Electronic Coupling Calculations for Bridge-Mediated Charge Transfer Using Constrained Density Functional Theory (CDFT) and Effective Hamiltonian Approaches at the Density Functional Theory (DFT) and Fragment-Orbital Density Functional Tight Binding (FODFTB) Level

Unraveling the electronic origin of a special feature in the triplet-minus-singlet spectra of carotenoids in natural photosystems

The influence of carotenoid triplet states on the Qy electronic transitions of chlorophylls has been observed in experiments on light-harvesting complexes over the past three decades, but the interpretation of the resulting spectral feature in the triplet minus singlet (T-S) absorption spectra of photosystems is still debated, as the physical-chemical explanation of this feature has been elusive. Here, we resolve this debate, by explaining the T-S spectra of pigment complexes over the Qy-band spectral region through a comparative study of chlorophyll-carotenoid model dyads and larger pigment complexes from the main light harvesting complex of higher plants (LHCII). This goal is achieved by combining state-of-the-art time-dependent density functional theory with analysis of the relationship between electronic properties and nuclear structure, and by comparison to the experiment. We find that the special signature in the T-S spectra of both model and natural photosystems is determined by singlet-like triplet excitations that can be described as effective singlet excitations on chlorophylls influenced by a stable electronic triplet on the carotenoid. The comparison with earlier experiments on different light-harvesting complexes confirms our theoretical interpretation of the T-S spectra in the Qy spectral region. Our results indicate an important role for the chlorophyll-carotenoid electronic coupling, which is also responsible for the fast triplet-triplet energy transfer, suggesting a fast trapping of the triplet into the relaxed carotenoid structure. The gained understanding of the interplay between the electronic and nuclear structures is potentially informative for future studies of the mechanism of photoprotection by carotenoids.

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.

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.

Electron hopping heat transport in molecules

The realization of single-molecule thermal conductance measurements has driven the need for theoretical tools to describe conduction processes that occur over atomistic length scales. In macroscale systems, the principle that is typically used to understand thermal conductivity is Fourier's law. At molecular length scales, however, deviations from Fourier's law are common in part because microscale thermal transport properties typically depend on the complex interplay between multiple heat conduction mechanisms. Here, the thermal transport properties that arise from electron transfer across a thermal gradient in a molecular conduction junction are examined theoretically. We illustrate how transport in a model junction is affected by varying the electronic structure and length of the molecular bridge in the junction as well as the strength of the coupling between the bridge and its surrounding environment. Three findings are of note: First, the transport properties can vary significantly depending on the characteristics of the molecular bridge and its environment; second, the system's thermal conductance commonly deviates from Fourier's law; and third, in properly engineered systems, the magnitude of electron hopping thermal conductance is similar to what has been measured in single-molecule devices.

Understanding Electron Transfer Reactions Using Constrained Density Functional Theory: Complications Due to Surface Interactions

The kinetic rates of electrochemical reactions depend on electrodes and molecules in question. In a flow battery, where the electrolyte molecules are charged and discharged on the electrodes, the efficiency of the electron transfer is of crucial importance for the performance of the device. The purpose of this work is to present a systematic atomic-level computational protocol for studying electron transfer between electrolyte and electrode. The computations are done by using constrained density functional theory (CDFT) to ensure that the electron is either on the electrode or in the electrolyte. The ab initio molecular dynamics (AIMD) is used to simulate the movement of the atoms. We use the Marcus theory to predict electron transfer rates and the combined CDFT-AIMD approach to compute the parameters for the Marcus theory where it is needed. We model the electrode with a single layer of graphene and methylviologen, 4,4'-dimethyldiquat, desalted basic red 5, 2-hydroxy-1,4-naphthaquinone, and 1,1-di(2-ethanol)-4,4-bipyridinium were selected for the electrolyte molecules. All of these molecules undergo consecutive electrochemical reactions with one electron being transferred at each stage. Because of significant electrode-molecule interactions, it is not possible to evaluate outer-sphere ET. This theoretical study contributes toward the development of a realistic-level prediction of electron transfer kinetics suitable for energy storage applications.

