Recent Advances in the Theory and Molecular Simulation of Biological Electron Transfer Reactions

Protein Medium Facilitates Electron Transfer in Photosynthetic Heliobacterial Reaction Center

This computational study addresses the question of how large membrane-bound proteins of electron transport chains facilitate fast vector-based charge transport. We study electron transfer reactions following ultrafast initial charge separation induced by absorption of light by P800 primary pair and leading to the electron localization at the A0 cofactor. Two subsequent, much slower reactions, electron transfer to the iron-sulfur cluster Fx and reduction of the menaquinone (MQ) cofactor, are studied by combining molecular dynamics simulations, electronic structure calculations, and theoretical modeling. The low value of the electronic coupling between A0 and Fx brings this reaction to the microsecond time scale even at the zero activation barrier. In contrast, A0-MQ electron transfer occurs on a subnanosecond time scale and might become the preferred route for charge transport. We elucidate mechanistic properties of the protein medium allowing fast, vectorial charge transfer. The electric field is high and inhomogeneous inside the protein and is coupled to high polarizabilities of cofactors to significantly lower the reaction barrier. The A0-MQ separation puts this reaction at the edge between the plateau characterizing the reaction dynamical control and exponential falloff due to electronic tunneling. A strong separation in relaxation times of the medium dynamics for the forward and backward reactions promotes vectorial charge transfer.

Electron transport chain-inspired coordination polymers for macroscopic spatiotemporal scales of charge separation and transport in photocatalysis

Classic homogeneous photocatalysis is limited by the temporal transience and the spatial proximity of photoinduced charge separation and transport. The electron transfer chain (ETC) in cellular respiration can mediate unidirectional and long-range electron transfer to isolate the oxidation and reduction centres. Inspired by this, we modified electron-accepting (A) viologen with π-extending thiazolothiazole and electron-donating (D) phenyl carboxylate into a D-A-π-A-D-type ligand and assembled segregated dye stacking in coordination polymer Cd-TzBDP for breaking the spatiotemporal limitation of single-molecule photocatalysis. The offset characteristics of D-A segregated stacking not only allowed the photoinduced-2e- transfer from the D-type carboxylate terminal to the spatially adjacent A-type viologen motif within 1 ps but also permitted the following delocalization of e- and h+ along stacked columns. These advantages endowed Cd-TzBDP with long-lived photochromic visualization of intermittent aerobic photooxidation steps, which enabled the bioinspired ETC-mediated aerobic respiration of mitochondria, achieving the continuous photocatalytic α-C(sp3)-H functionalization of tertiary amines with pharmaceutical interest. Enlightened by ETC-mediated electron leak in hypoxia, the coordination polymer was further employed in a photocatalytic membrane reactor, which visually illustrated the photo-driven cross-membrane long-range transfers of multiple electrons and protons from the hypoxic compartment to normoxic one, benefiting the distal photooxidation and photoreduction with biomimetic compartment selectivity.

Semiclassical dynamics in Wigner phase space II: Nonadiabatic hybrid Wigner dynamics

We present an approximate semiclassical (SC) framework for mixed quantized dynamics in Wigner phase space in a two-part series. In the first article, we introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method that allows for a few important "system" degrees of freedom to be quantized using high-level double Herman-Kluk SC theory while describing the rest (the "bath") using classical-limit linearized SC theory. In this second article, we extend our hybrid Wigner dynamics to nonadiabatic processes. The resulting Nonadiabatic Hybrid Wigner Dynamics (NHWD) has two variants that differ in the choice of degrees of freedom to be quantized. Specifically, we introduce NHWD(E) where only the electronic state variables are quantized and the NHWD(V) where both electronic state variables and a handful of strongly coupled nuclear modes are quantized. We show that while NHWD(E) proves accurate for a wide range of scattering models and spin-boson models, systems where a few nuclear modes are strongly coupled to electronic states require NHWD(V) to accurately capture the long-time dynamics. Taken together, we show that AHWD and NHWD represent a new framework for SC simulations of high-dimensional systems with significant quantum effects.

Multiconfigurational Surface Hopping: a Time-Dependent Variational Approach with Momentum-Jump Trajectories

The Ehrenfest mean field dynamics and trajectory surface hopping have been widely used in nonadiabatic dynamics simulations. Based on the time-dependent variational principle (TDVP), the multiconfigurational Ehrenfest (MCE) method has also been developed and can be regarded as a multiconfigurational extension of the traditional Ehrenfest dynamics. However, it is not straightforward to apply the TDVP to surface hopping trajectories because there exists momentum jump during surface hops. To solve this problem, we here propose a multiconfigurational surface hopping (MCSH) method, where continuous momenta are obtained by linear interpolation and the interpolated trajectories are used to construct the basis functions for TDVP in a postprocessing manner. As demonstrated in a series of representative spin-boson models, MCSH achieves high accuracy with only several hundred trajectory bases and can uniformly improve the performance of surface hopping. In principle, MCSH can be combined with all kinds of mixed quantum-classical trajectories and thus has the potential to properly describe general nonadiabatic dynamics.

Electrochemical and quantum chemical approaches to the study of dopamine sensing using bentonite and l-cysteine modified carbon paste electrode

This work presents a significant investigation involving both electrochemical experiment and quantum chemical simulation approaches. The objective was to characterize the electrochemical detection of dopamine (DA). The detection was carried out using a modified carbon paste electrode (CPE) incorporating bentonite (Bent) and l-cysteine (CySH) (named as CySH/Bent/CPE). To understand and explain the oxidation mechanism of DA on the CySH/Bent modified electrode surface, the coupling of the two approaches were exploited. The CySH/Bent/CPE showed excellent electroactivity toward DA such as good sensibility, selectivity, stability, and regenerative ability. The developed sensor shows a dynamic linear range from 0.8 to 80 μM with a limit of detection and quantification of 0.5 μM and 1.5 μM, respectively. During the quantitative analysis of DA in presence of ascorbic acid (AA) and uric acid (UA) the electrochemical oxidation signals of AA, DA, and UA distinctly appear as three separate peaks. The potential differences between the peaks are 190 mv, 150 mv, and 340 mV for the AA-DA, DA-UA, and AA-UA oxidation pairs, respectively. These observations stem from square wave voltammetry (SWV) studies, along with the corresponding redox peak potential separations. The developed sensor is simple and accurate to monitor DA in human serum samples. On the other hand, CySH acts as an electrocatalyst on the CySH/Bent/CPE surface by increasing its active electron transfer sites, as suggested by the quantum chemical modeling with analytical results of Fukui. Furthermore, the voltammetric results obtained agree well with the theoretical calculations.

