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We unveil a rich solvation dynamics of water molecules at the hematite/liquid water interface spanning three different time scales. This is made possible through extensive hybrid DFT molecular dynamics simulations, accelerated by machine learning.

Bacterial cytochromes P450 BM3 (CYP450 BM3) catalyze reactions of industrial importance. Despite many successful biotransformations, robust (re)design for novel applications remains challenging. Rational design and evolutionary approaches are not always successful, highlighting a lack of complete understanding of the mechanisms of electron transfer (ET) modulations. Thus, the full potential of CYP450 reactions remains under-exploited. In this work, we report the first molecular dynamics (MD)-based explicit prediction of BM3 ET parameters (reorganization energies; λ and ET free energies; Δ

Hemoglobin-mediated transport of dioxygen (O(2)) critically depends on the stability of the reduced (Fe(2+)) form of the heme cofactors. Some protein mutations stabilize the oxidized (Fe(3+)) state (methemoglobin, Hb M), causing methemoglobinemia, and can be lethal above 30%. The majority of the analyses of factors influencing Hb oxidation are retrospective and give insights only for inner-sphere mutations of heme (His58, His87). Herein, we report the first all-atom molecular dynamics simulations on both redox states and calculations of the Marcus electron transfer (ET) parameters for the α chain Hb oxidation and reduction rates for Hb M. The Hb wild-type (WT) and most of the studied α chain variants maintain globin structure except the Hb M Iwate (H87Y). The mutants forming Hb M tend to have lower redox potentials and thus stabilize the oxidized (Fe(3+)) state (in particular, the Hb Miyagi variant with K61E mutation). Solvent reorganization (λ(solv) 73–96%) makes major contributions to reorganization free energy, whereas protein reorganization (λ(prot)) accounts for 27–30% except for the Miyagi and J-Buda variants (λ(prot) ∼4%). Analysis of heme-solvent H-bonding interactions among variants provide insights into the role of Lys61 residue in stabilizing the Fe(2+) state. Semiclassical Marcus ET theory-based calculations predict experimental k(ET) for the Cyt b5-Hb complex and provide insights into relative reduction rates for Hb M in Hb variants. Thus, our methodology provides a rationale for the effect of mutations on the structure, stability, and Hb oxidation reduction rates and has potential for identification of mutations that result in methemoglobinemia.

Quantum dynamical simulations are essential for a molecular-level understanding of light-induced processes in optoelectronic materials, but they tend to be computationally demanding. We introduce an efficient mixed quantum-classical nonadiabatic molecular dynamics method termed eXcitonic state-based Surface Hopping (X-SH), which propagates the electronic Schrödinger equation in the space of local excitonic and charge-transfer electronic states, coupled to the thermal motion of the nuclear degrees of freedom. The method is applied to exciton decay in a 1D model of a fullerene-oligothiophene junction, and the results are compared to the ones from a fully quantum dynamical treatment at the level of the Multilayer Multiconfigurational Time-Dependent Hartree (ML-MCTDH) approach. Both methods predict that charge-separated states are formed on the 10-100 fs time scale via multiple "hot-exciton dissociation" pathways. The results demonstrate that X-SH is a promising tool advancing the simulation of photoexcited processes from the molecular to the true nanomaterials scale.

Microbial nanowires are fascinating biological structures that allow bacteria to transport electrons over micrometers for reduction of extracellular substrates. It was recently established that the nanowires of both Shewanella and Geobacter are made of multi-heme proteins; but, while Shewanella employs the 20-heme protein complex MtrCAB, Geobacter uses a redox polymer made of the hexa-heme protein OmcS, begging the question as to which protein architecture is more efficient in terms of long-range electron transfer. Using a multiscale computational approach we find that OmcS supports electron flows about an order of magnitude higher than MtrCAB due to larger heme-heme electronic couplings and better insulation of hemes from the solvent. We show that heme side chains are an essential structural element in both protein complexes, accelerating rate-limiting electron tunnelling steps up to 1000-fold. Our results imply that the alternating stacked/T-shaped heme arrangement present in both protein complexes may be an evolutionarily convergent design principle permitting efficient electron transfer over very long distances.

