Coherent Nuclear and Electronic Dynamics in Primary Charge Separation in Photosynthetic Reaction Centers: A Redfield Theory Approach

Tensor-Train Thermo-Field Memory Kernels for Generalized Quantum Master Equations

The generalized quantum master equation (GQME) approach provides a rigorous framework for deriving the exact equation of motion for any subset of electronic reduced density matrix elements (e.g., the diagonal elements). In the context of electronic dynamics, the memory kernel and inhomogeneous term of the GQME introduce the implicit coupling to nuclear motion and dynamics of electronic density matrix elements that are projected out (e.g., the off-diagonal elements), allowing for efficient quantum dynamics simulations. Here, we focus on benchmark quantum simulations of electronic dynamics in a spin-boson model system described by various types of GQMEs. Exact memory kernels and inhomogeneous terms are obtained from short-time quantum-mechanically exact tensor-train thermo-field dynamics (TT-TFD) simulations and are compared with those obtained from an approximate linearized semiclassical method, allowing for assessment of the accuracy of these approximate memory kernels and inhomogeneous terms. Moreover, we have analyzed the computational cost of the full and reduced-dimensionality GQMEs. The scaling of the computational cost is dependent on several factors, sometimes with opposite scaling trends. The TT-TFD memory kernels can provide insights on the main sources of inaccuracies of GQME approaches when combined with approximate input methods and pave the road for the development of quantum circuits that implement GQMEs on digital quantum computers.

In memory of Vladimir Anatolievich Shuvalov (1943-2022): an outstanding biophysicist

We present here a tribute to one of the foremost biophysicists of our time, Vladimir Anatolievich Shuvalov, who made important contributions in bioenergetics, especially on the primary steps of conversion of light energy into charge-separated states in both anoxygenic and oxygenic photosynthesis. For this, he and his research team exploited pico- and femtosecond transient absorption spectroscopy, photodichroism & circular dichroism spectroscopy, light-induced FTIR (Fourier-transform infrared) spectroscopy, and hole-burning spectroscopy. We remember him for his outstanding leadership and for being a wonderful mentor to many scientists in this area. Reminiscences by many [Suleyman Allakhverdiev (Russia); Robert Blankenship (USA); Richard Cogdell (UK); Arvi Freiberg (Estonia); Govindjee Govindjee (USA); Alexander Krasnovsky, jr, (Russia); William Parson (USA); Andrei Razjivin (Russia); Jian- Ren Shen (Japan); Sergei Shuvalov (Russia); Lyudmilla Vasilieva (Russia); and Andrei Yakovlev (Russia)] have included not only his wonderful personal character, but his outstanding scientific research.

Electronic Absorption Spectra from Off-Diagonal Quantum Master Equations

Quantum master equations (QMEs) provide a general framework for describing electronic dynamics within a complex molecular system. Off-diagonal QMEs (OD-QMEs) correspond to a family of QMEs that describe the electronic dynamics in the interaction picture based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. The fact that OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrodinger picture electronic coherences from them. A key experimental quantity that relies on the ability to obtain accurate Schrodinger picture electronic coherences is the absorption spectrum. In this paper, we propose using a recently introduced procedure for extracting Schrodinger picture electronic coherences from interaction picture inputs to calculate electronic absorption spectra from electronic dynamics generated by OD-QMEs. The accuracy of the absorption spectra obtained in this way is studied in the context of a biexciton benchmark model, by comparing spectra calculated based on time-local and time-nonlocal OD-QMEs to spectra calculated based on a Redfield-type QME and the non-perturbative and quantum-mechanically exact hierarchical equations of motion (HEOM) method.

Dynamics of diverse coherences in primary charge separation of bacterial reaction center at 77 K revealed by wavelet analysis

To uncover the mechanism behind the high photo-electronic conversion efficiency in natural photosynthetic complexes it is essential to trace the dynamics of electronic and vibrational quantum coherences. Here we apply wavelet analysis to two-dimensional electronic spectroscopy data for three purple bacterial reaction centers with mutations that produce drastically different rates of primary charge separation. From the frequency distribution and dynamic evolution features of the quantum beating, electronic coherence with a dephasing lifetime of ~50 fs, vibronic coherence with a lifetime of ~150 fs and vibrational/vibronic coherences with a lifetime of 450 fs are distinguished. We find that they are responsible for, or couple to, different specific steps during the primary charge separation process, i.e., intradimer charge transfer inside the special bacteriochlorophyll pair followed by its relaxation and stabilization of the charge-transfer state. The results enlighten our understanding of how quantum coherences participate in, and contribute to, a biological electron transfer reaction.

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.