Revisiting Solar Energy Flow in Nanomaterial-Microorganism Hybrid Systems

Nanomaterial-microorganism hybrid systems (NMHSs), integrating semiconductor nanomaterials with microorganisms, present a promising platform for broadband solar energy harvesting, high-efficiency carbon reduction, and sustainable chemical production. While studies underscore its potential in diverse solar-to-chemical energy conversions, prevailing NMHSs grapple with suboptimal energy conversion efficiency. Such limitations stem predominantly from an insufficient systematic exploration of the mechanisms dictating solar energy flow. This review provides a systematic overview of the notable advancements in this nascent field, with a particular focus on the discussion of three pivotal steps of energy flow: solar energy capture, cross-membrane energy transport, and energy conversion into chemicals. While key challenges faced in each stage are independently identified and discussed, viable solutions are correspondingly postulated. In view of the interplay of the three steps in affecting the overall efficiency of solar-to-chemical energy conversion, subsequent discussions thus take an integrative and systematic viewpoint to comprehend, analyze and improve the solar energy flow in the current NMHSs of different configurations, and highlighting the contemporary techniques that can be employed to investigate various aspects of energy flow within NMHSs. Finally, a concluding section summarizes opportunities for future research, providing a roadmap for the continued development and optimization of NMHSs.

Understanding Nanoscale Interactions between Minerals and Microbes: Opportunities for Green Remediation of Contaminated Sites

In situ contaminant degradation and detoxification mediated by microbes and minerals is an important element of green remediation. Improved understanding of microbe-mineral interactions on the nanoscale offers promising opportunities to further minimize the environmental and energy footprints of site remediation. In this Perspective, we describe new methodologies that take advantage of an array of multidisciplinary tools─including multiomics-based analysis, bioinformatics, machine learning, gene editing, real-time spectroscopic and microscopic analysis, and computational simulations─to identify the key microbial drivers in the real environments, and to characterize in situ the dynamic interplay between minerals and microbes with high spatiotemporal resolutions. We then reflect on how the knowledge gained can be exploited to modulate the binding, electron transfer, and metabolic activities at the microbe-mineral interfaces, to develop new in situ contaminant degradation and detoxication technologies with combined merits of high efficacy, material longevity, and low environmental impacts. Two main strategies are proposed to maximize the synergy between minerals and microbes, including using mineral nanoparticles to enhance the versatility of microorganisms (e.g., tolerance to environmental stresses, growth and metabolism, directed migration, selectivity, and electron transfer), and using microbes to synthesize and regenerate highly dispersed nanostructures with desired structural/surface properties and reactivity.

Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime

Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus-Levich-Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane-anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes.

Electronic Transport Properties of Molecular Clusters Sb4O6, P4Se3, and P4O6

Inorganic molecular crystal (IMC) is a trending class of materials in which structural units comprise molecular cages or clusters bonded via van der Waal forces. The structure-property relationship in IMCs is less known due to the unusual assembly of molecular clusters in these materials. In this paper, the density functional theory-calculated electronic transport properties of the molecular clusters of antimony oxide (Sb4O6), phosphorus triselenide (P4Se3), and phosphorus trioxide (P4O6) are described in detail. The calculated values of highest occupied molecular orbital-lowest unoccupied molecular orbital gaps appeared as 5.487, 2.296, and 4.425 eV for Sb4O6, P4Se3, and P4O6, respectively. The work was carried out to explore the charge transport mechanism in IMCs in order to disclose their potential in practical applications. The calculations involved charge-transfer integral based on Marcus theory to compute the electronic coupling (V), reorganization energies (λ), and hopping rate (k) in the structures. The hopping rate for Sb4O6, P4Se3, and P4O6 is found as 8.49 × 10-12, 1.28 × 10-14, and 2.51 × 10-20 s-1, respectively. The transport properties of Sb4O6 are found better, which predicts the application of the relevant IMC for device grade applications. The findings of this study are important for future application of the IMCs in electronic and optoelectronic applications.

Long-range charge transfer mechanism of the III2IV2 mycobacterial supercomplex

Aerobic life is powered by membrane-bound redox enzymes that shuttle electrons to oxygen and transfer protons across a biological membrane. Structural studies suggest that these energy-transducing enzymes operate as higher-order supercomplexes, but their functional role remains poorly understood and highly debated. Here we resolve the functional dynamics of the 0.7 MDa III2IV2 obligate supercomplex from Mycobacterium smegmatis, a close relative of M. tuberculosis, the causative agent of tuberculosis. By combining computational, biochemical, and high-resolution (2.3 Å) cryo-electron microscopy experiments, we show how the mycobacterial supercomplex catalyses long-range charge transport from its menaquinol oxidation site to the binuclear active site for oxygen reduction. Our data reveal proton and electron pathways responsible for the charge transfer reactions, mechanistic principles of the quinone catalysis, and how unique molecular adaptations, water molecules, and lipid interactions enable the proton-coupled electron transfer (PCET) reactions. Our combined findings provide a mechanistic blueprint of mycobacterial supercomplexes and a basis for developing drugs against pathogenic bacteria.

Properties of the iron-sulfur cluster electron transfer relay in an [FeFe]-hydrogenase that is tuned for H2 oxidation catalysis

[FeFe]-hydrogenases catalyze the reversible oxidation of H2 from electrons and protons at an organometallic active site cofactor named the H-cluster. In addition to the H-cluster, most [FeFe]-hydrogenases possess accessory FeS cluster (F-cluster) relays that function in mediating electron transfer with catalysis. There is significant variation in the structural properties of F-cluster relays among the [FeFe]-hydrogenases; however, it is unknown how this variation relates to the electronic and thermodynamic properties, and thus the electron transfer properties, of enzymes. Clostridium pasteurianum [FeFe]-hydrogenase II (CpII) exhibits a large catalytic bias for H2 oxidation (compared to H2 production), making it a notable system for examining if F-cluster properties contribute to the overall function and efficiency of the enzyme. By applying a combination of multifrequency and potentiometric electron paramagnetic resonance, we resolved two electron paramagnetic resonance signals with distinct power- and temperature-dependent properties at g = 2.058 1.931 1.891 (F2.058) and g = 2.061 1.920 1.887 (F2.061), with assigned midpoint potentials of -140 ± 18 mV and -406 ± 12 mV versus normal hydrogen electrode, respectively. Spectral analysis revealed features consistent with spin-spin coupling between the two [4Fe-4S] F-clusters, and possible functional models are discussed that account for the contribution of coupling to the electron transfer landscape. The results signify the interplay of electronic coupling and free energy properties and parameters of the FeS clusters to the electron transfer mechanism through the relay and provide new insight as to how relays functionally complement the catalytic directionality of active sites to achieve highly efficient catalysis.