Constrained density functional theory (CDFT) is a powerful tool for the prediction of electron transfer parameters in condensed phase simulations at a reasonable computational cost. In this work we present an extension to CDFT in the popular mixed Gaussian/plane wave electronic structure package CP2K, implementing the additional force terms arising from a constraint based on Hirshfeld charge partitioning. This improves upon the existing Becke partitioning scheme, which is prone to give unphysical atomic charges. We verify this implementation for a variety of systems: electron transfer in (H

Transition metal oxide materials have attracted much attention for photoelectrochemical water splitting, but problems remain, e.g. the sluggish transport of excess charge carriers in these materials, which is not well understood. Here we use periodic, spin-constrained and gap-optimized hybrid density functional theory to uncover the nature and transport mechanism of holes and excess electrons in a widely used water splitting material, bulk-hematite (α-Fe

Investigation of many electronic processes in molecules and materials, such as charge and exciton transport, requires a computational framework that incorporates both non-adiabatic electronic effects and nuclear quantum effects, in particular at low temperatures. We have recently developed an efficient semi-empirical fewest switches surface hopping method, denoted fragment orbital-based surface hopping (FOB-SH), that was tailored towards highly efficient simulation of charge transport in molecular materials, yet with nuclei treated classically. In this work, we extend FOB-SH and include nuclear quantum effects by combining it with ring-polymer molecular dynamics (RPMD) in three different flavours: (i) RPSH with bead approximation (RPSH-BA) as suggested in Shushkov et al., J. Chem. Phys., 2012, 137, 22A549, (ii) a modification of (i) denoted RPSH with weighted bead approximation (RPSH-wBA) and (iii) the isomorphic Hamiltonian method of Tao et al., J. Chem. Phys., 2018, 148, 10237 (SH-RP-iso). We present here applications to hole transfer in a molecular dimer model and analyze detailed balance and internal consistency of all three methods and investigate the temperature and driving force dependence of the hole transfer rate. We find that RPSH-BA strongly underestimates and RPSH-wBA overestimates the exact excited state population, while SH-RP-iso gives satisfactory results. We also find that the latter predicts a flattening of the rate vs. driving force dependence in the Marcus inverted regime at low temperature, as often observed experimentally. Overall, our results suggest that FOB-SH combined with SH-RP-iso is a promising method for including zero point motion and tunneling in charge transport simulations in molecular materials and biological systems.

Iron oxides such as hematite (α-Fe2O3) play an important role in diverse fields ranging from biogeochemistry to photocatalysis. Here we perform calculations of both the electron and electron hole polaron structures and associated reorganisation energies for a series of bulk iron oxides: hematite (α-Fe2O3), lepidocrocite (γ-FeOOH), goethite (α-FeOOH) and white rust (Fe(OH)2). Through the use of gap-optimized hybrid functionals and large supercells under periodic boundary conditions, we remove some of the complications and uncertainties present in earlier cluster model calculations. It is found that while the electron hole polaron in these materials generally localises onto a single iron site, the electron polaron localises across two iron sites of the same spin layer as a consequence of the lower reorganisation energy for electrons compared to holes. An exception to these trends is the hole of goethite, which according to our calculations does not form a localised polaron.

The search for conductive soft matter materials with significant charge mobility under ambient conditions has been a major priority in organic electronics (OE) research. Alkylated tetracenes are promising cost-effective candidate molecules that can be synthesized using wet chemistry methods, resulting in columnar single crystals with pronounced structural stability at and above room temperature. A remarkable characteristic of these materials is the capability of tuning the tetracene core intracolumnar stacking pattern and the crystal melting point via the side chain length and type modifications. In this study, we examine the performance of a series of alkylated tetracenes as hole conducting materials using a novel atomistic simulation technique that allows us to predict both the charge transport mechanism and mobilities. Our simulations demonstrate that molecular wires of alkylated tetracenes are capable of polaronic hole conduction at room temperature, with mobility values ranging up to 21 cm2 V−1 s−1, thus rendering such materials a highly promising choice for flexible OE applications. As regards the charge transfer robustness, two promising tetracene derivatives are identified with the capability of seamless inter-wire polaron delocalization, alleviating possible transfer bottlenecks due to local molecular defects. Our findings suggest that alkylated tetracenes offer an attractive route towards flexible columnar OE materials with unprecedented hole mobilities.

