Two-dimensional spectroscopy can distinguish between decoherence and dephasing of zero-quantum coherences

Recent experiments on a variety of photosynthetic antenna systems have revealed that coherences among electronic states persist longer than previously anticipated. In an ensemble measurement, the observed dephasing of a coherent state can occur because of either disorder across the ensemble or decoherence from interactions with the bath. Distinguishing how much such disorder affects the experimentally observed dephasing rate is paramount for understanding the role that quantum coherence may play in energy transfer through these complexes. Here, we show that two-dimensional electronic spectra can distinguish between the limiting cases of homogeneous dephasing (decoherence) and inhomogeneous dephasing by examining how the quantum beat frequency changes within a cross peak. For the antenna complex LH2 isolated from Rhodobacter sphaeroides , we find that dephasing of the coherence between the B850 and B800 rings arises predominantly from inhomogeneity. In contrast, within the Fenna-Matthews-Olson (FMO) complex from Chlorobium tepidum , dephasing of the coherence between the first two excitons appears quite homogeneous. Thus, the observed dephasing rate sets an upper bound on decoherence for the LH2 complex while establishing both an upper and lower bound for the FMO complex.     

Quantum coherence in photosynthesis

Quantum coherence improves the quantum efficiency of excitonic energy transport within the Fenna-Matthews-Olson photosynthetic complex from the green sulphur bacterium, Chlorobium tepidum. Experimental evidence from third-order nonlinear spectroscopies provides clear evidence of quantum coherence among excited states persisting for picoseconds despite rapid (<100fs) dephasing of quantum coherence between ground and excited states. This protection of quantum coherence can arise from multiple mechanisms, but the net effect is the same: the energetic landscape is course-grained thereby improving efficiency by effectively smoothing the rugged energetic landscape while simultaneously eliminating trap states. The protein bath enables the unusual observed dynamics and illustrates some simple design principles that provide direction to synthetic efforts to mimic the effect. This communication provides an overview of experimental and theoretical notions for those interested in exploiting design principles of photosynthetic energy transfer in synthetic systems.     

Characterization and quantification of the role of coherence in ultrafast quantum biological experiments using quantum master equations,atomistic simulations,and quantum process tomography

Long-lived electronic coherences in various photosynthetic complexes at cryogenic and room temperature have generated vigorous efforts both in theory and experiment to understand their origins and explore their potential role to biological function. The ultrafast signals resulting from the experiments that show evidence for these coherences result from many contributions to the molecular polarization. Quantum process tomography (QPT) is a technique whose goal is that of obtaining the time-evolution of all the density matrix elements based on a designed set of experiments with different preparation and measurements. The QPT procedure was conceived in the context of quantum information processing to characterize and understand general quantum evolution of controllable quantum systems, for example while carrying out quantum computational tasks. We introduce our QPT method for ultrafast experiments, and as an illustrative example, apply it to a simulation of a two-chromophore subsystem of the Fenna-Matthews-Olson photosynthetic complex, which was recently shown to have long-lived quantum coherences. Our Fenna-Matthews-Olson model is constructed using an atomistic approach to extract relevant parameters for the simulation of photosynthetic complexes that consists of a quantum mechanics/molecular mechanics approach combined with molecular dynamics and the use of state-of-the-art quantum master equations. We provide a set of methods that allow for quantifying the role of quantum coherence, dephasing, relaxation and other elementary processes in energy transfer efficiency in photosynthetic complexes, based on the information obtained from the atomistic simulations, or, using QPT, directly from the experiment. The ultimate goal of the combination of this diverse set of methodologies is to provide a reliable way of quantifying the role of long-lived quantum coherences and obtain atomistic insight of their causes.     