Light-Induced Conformational Alterations in Heliorhodopsin Triggered by the Retinal Excited State

Heliorhodopsins are a recently discovered diverse retinal protein family with an inverted topology of the opsin where the retinal protonated Schiff base proton is facing the cell cytoplasmic side in contrast to type 1 rhodopsins. To explore whether light-induced retinal double-bond isomerization is a prerequisite for triggering protein conformational alterations, we utilized the retinal oxime formation reaction and thermal denaturation of a native heliorhodopsin of Thermoplasmatales archaeon SG8-52-1 (TaHeR) as well as a trans-locked retinal analogue (TaHeR_L) in which the critical C₁₃=C₁₄ double-bond isomerization is prevented. We found that both reactions are light-accelerated not only in the native but also in the “locked” pigment despite lacking any isomerization. It is suggested that light-induced charge redistribution in the retinal excited state polarizes the protein and triggers protein conformational perturbations that thermally decay in microseconds. The extracted activation energy and the frequency factor for both the reactions reveal that the light enhancement of TaHeR differs distinctly from the earlier studied type 1 microbial rhodopsins.

Simulating energy transfer dynamics in the Fenna-Matthews-Olson complex via the modified generalized quantum master equation

The generalized quantum master equation (GQME) provides a general and formally exact framework for simulating the reduced dynamics of open quantum systems. The recently introduced modified approach to the GQME (M-GQME) corresponds to a specific implementation of the GQME that is geared toward simulating the dynamics of the electronic reduced density matrix in systems governed by an excitonic Hamiltonian. Such a Hamiltonian, which is often used for describing energy and charge transfer dynamics in complex molecular systems, is given in terms of diabatic electronic states that are coupled to each other and correspond to different nuclear Hamiltonians. Within the M-GQME approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic density matrix is fully captured by a memory kernel superoperator, which can be obtained from short-lived (compared to the time scale of energy/charge transfer) projection-free inputs. In this paper, we test the ability of the M-GQME to predict the energy transfer dynamics within a seven-state benchmark model of the Fenna-Matthews-Olson (FMO) complex, with the short-lived projection-free inputs obtained via the Ehrenfest method. The M-GQME with Ehrenfest-based inputs is shown to yield accurate results across a wide parameter range. It is also found to dramatically outperform the direct application of the Ehrenfest method and to provide better-behaved convergence with respect to memory time in comparison to an alternative implementation of the GQME approach previously applied to the same FMO model.

Photoinduced charge transfer in Zn(II) and Au(III)-ligated symmetric and asymmetric bacteriochlorin dyads: A computational study

The excited-state properties and photoinduced charge-transfer (CT) kinetics in a series of symmetrical and asymmetrical Zn- and Au-ligated meso-meso-connected bacteriochlorin (BChl) complexes are studied computationally. BChl derivatives, which are excellent near-IR absorbing chromophores, are found to play a central role in bacterial photosynthetic reaction centers but are rarely used in artificial solar energy harvesting systems. The optical properties of chemically linked BChl complexes can be tuned by varying the linking group and involving different ligated metal ions. We investigate charge transfer in BChl dyads that are either directly linked or through a phenylene ring (1,4-phenylene) and which are ligating Zn or Au ions. The directly linked dyads with a nearly perpendicular arrangement of the BChl units bear markedly different properties than phenylene linked dyads. In addition, we find that the dielectric dependence of the intramolecular CT rate is very strong in neutral Zn-ligated dyads, whereas cationic Au-ligated dyads show negligible dielectric dependence of the CT rate. Rate constants of the photo induced CT process are calculated at the semiclassical Marcus level and are compared to fully quantum mechanical Fermi's golden rule based values. The rates are calculated using a screened range separated hybrid functional that offers a consistent framework for addressing environment polarization. We study solvated systems in two solvents of a low and a high scalar dielectric constant.

On the role of non-diagonal system-environment interactions in bridge-mediated electron transfer

Bridge-mediated electron transfer (ET) between a donor and an acceptor is prototypical for the description of numerous most important ET scenarios. While multi-step ET and the interplay of sequential and direct superexchange transfer pathways in the donor-bridge-acceptor (D-B-A) model are increasingly understood, the influence of off-diagonal system-bath interactions on the transfer dynamics is less explored. Off-diagonal interactions account for the dependence of the ET coupling elements on nuclear coordinates (non-Condon effects) and are typically neglected. Here, we numerically investigate with quasi-adiabatic propagator path integral simulations the impact of off-diagonal system-environment interactions on the transfer dynamics for a wide range of scenarios in the D-B-A model. We demonstrate that off-diagonal system-environment interactions can have profound impact on the bridge-mediated ET dynamics. In the considered scenarios, the dynamics itself does not allow for a rigorous assignment of the underlying transfer mechanism. Furthermore, we demonstrate how off-diagonal system-environment interaction mediates anomalous localization by preventing long-time depopulation of the bridge B and how coherent transfer dynamics between donor D and acceptor A can be facilitated. The arising non-exponential short-time dynamics and coherent oscillations are interpreted within an equivalent Hamiltonian representation of a primary reaction coordinate model that reveals how the complex vibronic interplay of vibrational and electronic degrees of freedom underlying the non-Condon effects can impose donor-to-acceptor coherence transfer on short timescales.