Iron oxides such as hematite (α-Fe2O3) play an important role in diverse fields ranging from biogeochemistry to photocatalysis. In the majority of these cases their electrical properties are key because they facilitate electron transfer reactions occurring at their interfaces. The iron oxides tend to be wide band gap semiconductors with a narrow d band. Consequently, electron and hole charge carriers localize by self-trapping to form polarons, carriers whose mobilities are tied to the lattice distortions they create. Site-to-site polaron transport is thermally activated and the rate depends on the energy to reorganize the local structure into a suitable transition state, as well as the strength of the electronic coupling in that transient configuration. In turn, these depend on factors that determine the atomic and electronic structure, including crystallographic direction. Because the structure of polarons, the reorganization energy, and the electronic coupling matrix element are not readily experimentally accessible, quantum mechanical calculations have been extraordinarily useful. However, this also means that the accuracy of predicting polaronic charge carrier mobilities depends strongly on the computational method used. In the ~20 years since the first application of ab initio cluster model computations to this topic for hematite, both the methodological rigor and the supporting computational power have greatly advanced. After a brief historical overview, this talk will highlight current findings obtained with gap-optimized hybrid density functional theory with periodic boundary conditions performed on massively parallel supercomputers. Comparisons will be made to the original calculations for hematite published in 2003. The DFT-based predictions for other iron oxide phases will also be discussed. Specifically, we will present calculations of both the electron and hole polaron structures and associated reorganization energies for the bulk of hematite, lepidocrocite (γ-FeOOH), goethite (α-FeOOH) and white rust (Fe(OH)2).1 Through the use of gap-optimized hybrid functionals and large supercells under periodic boundary conditions, we remove some of the complications and uncertainties present in earlier cluster model calculations. It is found that while the hole polaron in these materials generally localizes onto a single iron site, the electron polaron delocalizes across two iron sites of the same spin layer as a consequence of the lower reorganization energy for electrons compared to holes. An exception to these trends is the hole of goethite, which according to our calculations does not form a localized polaron. For hematite,2 we find that upon ionization the hole relaxes from a delocalized band state to a polaron localized on a single iron atom with localization induced by tetragonal distortion of the six surrounding iron-oxygen bonds. This distortion is responsible for sluggish hopping transport in the Fe-bilayer, characterized by an activation energy of 70 meV and a hole mobility of 0.031 cm2/(V s). By contrast, the excess electron induces a smaller distortion of the iron-oxygen bonds resulting in delocalization over two neighboring Fe units. We find that 2-site delocalization is advantageous for charge transport due to the larger spatial displacements per transfer step. As a result, the electron mobility is predicted to be a factor of three higher than the hole mobility, 0.098 cm2/(V s), in qualitative agreement with experimental observations. The advances made on the theory and simulation front have provided increasing insight into the nature of polaronic transport in the iron oxides, and the methods have been widely duplicated successfully to a variety of materials. However, there is tremendous room for expansion of the work to treat the more challenging aspects governing iron oxide behavior in natural systems and in device application, including the role of interfaces, surface potential, and defects to name a few. Theoretical computations seem poised now more than ever to help unlock the fundamental insight into charge carrier transport in polaronic materials needed to understand and adapt their electrical transport properties. References Ahart C.S., Blumberger J., Rosso K.M. (2020) Polaronic structure of excess electrons and holes for a series of bulk iron oxides. Physical Chemistry Chemical Physics, 22, 10699-10709. Ahart C.S., Rosso K.M., Blumberger J. (2022) Electron and hole mobilities in bulk hematite from spin-constrained density functional theory. Journal of the American Chemical Society, 144, 4623-4632.

