Electron Transfer-from Isolated Molecules to Biomolecules

What Can CISS Teach Us about Electron Transfer?

Electron transfer (eT) processes have garnered the attention of chemists and physicists for more than seven decades, and it is commonly believed that the essential features of the electron transfer mechanism are well understood─despite some open questions relating to the efficiency of long-range eT in some systems and temperature effects that are difficult to reconcile with the existing theories. The chiral induced spin selectivity (CISS) effect, which has been studied experimentally since 1999, demonstrates that eT through chiral systems depends on the electron's spin. Attempts to explain the CISS effect by adding spin-orbit coupling to the existing eT theories fails to reproduce the experimental results quantitatively, and it has become evident that the theory for explaining CISS must consider electron-vibration and/or electron-electron interactions. In this Perspective we identify some features of the CISS effect that imply that we should reconsider and refine the Marcus-Levich-Jortner mechanistic description for eT processes, especially for nonlinear systems and in the case of long-range eT.

Interlayer Charge Transport in 2D Lead Halide Perovskites from First Principles

We report on the implementation of a versatile projection-operator diabatization approach to calculate electronic coupling integrals in layered periodic systems. The approach is applied to model charge transport across the saturated organic spacers in two-dimensional (2D) lead halide perovskites. The calculations yield out-of-plane charge transfer rates that decay exponentially with the increasing length of the alkyl chain, range from a few nanoseconds to milliseconds, and are supportive of a hopping mechanism. Most importantly, we show that the charge carriers strongly couple to distortions of the Pb-I framework and that accounting for the associated nonlocal dynamic disorder increases the thermally averaged interlayer rates by a few orders of magnitude compared to the frozen-ion 0 K-optimized structure. Our formalism provides the first comprehensive insight into the role of the organic spacer cation on vertical transport in 2D lead halide perovskites and can be readily extended to functional π-conjugated spacers, where we expect the improved energy alignment with the inorganic layout to speed up the charge transfer between the semiconducting layers.

First-Principles Calculations of Excited-State Decay Rate Constants in Organic Fluorophores

In this Perspective, we discuss recent advances made to evaluate from first-principles the excited-state decay rate constants of organic fluorophores, focusing on the so-called static strategy. In this strategy, one essentially takes advantage of Fermi's golden rule (FGR) to evaluate rate constants at key points of the potential energy surfaces, a procedure that can be refined in a variety of ways. In this way, the radiative rate constant can be straightforwardly obtained by integrating the fluorescence line shape, itself determined from vibronic calculations. Likewise, FGR allows for a consistent calculation of the internal conversion (related to the non-adiabatic couplings) in the weak-coupling regime and intersystem crossing rates, therefore giving access to estimates of the emission yields when no complex photophysical phenomenon is at play. Beyond outlining the underlying theories, we summarize here the results of benchmarks performed for various types of rates, highlighting that both the quality of the vibronic calculations and the accuracy of the relative energies are crucial to reaching semiquantitative estimates. Finally, we illustrate the successes and challenges in determining the fluorescence quantum yields using a series of organic fluorophores.

Anti-Arrhenius behavior of electron transfer reactions in molecular dimers

Rates of chemical reactions typically accelerate as the temperature rises, following the Arrhenius law. However, electron transfer reactions may exhibit weak temperature dependence or counterintuitive behavior, known as anti-Arrhenius behavior, wherein reaction rates decrease as temperature increases. Solvent reorganization energy and torsion-induced changes in electronic couplings could contribute to this unusual behavior, but how each contributes to the overall temperature dependence is unclear. One can decelerate the charge recombination process in photogenerated radical pairs or charge-separated states by harnessing this often-overlooked phenomenon. This means that we could achieve long-lived radical pairs without relying on conventional cooling. Using a series of homo molecular dimers, we showed that the degree of torsional hindrance dictates temperature-dependent torsion-induced changes in electronic coupling and, therefore, charge recombination rates. The overall temperature dependence is controlled by how changes in electronic coupling and the temperature-dependent solvent reorganization energy contribute to the rates of charge recombination. Our findings pave the way for rationally designing molecules that exhibit anti-Arrhenius behavior to slow down charge recombination, opening possibilities for applications in energy-related and quantum information technologies.