Tunneling-to-Hopping Transition in Multiheme Cytochrome Bioelectronic Junctions

Multiheme cytochromes (MHCs) have attracted much interest for use in nanobioelectronic junctions due to their high electronic conductances. Recent measurements on dry MHC junctions suggested that a coherent tunneling mechanism is operative over surprisingly long long distances (>3 nm), which challenges our understanding of coherent transport phenomena. Here we show that this is due to (i) a low exponential distance decay constant for coherent conduction in MHCs (β = 0.2 Å^-1) and (ii) a large density of protein electronic states which prolongs the coherent tunneling regime to distances that exceed those in molecular wires made of small molecules. Incoherent hopping conduction is uncompetitive due to the large energy level offset at the protein-electrode interface. Removing this offset, e.g., by gating, we predict that the transport mechanism crosses over from coherent tunneling to incoherent hopping at a protein size of ∼7 nm, thus enabling transport on the micrometer scale with a shallow polynomial (∼1/r) distance decay.

Implementation and Validation of Constrained Density Functional Theory Forces in the CP2K Package

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 (H₂O)₂⁺ in a vacuum, electron tunnelling between oxygen vacancy centers in solid MgO, and electron self-exchange in aqueous Ru²⁺–Ru³⁺. We find good agreement with previous plane-wave CDFT results for the same systems, but at a significantly lower computational cost, and we discuss the general reliability of condensed phase CDFT calculations.

Controllable Electron Transfer in Mixed-Valence Bridged Norbornylogous Compounds: Ab Initio Calculation Combined with a Parametric Model and Through-Bond and Through-Space Interpretation

In the context of a computationally guided approach to the controllable electron transfer in mixed-valence (MV) systems, in this article, we study the electron transfer (ET) in the series of oxidized norbornadiene C₇H₈ (I) and its polycyclic derivatives, C₁₂H₁₂ (II), C₁₇H₁₆, (III), C₂₇H₂₄ (IV), and C₃₂H₂₈ (V), with variable lengths of the bridge connecting redox sites. The work combines an ab initio CASSCF evaluation of the electronic structure of systems I-V with the parametric description in the framework of the biorbital two-mode vibronic model. The model involves coupling with the "breathing" mode and intercenter vibration modulating the distances between the redox fragments. The ab initio calculations were performed for two types of optimized structures of I-V: (a) charge-localized global minimum (C_s) and (b) symmetric configuration (C_2v) with the delocalized charge. This allows one to estimate the potential barrier separating charge-localized configurations as well as vibronic coupling parameters and the electron transfer integral. Along with the adiabatic approach, the quantum-mechanical analysis of the vibronic levels has been applied to precisely estimate the quantum effect of tunneling splitting. We estimate the "through-space" and "through-bond" contributions to the parameters interrelated with the charge transfer (CT). The through-space effect proves to be a major factor of ET at a short distance between the redox centers, whereas the through-bond contribution is dominant at a long distance. Vibronic coupling under the condition of through-space ET leads to the localization of the positive charge on the π-chromophore, while the through-bond component of ET results in compensating σ-shifts and subsequent charge delocalization over the bridge. The limitations of the parametric approach were discussed in the context of the two components contributing to the ET. Particularly, the bridge polarization in the course of through-bond ET proves to be beyond the basis of the employed parametric model.