Time-resolved coherent anti-Stokes Raman-scattering measurements of I2 in solid Kr: vibrational dephasing on the ground electronic state at 2.6-32 K

Time-resolved coherent anti-Stokes Raman-scattering (CARS) measurements are carried out for iodine (I2) in solid krypton matrices. The dependence of vibrational dephasing time on temperature and vibrational quantum number v is studied. The v dependence is approximately quadratic, while the temperature dependence of both vibrational dephasing and spectral shift, although weak, fits the exponential form characteristic of dephasing by pseudolocal phonons. The analysis of the data indicates that the frequency of the pseudolocal phonons is approximately 30 cm(-1). The longest dephasing times are observed for v = 2 being approximately 300 ps and limited by inhomogeneous broadening. An increase in the dephasing rate of v = 2 as the temperature is lowered to T = 2.6 K is taken as a clear indication of lattice-strain-induced inhomogeneity of the ensemble coherence.     

The nature of the low energy band of the Fenna-Matthews-Olson complex: vibronic signatures

Based entirely upon actual experimental observations on electron-phonon coupling, we develop a theoretical framework to show that the lowest energy band of the Fenna-Matthews-Olson complex exhibits observable features due to the quantum nature of the vibrational manifolds present in its chromophores. The study of linear spectra provides us with the basis to understand the dynamical features arising from the vibronic structure in nonlinear spectra in a progressive fashion, starting from a microscopic model to finally performing an inhomogeneous average. We show that the discreteness of the vibronic structure can be witnessed by probing the diagonal peaks of the nonlinear spectra by means of a relative phase shift in the waiting time resolved signal. Moreover, we demonstrate that the photon-echo and non-rephasing paths are sensitive to different harmonics in the vibrational manifold when static disorder is taken into account. Supported by analytical and numerical calculations, we show that non-diagonal resonances in the 2D spectra in the waiting time, further capture the discreteness of vibrations through a modulation of the amplitude without any effect in the signal intrinsic frequency. This fact generates a signal that is highly sensitive to correlations in the static disorder of the excitonic energy albeit protected against dephasing due to inhomogeneities of the vibrational ensemble.     

Electronic coherence effects in photosynthetic light harvesting

Photosynthetic light harvesting is a paradigmatic example for quantum effects in biology. In this work, we review studies on quantum coherence effects in the LH2 antenna complex from purple bacteria to demonstrate how quantum mechanical rules play important roles in the speedup of excitation energy transfer, the stabilization of electronic excitations, and the robustness of light harvesting in photosynthesis. Subsequently, we present our recent theoretical studies on exciton dynamical localization and excitonic coherence generation in photosynthetic systems. We apply a variational-polaron approach to investigate decoherence of exciton states induced by dynamical fluctuations due to system-environment interactions. The results indicate that the dynamical localization of photoexcitations in photosynthetic complexes is significant and imperative for a complete understanding of coherence and excitation dynamics in photosynthesis. Moreover, we use a simple model to investigate quantum coherence effects in intercomplex excitation energy transfer in natural photosynthesis, with a focus on the likelihoods of generating excitonic coherences during the process. Our model simulations reveal that excitonic coherence between acceptor exciton states and transient nonlocal quantum correlation between distant pairs of chromophores can be generated through intercomplex energy transfer. Finally, we discuss the implications of these theoretical works and important open questions that remain to be answered.     

Smoothing techniques of global optimization: Distance scaling method in searches for most stable Lennard–Jones atomic clusters

Spatial averaging of the potential energy function facilitates the search for the most stable configuration of a molecular system. Recently some global optimization methods of this kind have been designed in the literature that rely on physical phenomena such as diffusion, wave function evolution in quantum mechanics, Smoluchowski dynamics, evolution in temperature of canonical ensembles, etc. In the present article we highlight the fact that all these methods, when applied to the Gaussian distributions of an ensemble, represent special cases of a set of differential equations involving the spatially averaged potential energy. Their structure suggests that the nature's strategy to cope with the global optimization is robust and differs only in the details in particular applications. The strategy consists of going downhill of the averaged potential energy, removing the barriers, and hunting for low energy regions by a selective increasing of the spatial averaging. In this study we explore the deformation of the potential rather than its averaging. The deformation comes from scaling of atomic distances and reduces the barriers even more effectively than the Gaussian averaging. The position and widths of the Gaussian distribution evolve similarly to the Gaussian density annealing (GDA), but we allow elliptical instead of spherical Gaussians as well as branching of the single trajectory of the system into multiple ones. When the temperature reaches 0 K, one has a number of independent Gaussian distributions, each corresponding to a structure and (usually low) energy of the system. The multiple elliptic-Gaussian distance scaling method has been applied to clusters of argon atoms (N=5,…,31), a system serving usually as a benchmark domain. The method found the global minima for all but three clusters (of very low energy). The procedure is 20 or more times less expensive than the GDA one. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2040–2049, 1997     