Consciousness as an Emergent Phenomenon: A Tale of Different Levels of Description

One of the biggest queries in cognitive sciences is the emergence of consciousness from matter. Modern neurobiological theories of consciousness propose that conscious experience is the result of interactions between large-scale neuronal networks in the brain, traditionally described within the realm of classical physics. Here, we propose a generalized connectionist framework in which the emergence of "conscious networks" is not exclusive of large brain areas, but can be identified in subcellular networks exhibiting nontrivial quantum phenomena. The essential feature of such networks is the existence of strong correlations in the system (classical or quantum coherence) and the presence of an optimal point at which the system's complexity and energy dissipation are maximized, whereas free-energy is minimized. This is expressed either by maximization of the information content in large scale functional networks or by achieving optimal efficiency through the quantum Goldilock effect.

On the Role of the Special Pair in Photosystems as a Charge Transfer Rectifier

The special pair, a bacteriochlorophyll a (BChl) dimer found at the core of bacterial reaction centers, is known to play a key role in the functionality of photosystems as a precursor to the photosynthesis process. In this paper, we analyze the inherent affinity of the special pair to rectify the intrapair photo-induced charge transfer (CT). In particular, we show that the molecular environment affects the nuclear geometry, resulting in symmetry breaking between the two possible intrapair CT processes. To this end, we study the relationships of the intrapair CT and the molecular geometry with respect to the effective dielectric constant provided by the molecular environment. We identify the special pair structural feature that breaks the symmetry between the two molecules, leading to CT rectification. Excited state energies, oscillator strengths, and electronic coupling values are obtained via time-dependent density functional theory, employing a recently developed framework based on a screened range-separated hybrid functional within a polarizable continuum model (SRSH-PCM). We analyze the rectification capability of the special pair by calculating the CT rates using a first-principles-based Fermi's golden rule approach.

Coherent intradimer dynamics in reaction centers of photosynthetic green bacterium Chloroflexus aurantiacus

Early-time dynamics of absorbance changes (light minus dark) in the long-wavelength Q_y absorption band of bacteriochlorophyll dimer P of isolated reaction centers (RCs) from thermophilic green bacterium Chloroflexus (Cfx.) aurantiacus was studied by difference pump-probe spectroscopy with 18-fs resolution at cryogenic temperature. It was found that the stimulated emission spectrum gradually moves to the red on the ~100-fs time scale and subsequently oscillates with a major frequency of ~140 cm⁻¹. By applying the non-secular Redfield theory and linear susceptibility theory, the coherent dynamics of the stimulated emission from the excited state of the primary electron donor, bacteriochlorophyll dimer P*, was modeled. The model showed the possibility of an extremely fast transition from the locally excited state P₁* to the spectrally different excited state P₂*. This transition is clearly seen in the kinetics of the stimulated emission at 880 and 945 nm, where mostly P₁* and P₂* states emit, respectively. These findings are similar to those obtained previously in RCs of the purple bacterium Rhodobacter (Rba.) sphaeroides. The assumption about the existence of the second excited state P₂* helps to explain the complicated temporal behavior of the ΔA spectrum measured by pump-probe spectroscopy. It is interesting that, in spite of the strong coupling between the P₁* and P₂* states assumed in our model, the form of the coherent oscillations is mainly defined by pure vibrational coherence in the excited states. A possible nature of the P₂* state is discussed.