Ultrafast estimation of electronic couplings for electron transfer between pi-conjugated organic molecules. II

The development of highly efficient methods for the calculation of electronic coupling matrix elements between the electron donor and acceptor is an important goal in theoretical organic semiconductor research. In Paper I [F. Gajdos, S. Valner, F. Hoffmann, J. Spencer, M. Breuer, A. Kubas, M. Dupuis, and J. Blumberger, J. Chem. Theory Comput. 10, 4653 (2014)], we introduced the analytic overlap method (AOM) for this purpose, which is an ultrafast electronic coupling estimator parameterized to and orders of magnitude faster than density functional theory (DFT) calculations at a reasonably small loss in accuracy. In this work, we reparameterize and extend the AOM to molecules containing nitrogen, oxygen, fluorine, and sulfur heteroatoms using 921 dimer configurations from the recently introduced HAB79 dataset. We find again a very good linear correlation between the frontier orbital overlap, calculated ultrafast in an optimized minimum Slater basis, and DFT reference electronic couplings. The new parameterization scheme is shown to be transferable to sulfur-containing polyaromatic hydrocarbons in experimentally resolved dimeric configurations. Our extension of the AOM enables high-throughput screening of very large databases of chemically diverse organic crystal structures and the application of computationally intense non-adiabatic molecular dynamics methods to charge transport in state-of-the-art organic semiconductors, e.g., non-fullerene acceptors.

HAB79: A new molecular dataset for benchmarking DFT and DFTB electronic couplings against high-level ab initio calculations

A new molecular dataset called HAB79 is introduced to provide ab initio reference values for electronic couplings (transfer integrals) and to benchmark density functional theory (DFT) and density functional tight-binding (DFTB) calculations. The HAB79 dataset is composed of 79 planar heterocyclic polyaromatic hydrocarbon molecules frequently encountered in organic (opto)electronics, arranged to 921 structurally diverse dimer configurations. We show that CASSCF/NEVPT2 with a minimal active space provides a robust reference method that can be applied to the relatively large molecules of the dataset. Electronic couplings are largest for cofacial dimers, in particular, sulfur-containing polyaromatic hydrocarbons, with values in excess of 0.5 eV, followed by parallel displaced cofacial dimers. V-shaped dimer motifs, often encountered in the herringbone layers of organic crystals, exhibit medium-sized couplings, whereas T-shaped dimers have the lowest couplings. DFT values obtained from the projector operator-based diabatization (POD) method are initially benchmarked against the smaller databases HAB11 (HAB7-) and found to systematically improve when climbing Jacob's ladder, giving mean relative unsigned errors (MRUEs) of 27.7% (26.3%) for the generalized gradient approximation (GGA) functional BLYP, 20.7% (15.8%) for hybrid functional B3LYP, and 5.2% (7.5%) for the long-range corrected hybrid functional omega-B97X. Cost-effective POD in combination with a GGA functional and very efficient DFTB calculations on the dimers of the HAB79 database give a good linear correlation with the CASSCF/NEVPT2 reference data, which, after scaling with a multiplicative constant, gives reasonably small MRUEs of 17.9% and 40.1%, respectively, bearing in mind that couplings in HAB79 vary over 4 orders of magnitude. The ab initio reference data reported here are expected to be useful for benchmarking other DFT or semi-empirical approaches for electronic coupling calculations.

The mystery of sub-picosecond charge transfer following irradiation of hydrated uridine monophosphate

The early mechanisms by which ionizing rays damage biological structures by so-called direct effects are largely elusive. In a recent picosecond pulse radiolysis study of concentrated uridine monophosphate solutions [J. Ma, S. A. Denisov, J.-L. Marignier, P. Pernot, A. Adhikary, S. Seki and M. Mostafavi, J. Phys. Chem. Lett., 2018, 9, 5105], unexpected results were found regarding the oxidation of the nucleobase. The signature of the oxidized nucleobase could not be detected 5 ps after the electron pulse, but only the oxidized phosphate, raising intriguing questions about the identity of charge-transfer mechanisms that could explain the absence of U⁺. We address here this question by means of advanced first-principles atomistic simulations of solvated uridine monophosphate, combining Density Functional Theory (DFT) with polarizable embedding schemes. We contrast three very distinct mechanisms of charge transfer covering the atto-, femto- and pico-second timescales. We first investigate the ionization mechanism and subsequent hole/charge migrations on a timescale of attoseconds to a few femtoseconds under the frozen nuclei approximation. We then consider a nuclear-driven phosphate-to-oxidized-nucleobase electron transfer, showing that it is an uncompetitive reaction channel on the sub-picosecond timescale, despite its high exothermicity and significant electronic coupling. Finally, we show that non-adiabatic charge transfer is enabled by femtosecond nuclear relaxation after ionization. We show that electronic decoherence and the electronic coupling strength are the key parameters that determine the hopping probabilities. Our results provide important insight into the interplay between electronics and nuclear motions in the early stages of the multiscale responses of biological matter subjected to ionizing radiation.