Direct observation of electron transfer in solids through X-ray crystallography

Nanoscale electron transfer (ET) in solids is fundamental to the design of multifunctional nanomaterials, yet its process is not fully understood. Herein, through X-ray crystallography, we directly observe solid-state ET via a crystal-to-crystal process. We first demonstrate the creation of a robust and flexible electron acceptor/acceptor (A/A) double-wall nanotube crystal ([(Zn2+)4(LA)4(LA=O)4]n) with a large window (0.90 nm × 0.92 nm) through the one-dimensional porous crystallization of heteroleptic Zn4 metallocycles ((Zn2+)4(LA)4(LA=O)4) with two different acceptor ligands (2,7-bis((1-ethyl-1H-imidazol-2-yl)ethynyl)acridine (LA) and 2,7-bis((1-ethyl-1H-imidazol-2-yl)ethynyl)acridin-9(10H)-one (LA=O)) in a slow-oxidation-associated crystallization procedure. We then achieve the bottom-up construction of the electron donor incorporated-A/A nanotube crystal ([(D)2⊂(Zn2+)4(LA)4(LA=O)4]n) through the subsequent absorption of electron donor guests (D = tetrathiafulvalene (TTF) and ferrocene (Fc)). Finally, we remove electrons from the electron donor guests inside the nanotube crystal through facile ET in the solid state to accumulate holes inside the nanotube crystal ([(D•+)2⊂(Zn2+)4(LA)4(LA=O)4]n), where the solid-state ET process (D - e- → D•+) is thus observed directly by X-ray crystallography.

Unraveling the mechanisms of triplet state formation in a heavy-atom free photosensitizer

Triplet excited state generation plays a pivotal role in photosensitizers, however the reliance on transition metals and heavy atoms can limit the utility of these systems. In this study, we demonstrate that an interplay of competing quantum effects controls the high triplet quantum yield in a prototypical boron dipyrromethene-anthracene (BD-An) donor-acceptor dyad photosensitizer, which is only captured by an accurate treatment of both inner and outer sphere reorganization energies. Our ab initio-derived model provides excellent agreement with experimentally measured spectra, triplet yields and excited state kinetic data, including the triplet lifetime. We find that rapid triplet state formation occurs primarily via high-energy triplet states through both spin-orbit coupled charge transfer and El-Sayed's rule breaking intersystem crossing, rather than direct spin-orbit coupled charge transfer to the lowest lying triplet state. Our calculations also reveal that competing effects of nuclear tunneling, electronic state recrossing, and electronic polarizability dictate the rate of non-productive ground state recombination. This study sheds light on the quantum effects driving efficient triplet formation in the BD-An system, and offers a promising simulation methodology for diverse photochemical systems.

Controlling the charge-transfer dynamics of two-level systems around avoided crossings

Two-level quantum systems are fundamental physical models that continue to attract growing interest due to their crucial role as a building block of quantum technologies. The exact analytical solution of the dynamics of these systems is central to control theory and its applications, such as that to quantum computing. In this study, we reconsider the two-state charge transfer problem by extending and using a methodology developed to study (pseudo)spin systems in quantum electrodynamics contexts. This approach allows us to build a time evolution operator for the charge transfer system and to show new opportunities for the coherent control of the system dynamics, with a particular emphasis on the critical dynamic region around the transition state coordinate, where the avoided crossing of the energy levels occurs. We identify and propose possible experimental implementations of a class of rotations of the charge donor (or acceptor) that endow the electronic coupling matrix element with a time-dependent phase that can be employed to realize controllable coherent dynamics of the system across the avoided level crossing. The analogy of these rotations to reference frame rotations in generalized semiclassical Rabi models is discussed. We also show that the physical rotations in the charge-transfer systems can be performed so as to implement quantum gates relevant to quantum computing. From an exquisitely physical-mathematical viewpoint, our approach brings to light situations in which the time-dependent state of the system can be obtained without resorting to the special functions appearing in the Landau-Zener approach.

Probing Nonadiabaticity of Proton-Coupled Electron Transfer in Ribonucleotide Reductase

The enzyme ribonucleotide reductase, which is essential for DNA synthesis, initiates the conversion of ribonucleotides to deoxyribonucleotides via radical transfer over a 32 Å pathway composed of proton-coupled electron transfer (PCET) reactions. Previously, the first three PCET reactions in the α subunit were investigated with hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations. Herein, the fourth PCET reaction in this subunit between C439 and guanosine diphosphate (GDP) is simulated and found to be slightly exoergic with a relatively high free energy barrier. To further elucidate the mechanisms of all four PCET reactions, we analyzed the vibronic and electron-proton nonadiabaticities. This analysis suggests that interfacial PCET between Y356 and Y731 is vibronically and electronically nonadiabatic, whereas PCET between Y731 and Y730 and between C439 and GDP is fully adiabatic and PCET between Y730 and C439 is in the intermediate regime. These insights provide guidance for selecting suitable rate constant expressions for these PCET reactions.

Calculation of Charge Transport Phenomena and Mobility Analysis in the Insulating Oil Using First Principle and Marcus Theory

Oil-paper insulation is widely used as a reliable composite insulation system in power transformers. The dielectric property of oil insulation plays an important role in the reliable operation of power equipment. To recognize the charge transfer process in composite insulation, the mobility of the charge in aged insulating oil is studied. However, few studies have been conducted on the microscopic mechanism of charge transport phenomena at the molecular level. In this research, we have studied the molecular electronic structure and the distribution of holes and electrons in the insulating oil by first-principles calculation. By combining with Marcus theory, the corresponding electron coupling energy, reorganization energy, and free energy are obtained. The corresponding charge hopping model is chosen by the parameter relation, and the hopping rate is calculated. At last, the mobility of holes and electrons in insulating oil within the insulation is simulated by the Monte Carlo method. Other possible charge migration methods are also studied and discussed for the comparison. It is observed that the transfer integral of electrons is 2 orders of magnitude larger than that of holes, which is mostly due to the localization of lowest unoccupied molecular orbitals (LUMO). The hole and charge transfers accord with Marcus hopping, the adiabatic charge transfer model, and the charge hopping rate is obtained. The actual free energy action under an external electric field is obtained by calculating polarizability and permittivity. Monte Carlo simulation is used to obtain the charge transfer image and mobility under an actual electric field. Possible types of traps and mobility of ions and clusters in the insulating oil are also studied.

