Charge constrained density functional molecular dynamics for simulation of condensed phase electron transfer reactions

We present a plane-wave basis set implementation of charge constrained density functional molecular dynamics (CDFT-MD) for simulation of electron transfer reactions in condensed phase systems. Following earlier work of Wu et al. Phys. Rev. A 72, 024502 (2005), the density functional is minimized under the constraint that the charge difference between donor and acceptor is equal to a given value. The classical ion dynamics is propagated on the Born-Oppenheimer surface of the charge constrained state. We investigate the dependence of the constrained energy and of the energy gap on the definition of the charge, and present expressions for the constraint forces. The method is applied to the Ru2+-Ru3+ electron self-exchange reaction in aqueous solution. Sampling the vertical energy gap along CDFT-MD trajectories, and correcting for finite size effects, a reorganization free energy of 1.6 eV is obtained. This is 0.1-0.2 eV lower than a previous estimate based on a continuum model for solvation. smaller value for reorganization free energy can be explained by fact that the Ru-O distances of the divalent and trivalent Ru-hexahydrates are predicted to be more similar in the electron transfer complex than for the separated aqua-ions.Comment: 12 pages, 7 figure

Electron transfer and transport through multi-heme proteins: recent progress and future directions

I review recent experimental measurements probing electron transfer (ET) and electron transport (ETp) through multi-heme cytochromes (MHCs) as well as their theoretical interpretation. Examples include pump-probe spectroscopy of Ru-labeled MHCs aimed at determining heme–heme ET rates in MHCs and the measurement of the I–V characteristics of MHCs in bioelectronic junctions. While the ET mechanism appears to be well established for MHCs in aqueous solution, the ETp mechanism in bioelectronic junctions such as STM remains elusive partly due to the complexities of the electrode–protein interface

Water at an electrochemical interface - a simulation study

The results of molecular dynamics simulations of the properties of water in an aqueous ionic solution close to an interface with a model metallic electrode are described. In the simulations the electrode behaves as an ideally polarizable hydrophilic metal, supporting image charge interactions with charged species, and it is maintained at a constant electrical potential with respect to the solution so that the model is a textbook representation of an electrochemical interface through which no current is passing. We show how water is strongly attracted to and ordered at the electrode surface. This ordering is different to the structure that might be imagined from continuum models of electrode interfaces. Further, this ordering significantly affects the probability of ions reaching the surface. We describe the concomitant motion and configurations of the water and ions as functions of the electrode potential, and we analyze the length scales over which ionic atmospheres fluctuate. The statistics of these fluctuations depend upon surface structure and ionic strength. The fluctuations are large, sufficiently so that the mean ionic atmosphere is a poor descriptor of the aqueous environment near a metal surface. The importance of this finding for a description of electrochemical reactions is examined by calculating, directly from the simulation, Marcus free energy profiles for transfer of charge between the electrode and a redox species in the solution and comparing the results with the predictions of continuum theories. Significant departures from the electrochemical textbook descriptions of the phenomenon are found and their physical origins are characterized from the atomistic perspective of the simulations.Comment: 29 pages, 15 figure

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

Charge Transport in Organic Semiconductors: The Perspective from Nonadiabatic Molecular Dynamics