Computational evaluation of transport parameters and logic circuit designing of L-Lysine amino acid stringed to Au, Ag, Cu, Pt, and Pd electrodes

The integrants of proteins, i.e., amino acids, have grossed exceptional recognition for their applications towards designing imminent switching devices. Among 20 amino acids, L-Lysine (i.e., positively charged) has the highest number of CH₂ chains, and such chains affect the rectification ratio in several biomolecules. Towards molecular rectification, we investigate the transport parameters of L-Lysine in conjunction with five different coinage metal electrodes, i.e., Au, Ag, Cu, Pt and Pd to form five distinct devices. We deputize the NEGF-DFT formulism for computing conductance, frontier molecular orbitals, current-voltage, and molecular projected self-Hamiltonian calculations using a self-consistent function. We focus on the most widely used electron exchange correlation combination, i.e., the PBE version of GGA with DZDP basis set. The molecular devices under inquisition exhibit phenomenal rectification ratios (RR) in conjunction with negative differential resistance (NDR) regimes. The nominated molecular device offers a substantial rectification ratio of 45.6 with platinum electrodes and a prominent peak to valley current ratio of 1.78 with copper electrodes. We deduce from these findings that L-Lysine based molecular devices would implicit in future bio-nanoelectronic devices. The OR and AND logic gates are also proposed hinged on highest rectification ratio of L-Lysine-based devices.

Surface hopping modeling of charge and energy transfer in active environments

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.

Hybrid Functional and Plane Waves based Ab Initio Molecular Dynamics Study of the Aqueous Fe2+ /Fe3+ Redox Reaction

Kohn-Sham density functional theory and plane wave basis set based ab initio molecular dynamics (AIMD) simulation is a powerful tool for studying complex reactions in solutions, such as electron transfer (ET) reactions involving Fe²⁺ /Fe³⁺ ions in water. In most cases, such simulations are performed using density functionals at the level of Generalized Gradient Approximation (GGA). The challenge in modelling ET reactions is the poor quality of GGA functionals in predicting properties of such open-shell systems due to the inevitable self-interaction error (SIE). While hybrid functionals can minimize SIE, standard plane-wave based AIMD at that level of theory is typically 150 times slower than GGA for systems containing ∼100 atoms. Among several approaches reported to speed-up AIMD simulations with hybrid functionals, the noise-stabilized MD (NSMD) procedure, together with the use of localized orbitals to compute the required exchange integrals, is an attractive option. In this work, we demonstrate the application of the NSMD approach for studying the Fe²⁺ /Fe³⁺ redox reaction in water. It is shown here that long AIMD trajectories at the level of hybrid density functionals can be obtained using this approach. Redox properties of the aqueous Fe²⁺ /Fe³⁺ system computed from these simulations are compared with the available experimental data for validation.

Plenty of Room on the Top: Pathways and Spectroscopic Signatures of Singlet Fission from Upper Singlet States

We investigate dynamic signatures of the singlet fission (SF) process triggered by the excitation of a molecular system to an upper singlet state S_N (N > 1) and develop a computational methodology for the simulation of nonlinear spectroscopic signals revealing the S_N → TT₁ SF in real time. We demonstrate that SF can proceed directly from the upper state S_N, bypassing the lowest excited state, S₁. We determine the main S_N → TT₁ reaction pathways and show by computer simulation and spectroscopic measurements that the S_N-initiated SF can be faster and more efficient than the traditionally studied S₁ → TT₁ SF. We claim that the S_N → TT₁ SF offers novel promising opportunities for engineering SF systems and enhancing SF yields.

Photoexcited Intramolecular Charge Transfer in Dye Sensitizers: Predictive In Silico Screening for Dye-Sensitized Solar Cell Devices

Efficient photoinduced intramolecular charge transfer (ICT) from donor to acceptor in dye molecules is the functional basis and key property in the working of a dye-sensitized solar cell (DSSC). To understand the ICT process in photoexcited dye molecules, we analyze the electronic properties and structural parameters of a chosen set of experimentally synthesized donor-acceptor (D-A) and donor-π-spacer-acceptor (D-π-A) type dye molecules in their ground, excited, and cationic states. The correlation between structural modification and charge redistribution in different parts of the molecule helps to identify the extent of π-conjugation and spatial rearrangement of electron density localization along the molecular skeleton. We find that prominent twisting of several groups and the resulting molecular bond rearrangements in larger parts of the molecule promote efficient donor to acceptor ICT, such as in D-A type ADEKA1 and C275 dyes. Thus, based on the modest computation of structural and electronic properties of dye molecules in their respective ground, excited, and cationic states, we identify the desired structural changes that facilitate tunable intramolecular charge transfer to highlight a simple and direct prescription to screen out probable efficient dye molecules among many samples. Our approach complements recent experimental evidence of capturing the structural view of the excited-state charge transfer in molecules.