Proteins achieve efficient energy storage and conversion through electron transfer along a series of redox cofactors. Multiheme cytochromes are notable examples. These proteins transfer electrons over distance scales of several nanometers to >10 μm and in so doing they couple cellular metabolism with extracellular redox partners including electrodes. Here we report pump-probe spectroscopy that provides a direct measure of the intrinsic rates of heme-heme electron transfer in this fascinating class of proteins. Our study took advantage of a spectrally unique His/Met ligated heme introduced at a defined site within the decaheme extracellular MtrC protein of Shewanella oneidensis. We observed rates of heme-to-heme electron transfer on the order of 109 s-1 (3.7-4.3 A edge-to-edge distance), in good agreement with predictions based on density functional and molecular dynamics calculations. These rates are amongst the highest reported for ground state electron transfer in biology. Yet, some fall 2-3 orders of magnitude below the Moser-Dutton ruler because electron transfer at these short distances is through-space and therefore associated with a higher tunneling barrier than the through-protein tunneling scenario that is usual at longer distances. Moreover, we show that the His/Met ligated heme creates an electron sink that stabilizes the charge separated state on the 100 microsecond time scale. This feature could be exploited in future designs of multiheme cytochromes as components of versatile photosynthetic biohybrid assemblies.

The treatment of electrostatic interactions is a key ingredient in the force field-based simulation of condensed phase systems. Most approaches used fixed, site-specific point charges. Yet, it is now clear that many applications of force fields (FFs) demand more sophisticated treatments, prompting the implementation of charge equilibration methods in polarizable FFs to allow the redistribution of charge within the system. One approach allowing both, charge redistribution and site-specific polarization, while at the same time solving methodological shortcomings of earlier methods, is the first-principles-derived atom-condensed Kohn-Sham density functional theory method approximated to the second order (ACKS2). In this work, we present two fragment approaches to ACKS2, termed f-ACKS2 and a self-consistent version, scf-ACKS2, that treat condensed phase systems as a collection of electronically polarizable molecular fragments. The fragmentation approach to ACKS2 not only leads to a more transferable and less system-specific collection of electronic response parameters but also opens up the method to large condensed phase systems. We validate the accuracies of f-ACKS2 and scf-ACKS2 by comparing polarization energies and induced dipole moments for a number of charged hydrocarbon dimers against DFT reference calculations. Finally, we also apply both fragmented ACKS2 variants to calculate the polarization energy for electron-hole pair separation along a chain of anthracene molecules and find excellent agreement with reference DFT calculations.

International audience; Progress in the design of high‐mobility organic semiconductors has been hampered by an incomplete fundamental understanding of the elusive charge carrier dynamics mediating electrical current in these materials. To address this problem, a novel fully atomistic non‐adiabatic molecular dynamics approach termed fragment orbital‐based surface hopping (FOB‐SH) that propagates the electron‐nuclear motion has been further improved and, for the first time, used to calculate the full 2D charge mobility tensor for the conductive planes of six structurally well characterized organic single crystals, in good agreement with available experimental data. The nature of the charge carrier in these materials is best described as a flickering polaron constantly changing shape and extensions under the influence of thermal disorder. Thermal intra‐band excitations from modestly delocalized band edge states (up to 5 nm or 10–20 molecules) to highly delocalized tail states (up to 10 nm or 40–60 molecules in the most conductive materials) give rise to short, ≈ 10 fs‐long bursts of the charge carrier wavefunction that drives the spatial displacement of the polaron, resulting in carrier diffusion and mobility. This study implies that key to the design of high‐mobility materials is a high density of strongly delocalized and thermally accessible tail states.

This themed collection is a collection of articles on frontiers in molecular simulation of solvated ions, molecules and interfaces.

Charge transport in high mobility organic semiconductors is in an intermediate regime between small polaron hopping and band transport limits. We have recently shown that surface hopping non-adiabatic molecular dynamics is a powerful method for prediction of charge transport mechanisms in organic materials and for near-quantitative prediction of charge mobilities at room temperature where the effects of nuclear zero-point motion and tunneling are still relatively small [S. Giannini et al., Nat. Commun., 2019, 10, 3843]. Here we assess and critically discuss the extensions to Tully's original method that have led to this success: (i) correction for missing electronic decoherence, (ii) detection of trivial crossings and (iii) removal of decoherence correction-induced spurious charge transfer. If any one of these corrections is not included, the charge mobility diverges with system size, each for different physical reasons. Yet if they are included, convergence with system size, detailed balance and good internal consistency are achieved.