Protein conformational alterations induced by the retinal excited state in proton and sodium pumping rhodopsins

Retinal proteins' biological activity is triggered by the retinal chromophore's light absorption, which initiates a photocycle. However, the mechanism by which retinal light excitation induces the protein's response is not completely understood. Recently, two new retinal proteins were discovered, namely, King Sejong 1-2 (KS1-2) and Nonlabens (Donghaeana) dokdonensis (DDR2), which exhibit H+ and Na+ pumping activities, respectively. To pinpoint whether protein conformation alterations can be achieved without light-induced retinal C13[double bond, length as m-dash]C14 double-bond isomerization, we utilized the hydroxylamine reaction, which cleaves the protonated Schiff base bond through which the retinal chromophore is covalently bound to the protein. The reaction is accelerated by light even though the cleavage is not a photochemical reaction. Therefore, the cleavage reaction may serve as a tool to detect protein conformation alterations. We discovered that in both KS1-2 and DDR2, the hydroxylamine reaction is light accelerated, even in artificial pigments derived from synthetic retinal in which the crucial C13[double bond, length as m-dash]C14 double-bond isomerization is prevented. Therefore, we propose that in both proteins the light-induced retinal charge redistribution taking place in the retinal excited state polarizes the protein, which, in turn, triggers protein conformation alterations. A further general possible application of the present finding is associated with other photoreceptor proteins having retinal or other non-retinal chromophores whose light excitation may affect the protein conformation.

Both electronic and vibrational coherences are involved in primary electron transfer in bacterial reaction center

Understanding the mechanism behind the near-unity efficiency of primary electron transfer in reaction centers is essential for designing performance-enhanced artificial solar conversion systems to fulfill mankind’s growing demands for energy. One of the most important challenges is distinguishing electronic and vibrational coherence and establishing their respective roles during charge separation. In this work we apply two-dimensional electronic spectroscopy to three structurally-modified reaction centers from the purple bacterium Rhodobacter sphaeroides with different primary electron transfer rates. By comparing dynamics and quantum beats, we reveal that an electronic coherence with dephasing lifetime of ~190 fs connects the initial excited state, P*, and the charge-transfer intermediate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}_{\mathrm{A}}^ + {\mathrm{P}}_{\mathrm{B}}^ -$$\end{document}PA+PB-; this \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}^ \ast \to {\mathrm{P}}_{\mathrm{A}}^ + {\mathrm{P}}_{\mathrm{B}}^ -$$\end{document}P*→PA+PB- step is associated with a long-lived quasi-resonant vibrational coherence; and another vibrational coherence is associated with stabilizing the primary photoproduct, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}^ + {\mathrm{B}}_{\mathrm{A}}^ -$$\end{document}P+BA-. The results show that both electronic and vibrational coherences are involved in primary electron transfer process and they correlate with the super-high efficiency.

Distinguishing electronic and vibrational coherences helps to clarify the near-unity efficiency of primary electron transfer in reaction centres. Here, the authors report their respective correlation with the electron transfer rate by comparing the 2D electronic spectra of three mutant reaction centres.

Coupled excitation energy and charge transfer dynamics in reaction centre inspired model systems

Functional operation conditions of reaction centre core complexes require the tight coupling of exciton states to concomitant charge separation. Rigorous theoretical treatment of such integrated excitation energy transfer (EET) and charge transfer (CT) dynamics is particularly challenging due to (i) appreciable system sizes, (ii) inter-site and system-bath couplings of similar magnitude that render the Born-Markov approximation invalid, (iii) substantial reorganization energies of CT states, and (iv) the presence of complex structured spectral densities due to vibrational modes of the surroundings. We present numerical simulations on bacterial reaction centre (bRC) inspired model systems that utilize the recently developed MACGIC-iQUAPI method [Richter et al., J. Chem. Phys., 2017, 146, 214101]. The simulations demonstrate that the method provides a rigorous framework for the investigation of such integrated EET-CT dynamics. First, the applicability of the MACGIC-iQUAPI method is explored for a transition from monotonically decaying to oscillatory system-bath influence coefficients, a behavior inherently imposed by structured bath spectral densities. Tightly coupled EET and CT dynamics is further addressed for an excitonic subsystem that resembles strong coupling of special pair states and serves as donor towards a generic bridge-acceptor system. By solving the dissipative quantum dynamics of such bRC inspired model systems, the quenching of excitonic coherence on the hundreds of femtoseconds timescale is explored via a variation of the bridge state energetics, resembling a continuous transition from sequential to superexchange mediated CT regimes. Further, the simulations explore the influence of resonant vibrational modes on the quenching of excitonic coherence via CT. The results reveal a moderate influence of vibrational mode on charge separation dynamics in regimes of biologically relevant EET and CT dynamics.

The future of quantum biology

Biological systems are dynamical, constantly exchanging energy and matter with the environment in order to maintain the non-equilibrium state synonymous with living. Developments in observational techniques have allowed us to study biological dynamics on increasingly small scales. Such studies have revealed evidence of quantum mechanical effects, which cannot be accounted for by classical physics, in a range of biological processes. Quantum biology is the study of such processes, and here we provide an outline of the current state of the field, as well as insights into future directions.