Heat transport induced by electron transfer: A general temperature quantum calculation

Electron transfer dominates chemical processes in biological, inorganic, and material chemistry. Energetic aspects of such phenomena, in particular, the energy transfer associated with the electron transfer process, have received little attention in the past but are important in designing energy conversion devices. This paper generalizes our earlier work in this direction, which was based on the semiclassical Marcus theory of electron transfer. It provides, within a simple model, a unified framework that includes the deep (nuclear) tunneling limit of electron transfer and the associated heat transfer when the donor and acceptor sites are seated in environments characterized by different local temperatures. The electron transfer induced heat conduction is shown to go through a maximum at some intermediate average temperature where quantum effects are already appreciable, and it approaches zero when the average temperature is very high (the classical limit) or very low (deep tunneling).

Vibrational Dephasing along the Reaction Coordinate of an Electron Transfer Reaction

The role of molecular vibration in photoinduced electron transfer (ET) reactions has been extensively debated in recent years. In this study, we investigated vibrational wavepacket dynamics in a model ET system consisting of an organic dye molecule as an electron acceptor dissolved in various electron donating solvents. By using broad band pump-probe (BBPP) spectroscopy with visible laser pulses of sub-10 fs duration, coherent vibrational wavepackets of naphthacene dye with frequencies spanning 170-1600 cm-1 were observed in the time domain. The coherence properties of 11 vibrational modes were analyzed by an inverse Fourier filtering procedure, and we discovered that the dephasing times of some vibrational coherences are reduced with increasing ET rates. Density functional theory calculations indicated that the corresponding vibrational modes have a large Huang-Rhys factor between the reactant and the product states, supporting the hypothesis that the loss of phase coherence along certain vibrational modes elucidates that those vibrations are coupled to the reaction coordinate of an ET reaction.

De Novo Design of Molecules with Low Hole Reorganization Energy Based on a Quarter-Million Molecule DFT Screen

Materials exhibiting higher mobilities than conventional organic semiconducting materials such as fullerenes and fused thiophenes are in high demand for applications in printed electronics. To discover new molecules in the heteroacene family that might show improved hole mobility, three de novo design methods were applied. Machine learning (ML) models were generated based on previously calculated hole reorganization energies of a quarter million examples of heteroacenes, where the energies were calculated by applying density functional theory (DFT) and a massive cloud computing environment. The three generative methods applied were (1) the continuous space method, where molecular structures are converted into continuous variables by applying the variational autoencoder/decoder technique; (2) the method based on reinforcement learning of SMILES strings (the REINVENT method); and (3) the junction tree variational autoencoder method that directly generates molecular graphs. Among the three methods, the second and third methods succeeded in obtaining chemical structures whose DFT-calculated hole reorganization energy was lower than the lowest energy in the training dataset. This suggests that an extrapolative materials design protocol can be developed by applying generative modeling to a quantitative structure-property relationship (QSPR) utility function.

Photoinduced Electron Transfer between DNA and Water-Soluble Porphyrins

Photophysical properties of five kinds of porphyrins (H₂TMPyP, ZnTMPyP, PdTMPyP, H₂TPPS, and ZnTPPS) complexed with model DNAs (ctDNA and dGMP) have been investigated using steady-state absorption, circular dichroism (CD), and femtosecond transient absorption spectroscopy. Upon addition of ctDNA (or dGMP), larger hypochromism and red shifts are observed for H₂TMPyP and PdTMPyP compared to the other samples. The steady-state measurements have suggested that the binding modes of H₂TMPyP-ctDNA and PdTMPyP-ctDNA are partial intercalation and full intercalation, respectively, while ZnTMPyP-ctDNA shows outside groove binding. No significant interaction was observed between both H₂TPPS and ZnTPPS with two kinds of DNA. Upon excitation of the porphyrins into the higher excited state S₂ (Soret band), the appearance of the transient absorption from ∼500 to ∼620 nm at about 0.05 ps in H₂TMPyP-ctDNA, H₂TMPyP-dGMP, and PdTMPyP-dGMP indicates the occurrence of the electron transfer (ET) from guanine to H₂TMPyP and PdTMPyP. The forward ET are extremely fast (k_f ≥ 1.0 × 10¹³ s^-1), and the backward ET rates are ∼5.6 × 10¹² and ∼4.0 × 10¹² s^-1, respectively. The complexation with DNA may lead to the shorter lifetime of the fluorescence of H₂TMPyP and PdTMPyP.

Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?