On the application of Marcus-Hush theory to small polaron chemical dynamics in oxides: its relationship to the Holstein model and the importance of lattice-orbital symmetries

The chemical dynamics of small polaron hopping within oxides is often interpreted through two-site variations on Marcus-Hush theory, while from a physics perspective small polaron hopping is more often approached from Holstein's solid-state formalism. Here we seek to provide a chemically oriented viewpoint, focusing on small polaron hopping in oxides, concerning these two phenomenological frameworks by employing both tight-binding modelling and first-principles calculations. First, within a semiclassical approach the Marcus-Hush relations are overviewed as a two-site reduction of Holstein's model. Within the single-band regime, similarities and differences between Holstein derived small polaron hopping and the Marcus-Hush model are also discussed. In this context the emergence of adiabaticity (or, conversely, diabaticity) is also explored within each framework both analytically and by directly evolving the system wavefunction. Then, through first-principles calculations of select oxides we explore how coupled lattice and orbital symmetries can impact on hopping properties - in a manner that is quite distinct typical chemical applications of Marcus-Hush theory. These results are then related back to the Holstein model to explore the relative applicability of the two frameworks towards interpreting small polaron hopping properties, where it is emphasized that the Holstein model offers an increasingly more appealing physicochemical interpretation of hopping processes as band and/or coupling interactions increase. Overall, this work aims to strengthen the physically oriented exploration of small polarons and their physicochemical properties in the growing oxide chemistry community.

Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping

It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.

A model analysis of centimeter-long electron transport in cable bacteria

The recent discovery of cable bacteria has greatly expanded the known length scale of biological electron transport, as these multi-cellular bacteria are capable of mediating electrical currents across centimeter-scale distances. To enable such long-range conduction, cable bacteria embed a network of regularly spaced, parallel protein fibers in their cell envelope. These fibers exhibit extraordinary electrical properties for a biological material, including an electrical conductivity that can exceed 100 S cm-1. Traditionally, long-range electron transport through proteins is described as a multi-step hopping process, in which the individual hopping steps are described by Marcus electron transport theory. Here, we investigate to what extent such a classical hopping model can explain the conductance data recorded for individual cable bacterium filaments. To this end, the conductive fiber network in cable bacteria is modelled as a set of parallel one-dimensional hopping chains. Comparison of model simulated and experimental current(I)/voltage(V) curves, reveals that the charge transport is field-driven rather than concentration-driven, and there is no significant injection barrier between electrodes and filaments. However, the observed high conductivity levels (>100 S cm-1) can only be reproduced, if we include much longer hopping distances (a > 10 nm) and lower reorganisation energies (λ < 0.2 eV) than conventionally used in electron relay models of protein structures. Overall, our model analysis suggests that the conduction mechanism in cable bacteria is markedly distinct from other known forms of long-range biological electron transport, such as in multi-heme cytochromes.

Electron transfer reaction of TEMPO-based organic radical batteries in different solvent environments: comparing quantum and classical approaches

In this study, we delve into the complex electron transfer reactions associated with the redox-active (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO), a common component in organic radical batteries (ORBs). Our approach estimates quantum electron-transfer (ET) energies using Density Functional Theory (DFT) calculations by sampling from structures simulated classically. This work presents a comparative study of reorganization energies in ET reactions across different solvents. Furthermore, we investigate how changes in the electrolyte environment can modify the reorganization energy and, consequently, impact ET dynamics. We also explore the relationship between classical and quantum vertical energies using linear regression models. Importantly, this comparison between quantum and classical vertical energies underscores the role of quantum effects, like charge delocalization, in offering added stabilization post-redox reactions. These effects are not adequately represented by the classical vertical energy distribution. Our study shows that, although we find a significant correlation between the vertical energies computed by DFT and the classical force field, the regression parameters depend on the solvent, highlighting that classical methods should be benchmarked by DFT before applying them to novel electrolyte materials.

Tryptophan to Tryptophan Hole Hopping in an Azurin Construct

Electron transfer (ET) between neutral and cationic tryptophan residues in the azurin construct [ReI(H126)(CO)3(dmp)](W124)(W122)CuI (dmp = 4,7-Me2-1,10-phenanthroline) was investigated by Born-Oppenheimer quantum-mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) simulations. We focused on W124•+ ← W122 ET, which is the middle step of the photochemical hole-hopping process *ReII(CO)3(dmp•-) ← W124 ← W122 ← CuI, where sequential hopping amounts to nearly 10,000-fold acceleration over single-step tunneling (ACS Cent. Sci. 2019, 5, 192-200). In accordance with experiments, UKS-DFT QM/MM/MD simulations identified forward and reverse steps of W124•+ ↔ W122 ET equilibrium, as well as back ET ReI(CO)3(dmp•-) → W124•+ that restores *ReII(CO)3(dmp•-). Strong electronic coupling between the two indoles (≥40 meV in the crossing region) makes the productive W124•+ ← W122 ET adiabatic. Energies of the two redox states are driven to degeneracy by fluctuations of the electrostatic potential at the two indoles, mainly caused by water solvation, with contributions from the protein dynamics in the W122 vicinity. ET probability depends on the orientation of Re(CO)3(dmp) relative to W124 and its rotation diminishes the hopping yield. Comparison with hole hopping in natural systems reveals structural and dynamics factors that are important for designing efficient hole-hopping processes.

