl atoms and single-photon ionization of the C3H3 radicals were performed, along with measurements of the Cl + C3H3 and HCl + C3H2 recoil kinetic energy distributions, using a scattering apparatus with electron bombardment ionization detection to resolve the competing Cl and HCl elimination channels. The experiments allow the determination of the Cl (2P3/2) and Cl (2P1/2) (hereafter Cl) branching fractions associated with the C-Cl bond fission, which are determined to be 0.5 +/- 0.1 for both channels. Although prior translational spectroscopy studies by others had concluded that the low velocity signal at the Cl+ mass was due to daughter fragments of the HCl elimination products, the present work shows that Cl atoms are produced with a bimodal recoil kinetic energy distribution. The major C-Cl bond fission channel, with a narrow recoil kinetic energy distribution peaking near 40 kcal/mol, produces both Cl and Cl, whereas the minor (5%) channel, partitioning much less energy to relative kinetic energy, produces only ground spin-orbit state Cl atoms. The maximum internal energy of the radicals produced in the low-recoil-kinetic-energy channel is consistent with this channel producing electronically excited propargyl radicals. Finally, in contrast to previous studies, the present work determines the HCl recoil kinetic energy distribution and identifies the possible contribution to this spectrum from propargyl radicals cracking to C3+ ions in the mass spectrometer.