Intramolecular Vibrations Complement the Robustness of Primary Charge Separation in a Dimer Model of the Photosystem II Reaction Center

The energy conversion of oxygenic photosynthesis is triggered by primary charge separation in proteins at the photosystem II reaction center. Here, we investigate the impacts of the protein environment and intramolecular vibrations on primary charge separation at the photosystem II reaction center. This is accomplished by combining the quantum dynamic theories of condensed phase electron transfer with quantum chemical calculations to evaluate the vibrational Huang-Rhys factors of chlorophyll and pheophytin molecules. We report that individual vibrational modes play a minor role in promoting charge separation, contrary to the discussion in recent publications. Nevertheless, these small contributions accumulate to considerably influence the charge separation rate, resulting in subpicosecond charge separation almost independent of the driving force and temperature. We suggest that the intramolecular vibrations complement the robustness of the charge separation in the photosystem II reaction center against the inherently large static disorder of the involved electronic energies.

Vibronic Coherence in the Charge Separation Process of the Rhodobacter sphaeroides Reaction Center

Two-dimensional electronic spectroscopy was applied to a variant of the reaction center (RC) of purple bacterium Rhodobacter sphaeroides lacking the primary acceptor ubiquinone in order to understand the ultrafast separation and transfer of charge between the bacteriochlorin cofactors. For the first time, characteristic 2D spectra were obtained for the participating excited and charge-transfer states, and the electron-transfer cascade (including two different channels, the P* and B* channels) was fully mapped. By analyzing quantum beats using 2D frequency maps, excited-state vibrational modes at 153 and 33 cm-1 were identified. We speculate that these modes couple to the charge separation (CS) process and collectively optimize the CS and are responsible for the superhigh efficiency.

Exciton-vibrational resonance and dynamics of charge separation in the photosystem II reaction center

The dynamics of charge separation in the photosystem II reaction center (PSII-RC) in the presence of intramolecular vibrations with their frequency matching the energy gap between the exciton state acting as the primary electron donor and the first charge-transfer (CT) state are investigated. A reduced PSII-RC 4-state model explicitly including a CT state is analyzed within Redfield relaxation theory in the multidimensional exciton-vibrational (vibronic) basis. This model is used to study coherent energy/electron transfers and their spectral signatures obtained by two-dimensional electronic spectroscopy (2DES). Modeling of the time-resolved 2D frequency maps obtained by wavelet analysis reveals the origins of the coherences which produce the observed oscillating features in 2DES and allows comparing the lifetimes of the coherences. The results suggest faster excitonic decoherence as compared with longer-lived vibronic oscillations. The emerging picture of the dynamics unravels the role of resonant vibrations in sustaining the effective energy conversion in the PSII-RC. We demonstrate that the mixing of the exciton and CT states promoted by a resonant vibrational quantum allows faster penetration of excitation energy into the CT with subsequent dynamic localization at the bottom of the CT potential induced by the remaining non-resonant nuclear modes. The degree of vibration-assisted mixing and, correspondingly, the rate of primary charge separation, increases significantly in the case of electron-vibrational resonance. The observed features illustrate the principles of quantum design of the photosynthetic unit. These principles are connected with the phenomenon of coherent mixing within vibronic eigenstates, increasing the effectiveness of charge separation not only upon coherent and impulsive laser excitation utilized in the 2DES experiment, but also under natural conditions under non-coherent non-impulsive solar light illumination.

Protein Vibration Effects on Primary Electron Transfer Dynamics in Rhodobacter sphaeroides Photosynthetic Reaction Center

Primary electron transfer (ET) in the chromophore subsystem in a bacterial reaction center (RC) is a unique process, and is coupled with the protein motion, which, like the ET, is caused by photoexcitation of these chromophores. ET is also coupled with dissipative processes, which are caused by interaction between chromophores and vibrations of its surrounding protein. We propose a new dynamics calculation method that accounts for both these effects of protein vibrations. Within this method, the photoinduced protein motion causes an addition of coherent component to the ET rate. We performed dynamics calculation using this method and parameters, which were determined from the ab initio wave functions of the chromophore subsystem and protein normal vibrational modes. We showed that it is this protein motion that causes oscillations in the time-dependencies of stimulated emission intensities and of absorption at 1020 nm. Moreover, the latter oscillations are related to the coherent component of the ET rate.