Fluctuation Relations to Calculate Protein Redox Potentials from Molecular Dynamics Simulations

The tunable design of protein redox potentials promises to open a range of applications in biotechnology and catalysis. Here, we introduce a method to calculate redox potential changes by combining fluctuation relations with molecular dynamics simulations. It involves the simulation of reduced and oxidized states, followed by the instantaneous conversion between them. Energy differences introduced by the perturbations are obtained using the Kubo-Onsager approach. Using a detailed fluctuation relation coupled with Bayesian inference, these are postprocessed into estimates for the redox potentials in an efficient manner. This new method, denoted MD + CB, is tested on a de novo four-helix bundle heme protein (the m4D2 "maquette") and five designed mutants, including some mutants characterized experimentally in this work. The MD + CB approach is found to perform reliably, giving redox potential shifts with reasonably good correlation (0.85) to the experimental values for the mutants. The MD + CB approach also compares well with redox potential shift predictions using a continuum electrostatic method. The estimation method employed within the MD + CB approach is straightforwardly transferable to standard equilibrium MD simulations and holds promise for redox protein engineering and design applications.

Energy-Conserving and Thermally Corrected Neglect of Back-Reaction Approximation Method for Nonadiabatic Molecular Dynamics

In this work, the energy-conserving and thermally corrected neglect of the back-reaction approximation approach for nonadiabatic molecular dynamics in extended atomistic systems is developed. The new approach introduces three key corrections to the original method: (1) it enforces the total energy conservation, (2) it introduces an explicit coupling of the system to its environment, and (3) it introduces a renormalization of nonadiabatic couplings to account for a difference between the instantaneous nuclear kinetic energy and the kinetic energy of guiding trajectories. In the new approach, an auxiliary kinetic energy variable is introduced as an independent dynamical variable. The new approach produces nonzero equilibrium populations, whereas the original neglect of the back-reaction approximation method does not. It yields population relaxation time scales that are favorably comparable to the reference values, and it introduces an explicit and controllable way of dissipating energy into a bath without an assumption of the bath being at equilibrium.

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.

Phonon-assisted nearly pure spin current in DNA molecular chains: a multifractal analysis

Motivated by the development of molecular spintronics, we studied the phonon-assisted spin transport along a DNA chain in the presence of environmental-induced dephasing using multifractal analysis. The results demonstrate that a nearly pure spin current is generated in the presence of the voltage gate. The pure spin current is enhanced by increasing thermal effects. The vibration modes due to the thermal phonon bath assist in generating the spin current, so the spin state is more delocalized in strong electron-phonon coupling. The phonon chirality can translate to the electron spin to create a nontrivial spin texture, including spin currents. The spin states become more extended by increasing the phonon temperature. On the other hand, the spin states are less localized in longer chains as the spin selectivity is higher in longer chains than in short ones. Therefore, we can engineer a molecular spintronic device by controlling phonon effects on the storage and transport of binary digits.

Simulating Electron Transfer Reactions in Solution: Radical-Polar Crossover

Single-electron transfer (SET) promotes a wide variety of interesting chemical transformations, but modeling of SET requires a careful treatment of electronic and solvent effects to give meaningful insight. Therefore, a combined constrained density functional theory and molecular mechanics (CDFT/MM) tool is introduced specifically for SET-initiated reactions. Mechanisms for two radical-polar crossover reactions involving the organic electron donors tetrakis(dimethylamino)ethylene (TDAE) and tetrathiafulvalene (TTF) were studied with the new tool. An unexpected tertiary radical intermediate within the TDAE system was identified, relationships between kinetics and substitution in the TTF system were explained, and the impact of the solvent environments on the TDAE and TTF reactions were examined. The results highlight the need for including solvent dynamics when quantifying SET kinetics and thermodynamics, as a free energy difference of >20 kcal/mol was observed. Overall, the new method informs mechanistic analysis of SET-initiated reactions and therefore is envisioned to be useful for studying reactions in the condensed phase.

An energy decomposition and extrapolation scheme for evaluating electron transfer rate constants: a case study on electron self-exchange reactions of transition metal complexes

A simple approach to the analysis of electron transfer (ET) reactions based on energy decomposition and extrapolation schemes is proposed. The present energy decomposition and extrapolation-based electron localization (EDEEL) method represents the diabatic energies for the initial and final states using the adiabatic energies of the donor and acceptor species and their complex. A scheme for the efficient estimation of ET rate constants is also proposed. EDEEL is semi-quantitative by directly evaluating the seam-of-crossing region of two diabatic potentials. In a numerical test, EDEEL successfully provided ET rate constants for electron self-exchange reactions of thirteen transition metal complexes with reasonable accuracy. In addition, its energy decomposition and extrapolation schemes provide all the energy values required for activation-strain model (ASM) analysis. The ASM analysis using EDEEL provided rational interpretations of the variation of the ET rate constants as a function of the transition metal complexes. These results suggest that EDEEL is useful for efficiently evaluating ET rate constants and obtaining a rational understanding of their magnitudes.

Charge carrier dynamics in conducting polymer PEDOT using ab initio molecular dynamics simulations

As conducting polymers become increasingly important in electronic devices, understanding their charge transport is essential for material and device development. Various semi-empirical approaches have been used to describe temporal charge carrier dynamics in these materials, but there have yet to be any theoretical approaches utilizing ab initio molecular dynamics. In this work, we develop a computational technique based on ab initio Car-Parrinello molecular dynamics to trace charge carrier temporal motion in archetypical conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT). Particularly, we analyze charge dynamics in a single PEDOT chain and in two coupled chains with different degrees of coupling and study the effect of temperature. In our model we first initiate a positively charged polaron (compensated by a negative counterion) at one end of the chain, and subsequently displace the counterion to the other end of the chain and trace polaron dynamics in the system by monitoring bond length alternation in the PEDOT backbone and charge density distribution. We find that at low temperature (T = 1 K) the polaron distortion gradually disappears from its initial location and reappears near the new position of the counterion. At the room temperature (T = 300 K), we find that the distortions induced by polaron, and atomic vibrations are of the same magnitude, which makes tracking the polaron distortion challenging because it is hidden behind the temperature-induced vibrations. The novel approach developed in this work can be used to study polaron mobility along and between the chains, investigate charge transport in highly doped polymers, and explore other flexible polymers, including n-doped ones.