Electron transfer pathways from quantum dynamics simulations

This work explores the possibility of simulating an electron transfer process between a donor and an acceptor in real time using time-dependent density functional theory electron dynamics. To achieve this objective, a central issue to resolve is the definition of the initial state. This must be a non-equilibrium electronic state able to trigger the charge transfer dynamics; here, two schemes are proposed to prepare such states. One is based on the combination of the density matrices of the donor and acceptor converged separately with appropriate charges (for example, -1 for the donor and +1 for the acceptor). The second approach relied on constrained DFT to localize the charge on each fragment. With these schemes, electron transfer processes are simulated in different model systems of increasing complexity: an atomic hydrogen dimer, a polyacetylene chain, and the active site of the T. cruzi hybrid type A heme peroxidase, for which two possible electron transfer paths have been postulated. For the latter system, the present methodology applied in a hybrid Quantum Mechanics - Molecular Mechanics framework allows us to establish the relative probabilities of each path and provides insight into the inhibition of the electron transfer provoked by the substitution of tryptophan by phenylalanine in the W233F mutant.

Tunneling matrix element and tunneling pathways of protein electron transfer calculated with a fragment molecular orbital method

Practical ways to calculate the tunneling matrix elements and analyze the tunneling pathways for protein electron-transfer (ET) reactions with a fragment molecular orbital (FMO) method are presented. The straightforward use of minimal basis sets only for the atoms involved in the covalent bond detachment in FMO can properly describe the ETs through the protein main-chains with the cost-effective two-body corrections (FMO2) without losing the quality of double-zeta basis sets. The current FMO codes have been interfaced with density functional theory, polarizable continuum model, and model core potentials, with which the FMO-based protein ET calculations can consider the effects of electron correlation, solvation, and transition-metal redox centers. The reasonable performance of the FMO-based ET calculations is demonstrated for three different sets of protein-ET model molecules: (1) hole transfer between two tryptophans covalently bridged by a polyalanine linker in the ideal α-helix and β-strand conformations, (2) ET between two plastoquinones covalently bridged by a polyalanine linker in the ideal α-helix and β-strand conformations, and (3) hole transfer between ruthenium (Ru) and copper (Cu) complexes covalently bridged by a stretch of a polyglycine linker as a model for Ru-modified derivatives of azurin.

Uniform potential difference scheme to evaluate effective electronic couplings for superexchange electron transfer in donor-bridge-acceptor systems

This article proposes an ab initio quantum chemical method to evaluate the effective electronic coupling that determines the rate of superexchange electron transfer in donor-bridge-acceptor (D-B-A) systems. The method utilizes the fragment charge difference to define electronic diabatic states and to apply an electrostatic potential in a form of a uniform potential difference that mimics solvation effects on the relative energies of the electronic states. The two-state generalized Mulliken-Hush method is used to obtain the effective electronic coupling as the nondiagonal element of the effective Hamiltonian that is derived based on the Green's function approach and the quasi-degenerate perturbation theory. A theoretical basis is provided for the dependence of the calculated effective electronic coupling on the applied potential and for how to find the optimal potential to give the desired effective electronic coupling that coincides with the result of the minimum energy splitting method. The method is applied to typical D-B-A molecules and gives the effective electronic couplings in reasonable agreement with the experimental estimates.

