Ultrafast energy transfer with competing channels: Non-equilibrium Förster and Modified Redfield theories

Theory of 2D electronic spectroscopy of water soluble chlorophyll-binding protein (WSCP): Signatures of Chl b derivate

We investigate how electronic excitations and subsequent dissipative dynamics in the water soluble chlorophyll-binding protein (WSCP) are connected to features in two-dimensional (2D) electronic spectra, thereby comparing results from our theoretical approach with experimental data from the literature. Our calculations rely on third-order response functions, which we derived from a second-order cumulant expansion of the dissipative dynamics involving the partial ordering prescription, assuming a fast vibrational relaxation in the potential energy surfaces of excitons. Depending on whether the WSCP complex containing a tetrameric arrangement of pigments composed of two dimers with weak excitonic coupling between them binds the chlorophyll variant Chl a or Chl b, the resulting linear absorption and circular dichroism spectra and particularly the 2D spectra exhibit substantial differences in line shapes. These differences between Chl a WSCP and Chl b WSCP cannot be explained by the slightly modified excitonic couplings within the two variants. In the case of Chl a WSCP, the assumption of equivalent dimer subunits facilitates a reproduction of substantial features from the experiment by the calculations. In contrast, for Chl b WSCP, we have to assume that the sample, in addition to Chl b dimers, contains a small but distinct fraction of chemically modified Chl b pigments. The existence of such Chl b derivates has been proposed by Pieper et al. [J. Phys. Chem. B 115, 4042 (2011)] based on low-temperature absorption and hole-burning spectroscopy. Here, we provide independent evidence.

Interplay of decoherence and relaxation in a two-level system interacting with an infinite-temperature reservoir

We study the time evolution of a single qubit in contact with a bath, within the framework of projection operator methods. Employing the so-called modified Redfield theory, which also treats energy conserving interactions nonperturbatively, we are able to study the regime beyond the scope of the ordinary approach. Reduced equations of motion for the qubit are derived in an idealistic system where both the bath and system-bath interactions are modeled by Gaussian distributed random matrices. In the strong decoherence regime, a simple relation between the bath correlation function and the decoherence process induced by the energy conserving interaction is found. It implies that energy conserving interactions slow down the relaxation process, which leads to a Zeno freezing if they are sufficiently strong. Furthermore, our results are also confirmed in numerical simulations.

Controlling photosynthetic energy conversion by small conformational changes

Control phenomena in biology usually refer to changes in gene expression and protein translation and modification. In this paper, another mode of regulation is highlighted; we propose that photosynthetic organisms can harness the interplay between localization and delocalization of energy transfer by utilizing small conformational changes in the structure of light-harvesting complexes. We examine the mechanism of energy transfer in photosynthetic pigment-protein complexes, first through the scope of theoretical work and then by in vitro studies of these complexes. Next, the biological relevance to evolutionary fitness of this localization-delocalization switch is explored by in vivo experiments on desert crust and marine cyanobacteria, which are both exposed to rapidly changing environmental conditions. These examples demonstrate the flexibility and low energy cost of this mechanism, making it a competitive survival strategy.

On simulating the dynamics of electronic populations and coherences via quantum master equations based on treating off-diagonal electronic coupling terms as a small perturbation

Quantum master equations provide a general framework for describing the dynamics of electronic observables within a complex molecular system. One particular family of such equations is based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. In this paper, we show how different choices of projection operators, as well as whether one starts out with the time-convolution or the time-convolutionless forms of the generalized quantum master equation, give rise to four different types of such off-diagonal quantum master equations (OD-QMEs), namely, time-convolution and time-convolutionless versions of a Pauli-type OD-QME for only the electronic populations and an OD-QME for the full electronic density matrix (including both electronic populations and coherences). The fact that those OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrödinger picture electronic coherences from them. To address this, we also extend a procedure for extracting Schrödinger picture electronic coherences from interaction picture populations recently introduced by Trushechkin in the context of time-convolutionless Pauli-type OD-QME to the other three types of OD-QMEs. The performance of the aforementioned four types of OD-QMEs is explored in the context of the Garg-Onuchic-Ambegaokar benchmark model for charge transfer in the condensed phase across a relatively wide parameter range. The results show that time-convolution OD-QMEs can be significantly more accurate than their time-convolutionless counterparts, particularly in the case of Pauli-type OD-QMEs, and that rather accurate Schrödinger picture coherences can be obtained from interaction picture electronic inputs.

Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics Using the Polaron Transformation in HEOM Space

In Frenkel exciton dynamics of aggregated molecules, the polaron transformation (PT) technique leads to decoupling of diagonal elements in the subspace of excited electronic states from vibrations. In this article we describe for the first time how PT becomes applicable in the framework of the "Hierarchical Equations of Motion" (HEOM) approach for treatment of open quantum systems. We extend the concept of formulating operators in HEOM space by deriving hierarchical equations of PT which lead to a shift in the excited state potential energy surface to compensate its displacement. While the assumption of thermal equilibration of the vibrational oscillators, introduced by PT, results in a stationary state in a monomer, in a dimer under the same assumption nonequilibrium dynamics appears because of the interplay of the transfer process and vibrational equilibration. Both vertical transitions generating a vibrationally hot state and initially equilibrated vibrational oscillators evolve toward the same stationary asymptotic state associated with polaron formation. The effect of PT on the dynamics of this process depends on initial excitation and basis representation of the electronic system. The developed approach facilitates a generic formulation of quantum master equations involving perturbative treatment of polaron dynamics.

An exact solution in the theory of fluorescence resonance energy transfer with vibrational relaxation

The elegant expression of Förster that predicts the well-known 1/R⁶ distance (R) dependence of the rate of energy transfer, although widely used, was derived using several approximations. Notable among them is the neglect of the vibrational relaxation in the reactant (donor) and product (acceptor) manifolds. Vibrational relaxation can play an important role when the energy transfer rate is faster than the vibrational relaxation rate. Under such conditions, donor to acceptor energy transfer can occur from the excited vibrational states. This phenomenon is not captured by the usual formulation based on the overlap of donor emission and acceptor absorption spectra. Here, we develop a Green's function-based generalized formalism and obtain an exact solution for the excited state population relaxation and the rate of energy transfer in the presence of vibrational relaxation. We find that the application of the well-known Förster's expression might lead to overestimation of R.

Exact description of excitonic dynamics in molecular aggregates weakly driven by light

We present a rigorous theoretical description of excitonic dynamics in molecular light-harvesting aggregates photoexcited by weak-intensity radiation of arbitrary properties. While the interaction with light is included up to the second order, the treatment of the excitation-environment coupling is exact and results in an exact expression for the reduced excitonic density matrix that is manifestly related to the spectroscopic picture of the photoexcitation process. This expression takes fully into account the environmental reorganization processes triggered by the two interactions with light. This is particularly important for slow environments and/or strong excitation-environment coupling. Within the exponential decomposition scheme, we demonstrate how our result can be recast as the hierarchy of equations of motion (HEOM) that explicitly and consistently includes the photoexcitation step. We analytically describe the environmental reorganization dynamics triggered by a delta-like excitation of a single chromophore and demonstrate how our HEOM, in appropriate limits, reduces to the Redfield equations comprising a pulsed photoexcitation and the nonequilibrium Förster theory. We also discuss the relation of our formalism to the combined Born-Markov-HEOM approaches in the case of excitation by thermal light.

Normal mode analysis of spectral density of FMO trimers: Intra- and intermonomer energy transfer

The intermolecular contribution to the spectral density of the exciton-vibrational coupling of the homotrimeric Fenna-Matthews-Olson (FMO) light-harvesting protein of green sulfur bacteria P. aestuarii is analyzed by combining a normal mode analysis of the protein with the charge density coupling method for the calculation of local transition energies of the pigments. Correlations in site energy fluctuations across the whole FMO trimer are found at low vibrational frequencies. Including, additionally, the high-frequency intrapigment part of the spectral density, extracted from line-narrowing spectra, we study intra- and intermonomer exciton transfer. Whereas the intrapigment part of the spectral density is important for fast intramonomer exciton relaxation, the intermolecular contributions (due to pigment-environment coupling) determine the intermonomer exciton transfer. Neither the variations of the local Huang-Rhys factors nor the correlations in site energy fluctuations have a critical influence on energy transfer. At room temperature, the intermonomer transfer in the FMO protein occurs on a 10 ps time scale, whereas intramonomer exciton equilibration is roughly two orders of magnitude faster. At cryogenic temperatures, intermonomer transfer limits the lifetimes of the lowest exciton band. The lifetimes are found to increase between 20 ps in the center of this band up to 100 ps toward lower energies, which is in very good agreement with the estimates from hole burning data. Interestingly, exciton delocalization in the FMO monomers is found to slow down intermonomer energy transfer, at both physiological and cryogenic temperatures.