A tremendous effort is currently devoted to the generation of novel hybrid materials with enhanced electronic properties for the creation of artificial photosynthetic systems. This compelling and challenging problem is well-defined from an experimental point of view, as the design of such materials relies on combining organic materials or metals with biological systems like light harvesting and redox-active proteins. Such hybrid systems can be used, e.g., as bio-sensors, bio-fuel cells, biohybrid photoelectrochemical cells, and nanostructured photoelectronic devices. Despite these efforts, the main bottleneck is the formation of efficient interfaces between the biological and the organic/metal counterparts for efficient electron transfer (ET). It is within this aspect that computation can make the difference and improve the current understanding of the mechanisms underneath the interface formation and the charge transfer efficiency. Yet, the systems considered (i.e., light harvesting protein, self-assembly monolayer and surface assembly) are more and more complex, reaching (and often passing) the limit of current computation power. In this review, recent developments in computational methods for studying complex interfaces for artificial photosynthesis will be provided and selected cases discussed, to assess the inherent ability of computation to leave a mark in this field of research.

Interplay of vibrational wavepackets during an ultrafast electron transfer reaction

Electron transfer reactions facilitate energy transduction and photoredox processes in biology and chemistry. Recent findings show that molecular vibrations can enable the dramatic acceleration of some electron transfer reactions, and control it by suppressing and enhancing reaction paths. Here, we report ultrafast spectroscopy experiments and quantum dynamics simulations that resolve how quantum vibrations participate in an electron transfer reaction. We observe ballistic electron transfer (~30 fs) along a reaction coordinate comprising high-frequency promoting vibrations. Along another vibrational coordinate, the system becomes impulsively out of equilibrium as a result of the electron transfer reaction. This leads to the generation (by the electron transfer reaction, not the laser pulse) of a new vibrational coherence along this second reaction coordinate in a mode associated with the reaction product. These results resolve a complex reaction trajectory composed of multiple vibrational coordinates that, like a sequence of ratchets, progressively diminish the recurrence of the reactant state.

The Efficiency of Photoinduced Intramolecular Charge Separation from the Second Excited State: What Factors Can Control It?

The efficiency of photoinduced charge separation (CS) in electron donor-acceptor compounds is commonly limited due to fast deactivation processes, such as the excited-state internal conversion and ultrafast hot reverse electron transfer to the acceptor, charge recombination (CR). A traditional way to avoid undesired energy losses due to CR is to put the reverse electron transfer into the Marcus inverted region, thus effectively suppressing it. This method, however, is not generally applicable when considering CS from the second locally excited state because the driving force of CR to the first excited state is small, and thus charge recombination is ultrafast and efficient. In this paper, we study the kinetic features of CS/CR from the second locally excited state of the donor using a semiclassical stochastic model of electron transfer. Particular attention is paid to the CS efficiency as well as the influence of the polar environment and intramolecular high-frequency vibrational modes on the kinetics of the charge-separated state. The influence of a number of model parameters on the CS yield and the energy efficiency has been analyzed using the results of numerical simulations. Several simple practical recipes for creating molecular compounds with high CS yields have been suggested. Simulations have also revealed a strong and non-monotonous (double-humped) dependence of both the yield and energy efficiency of CS on the driving force.

Molecular Dynamics Simulations of Bimolecular Electron Transfer: Testing the Coulomb Term in the Weller Equation

Reliable estimation of the driving force for photoinduced electron transfer between neutral reactants is of utmost importance for most practical applications of these reactions. The driving force is usually calculated from the Weller equation, which contains a Coulomb term, C, whose magnitude in polar solvents is debated. We have performed umbrella sampling molecular dynamics simulations to determine C from the potentials of mean force between neutral and ionic donor/acceptor pairs of different sizes in solvents of varying polarity. According to the simulations, C in polar solvents is a factor of 2 more negative than typically calculated according to the Weller equation. Use of the π-stack contact distance in the Weller equation instead of the van der Waals radius recovers the correct value of C, but this is mostly fortuitous due to the compensating effects of overestimating the dielectric screening at contact and neglecting both charge dilution and desolvation.