PyCDFT: A Python package for constrained density functional theory

We present PyCDFT, a Python package to compute diabatic states using constrained density functional theory (CDFT). PyCDFT provides an object-oriented, customizable implementation of CDFT, and allows for both single-point self-consistent-field calculations and geometry optimizations. PyCDFT is designed to interface with existing density functional theory (DFT) codes to perform CDFT calculations where constraint potentials are added to the Kohn-Sham Hamiltonian. Here, we demonstrate the use of PyCDFT by performing calculations with a massively parallel first-principles molecular dynamics code, Qbox, and we benchmark its accuracy by computing the electronic coupling between diabatic states for a set of organic molecules. We show that PyCDFT yields results in agreement with existing implementations and is a robust and flexible package for performing CDFT calculations. The program is available at https://dx.doi.org/10.5281/zenodo.3821097.

Neutral excitation density-functional theory: an efficient and variational first-principles method for simulating neutral excitations in molecules

We introduce neutral excitation density-functional theory (XDFT), a computationally light, generally applicable, first-principles technique for calculating neutral electronic excitations. The concept is to generalise constrained density functional theory to free it from any assumptions about the spatial confinement of electrons and holes, but to maintain all the advantages of a variational method. The task of calculating the lowest excited state of a given symmetry is thereby simplified to one of performing a simple, low-cost sequence of coupled DFT calculations. We demonstrate the efficacy of the method by calculating the lowest single-particle singlet and triplet excitation energies in the well-known Thiel molecular test set, with results which are in good agreement with linear-response time-dependent density functional theory (LR-TDDFT). Furthermore, we show that XDFT can successfully capture two-electron excitations, in principle, offering a flexible approach to target specific effects beyond state-of-the-art adiabatic-kernel LR-TDDFT. Overall the method makes optical gaps and electron-hole binding energies readily accessible at a computational cost and scaling comparable to that of standard density functional theory. Owing to its multiple qualities beneficial to high-throughput studies where the optical gap is of particular interest; namely broad applicability, low computational demand, and ease of implementation and automation, XDFT presents as a viable candidate for research within materials discovery and informatics frameworks.

Unravelling electron transfer in peptide-cation complexes: a model for mimicking redox centres in proteins

We provide evidence that bound zinc promotes electron transfer in a peptide by changing the electronic properties of the peptide.

Electron transfer in extended systems: characterization by periodic density functional theory including the electronic coupling

We describe a new computer implementation of electron transfer (ET) theory in extended systems treated by periodic density functional theory (DFT), including the calculation of the electronic coupling transition element V_AB. In particular, the development opens up the full characterization of electron transfer in the solid state. The approach is valid for any single-determinant wavefunction with localized character representing the electronic structure of the system, from Hartree-Fock (HF) theory, to density functional theory (DFT), hybrid DFT theory, DFT+U theory, and constrained DFT (cDFT) theory. The implementation in CP2K reuses the high-performance functions of the code. The computational cost is equivalent to only one iteration of an HF calculation. We present test calculations for electron transfer in a number of systems, including a 1D-model of ferric oxide, hematite Fe₂O₃, rutile TiO₂, and finally bismuth vanadate BiVO₄.

Machine Learning for Predicting Electron Transfer Coupling

Electron transfer coupling is a critical factor in determining electron transfer rates. This coupling strength can be sensitive to details in molecular geometries, especially intermolecular configurations. Thus, studying charge transporting behavior with a full first-principle approach demands a large amount of computation resources in quantum chemistry (QC) calculation. To address this issue, we developed a machine learning (ML) approach to evaluate electronic coupling. A prototypical ML model for an ethylene system was built by kernel ridge regression with Coulomb matrix representation. Since the performance of the ML models highly dependent on their building strategies, we systematically investigated the generality of the ML models, the choice of features and target labels. The best ML model trained with 40 000 samples achieved a mean absolute error of 3.5 meV and greater than 98% accuracy in predicting phases. The distance and orientation dependence of electronic coupling was successfully captured. Bypassing QC calculation, the ML model saved 10-10⁴ times the computation cost. With the help of ML, reliable charge transport models and mechanisms can be further developed.