It was recently suggested that cytochrome c operates in an ergodicity-breaking regime characterized by unusually large energy gap thermal fluctuations and associated reorganization free energies for heme oxidation of up to 3.0 eV. The large fluctuations were reported to lower activation free energy for oxidation of the heme cofactor by almost a factor of 2 compared to the case where ergodicity is maintained. Our group has recently investigated this claim computationally at several levels of theory and found no evidence for such large energy gap fluctuations. Here we address the points of our earlier work that have raised criticism and we also extend our previous investigation by considering a simple linear polarizability model for cytochrome c oxidation. We find very consistent results among all our computational approaches, ranging from classical molecular dynamics, to the linear polarizability model to QM(PMM)/MM to full QM(DFT)/MM electrostatic emdedding. None of them support the notion of very large energy gap fluctuations or ergodicity breaking. The deviation between our simulations and the ones reported in [

The interface between transition metal oxides (TMO) and liquid water plays a crucial role in environmental chemistry, catalysis, and energy science. Yet, the mechanism and energetics of chemical transformations at solvated TMO surfaces is often unclear, largely because of the difficulty to characterize the active surface species experimentally. The hematite (α-Fe2O3)-liquid water interface is a case in point. Here we demonstrate that ab initio molecular dynamics is a viable tool for determining the protonation states of complex interfaces. The pKa values of the oxygen-terminated (001) surface group of hematite, ≡OH, and half-layer terminated (012) surface groups, ≡2OH and ≡1OH2, are predicted to be (18.5 ± 0.3), (18.9 ± 0.6), and (10.3 ± 0.5) pKa units, respectively. These are in good agreement with recent bond-valence theory based estimates, and suggest that the deprotonation of these surfaces require significantly more free energy input than previously thought.

Electronic coupling matrix elements are important to the theoretical description of electron transfer processes. However, they are notoriously difficult to obtain accurately from time- dependent density functional theory (TDDFT). Here, we use the HAB11 benchmark dataset of coupling matrix elements to assess whether TDDFT using optimally-tuned range-separated hybrid functionals, already known to be successful for the description of charge transfer excitation energies, also allows for an improved accuracy in the prediction of coupling matrix elements. We find that this approach outperforms all previous TDDFT calculations, based on semi-local, hybrid, or non-tuned range-separated hybrid functionals, with a remaining average deviation as low as ~12%. We discuss potential sources for the remaining error., Mol. Phys., in press (Michael Baer festschrift)

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

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.

The last 20 years of force field development have shown that even well parametrized classical models need to at least approximate the dielectric response of molecular systems-based, e.g., on atomic polarizabilities-in order to correctly render their structural and dynamic properties. Yet, despite great advances most approaches tend to be based on ad hoc assumptions and often insufficiently capture the dielectric response of the system to external perturbations, such as, e.g., charge carriers in semiconducting materials. A possible remedy was recently introduced with the atom-condensed Kohn-Sham density-functional theory approximated to second order (ACKS2), which is fully derived from first principles. Unfortunately, specifically its reliance on first-principles derived parameters so far precluded the widespread adoption of ACKS2. Opening up ACKS2 for general use, we here present a reformulation of the method in terms of Gaussian basis functions, which allows us to determine many of the ACKS2 parameters analytically. Two sets of parameters depending on exchange-correlation interactions are still calculated numerically, but we show that they could be straightforwardly parametrized owing to the smoothness of the new basis. Our approach exhibits three crucial benefits for future applications in force fields: i) efficiency, ii) accuracy, and iii) transferability. We numerically validate our Gaussian augmented ACKS2 model for a set of small hydrocarbons which shows a very good agreement with density-functional theory reference calculations. To further demonstrate the method's accuracy and transferability for realistic systems, we calculate polarization responses and energies of anthracene and tetracene, two major building blocks in organic semiconductors.