Machine-Learning Guided Quantum Chemical and Molecular Dynamics Calculations to Design Novel Hole-Conducting Organic Materials

Materials exhibiting higher mobilities than conventional organic semiconducting materials such as fullerenes and fused thiophenes are in high demand for applications such as printed electronics, organic solar cells, and image sensors. In order to discover new molecules that might show improved charge mobility, combined density functional theory (DFT) and molecular dynamics (MD) calculations were performed, guided by predictions from machine learning (ML). A ML model was constructed based on 32 values of theoretically calculated hole mobilities for thiophene derivatives, benzodifuran derivatives, a carbazole derivative and a perylene diimide derivative with the maximum value of 10^-1.96 cm²/(V s). Sequential learning, also known as active learning, was applied to select compounds on which to perform DFT/MD calculation of hole mobility to simultaneously improve the mobility surrogate model and identify high mobility compounds. By performing 60 cycles of sequential learning with 165 DFT/MD calculations, a molecule having a fused thioacene structure with its calculated hole mobility of 10^-1.86 cm²/(V s) was identified. This values is higher than the maximum value of mobility in the initial training data set, showing that an extrapolative discovery could be made with the sequential learning.

Quantum yield and energy efficiency of photoinduced intramolecular charge separation

Kinetics of photoinduced intramolecular charge separation (CS) and the ensuing ultrafast charge recombination (CR) in electron-donor-acceptor dyads are studied numerically, taking into account the excitation of charge-transfer active intramolecular vibrations and multiple relaxation time scales of the surrounding polar solvent. Both energetic and dynamic properties of intramolecular and solvent reorganization are considered, and their influence on the CS/CR kinetics and quantum yield of ultrafast CS is explored. Particular attention is paid to the energy efficiency of CS, as one of the most important parameters indicating the promise of using a molecular compound as a basis for emerging optoelectronic devices. The CS quantum yield and the energy efficiency of CS are shown to depend differently on the key model parameters. Necessary conditions for the highly efficient CS are evaluated using analytic formulae for the electron transfer rates and derived from numerical simulation data. The reasons why low-exergonic CS taking place in the Marcus normal region can be much slower than CR in the deep inverted region are discussed.

Charge transport in semiconductors assembled from nanocrystal quantum dots

The potential of semiconductors assembled from nanocrystals has been demonstrated for a broad array of electronic and optoelectronic devices, including transistors, light emitting diodes, solar cells, photodetectors, thermoelectrics, and phase change memory cells. Despite the commercial success of nanocrystal quantum dots as optical absorbers and emitters, applications involving charge transport through nanocrystal semiconductors have eluded exploitation due to the inability to predictively control their electronic properties. Here, we perform large-scale, ab initio simulations to understand carrier transport, generation, and trapping in strongly confined nanocrystal quantum dot-based semiconductors from first principles. We use these findings to build a predictive model for charge transport in these materials, which we validate experimentally. Our insights provide a path for systematic engineering of these semiconductors, which in fact offer previously unexplored opportunities for tunability not achievable in other semiconductor systems.

Establishing charge-transfer excitons in 2D perovskite heterostructures

Charge-transfer excitons (CTEs) immensely enrich property-tuning capabilities of semiconducting materials. However, such concept has been remaining as unexplored topic within halide perovskite structures. Here, we report that CTEs can be effectively formed in heterostructured 2D perovskites prepared by mixing PEA₂PbI₄:PEA₂SnI₄, functioning as host and guest components. Remarkably, a broad emission can be demonstrated with quick formation of 3 ps but prolonged lifetime of ~0.5 μs. This broad PL presents the hypothesis of CTEs, verified by the exclusion of lattice distortion and doping effects through demonstrating double-layered PEA₂PbI₄/PEA₂SnI₄ heterostructure when shearing-away PEA₂SnI₄ film onto the surface of PEA₂PbI₄ film by using hand-finger pressing method. The below-bandgap photocurrent indicates that CTEs are vital states formed at PEA₂PbI₄:PEA₂SnI₄ interfaces in 2D perovskite heterostructures. Electroluminescence shows that CTEs can be directly formed with electrically injected carriers in perovskite LEDs. Clearly, the CTEs presents a new mechanism to advance the multifunctionalities in 2D perovskites.

Forming charge transfer excitons (CTEs) exclusively within perovskite structures remains as an unexplored issue. Here, the authors report the establishment of CTEs for demonstrating broad light emission within quasi-2D perovskite heterostructures, presenting “intermolecular-type” excited states.