How To Extract Quantitative Information on Electronic Transitions from the Density Functional Theory "Black Box"

Electronic couplings and vertical excitation energies are crucial determinants of charge and excitation energy transfer rates in a broad variety of processes ranging from biological charge transfer to charge transport through inorganic materials, from molecular sensing to intracellular signaling. Density Functional Theory (DFT) is generally used to calculate these critical parameters, but the quality of the results is unpredictable because of the semiempirical nature of the available DFT approaches. This study identifies a small set of fundamental rules that enables accurate DFT computation of electronic couplings and vertical excitation energies in molecular complexes and materials. These rules are applied to predict efficient DFT approaches to coupling calculations. The result is an easy-to-use guide for reliable DFT descriptions of electronic transitions.

Biological relevance of charge transfer branching pathways in photolyases

The repair of sun-induced DNA lesions by photolyases is driven by a photoinduced electron transfer from a fully reduced FAD to the damaged DNA. A chain of several aromatic residues connecting FAD to solvent ensures the prior photoreduction of the FAD cofactor. In PhrA, a class III CPD photolyase, two branching tryptophan charge transfer pathways have been characterized. According to previous experiments, both pathways play a role in the FAD photoreduction. To provide a molecular insight to the charge transfer abilities of both pathways, we perform multiscales simulations where the protein motion and the positive charge are simultaneously propagated. Our computational approach reveals that one pathway drives a very fast charge transfer whereas the other pathway provides a very good thermodynamic stabilization of the positive charge. During the simulations, the positive charge firstly moves on the fast triad, while a reorganization of the close FAD˙^- environment occurs. Then, backward transfers can lead to the propagation of the positive charge on the second pathway. After one nanosecond, we observe a nearly equal probability to find the charge at ending tryptophan of either pathway; eventually the charge distribution will likely evolve towards a charge stabilization on the last tryptophan of the slowest pathway. Our results highlight the role the protein environment, which manages the association of a kinetic and a thermodynamic pathways to trigger a fast and efficient FAD photoreduction.

Computational construction of the electronic Hamiltonian for photoinduced electron transfer and Redfield propagation

The construction of open-system diabatic Hamiltonians relevant for the investigation of electron transfer processes is a computational challenge. Here all relevant parameters for Redfield propagations are extracted fromab initiocomputations.

Electron transfer characteristics of 2'-deoxy-2'-fluoro-arabinonucleic acid, a nucleic acid with enhanced chemical stability

The non-biological nucleic acid 2'-deoxy-2'-fluoro-arabinonucleic acid (2'F-ANA) may be of use because of its higher chemical stability than DNA in terms of resistance to hydrolysis and nuclease degradation. In order to investigate the charge transfer characteristics of 2'F-ANA, of relevance to applications in nucleic acid-based biosensors and chip technologies, we compare the electronic couplings for hole transfer between stacked nucleobase pairs in DNA and 2'F-ANA by carrying out density functional theory (DFT) calculations on geometries taken from molecular dynamics simulations. We find similar averages and distribution widths of the base-pair couplings in the two systems. On the basis of this result, 2'F-ANA is expected to have charge transfer properties similar to those of DNA, while offering the advantage of enhanced chemical stability. As such, 2'F-ANA may serve as a possible alternative to DNA for use in a broad range of nanobiotechnological applications. Furthermore, we show that the (experimentally observed) enhanced chemical stability resulting from the backbone modifications does not cause reduced fluctuations of the base-pair electronic couplings around the values found for "ideal" B-DNA (with standard step parameter values). Our study also supports the use of a DFT implementation, with the M11 functional, of the wave function overlap method to compute effective electronic couplings in nucleic acid systems.