Algorithms for sampling a quantum microcanonical ensemble of harmonic oscillators at potential minima and conical intersections

Algorithms are presented for sampling quantum microcanonical ensembles for a potential energy minimum and for the conical intersection at the minimum energy crossing point of two coupled electronic states. These ensembles may be used to initialize trajectories for chemical dynamics simulations. The unimolecular dynamics of a microcanonical ensemble about a potential energy minimum may be compared with the dynamics predicted by quantum Rice-Ramsperger-Kassel-Marcus (RRKM) theory. If the dynamics is non-RRKM, it will be of particular interest to determine which states have particularly long lifetimes. Initializing a microcanonical ensemble for the electronically excited state at a conical intersection is a model for electronic nonadiabatic dynamics. The trajectory surface-hopping approach may be used to study the ensuing chemical dynamics. A strength of the model is that zero-point energy conditions are included for the initial nonadiabatic dynamics at the conical intersection.     

Communication: Exciton-phonon information flow in the energy transfer process of photosynthetic complexes

Non-Markovian and nonequilibrium phonon effects are believed to be key ingredients in the energy transfer in photosynthetic complexes, especially in complexes which exhibit a regime of intermediate exciton-phonon coupling. In this work, we utilize a recently developed measure for non-Markovianity to elucidate the exciton-phonon dynamics in terms of the information flow between electronic and vibrational degrees of freedom. We study the measure in the hierarchical equation of motion approach which captures strong coupling effects and nonequilibrium molecular reorganization. We propose an additional trace distance measure for the information flow that could be extended to other master equations. We find that for a model dimer system and for the Fenna-Matthews-Olson complex the non-Markovianity is significant under physiological conditions.     

Massively parallel spin–orbit configuration interaction

We describe a new approach to incorporating quantum effects into chemical reaction rate theory using quantum trajectories. Our development is based on the entangled trajectory molecular dynamics method for simulating quantum processes using trajectory integration and ensemble averaging. By making dynamical approximations similar to those underlying classical transition state theory, quantum corrections are incorporated analytically into the quantum rate expression. We focus on a simple model of quantum decay in a metastable system and consider the deep tunneling limit where the classical rate vanishes and the process is entirely quantum mechanical. We compare our approximate estimate with the well-known WKB tunneling rate and find qualitative agreement.     

Independent trajectory implementation of the semiclassical Liouville method: application to multidimensional reaction dynamics

We describe an independent trajectory implementation of semiclassical Liouville method for simulating quantum processes using classical trajectories. In this approach, a single ensemble of trajectories describes all semiclassical density matrix elements of a coupled electronic state problem, with the ensemble evolving classically under a single reference Hamiltonian chosen on the basis of physical grounds. In this paper, we introduce an additional uncoupled trajectory approximation, allowing the members of the ensemble to evolve independently of one another and eliminating the major computational costs of our previous coupled trajectory implementation. The accuracy of the method is demonstrated for model one-dimensional problems. In addition, the approach is applied to the chemical reaction dynamics of a collinear triatomic system, yielding excellent agreement with exact calculations. This method allows molecular dynamics involving coupled electronic surfaces to be modeled with essentially the same effort as classical molecular dynamics and ensemble averaging.     