Long-Range Exciton Diffusion via Singlet Revival Mechanism

We clarify the mechanism that leads to extended exciton diffusion length in organic materials which exhibit a strong anisotropy of electronic coupling. We analyze the cooperative effects of singlet fission and triplet-triplet annihilation in the exciton diffusion by means of the dynamic Monte Carlo simulations. As a model system, we consider the rubrene crystal which exhibits a long-range exciton diffusion. The deexcitation of the singlet exciton is suppressed by singlet → triplet conversion via singlet fission. Even though the triplet exciton would hardly diffuse along the c-axis in the rubrene crystal (perpendicular to the high mobility plane) because of the small electronic coupling, the regeneration of the singlet exciton via triplet-triplet annihilation enables long-range exciton diffusion along the c-axis. This singlet revival mechanism can extend the overall lifetime and the diffusion length of the exciton, through back-and-forth transitions between an isotropically diffusing singlet exciton and a long-lived triplet exciton.

Unified Model for Photophysical and Electro-Optical Properties of Green Fluorescent Proteins

Green fluorescent proteins (GFPs) have become indispensable imaging and optogenetic tools. Their absorption and emission properties can be optimized for specific applications. Currently, no unified framework exists to comprehensively describe these photophysical properties, namely the absorption maxima, emission maxima, Stokes shifts, vibronic progressions, extinction coefficients, Stark tuning rates, and spontaneous emission rates, especially one that includes the effects of the protein environment. In this work, we study the correlations among these properties from systematically tuned GFP environmental mutants and chromophore variants. Correlation plots reveal monotonic trends, suggesting that all these properties are governed by one underlying factor dependent on the chromophore's environment. By treating the anionic GFP chromophore as a mixed-valence compound existing as a superposition of two resonance forms, we argue that this underlying factor is defined as the difference in energy between the two forms, or the driving force, which is tuned by the environment. We then introduce a Marcus-Hush model with the bond length alternation vibrational mode, treating the GFP absorption band as an intervalence charge transfer band. This model explains all of the observed strong correlations among photophysical properties; related subtopics are extensively discussed in the Supporting Information. Finally, we demonstrate the model's predictive power by utilizing the additivity of the driving force. The model described here elucidates the role of the protein environment in modulating the photophysical properties of the chromophore, providing insights and limitations for designing new GFPs with desired phenotypes. We argue that this model should also be generally applicable to both biological and nonbiological polymethine dyes.

Ergodicity-Breaking in Thermal Biological Electron Transfer? Cytochrome C Revisited

It was recently suggested that certain redox proteins operate in an ergodicity-breaking regime to facilitate biological electron transfer (ET). A signature for this is a large variance reorganization free energy (several electronvolts) but a significantly smaller Stokes reorganization free energy due to incomplete protein relaxation on the time scale of the ET event. Here we investigate whether this picture holds for oxidation of cytochrome c in aqueous solution, at various levels of theory including classical molecular dynamics with two additive and one electronically polarizable force field, and QM/MM calculations with the QM region treated by full electrostatic DFT embedding and by the perturbed matrix method. Sampling the protein and energy gap dynamics over more than 250 ns, we find no evidence for ergodicity-breaking effects. In particular, the inclusion of electronic polarizability of the heme group at QM/MM levels did not induce nonergodic effects, contrary to previous reports by Matyushov et al. The well-known problem of overestimation of reorganization free energies with additive force fields is cured when the protein and solvent are treated as electronically polarizable. Ergodicity-breaking effects may occur in other redox proteins, and our results suggest that long simulations, ideally on the ET time scale, with electronically polarizable force fields are required to obtain strong numerical evidence for them.

Regioselective Ultrafast Photoinduced Electron Transfer from Naphthols to Halocarbon Solvents

Excited state decay of 2-naphthol (2N) in halocarbon solvents has been observed to be significantly slower when compared to that of 1-naphthol (1N). In this study, we provide new physical insights behind this observation by exploring the regioselective electron transfer (ET) mechanism from photoexcited 1N and 2N to halocarbon solvents at a detailed molecular level. Using state-of-the-art electronic structure calculations, we explore several configurations of naphthol-chloroform complexes and find that the proximity of the electron-accepting chloroform molecule to the electron-rich -OH group of the naphthol is the dominant factor affecting electron transfer rates. The origin of significantly slower electron transfer rates for 2N is traced back to the notably smaller electronic coupling when the electron-accepting chloroform molecule is on top of the aromatic ring distal to the -OH group. Our findings suggest that regioselective photoinduced electron transfer could thus be exploited to control electron transfer in substituted acenes tailored for specific applications.