Modeling irreversible molecular internal conversion using the time-dependent variational approach with sD2 ansatz

A model of irreversible molecular internal conversion dynamics due to molecular thermal energy dissipation to the bath is presented.

Geometry Effects on Light-Harvesting Complex's Light Absorption and Energy Transfer in Purple Bacteria

Light-harvesting complexes (LHC) in photosynthetic organisms perform the major function of light absorption and energy transportation. Optical spectrum of LHC provides a detailed understanding of the molecular mechanisms involved in the excitation energy transfer (EET) processes, which has been widely studied. Here, we study how the geometric property of LHC in Rhodospirillum (Rs.) molischianum would affect its spectral characteristics and energy transfer process. By adopting the effective Hamiltonian and the dipole-dipole approximation, we calculate the exciton level structures for the LH2 ring and LH1 ring and the energy transfer time between different LHCs under various structural parameters and different rotational symmetries. Our numerical results show that the LHC's absorption peaks and the energy transfer time between different LHCs can be modified by changing the geometric configurations. Our study may be beneficial to the applications in designing highly efficient photovoltaic cell and other artificial photosynthetic systems.

Fluorescence Anisotropy Reloaded-Emerging Polarization Microscopy Methods for Assessing Chromophores' Organization and Excitation Energy Transfer in Single Molecules, Particles, Films, and Beyond

Fluorescence polarization is widely used to assess the orientation/rotation of molecules, and the excitation energy transfer between closely located chromophores. Emerging since the 1990s, single molecule fluorescence spectroscopy and imaging stimulate the application of light polarization for studying molecular organization and energy transfer beyond ensemble averaging. Here, traditional fluorescence polarization and linear dichroism methods used for bulk samples are compared with techniques specially developed for, or inspired by, single molecule fluorescence spectroscopy. Techniques for assessing energy transfer in anisotropic samples, where the traditional fluorescence anisotropy framework is not readily applicable, are discussed in depth. It is shown that the concept of a polarization portrait and the single funnel approximation can lay the foundation for alternative energy transfer metrics. Examples ranging from fundamental studies of photoactive materials (conjugated polymers, light-harvesting aggregates, and perovskite semiconductors) to Förster resonant energy transfer (FRET)-based biomedical imaging are presented. Furthermore, novel uses of light polarization for super-resolution optical imaging are mentioned as well as strategies for avoiding artifacts in polarization microscopy.

Unique Energy Transfer in Fluorescein-Conjugated Au22 Nanoclusters Leading to 160-Fold pH-Contrasting Photoluminescence

Accurate measurements of intracellular pH are of crucial importance in understanding the cellular activities and in the development of intracellular drug delivery systems. Here we report a highly sensitive pH probe based on a fluorescein-conjugated Au₂₂ nanocluster. Steady-state photoluminescence (PL) measurements have shown that, when conjugated to Au₂₂, fluorescein exhibits more than 160-fold pH-contrasting PL in the pH range of 4.3-7.8. Transient absorption measurements show that there are two competing ultrafast processes in the fluorescein-conjugated Au₂₂ nanocluster: the intracore-state relaxation and the energy transfer from the nonthermalized states of Au₂₂ to fluorescein. The latter becomes predominant at a higher pH, leading to dramatic PL enhancement of fluorescein. In addition to the intrinsically low toxicity, fluorescein-conjugated Au₂₂ nanoclusters exhibit high pH sensitivity, wide dynamic range, and excellent photostability, providing a powerful tool for the study of intracellular processes.

The Role of Quantum Decoherence in FRET

Resonance energy transfer has become an indispensable experimental tool for single-molecule and single-cell biophysics. Its physical underpinnings, however, are subtle: it involves a discrete jump of excitation from one molecule to another, and so we regard it as a strongly quantum-mechanical process. And yet its kinetics differ from what many of us were taught about two-state quantum systems, quantum superpositions of the states do not seem to arise, and so on. Although J. R. Oppenheimer and T. Förster navigated these subtleties successfully, it remains hard to find an elementary derivation in modern language. The key step involves acknowledging quantum decoherence. Appreciating that aspect can be helpful when we attempt to extend our understanding to situations in which Förster's original analysis is not applicable.