Charge carrier transport in organic semiconductors is at the heart of many revolutionary technologies ranging from organic transistors, light-emitting diodes, flexible displays and photovoltaic cells. Yet, the nature of charge carriers and their transport mechanism in these materials is still unclear. Here we show that by solving the time-dependent electronic Schrödinger equation coupled to nuclear motion for eight organic molecular crystals, the excess charge carrier forms a polaron delocalized over up to 10–20 molecules in the most conductive crystals. The polaron propagates through the crystal by diffusive jumps over several lattice spacings at a time during which it expands more than twice its size. Computed values for polaron size and charge mobility are in excellent agreement with experimental estimates and correlate very well with the recently proposed transient localization theory., Existing transport models for organic semiconductors are limited in their ability to accurately describe the transport mechanisms in these materials. Here, the authors report the fragment-orbital based surface hopping method for predicting charge transport in crystalline organic semiconductors.

A central challenge of organic semiconductor research is to make cheap, disordered materials that exhibit high electrical conductivity. Unfortunately, this endeavor is hampered by the poor fundamental understanding of the relationship between molecular packing structure and charge carrier mobility. Here a novel computational methodology is presented that fills this gap. Using a melt-quench procedure it is shown that amorphous pentacene spontaneously self-assembles to nanocrystalline structures that, at long quench times, form the characteristic herringbone layer of the single crystal. Quantum dynamical simulations of electron hole transport show a clear correlation between the crystallinity of the sample, the quantum delocalization, and the mobility of the charge carrier. Surprisingly, the long-held belief that charge carriers form relatively localized polarons in disordered OS is only valid for fully amorphous structures-for nanocrystalline and crystalline samples, significant charge carrier delocalization over several nanometers occurs that underpins their improved conductivities. The good agreement with experimentally available data makes the presented methodology a robust computational tool for the predictive engineering of disordered organic materials.

International audience; FeFe hydrogenases are the most efficient H2-producing enzymes. However, inactivation by O2 remains an obstacle that prevents them being used in many biotechnological devices. Here, we combine electrochemistry, site-directed mutagenesis, molecular dynamics and quantum chemical calculations to uncover the molecular mechanism of O2 diffusion within the enzyme and its reactions at the active site. We propose that the partial reversibility of the reaction with O2 results from the four-electron reduction of O2 to water. The third electron/proton transfer step is the bottleneck for water production, competing with formation of a highly reactive OH radical and hydroxylated cysteine. The rapid delivery of electrons and protons to the active site is therefore crucial to prevent the accumulation of these aggressive species during prolonged O2 exposure. These findings should provide important clues for the design of hydrogenase mutants with increased resistance to oxidative damage.

The bacterium Shewanella oneidensis has evolved a sophisticated electron transfer (ET) machinery to export electrons from the cytosol to extracellular space during extracellular respiration. At the heart of this process are decaheme proteins of the Mtr pathway, MtrC and MtrF, located at the external face of the outer bacterial membrane. Crystal structures have revealed that these proteins bind 10 c-type hemes arranged in the peculiar shape of a staggered cross that trifurcates the electron flow, presumably to reduce extracellular substrates while directing electrons to neighboring multiheme cytochromes at either side along the membrane. Especially intriguing is the design of the heme junctions trifurcating the electron flow: they are made of coplanar and T-shaped heme pair motifs with relatively large and seemingly unfavorable tunneling distances. Here, we use electronic structure calculations and molecular simulations to show that the side chains of the heme rings, in particular the cysteine linkages inserting in the space between coplanar and T-shaped heme pairs, strongly enhance electronic coupling in these two motifs. This results in an ≈ 10 3 -fold speedup of ET steps at heme junctions that would otherwise be rate limiting. The predicted maximum electron flux through the solvated proteins is remarkably similar for all possible flow directions, suggesting that MtrC and MtrF shuttle electrons with similar efficiency and reversibly in directions parallel and orthogonal to the outer membrane. No major differences in the ET properties of MtrC and MtrF are found, implying that the different expression levels of the two proteins during extracellular respiration are not related to redox function.