Intramolecular Long-Range Charge-Transfer Emission in Donor-Bridge-Acceptor Systems

Charge recombination to the electronic ground state typically occurs nonradiatively. We report a rational design of donor-bridge-acceptor molecules that exhibit charge-transfer (CT) emission through conjugated bridges over distances of up to 24 Å. The emission is enhanced by intensity borrowing and extends into the near-IR region. Efficient charge recombination to the initial excited state results in recombination fluorescence. We have established the identity of CT emission by solvent dependence, sensitivity to temperature, femtosecond transient absorption spectroscopy, and unique emission polarization patterns. Large excited-state electronic couplings and small energy gaps enable the observation of intramolecular long-range CT emission over the unprecedented long distance. These results open new possibilities of using intramolecular long-range CT emission in molecular electronic and biomedical imaging probe applications.

Electron transfer in confined electromagnetic fields

The interaction between molecular (atomic) electron(s) and the vacuum field of a reflective cavity generates significant interest, thanks to the rapid developments in nanophotonics. Such interaction which lies within the realm of cavity quantum electrodynamic can substantially affect the transport properties of molecular systems. In this work, we consider a nonadiabatic electron transfer process in the presence of a cavity mode. We present a generalized framework for the interaction between a charged molecular system and a quantized electromagnetic field of a cavity and apply it to the problem of electron transfer between a donor and an acceptor placed in a confined vacuum electromagnetic field. The effective system Hamiltonian corresponds to a unified Rabi and spin-boson model which includes a self-dipole energy term. Two limiting cases are considered: one where the electron is assumed much faster than the cavity mode and another in which the electron tunneling time is significantly larger than the mode period. In both cases, a significant rate enhancement can be produced by coupling to the cavity mode in the Marcus inverted region. The results of this work offer new possibilities for controlling electron transfer processes using visible and infrared plasmonics.

Two-Dimensional Electronic Transport in Rubrene: The Impact of Inter-Chain Coupling

Organic semi-conductors have unique electronic properties and are important systems both at the fundamental level and also for their applications in electronic devices. In this article we focus on the particular case of rubrene which has one of the best electronic transport properties for application purposes. We show that this system can be well simulated by simple tight-binding systems representing one-dimensional (1D) chains that are weakly coupled to their neighboring chains in the same plane. This makes in principle this rubrene system somehow intermediate between 1D and isotropic 2D models. We analyse in detail the dc-transport and terahertz conductivity in the 1D and in the anisotropic 2D models. The transient localisation scenario allows us to reproduce satisfactorily some basics results such as mobility anisotropy and orders of magnitude as well as ac-conductivity in the terahertz range. This model shows in particular that even a weak inter-chain coupling is able to improve notably the propagation along the chains. This suggest also that a strong inter-chain coupling is important to get organic semi-conductors with the best possible transport properties for applicative purposes.

Thermodynamics of Reactions Affected by Medium Reorganization

We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc.). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager's reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not allow reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved. Proteins provide several routes for achieving large entropic effects through incomplete (nonergodic) sampling of the complex energy landscape and by facilitating an active role of water in the reaction mechanism.

Salt Effect in Ion-Pair Dynamics after Bimolecular Photoinduced Electron Transfer in a Room-Temperature Ionic Liquid

Bimolecular photoinduced electron transfer between perylene and two quenchers was investigated in an imidazolium room-temperature ionic liquid (RTIL) and in a dipolar solvent mixture of the same viscosity using transient absorption on the subpicosecond to submicrosecond time scales. Whereas charge separation dynamics were similar in both solvents, significant differences were observed in the temporal evolution of the ensuing radical ions: although small, the free-ion yield is significantly larger in the RTIL, and recombination of the ion pair to the triplet state of perylene is more efficient in the dipolar solvent. The temporal evolution of reactant, ion, and triplet state populations could be well reproduced using unified encounter theory. This analysis reveals that the observed differences can be explained by the strong screening of the Coulomb potential in the ion pair by the ionic solvent. In essence, RTILs favor free ions compared to highly dipolar solvents of the same viscosity.

Coarse-grained representation of the quasi adiabatic propagator path integral for the treatment of non-Markovian long-time bath memory

The description of non-Markovian effects imposed by low frequency bath modes poses a persistent challenge for path integral based approaches like the iterative quasi-adiabatic propagator path integral (iQUAPI) method. We present a novel approximate method, termed mask assisted coarse graining of influence coefficients (MACGIC)-iQUAPI, that offers appealing computational savings due to substantial reduction of considered path segments for propagation. The method relies on an efficient path segment merging procedure via an intermediate coarse grained representation of Feynman-Vernon influence coefficients that exploits physical properties of system decoherence. The MACGIC-iQUAPI method allows us to access the regime of biological significant long-time bath memory on the order of hundred propagation time steps while retaining convergence to iQUAPI results. Numerical performance is demonstrated for a set of benchmark problems that cover bath assisted long range electron transfer, the transition from coherent to incoherent dynamics in a prototypical molecular dimer and excitation energy transfer in a 24-state model of the Fenna-Matthews-Olson trimer complex where in all cases excellent agreement with numerically exact reference data is obtained.