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

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

Approximate DFT-based methods for generating diabatic states and calculating electronic couplings: models of two and more states

Four types of density functional theory (DFT)-based approaches are assessed in this work for the approximate construction of diabatic states and the evaluation of electronic couplings between these states. These approaches include the constrained DFT (CDFT) method, the constrained noninteracting electron (CNE) model to post-process Kohn-Sham operators, the approximate block-diagonalization (BD) of the Kohn-Sham operators, and the generalized Mulliken-Hush method. It is shown that the first three approaches provide a good description for long-distance intermolecular electron transfer (ET) reactions. On the other hand, inconsistent results were found when applying these approaches to intramolecular ET in strongly coupled, mixed-valence systems. Model analysis shows that this discrepancy is caused by the inappropriate use of the two-state model rather than the defects of the approaches themselves. The situation is much improved when more states are included in the model electronic Hamiltonian. The CNE and BD approaches can thus serve as efficient and robust alternatives for building ET models based on DFT calculations.

Functional role of an unusual tyrosine residue in the electron transfer chain of a prokaryotic (6-4) photolyase

Cryptochromes and photolyases form a flavoprotein family in which the FAD chromophore undergoes light induced changes of its redox state. During this process, termed photoreduction, electrons flow from the surface via conserved amino acid residues to FAD. The bacterial (6-4) photolyase PhrB belongs to a phylogenetically ancient group. Photoreduction of PhrB differs from the typical pattern because the amino acid of the electron cascade next to FAD is a tyrosine (Tyr391), whereas photolyases and cryptochromes of other groups have a tryptophan as direct electron donor of FAD. Mutagenesis studies have identified Trp342 and Trp390 as essential for charge transfer. Trp342 is located at the periphery of PhrB while Trp390 connects Trp342 and Tyr391. The role of Tyr391, which lies between Trp390 and FAD, is however unclear as its replacement by phenylalanine did not block photoreduction. Experiments reported here, which replace Tyr391 by Ala, show that photoreduction is blocked, underlining the relevance of Tyr/Phe at position 391 and indicating that charge transfer occurs via the triad 391-390-342. This raises the question, why PhrB positions a tyrosine at this location, having a less favourable ionisation potential than tryptophan, which occurs at this position in many proteins of the photolyase/cryptochrome family. Tunnelling matrix calculations show that tyrosine or phenylalanine can be involved in a productive bridged electron transfer between FAD and Trp390, in line with experimental findings. Since replacement of Tyr391 by Trp resulted in loss of FAD and DMRL chromophores, electron transfer cannot be studied experimentally in this mutant, but calculations on a mutant model suggest that Trp might participate in the electron transfer cascade. Charge transfer simulations reveal an unusual stabilization of the positive charge on site 391 compared to other photolyases or cryptochromes. Water molecules near Tyr391 offer a polar environment which stabilizes the positive charge on this site, thereby lowering the energetic barrier intrinsic to tyrosine. This opens a second charge transfer channel in addition to tunnelling through the tyrosine barrier, based on hopping and therefore transient oxidation of Tyr391, which enables a fast charge transfer similar to proteins utilizing a tryptophan-triad. Our results suggest that evolution of the first site of the redox chain has just been possible by tuning the protein structure and environment to manage a downhill hole transfer process from FAD to solvent.

Density Functional Physicality in Electronic Coupling Estimation: Benchmarks and Error Analysis

Electronic coupling estimates from constrained density functional theory configuration interaction (CDFT-CI) depend critically on choice of density functional. In this Letter, the orbital multielectron self-interaction error (OMSIE), vertical electron affinity (VEA), and vertical ionization potential (VIP) are shown to be the key indicators inherited from the density functional that determine the accuracy of electronic coupling estimates. An error metric η is derived to connect the three properties, based on the linear proportionality between electronic coupling and overlap integral, and the hypothesis that the slope of this line is a function of VEA/VIP, η = (1/N_testset)Σ_i^testset|-VE^Ref × OMSIE + ΔVE - ΔVE × OMSIE|_i. Based on η, BH&HLYP and LRC-ωPBEh are suggested as the best functionals for electron and hole transfer, respectively. Error metric η is therefore a useful predictor of errors in CDFT-CI electronic coupling, showing that the physical correctness of the density functional has a direct effect on the accuracy of the electronic coupling.

Charge Transport in Molecular Materials: An Assessment of Computational Methods

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.