Multiheme cytochromes attract much attention for their electron transport properties. These proteins conduct electrons across bacterial cell walls, along extracellular filaments, and when purified can serve as bionanoelectronic junctions. Thus, it is important and necessary to identify and understand the factors governing electron transfer in this family of proteins. To this end we have used ultra-fast transient absorbance spectroscopy, to define heme-heme electron transfer dynamics in the representative multiheme cytochrome STC from Shewanella oneidensis in aqueous solution. STC was photo-sensitized by site-selective labelling with a Ru(II)(bipyridine)3 dye and the dynamics of light-driven electron transfer described by a kinetic model corroborated by molecular dynamics simulation and density functional theory calculations. With the dye attached adjacent to STC Heme IV, a rate constant of 87 x 106 s-1 was resolved for Heme IV → Heme III electron transfer. With the dye attached adjacent to STC Heme I, at the opposite terminus of the tetraheme chain, a rate constant of 125 x 106 s-1 was defined for Heme I → Heme II electron transfer. These rates are an order of magnitude faster than previously computed values for unlabeled STC. The Heme III/IV and I/II pairs exemplify the T-shaped heme packing arrangement, prevalent in multiheme cytochromes, whereby the adjacent porphyrin rings lie at 90o with edge-edge (Fe-Fe) distances of ≈6 (11) Å. The results are significant in demonstrating the opportunities for pump-probe spectroscopies to resolve inter-heme electron transfer in Ru-labeled multiheme cytochromes.

Multi-heme cytochrome c (CytC) proteins are key for transferring electrons out of cells, to enable intracellular oxidation to proceed, also in the absence of O2. In these proteins most of the hemes are arranged in a linear array suggesting a facile path for electronic conduction. To test this, we studied solvent free electron transport across two multi-heme CytC-type: MtrF (deca-heme CytC) and STC (tetra-heme CytC). Transport is measured across monolayers of these proteins in solid state configuration between Au electrodes. Both proteins showed 1,000x higher conductance than single heme, or heme-free proteins, but similar to monolayers of conjugated organics. Conductances are found to be temperature-independent (320-80K), suggesting tunneling as the transport mechanism based on present experimental data. This mechanism is consistent with modelling the I-V curves, results of which could be interpreted by having protein-electrode coupling as rate limiting, rather than transport within the proteins.

The pathways by which small molecules (substrates or inhibitors) access active sites are a key aspect of the function of enzymes and other proteins. A key problem in designing or altering such proteins is to identify sites for mutation which will have the desired effect on the substrate transport properties. While specific access channels have been invoked in the past, molecular simulations suggest that multiple routes are possible, complicating the analysis. This complexity, however, can be captured by a Markov State Model (MSM) of the ligand diffusion process. We have developed a sensitivity analysis of the resulting rate matrix, which identifies the locations where mutations should have the largest effect on the diffusive on rate. We apply this method to myoglobin, which is the best characterized example both from experiment and simulation. We validate the approach by translating the sensitivity parameter obtained from this method into the CO binding rates in myoglobin upon mutation, resulting in a semi-quantitative correlation with experiment. The model is further validated against an explicit simulation for one of the experimental mutants.

A new database (HAB7-) of electronic coupling matrix elements (Hab) for electron transfer in seven medium-sized negatively charged π-conjugated organic dimers is introduced. Reference data are obtained with spin-component scaled approximate coupled cluster method (SCS-CC2) and large basis sets. Assessed DFT-based approaches include constrained density functional theory (CDFT), fragment-orbital DFT (FODFT), self-consistent charge density functional tight-binding (FODFTB) and the recently described analytic overlap method (AOM). This complements the previously reported HAB11 database where only cationic dimers were considered. The CDFT method in combination with a functional based on PBE and including 50% of exact exchange (HFX) was found to provide best estimates, with a mean relative unsigned error (MRUE) of 8.2%. CDFT couplings systematically increase with decreasing fraction of HFX as a consequence of increasing delocalisation of the SOMO orbital. The FODFT method is found to be very robust underestimating electronic couplings by 28%. The FODFTB and AOM methods, although orders of magnitude more efficient in terms of computational effort than the DFT approaches, perform well with reasonably small errors of 54% and 29%, respectively, translating in errors in the non-adiabatic electron transfer rate of a factor of 2.4 and 1.7, respectively. We discuss carefully various sources of errors and the scope and limitations of all assessed methods taking into account the results obtained for both HAB7- and HAB11 databases.