On the performance of a photosystem II reaction centre-based photocell

The photosystem II reaction centre is the photosynthetic complex responsible for oxygen production on Earth. Its water splitting function is particularly favoured by the formation of a stable charge separated state via a pathway that starts at an accessory chlorophyll. Here we envision a photovoltaic device that places one of these complexes between electrodes and investigate how the mean current and its fluctuations depend on the microscopic interactions underlying charge separation in the pathway considered. Our results indicate that coupling to well resolved vibrational modes does not necessarily offer an advantage in terms of power output but can lead to photo-currents with suppressed noise levels characterizing a multi-step ordered transport process. Besides giving insight into the suitability of these complexes for molecular-scale photovoltaics, our work suggests a new possible biological function for the vibrational environment of photosynthetic reaction centres, namely, to reduce the intrinsic current noise for regulatory processes.

Quantum design of photosynthesis for bio-inspired solar-energy conversion

Photosynthesis is the natural process that converts solar photons into energy-rich products that are needed to drive the biochemistry of life. Two ultrafast processes form the basis of photosynthesis: excitation energy transfer and charge separation. Under optimal conditions, every photon that is absorbed is used by the photosynthetic organism. Fundamental quantum mechanics phenomena, including delocalization, underlie the speed, efficiency and directionality of the charge-separation process. At least four design principles are active in natural photosynthesis, and these can be applied practically to stimulate the development of bio-inspired, human-made energy conversion systems.

On thermodynamic inconsistencies in several photosynthetic and solar cell models and how to fix them

We analyze standard theoretical models of solar energy conversion developed to study solar cells and photosynthetic systems. We show that assuming the energy transfer to the reaction center/electric circuit is through a decay rate or "sink", contradicts the second law of thermodynamics. We put forward a thermodynamically consistent alternative by explicitly considering parts of the reaction center/electric circuit and by employing a Hamiltonian transfer. The predicted energy transfer by the new scheme differs from the one found using a decay rate, casting doubts on the validity of the conclusions obtained by models which include the latter.

How exciton-vibrational coherences control charge separation in the photosystem II reaction center

In photosynthesis absorbed sun light produces collective excitations (excitons) that form a coherent superposition of electronic and vibrational states of the individual pigments. Two-dimensional (2D) electronic spectroscopy allows a visualization of how these coherences are involved in the primary processes of energy and charge transfer. Based on quantitative modeling we identify the exciton-vibrational coherences observed in 2D photon echo of the photosystem II reaction center (PSII-RC). We find that the vibrations resonant with the exciton splittings can modify the delocalization of the exciton states and produce additional states, thus promoting directed energy transfer and allowing a switch between the two charge separation pathways. We conclude that the coincidence of the frequencies of the most intense vibrations with the splittings within the manifold of exciton and charge-transfer states in the PSII-RC is not occurring by chance, but reflects a fundamental principle of how energy conversion in photosynthesis was optimized.

The Role of Resonant Vibrations in Electronic Energy Transfer

Nuclear vibrations play a prominent role in the spectroscopy and dynamics of electronic systems. As recent experimental and theoretical studies suggest, this may be even more so when vibrational frequencies are resonant with transitions between the electronic states. Herein, a vibronic multilevel Redfield model is reported for excitonically coupled electronic two-level systems with a few explicitly included vibrational modes and interacting with a phonon bath. With numerical simulations the effects of the quantized vibrations on the dynamics of energy transfer and coherence in a model dimer are illustrated. The resonance between the vibrational frequency and energy gap between the sites leads to a large delocalization of vibronic states, which then results in faster energy transfer and longer-lived mixed coherences.

Elastic Vibrations in the Photosynthetic Bacterial Reaction Center Coupled to the Primary Charge Separation: Implications from Molecular Dynamics Simulations and Stochastic Langevin Approach

Primary electron transfer reactions in the bacterial reaction center are difficult for theoretical explication: the reaction kinetics, almost unalterable over a wide range of temperature and free energy changes, revealed oscillatory features observed initially by Shuvalov and coauthors (1997, 2002). Here the reaction mechanism was studied by molecular dynamics and analyzed within a phenomenological Langevin approach. The spectral function of polarization around the bacteriochlorophyll special pair PLPM and the dielectric response upon the formation of PL(+)PM(-) dipole within the special pair were calculated. The system response was approximated by Langevin oscillators; the respective frequencies, friction, and energy coupling coefficients were determined. The protein dynamics around PL and PM were distinctly asymmetric. The polarization around PL included slow modes with the frequency 30-80 cm(-1) and the total amplitude of 130 mV. Two main low-frequency modes of protein response around PM had frequencies of 95 and 155 cm(-1) and the total amplitude of 30 mV. In addition, a slowly damping mode with the frequency of 118 cm(-1) and the damping time >1.1 ps was coupled to the formation of PL(+)PM(-) dipole. It was attributed to elastic vibrations of α-helices in the vicinity of PLPM. The proposed trapping of P excitation energy in the form of the elastic vibrations can rationalize the observed properties of the primary electron transfer reactions, namely, the unusual temperature and ΔG dependences, the oscillating phenomena in kinetics, and the asymmetry of the charge separation reactions.