Electrochemistry in sensing of molecular interactions of proteins and their behavior in an electric field

Electrochemical methods can be used not only for the sensitive analysis of proteins but also for deeper research into their structure, transport functions (transfer of electrons and protons), and sensing their interactions with soft and solid surfaces. Last but not least, electrochemical tools are useful for investigating the effect of an electric field on protein structure, the direct application of electrochemical methods for controlling protein function, or the micromanipulation of supramolecular protein structures. There are many experimental arrangements (modalities), from the classic configuration that works with an electrochemical cell to miniaturized electrochemical sensors and microchip platforms. The support of computational chemistry methods which appropriately complement the interpretation framework of experimental results is also important. This text describes recent directions in electrochemical methods for the determination of proteins and briefly summarizes available methodologies for the selective labeling of proteins using redox-active probes. Attention is also paid to the theoretical aspects of electron transport and the effect of an external electric field on the structure of selected proteins. Instead of providing a comprehensive overview, we aim to highlight areas of interest that have not been summarized recently, but, at the same time, represent current trends in the field.

Contribution Factors of the First Kind Calculated for the Marcus Electron-Transfer Rate and Their Applications

In this study, we applied the concept of the "contribution factor of the first kind (CFFK)" to the original electron-transfer (ET) rate theory proposed by Marcus. Mathematical derivations provided simple and convenient formulas for estimating the relative contributions of ten physical and chemical parameters involved in the Marcus ET rate formula: (1) the maximum strength of the electronic coupling energy between two molecules, (2) the exponential decay rate of the electronic coupling energy versus the distance between both molecules, (3) the distance between both molecules, (4) the equilibrium distance between both molecules, (5) the Gibbs free energy, (6) reorganization free energy in the prefactor of the Marcus ET rate equation, (7) reorganization free energy in the denominator of the exponential term, (8) reorganization free energy in the argument of the exponential term, (9) Boltzmann constant times absolute temperature in the prefactor of the rate equation, and (10) Boltzmann constant times absolute temperature in the denominator of the exponential term. We applied our theories to (i) ET reactions at bacterial photosynthesis reaction centers, PSI and PSII, and soluble ferredoxins (Fd); (ii) intraprotein ET reactions for designed azurin mutants; and (iii) ET reactions in flavodoxin (Fld). The formulas and calculations suggest that the theory behind the CFFK is useful for quantitatively identifying major and minor physical and chemical factors and corresponding trade-offs, all of which affect the magnitude of the Marcus ET rate.

Comment on "Applicability of perturbed matrix method for charge transfer studies at bio/metallic interfaces: a case of azurin" by O. Kontkanen, D. Biriukov and Z. Futera, Phys. Chem. Chem. Phys., 2023, , 12479

Polarizability is a fundamental property of all molecular systems describing the deformation of the molecular electronic density in response to an applied electric field. The question of whether polarizability of the active site needs to be included in theories of enzymatic activity remains open. Hybrid quantum mechanical/molecular mechanical calculations are hampered by difficulties faced by many quantum-chemistry algorithms to provide sufficiently accurate estimates of the anisotropic second-rank tensor of molecular polarizability. In this Comment, we provide general theoretical arguments for the values of polarizability of the quantum region or a molecule which have to be reproduced by electronic structure calculations.

Competing quantum effects in heavy-atom tunnelling through conical intersections

Thermally activated chemical reactions are typically understood in terms of overcoming potential-energy barriers. However, standard rate theories break down in the presence of a conical intersection (CI) because these processes are inherently nonadiabatic, invalidating the Born-Oppenheimer approximation. Moreover, CIs give rise to intricate nuclear quantum effects such as tunnelling and the geometric phase, which are neglected by standard trajectory-based simulations and remain largely unexplored in complex molecular systems. We present new semiclassical transition-state theories based on an extension of golden-rule instanton theory to describe nonadiabatic tunnelling through CIs and thus provide an intuitive picture for the reaction mechanism. We apply the method in conjunction with first-principles electronic-structure calculations to the electron transfer in the bis(methylene)-adamantyl cation. Our study reveals a strong competition between heavy-atom tunnelling and geometric-phase effects.

Stereoselective amino acid synthesis by synergistic photoredox-pyridoxal radical biocatalysis

Developing synthetically useful enzymatic reactions that are not known in biochemistry and organic chemistry is an important challenge in biocatalysis. Through the synergistic merger of photoredox catalysis and pyridoxal 5'-phosphate (PLP) biocatalysis, we developed a pyridoxal radical biocatalysis approach to prepare valuable noncanonical amino acids, including those bearing a stereochemical dyad or triad, without the need for protecting groups. Using engineered PLP enzymes, either enantiomeric product could be produced in a biocatalyst-controlled fashion. Synergistic photoredox-pyridoxal radical biocatalysis represents a powerful platform with which to discover previously unknown catalytic reactions and to tame radical intermediates for asymmetric catalysis.

Multimodal investigation of electronic transport in PTMA and its impact on organic radical battery performance

Organic radical batteries (ORBs) represent a viable pathway to a more sustainable energy storage technology compared to conventional Li-ion batteries. For further materials and cell development towards competitive energy and power densities, a deeper understanding of electron transport and conductivity in organic radical polymer cathodes is required. Such electron transport is characterised by electron hopping processes, which depend on the presence of closely spaced hopping sites. Using a combination of electrochemical, electron paramagnetic resonance (EPR) spectroscopic, and theoretical molecular dynamics as well as density functional theory modelling techniques, we explored how compositional characteristics of cross-linked poly(2,2,6,6-tetramethyl-1-piperidinyloxy-4-yl methacrylate) (PTMA) polymers govern electron hopping and rationalise their impact on ORB performance. Electrochemistry and EPR spectroscopy not only show a correlation between capacity and the total number of radicals in an ORB using a PTMA cathode, but also indicates that the state-of-health degrades about twice as fast if the amount of radical is reduced by 15%. The presence of up to 3% free monomer radicals did not improve fast charging capabilities. Pulsed EPR indicated that these radicals readily dissolve into the electrolyte but a direct effect on battery degradation could not be shown. However, a qualitative impact cannot be excluded either. The work further illustrates that nitroxide units have a high affinity to the carbon black conductive additive, indicating the possibility of its participation in electron hopping. At the same time, the polymers attempt to adopt a compact conformation to increase radical-radical contact. Hence, a kinetic competition exists, which might gradually be altered towards a thermodynamically more stable configuration by repeated cycling, yet further investigations are required for its characterisation.