We have recently introduced an efficient semi-empirical non-adiabatic molecular dynamics method for the simulation of charge transfer/transport in molecules and molecular materials, denoted fragment orbital-based surface hopping (FOB-SH) [J. Spencer et al., J. Chem. Phys. 145, 064102 (2016)]. In this method, the charge carrier wavefunction is expanded in a set of charge localized, diabatic electronic states and propagated in the time-dependent potential due to classical nuclear motion. Here we derive and implement an exact expression for the non-adiabatic coupling vectors between the adiabatic electronic states in terms of nuclear gradients of the diabatic electronic states. With the non-adiabatic coupling vectors (NACVs) available, we investigate how different flavours of fewest switches surface hopping affect detailed balance, internal consistency, and total energy conservation for electron hole transfer in a molecular dimer with two electronic states. We find that FOB-SH satisfies detailed balance across a wide range of diabatic electronic coupling strengths provided that the velocities are adjusted along the direction of the NACV to satisfy total energy conservation upon a surface hop. This criterion produces the right fraction of energy-forbidden (frustrated) hops, which is essential for correct population of excited states, especially when diabatic couplings are on the order of the thermal energy or larger, as in organic semiconductors and DNA. Furthermore, we find that FOB-SH is internally consistent, that is, the electronic surface population matches the average quantum amplitudes, but only in the limit of small diabatic couplings. For large diabatic couplings, inconsistencies are observed as the decrease in excited state population due to frustrated hops is not matched by a corresponding decrease in quantum amplitudes. The derivation provided here for the NACV should be generally applicable to any electronic structure approach where the electronic Hamiltonian is constructed in a diabatic electronic state basis.

Multi-heme proteins have attracted much attention recently due to their prominent role in mediating extracellular electron transport (ET), but one of their key fundamental properties, the rate constants for ET between the constituent heme groups, have so far evaded experimental determination. Here we report the set of heme–heme theoretical ET rate constants that define electron flow in the tetra-heme protein STC by combining a novel projector-operator diabatization approach for electronic coupling calculation with molecular dynamics simulation of ET free energies. On the basis of our calculations, we find that the protein limited electron flux through STC in the thermodynamic downhill direction (heme 1→4) is ∼3 × 106 s–1. We find that cysteine linkages inserting in the space between the two terminal heme pairs 1-2 and 3-4 significantly enhance the overall electron flow, by a factor of about 37, due to weak mixing of the sulfur 3p orbital with the Fe-heme d orbitals. While the packing density model, and to...

We previously computed the redox potentials for the 10 hemes in the decaheme cytochrome MtrF using thermodynamic integration (TI) in combination with all-atom, explicit solvent molecular dynamics (MD) simulation (1). In a recent study, Watanabe et al. (2) recomputed these potentials using a Poisson–Boltzmann (PB) continuum approach. The potentials obtained from MD for the all-oxidized protein gave a nearly symmetrical free energy profile along the octaheme chain with a small overall driving force of −48 ± 66 meV from heme 10 to heme 5 and two symmetrical free energy maxima of ∼200 meV at heme 9 (domain IV) and heme 4 (domain II). The … [↵][1]1To whom correspondence should be addressed. Email: j.blumberger{at}ucl.ac.uk. [1]: #xref-corresp-1-1

Simulation of charge transport in organic semiconducting materials requires the development of strategies for very fast yet accurate estimation of electronic coupling matrix elements for electron transfer between organic molecules (transfer integrals, Hab). A well-known relation that is often exploited for this purpose is the approximately linear dependence of electronic coupling with respect to the overlap of the corresponding diabatic state wave functions for a given donor-acceptor pair. Here we show that a single such relation can be established for a large number of different π-conjugated organic molecules. In our computational scheme the overlap of the diabatic state wave function is simply estimated by the overlap of the highest singly occupied molecular orbital of donor and acceptor, projected on a minimum valence shell Slater-type orbital (STO) basis with optimized Slater decay coefficients. After calibration of the linear relation, the average error in Hab as obtained from the STO orbital overlap is a factor of 1.9 with respect to wave function-theory validated DFT calculations for a diverse set of π-conjugated organic dimers including small arenes, arenes with S, N, and O heteroatoms, acenes, porphins, and buckyballs. The crucial advantage of the scheme is that the STO orbital overlap calculation is analytic. This leads to speedups of 6 orders of magnitude with respect to reference DFT calculations, with little loss of accuracy in the regime relevant to charge transport in organics.