Termination of Biological Function at Low Temperatures: Glass or Structural Transition?

Energy of life is produced by electron transfer in energy chains of respiration or photosynthesis. A small input of free energy available to biology puts significant restrictions on how much free energy can be lost in each electron-transfer reaction. We advocate the view that breaking ergodicity, leading to violation of the fluctuation-dissipation theorem (FDT), is how proteins achieve high reaction rates without sacrificing the reaction free energy. Here we show that a significant level of nonergodicity, represented by a large extent of the configurational temperature over the kinetic temperature, is maintained in the entire physiological range for the cytochrome c electron transfer protein. The protein returns to the state consistent with the FDT below the crossover temperature close to the temperature of the protein glass transition. This crossover leads to a sharp increase in the activation barrier of electron transfer and is displayed by a kink in the Arrhenius plot for the reaction rate constant.

Charge-Transfer Knowledge Graph among Amino Acids Derived from High-Throughput Electronic Structure Calculations for Protein Database

The charge-transfer coupling is an important component in tight-binding methods. Because of the highly complex chemical structure of biomolecules, the anisotropic feature of charge-transfer couplings in realistic proteins cannot be ignored. In this work, we have performed the first large-scale quantitative assessment of charge-transfer preference by calculating the charge-transfer couplings in all 20 × 20 possible amino acid side-chain combinations, which are extracted from available high-quality structures of thousands of protein complexes. The charge-transfer database quantitatively shows distinct features of charge-transfer couplings among millions of amino acid side-chain combinations. The overall distribution of charge-transfer couplings reveals that only one average or representative structure cannot be regarded as the typical charge-transfer preference in realistic proteins. This work provides us an alternative route to comprehensively understand the charge-transfer couplings for the overall distribution of realistic proteins in the foreseen big data scenario.

Measuring the Vibrational Density of States of Nanocrystal-Based Thin Films with Inelastic X-ray Scattering

Knowledge of the vibrational structure of a semiconductor is essential for explaining its optical and electronic properties and enabling optimized materials selection for optoelectronic devices. However, measurement of the vibrational density of states of nanomaterials is challenging. Here, using the example of colloidal nanocrystals (quantum dots), we show that the vibrational density of states of nanomaterials can be accurately and efficiently measured with inelastic X-ray scattering (IXS). Using IXS, we report the first experimental measurements of the vibrational density of states for lead sulfide nanocrystals with different halide-ion terminations and for CsPbBr₃ perovskite nanocrystals. IXS findings are supported with ab initio molecular dynamics simulations, which provide insight into the origin of the measured vibrational structure and the effect of nanocrystal surface. Our findings highlight the advantages of IXS compared to other methods for measuring the vibrational density of states of nanocrystals such as inelastic neutron scattering and Raman scattering.

Reassessment of the Four-Point Approach to the Electron-Transfer Marcus-Hush Theory

The Marcus-Hush theory has been successfully applied to describe and predict the activation barriers and hence the electron-transfer (ET) rates in several physicochemical and biological systems. This theory assumes that in the ET reaction, the geometry of the free Gibbs energy landscape is parabolic, with equal curvature near the local minimum for both reactants and products. In spite of its achievements, more realistic models have included the assumption of the two parabolas having not the same curvature. This situation is analyzed by the Nelsen's four-point method. As a benchmark to compare the Marcus-Hush approximation to a precise calculation of the excitation energy, we studied the non-ET process of the electronic excitation of the aluminum dimer that has two local minima (³∑_g ^- and ³∏_u electronic states) and allows to obtain analytically the Marcus-Hush nonsymmetric parameters. We appraise the ability of the Marcus-Hush formula to approximate the analytical results by using several averages of the two reorganization energies associated with the forward and backward transitions and analyze the error. It is observed that the geometric average minimizes the relative error and that the analytical case is recovered. The main results of this paper are obtained by the application of the Nelsen's four-point method to compute the reorganization energies of a large set of potential π-conjugated molecules proposed for organic photovoltaic devices using the above-mentioned averages for the Marcus-Hush formula. The activation energies obtained with the geometric average are significantly larger for some donor-acceptor pairs in comparison with the previously employed arithmetic average, their differences being suitable for experimental testing.