Correlated particle transport enables biological free energy transduction

Studies of biological transport frequently neglect the explicit statistical correlations among particle site occupancies (i.e., they use a mean-field approximation). Neglecting correlations sometimes captures biological function, even for out-of-equilibrium and interacting systems. We show that neglecting correlations fails to describe free energy transduction, mistakenly predicting an abundance of slippage and energy dissipation, even for networks that are near reversible and lack interactions among particle sites. Interestingly, linear charge transport chains are well described without including correlations, even for networks that are driven and include site-site interactions typical of biological electron transfer chains. We examine three specific bioenergetic networks: a linear electron transfer chain (as found in bacterial nanowires), a near-reversible electron bifurcation network (as in complex III of respiration and other recently discovered structures), and a redox-coupled proton pump (as in complex IV of respiration).

Hybrid Quantum Mechanical/Molecular Mechanical Methods For Studying Energy Transduction in Biomolecular Machines

Hybrid quantum mechanical/molecular mechanical (QM/MM) methods have become indispensable tools for the study of biomolecules. In this article, we briefly review the basic methodological details of QM/MM approaches and discuss their applications to various energy transduction problems in biomolecular machines, such as long-range proton transports, fast electron transfers, and mechanochemical coupling. We highlight the particular importance for these applications of balancing computational efficiency and accuracy. Using several recent examples, we illustrate the value and limitations of QM/MM methodologies for both ground and excited states, as well as strategies for calibrating them in specific applications. We conclude with brief comments on several areas that can benefit from further efforts to make QM/MM analyses more quantitative and applicable to increasingly complex biological problems.

Applicability of perturbed matrix method for charge transfer studies at bio/metallic interfaces: a case of azurin

As the field of nanoelectronics based on biomolecules such as peptides and proteins rapidly grows, there is a need for robust computational methods able to reliably predict charge transfer properties at bio/metallic interfaces. Traditionally, hybrid quantum-mechanical/molecular-mechanical techniques are employed for systems where the electron hopping transfer mechanism is applicable to determine physical parameters controlling the thermodynamics and kinetics of charge transfer processes. However, these approaches are limited by a relatively high computational cost when extensive sampling of a configurational space is required, like in the case of soft biomatter. For these applications, semi-empirical approaches such as the perturbed matrix method (PMM) have been developed and successfully used to study charge-transfer processes in biomolecules. Here, we explore the performance of PMM on prototypical redox-active protein azurin in various environments, from solution to vacuum interfaces with gold surfaces and protein junction. We systematically benchmarked the robustness and convergence of the method with respect to the quantum-centre size, size of the Hamiltonian, number of samples, and level of theory. We show that PMM can adequately capture all the trends associated with the structural and electronic changes related to azurin oxidation at bio/metallic interfaces.

Ionogel-Electrode for the Study of Protein Tunnel Junctions under Physiologically Relevant Conditions

The study of charge transport through proteins is essential for understanding complicated electrochemical processes in biological activities while the reasons for the coexistence of tunneling and hopping phenomena in protein junctions still remain unclear. In this work, a flexible and conductive ionogel electrode is synthesized and is used as a top contact to form highly reproducible protein junctions. The junctions of proteins, including human serum albumin, cytochrome C and hemoglobin, show temperature-independent electron tunneling characteristics when the junctions are in solid states while with a different mechanism of temperature-dependent electron hopping when junctions are hydrated under physiologically relevant conditions. It is demonstrated that the solvent reorganization energy plays an important role in the electron-hopping process and experimentally shown that it requires ≈100 meV for electron hopping through one heme group inside a hydrated protein molecule connected between two electrodes.

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.

Reorganization energy of electron transfer

The theory of electron transfer reactions establishes the conceptual foundation for redox solution chemistry, electrochemistry, and bioenergetics. Electron and proton transfer across the cellular membrane provide all energy of life gained through natural photosynthesis and mitochondrial respiration. Rates of biological charge transfer set kinetic bottlenecks for biological energy storage. The main system-specific parameter determining the activation barrier for a single electron-transfer hop is the reorganization energy of the medium. Both harvesting of light energy in natural and artificial photosynthesis and efficient electron transport in biological energy chains require reduction of the reorganization energy to allow fast transitions. This review article discusses mechanisms by which small values of the reorganization energy are achieved in protein electron transfer and how similar mechanisms can operate in other media, such as nonpolar and ionic liquids. One of the major mechanisms of reorganization energy reduction is through non-Gibbsian (nonergodic) sampling of the medium configurations on the reaction time. A number of alternative mechanisms, such as electrowetting of active sites of proteins, give rise to non-parabolic free energy surfaces of electron transfer. These mechanisms, and nonequilibrium population of donor-acceptor vibrations, lead to a universal phenomenology of separation between the Stokes shift and variance reorganization energies of electron transfer.

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.

Learning pair potentials using differentiable simulations

Learning pair interactions from experimental or simulation data is of great interest for molecular simulations. We propose a general stochastic method for learning pair interactions from data using differentiable simulations (DiffSim). DiffSim defines a loss function based on structural observables, such as the radial distribution function, through molecular dynamics (MD) simulations. The interaction potentials are then learned directly by stochastic gradient descent, using backpropagation to calculate the gradient of the structural loss metric with respect to the interaction potential through the MD simulation. This gradient-based method is flexible and can be configured to simulate and optimize multiple systems simultaneously. For example, it is possible to simultaneously learn potentials for different temperatures or for different compositions. We demonstrate the approach by recovering simple pair potentials, such as Lennard-Jones systems, from radial distribution functions. We find that DiffSim can be used to probe a wider functional space of pair potentials compared with traditional methods like iterative Boltzmann inversion. We show that our methods can be used to simultaneously fit potentials for simulations at different compositions and temperatures to improve the transferability of the learned potentials.

Electrochemical Properties and Local Structure of the TEMPO/TEMPO+ Redox Pair in Ionic Liquids

Redox-active organic species play an important role in catalysis, energy storage, and biotechnology. One of the representatives is the 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) radical, used as a mediator in organic synthesis and considered a safe alternative to heavy metals. In order to develop a TEMPO-based system with well-controlled electrochemical and catalytic properties, a reaction medium should be carefully chosen. Being highly conductive, stable, and low flammability fluids, ionic liquids (ILs) seem to be promising solvents with easily adjustable physical and solvation properties. In this work, we give an insight into the local structure of ILs around TEMPO and its oxidized form, TEMPO⁺, underlining striking differences in the solvation of these two species. The analysis is coupled with a study of thermodynamics and kinetics of oxidation in the frame of Marcus theory. Our systematic investigation includes imidazolium, pyrrolydinium, and phosphonium families combined with anions of different size, polarity, and flexibility, opting to provide a clear and comprehensive picture of the impact of the nature of IL ions on the behavior of radical/cation redox pairs. The obtained results will help to explain experimentally observed effects and to rationalize the design of TEMPO/IL systems.