The role of retinal light induced dipole in halorhodopsin structural alteration

The present work studies the mechanism of light induced protein conformational changes in the over-expressed mutant of halorhodopsin (phR) from Natronomonas pharaonis. The catalytic effect of light is reflected in accelerating hydroxyl amine reaction rate of light adapted phR. Light catalysis was detected in native phR but also in artificial pigments derived from tailored retinal analogs locked at the crucial C13=C14 double bond. It is proposed that the photoexcited retinal chromophore induces protein concerted motion that decreases the energy gap between reactants ground and transition states. This energy gap is overcome by coupling to specific protein vibrations. Surprisingly, the rate constants show unusual decreasing trend following temperature increase both for native and artificial pigments.

Efficient tool to calculate two-dimensional optical spectra for photoactive molecular complexes

We combine the coherent modified Redfield theory (CMRT) with the equation of motion-phase matching approach (PMA) to calculate two-dimensional photon-echo spectra for photoactive molecular complexes with an intermediate strength of the coupling to their environment. Both techniques are highly efficient, yet they involve approximations at different levels. By explicitly comparing with the numerically exact quasiadiabatic path integral approach, we show for the Fenna-Matthews-Olson complex that the CMRT describes the decay rates in the population dynamics well, but final stationary populations and the oscillation frequencies differ slightly. In addition, we use the combined CMRT+PMA to calculate two-dimensional photon-echo spectra for a simple dimer model. We find excellent agreement with the exact path integral calculations at short waiting times where the dynamics is still coherent. For long waiting times, differences occur due to different final stationary states, specifically for strong system-bath coupling. For weak to intermediate system-bath couplings, which is most important for natural photosynthetic complexes, the combined CMRT+PMA gives reasonable results with acceptable computational efforts.

Biosolar cells: global artificial photosynthesis needs responsive matrices with quantum coherent kinetic control for high yield

This contribution discusses why we should consider developing artificial photosynthesis with the tandem approach followed by the Dutch BioSolar Cells consortium, a current operational paradigm for a global artificial photosynthesis project. We weigh the advantages and disadvantages of a tandem converter against other approaches, including biomass. Owing to the low density of solar energy per unit area, artificial photosynthetic systems must operate at high efficiency to minimize the land (or sea) area required. In particular, tandem converters are a much better option than biomass for densely populated countries and use two photons per electron extracted from water as the raw material into chemical conversion to hydrogen, or carbon-based fuel when CO₂ is also used. For the average total light sum of 40 mol m⁻² d⁻¹ for The Netherlands, the upper limits are many tons of hydrogen or carbon-based fuel per hectare per year. A principal challenge is to forge materials for quantitative conversion of photons to chemical products within the physical limitation of an internal potential of ca 2.9 V. When going from electric charge in the tandem to hydrogen and back to electricity, only the energy equivalent to 1.23 V can be stored in the fuel and regained. A critical step is then to learn from nature how to use the remaining difference of ca 1.7 V effectively by triple use of one overpotential for preventing recombination, kinetic stabilization of catalytic intermediates and finally generating targeted heat for the release of oxygen. Probably the only way to achieve this is by using bioinspired responsive matrices that have quantum–classical pathways for a coherent conversion of photons to fuels, similar to what has been achieved by natural selection in evolution. In appendix A for the expert, we derive a propagator that describes how catalytic reactions can proceed coherently by a convergence of time scales of quantum electron dynamics and classical nuclear dynamics. We propose that synergy gains by such processes form a basis for further progress towards high efficiency and yield for a global project on artificial photosynthesis. Finally, we look at artificial photosynthesis research in The Netherlands and use this as an example of how an interdisciplinary approach is beneficial to artificial photosynthesis research. We conclude with some of the potential societal consequences of a large-scale roll out of artificial photosynthesis.

A quantum protective mechanism in photosynthesis

Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life.

Quantum Coherence in Photosynthesis for Efficient Solar Energy Conversion

The crucial step in the conversion of solar to chemical energy in Photosynthesis takes place in the reaction center where the absorbed excitation energy is converted into a stable charge separated state by ultrafast electron transfer events. However, the fundamental mechanism responsible for the near unity quantum efficiency of this process is unknown. Here we elucidate the role of coherence in determining the efficiency of charge separation in the plant photosystem II reaction centre (PSII RC) by comprehensively combining experiment (two-dimensional electronic spectroscopy) and theory (Redfield theory). We reveal the presence of electronic coherence between excitons as well as between exciton and charge transfer states which we argue to be maintained by vibrational modes. Furthermore, we present evidence for the strong correlation between the degree of electronic coherence and efficient and ultrafast charge separation. We propose that this coherent mechanism will inspire the development of new energy technologies.