A stochastic surrogate Hamiltonian approach of coherent and incoherent exciton transport in the Fenna-Matthews-Olson complex

The capture and transduction of energy in biological systems is clearly necessary for life, and nature has evolved remarkable macromolecular entities to serve these purposes. The Fenna-Matthews-Olson (FMO) complex serves as an intermediate to transfer the energy from the chlorosome to the special pairs of different photo systems. Recent observations have both suggested the importance of coherent exciton transport within the FMO and motivated an elegant and appropriate theoretical construct for interpreting these observations. Here we employ a different approach to exciton transport in a relaxing environment, one based on the stochastic surrogate Hamiltonian method. With it, we calculate the quantum trajectories through the FMO complex both for the model involving seven bacteriochlorophylls that has been used before, and for one involving an eighth bacteriochlorophyll, which has been observed in some new and very important structural work. We find that in both systems, efficient energy transfer to the ultimate receptor occurs, but that because of the placement of, and energy relaxation among, the different bacteriochlorophyll subunits in the FMO complex, the importance of coherent oscillation that was discussed extensively for the seven site system is far less striking for the eight site system, effectively because of the weak mixing between the initial site and the remainder of the system. We suggest that the relevant spectral densities can be determinative for the energy transport route and may provide a new way to enhance energy transfer in artificial devices.     

The effects of connectivity, coherence, and trapping on energy transfer in simple light-harvesting systems studied using the Haken-Strobl model with diagonal disorder

The problem of electronic energy transfer in a network of two-level systems coupled to a single trapping site is investigated using a simple Haken-Strobl model with diagonal disorder. The goal is to illustrate how the trapping time T(trap), coherence time T(d), and molecular topology all affect the overall efficiency of a light-harvesting network. Several issues are identified that need to be considered in the design of an optimal energy transfer network, including the dephasing-induced decoupling the trap from the rest of the network, the nonlinear dependence of trapping rate on the coherence time, and the role of network size and connectivity in determining the effect of the coherence time on efficiency. There are two main conclusions from this work. First, there exists an optimum combination of trapping time and coherence time, which will give the most rapid population transfer to the trap. These values are not in general the shortest trapping time and the longest coherence time, as would be expected based on rate equation models and/or simple considerations from previous analytical results derived for the Haken-Strobl model in an infinite system. Second, in the coherent regime, where T(d) is longer than the other relevant timescales, population trapping in a finite system can be suppressed by quantum interference effects, whose magnitude is sensitive to the molecular geometry. Suggestions for possible methods of observing such effects are discussed. These results provide a qualitative framework for quantum coherence and molecular topology into account for the design of covalent light-harvesting networks with high energy transfer efficiencies.     

Theory and Simulation of the Environmental Effects on FMO Electronic Transitions

Long-lived quantum coherence has been experimentally observed in the Fenna-Matthews-Olson (FMO) light-harvesting complex. It is much debated which role thermal effects play and if the observed low-temperature behavior arises also at physiological temperature. To contribute to this debate we use molecular dynamics simulations to study the coupling between the protein environment and the vertical excitation energies of individual bacteriochlorophyll molecules in the FMO complex of the green sulphur bacterium Chlorobaculum tepidum. The so-called spectral densities, which account for the environmental influence on the excited state dynamics, are determined from temporal autocorrelation functions of the energy gaps between ground and first excited states of the individual pigments. Although the overall shape of the spectral density is found to be rather similar for all pigments, variations in their magnitude can be seen. Differences between the spectral densities for the pigments of the FMO monomer and FMO trimer are also presented.     

Intermittent electron transfer activity from single CdSe/ZnS quantum dots

Electron transfer activity from excited single CdSe/ZnS core/shell quantum dots (QDs) to adsorbed Fluorescein 27 was studied by single QD fluorescence spectroscopy. In comparison with QDs, the QD-acceptor complexes showed a shorter average and broader distribution of QD emission lifetimes due to electron transfer to adsorbates. Large fluctuation of lifetimes in single QD/dye complexes was observed, indicating intermittent electron transfer activity from QDs.