Non-Conventional Peptide Self-Assembly into a Conductive Supramolecular Rope

Structures composed of alternating α and β amino acids can give rise to peculiar secondary structural motifs, which could self-assemble into complex structures of controlled geometries. This work describes the self-assembly properties of an α,β-peptide, containing three units of syn H2-(2-F-Phe)-h-PheGly-OH, able to self-organize on surfaces into a fascinating supramolecular rope. This material was characterized by AFM, electronic conduction and fluorescence measurements. Molecular dynamics simulations showed that this hexapeptide can self-assemble into an antiparallel β-sheet layer, stabilized by intermolecular H-bonds, which, in turn, can self-assemble into many side-by-side layers, due to π-π interactions. As a matter of fact, we demonstrated that in this system, the presence of aromatic residues at the intramolecular interface promoted by the alternation of α,β-amino-acids in the primary sequence, endorses the formation of a super-secondary structure where the aromatic groups are close to each other, conferring to the system good electron conduction properties. This work demonstrates the capability and future potential of designing and fabricating distinctive nanostructures and efficient bioelectronic interfaces based on an α,β-peptide, by controlling structure and interaction processes beyond those obtained with α- or β-peptides alone.

Mixed Sulfur/Selenium Anions Weaken Electron-Vibrational Interaction in Cu2ZnSn(S,Se)4 Photoabsorber

Kesterite Cu₂ZnSn(S,Se)₄ (CZTSSe) solar absorbers have attracted intensive investigations for next-generation photovoltaic applications. Here, by using ab initio static and molecular dynamics simulations, we investigated the anion compositional dependence of electron-vibration interaction in CZTSSe materials. We found that the conduction band fluctuates more than the valence band, and as a result, the band gap variation is more sensitive to the change of the former, which can be understood in terms of p-d hybridization in the valence bands. Electron-phonon coupling is smaller in CZTSSe alloy compared to pure S- or Se-containing structures, as evidenced by the smaller fluctuation of excitation energy, and can be attributed to the weaker structural dynamics of the metal-anion bond. Small electron-phonon coupling strength may lead to better charge transport in these materials. We also elucidated the interplay between disordered structures and S/Se stoichiometry through analysis of optical line width. The results highlight the importance of anion composition engineering and provide new insights into the rational design of high-performing kesterite absorbers for solar cells.

Chances and challenges of long-distance electron transfer for cellular redox reactions

Biological redox reactions often use a set-up in which final redox partners are localized in different compartments and electron transfer (ET) among them is mediated by redox-active molecules. In enzymes, these ET processes occur over nm distances, whereas multi-protein filaments bridge μm ranges. Electrons are transported over cm ranges in cable bacteria, which are formed by thousands of cells. In this review, we describe molecular mechanisms that explain how respiration in a compartmentalized set-up ensures redox homeostasis. We highlight mechanistic studies on ET through metal-free peptides and proteins demonstrating that long-distance ET is possible because amino acids Tyr, Trp, Phe, and Met can act as relay stations. This cuts one long ET into several short reaction steps. The chances and challenges of long-distance ET for cellular redox reactions are then discussed.

New Perspective on Electron Transfer through Molecules

Motivated by experiments which display unusual length and temperature effects for electron transfer in the nanometer length regime, we propose a new approach for describing long-range electron transfer (ET) processes through molecules. We posit that the electron reorganization in the molecules (e.g., the electronic polarization of a macromolecule or organic film by an applied electric potential, or the injected charge generating a dipole moment) should be included in the description. We numerically solve a one-dimensional model for the electron transport, which includes electron-electron interactions explicitly, and we show that it generates a power law distance dependence for electron transport similar to that observed in experiments. The model does not include vibrations explicitly and should be consistent with the weak temperature dependences observed experimentally. This approach emphasizes the need to treat the electronic changes in the molecule(s) more explicitly to understand the behavior.

Accelerated constant-voltage quantum mechanical/molecular mechanical method for molecular systems at electrochemical interfaces

The structure and electronic properties of a molecule at an electrochemical interface are changed by interactions with the electrode surface and the electrolyte solution, which can be significantly modulated by an applied voltage. We present an efficient self-consistent quantum mechanics/molecular mechanics (QM/MM) approach to study a physisorbed molecule at a metal electrode-electrolyte interface under the constant-voltage condition. The approach employs a classical polarizable double electrode model, which enables us to study the QM/MM system in the constant-voltage ensemble. A mean-field embedding approximation is further introduced in order to overcome the difficulties associated with statistical sampling of the electrolyte configurations. The results of applying the method to a test system indicate that the adsorbed molecule is no less or slightly more polarized at the interface than in the bulk electrolyte solution. The geometry of the horizontally adsorbed molecule is modulated by their electrostatic interactions with the polarizable electrode surfaces and also the interactions with cations attracted toward the interface when the adsorbate is reduced. We also demonstrate that the approach can be used to quantitatively evaluate the reorganization energy of a one electron reduction reaction of a molecule in an electrochemical cell.

Semiclassical Theory of Multistage Nonequilibrium Electron Transfer in Macromolecular Compounds in Polar Media with Several Relaxation Timescales

Many specific features of ultrafast electron transfer (ET) reactions in macromolecular compounds can be attributed to nonequilibrium configurations of intramolecular vibrational degrees of freedom and the environment. In photoinduced ET, nonequilibrium nuclear configurations are often produced at the stage of optical excitation, but they can also be the result of electron tunneling itself, i.e., fast redistribution of charges within the macromolecule. A consistent theoretical description of ultrafast ET requires an explicit consideration of the nuclear subsystem, including its evolution between electron jumps. In this paper, the effect of the multi-timescale nuclear reorganization on ET transitions in macromolecular compounds is studied, and a general theory of ultrafast ET in non-Debye polar environments with a multi-component relaxation function is developed. Particular attention is paid to designing the multidimensional space of nonequilibrium nuclear configurations, as well as constructing the diabatic free energy surfaces for the ET states. The reorganization energies of individual ET transitions, the equilibrium energies of ET states, and the relaxation properties of the environment are used as input data for the theory. The effect of the system-environment interaction on the ET kinetics is discussed, and mechanisms for enhancing the efficiency of charge separation in macromolecular compounds are analyzed.