From localized excited States to excitons: changing of conceptions of primary photosynthetic processes in the twentieth century

A short description of two theories of the primary photosynthetic processes is given. Generally accepted in 1950s-1990s, the localized excited states theory has been changed to the modern exciton theory. Appearance of the new experimental data and the light-harvesting complex crystal structure are reasons why the exciton theory has become important. The bulk of data for the old theory and outstanding experiments that have been the driving force for a new theory are discussed in detail.

Modeling of reversible charge separation in reaction centers of photosynthesis: an incoherent approach

Primary charge separation in reaction centers (RCs) of bacterial photosynthesis is modeled in this work. An incoherent population dynamics of RCs states is formulated by kinetic equations. It is assumed that charge separation is accompanied by regular motion of the system along additional coordinates. This motion modulates an energetics of the reactions, and this modulation causes femtosecond oscillations in the population of the states. The best qualitative and quantitative accordance with experimental data on native, modified and mutant RCs of Rba. sphaeroides is achieved in the five states model that includes two excited states P(*)905BAHA and P(*)940BAHA and three charge separated states I, P(+)BA(-)HA and P(+)BAHA(-) (P is a primary electron donor, bacteriochlorophyll dimer, BA and HA are electron acceptors, monomeric bacteriochlorophyll and bacteriopheophytin in active A-branch respectively). The excited states emit at 905 and 940 nm and have approximately the same energy and high interaction rate. The intermediate state I is populated earlier than the P(+)BA(-)HA state and has energy close to the energy of the excited states, a high rate of population and depopulation and spectral identity to the BA(-). A sum of the I and P(+)BA(-)HA populations fits the experimental kinetics of the BA(-) absorption band at 1020 nm. The model explains an oscillatory phenomenon in the kinetics of the P(*) stimulated emission and of the BA(-) absorption. In the schemes without the I state, accordance with the experiment is achieved at unreal parameter values or is not achieved at all. A qualitative agreement of the model with the experiment can be achieved at a wide range of parameter values. The nature of the states I and P(*)940BAHA is discussed in terms of partial charge separation between P and BA and inside P respectively.

Non-classicality of the molecular vibrations assisting exciton energy transfer at room temperature

Advancing the debate on quantum effects in light-initiated reactions in biology requires clear identification of non-classical features that these processes can exhibit and utilize. Here we show that in prototype dimers present in a variety of photosynthetic antennae, efficient vibration-assisted energy transfer in the sub-picosecond timescale and at room temperature can manifest and benefit from non-classical fluctuations of collective pigment motions. Non-classicality of initially thermalized vibrations is induced via coherent exciton-vibration interactions and is unambiguously indicated by negativities in the phase-space quasi-probability distribution of the effective collective mode coupled to the electronic dynamics. These quantum effects can be prompted upon incoherent input of excitation. Our results therefore suggest that investigation of the non-classical properties of vibrational motions assisting excitation and charge transport, photoreception and chemical sensing processes could be a touchstone for revealing a role for non-trivial quantum phenomena in biology.

Femtosecond dynamics of short-range protein electron transfer in flavodoxin

Intraprotein electron transfer (ET) in flavoproteins is important for understanding the correlation of their redox, configuration, and reactivity at the active site. Here, we used oxidized flavodoxin as a model system and report our complete characterization of a photoinduced redox cycle from the initial charge separation in 135-340 fs to subsequent charge recombination in 0.95-1.6 ps and to the final cooling relaxation of the product(s) in 2.5-4.3 ps. With 11 mutations at the active site, we observed that these ultrafast ET dynamics, much faster than active-site relaxation, mainly depend on the reduction potentials of the electron donors with minor changes caused by mutations, reflecting a highly localized ET reaction between the stacked donor and acceptor at a van der Waals distance and leading to a gas-phase type of bimolecular ET reaction confined in the active-site nanospace. Significantly, these ultrafast ET reactions ensure our direct observation of vibrationally excited reaction product(s), suggesting that the back ET barrier is effectively reduced because of the decrease in the total free energy in the Marcus inverted region, leading to the accelerated charge recombination. Such vibrationally coupled charge recombination should be a general feature of flavoproteins with similar configurations and interactions between the cofactor flavin and neighboring aromatic residues.