ConspectusOrganic semiconductors (OSs) are an exciting class of materials that have enabled disruptive technologies in this century including large-area electronics, flexible displays, and inexpensive solar cells. All of these technologies rely on the motion of electrical charges within the material and the diffusivity of these charges critically determines their performance. In this respect, it is remarkable that the nature of the charge transport in these materials has puzzled the community for so many years, even for apparently simple systems such as molecular single crystals: some experiments would better fit an interpretation in terms of a localized particle picture, akin to molecular or biological electron transfer, while others are in better agreement with a wave-like interpretation, more akin to band transport in metals.Exciting recent progress in the theory and simulation of charge carrier transport in OSs has now led to a unified understanding of these disparate findings, and this Account will review one of these tools developed in our laboratory in some detail: direct charge carrier propagation by quantum-classical nonadiabatic molecular dynamics. One finds that even in defect-free crystals the charge carrier can either localize on a single molecule or substantially delocalize over a large number of molecules depending on the relative strength of electronic couplings between the molecules, reorganization, or charge trapping energy of the molecule and thermal fluctuations of electronic couplings and site energies, also known as electron-phonon couplings.Our simulations predict that in molecular OSs exhibiting some of the highest measured charge mobilities to date, the charge carrier forms "flickering" polarons, objects that are delocalized over 10-20 molecules on average and that constantly change their shape and extension under the influence of thermal disorder. The flickering polarons propagate through the OS by short (≈10 fs long) bursts of the wave function that lead to an expansion of the polaron to about twice its size, resulting in spatial displacement, carrier diffusion, charge mobility, and electrical conductivity. Arguably best termed "transient delocalization", this mechanistic scenario is very similar to the one assumed in transient localization theory and supports its assertions. We also review recent applications of our methodology to charge transport in disordered and nanocrystalline samples, which allows us to understand the influence of defects and grain boundaries on the charge propagation.Unfortunately, the energetically favorable packing structures of typical OSs, whether molecular or polymeric, places fundamental constraints on charge mobilities/electronic conductivity compared to inorganic semiconductors, which limits their range of applications. In this Account, we review the design rules that could pave the way for new very high-mobility OS materials and we argue that 2D covalent organic frameworks are one of the most promising candidates to satisfy them.We conclude that our nonadiabatic dynamics method is a powerful approach for predicting charge carrier transport in crystalline and disordered materials. We close with a brief outlook on extensions of the method to exciton transport, dissociation, and recombination. This will bring us a step closer to an understanding of the birth, survival, and annihiliation of charges at interfaces of optoelectronic devices

Nanosecond solvation dynamics of the hematite/liquid water interface at hybrid DFT accuracy using committee neural network potentials

Metal oxide/water interfaces play an important role in biology, catalysis, energy storage and photocatalytic water splitting. The atomistic structure at these interfaces is often difficult to characterize by experimental techniques, whilst results from ab initio molecular dynamics simulations tend to be uncertain due to the limited length and time scales accessible. In this work, we train a committee neural network potential to simulate the hematite/water interface at the hybrid DFT level of theory to reach the nanosecond timescale and systems containing more than 3000 atoms. The NNP enables us to converge dynamical properties, not possible with brute-force ab initio molecular dynamics. Our simulations uncover a rich solvation dynamics at the hematite/water interface spanning three different time scales: picosecond H-bond dynamics between surface hydroxyls and the first water layer, in-plane/out-of-plane tilt motion of surface hydroxyls on the 10 ps time scale, and diffusion of water molecules from the oxide surface characterized by a mean residence lifetime of about 60 ps. Calculation of vibrational spectra confirm that H-bonds between surface hydroxyls and first layer water molecules are stronger than H-bonds in bulk water. Our study showcases how state of the art machine learning approaches can routinely be utilized to explore the structural dynamics at transition metal oxide interfaces with complex electronic structure. It foreshadows that c-NNPs are a promising tool to tackle the sampling problem in ab initio electrochemistry with explicit solvent molecules

Flavin Binding to the Deca-heme Cytochrome MtrC: Insights from Computational Molecular Simulation

Certain dissimilatory bacteria have the remarkable ability to use extracellular metal oxide minerals instead of oxygen as terminal electron sinks, using a process known as "extracellular respiration". Specialized multiheme cytochromes located on the outer membrane of the microbe were shown to be crucial for electron transfer from the cell surface to the mineral. This process is facilitated by soluble, biogenic flavins secreted by the organism for the purpose of acting as an electron shuttle. However, their interactions with the outer-membrane cytochromes are not established on a molecular scale. Here, we study the interaction between the outer-membrane deca-heme cytochrome MtrC from Shewanella oneidensis and flavin mononucleotide (FMN in fully oxidized quinone form) using computational docking. We find that interaction of FMN with MtrC is significantly weaker than with known FMN-binding proteins, but identify a mildly preferred interaction site close to heme 2 with a dissociation constant (Kd) = 490 μM, in good agreement with recent experimental estimates, Kd = 255 μM. The weak interaction with MtrC can be qualitatively explained by the smaller number of hydrogen bonds that the planar headgroup of FMN can form with this protein compared to FMN-binding proteins. Molecular dynamics simulation gives indications for a possible conformational switch upon cleavage of the disulphide bond of MtrC, but without concomitant increase in binding affinities according to this docking study. Overall, our results suggest that binding of FMN to MtrC is reversible and not highly specific, which may be consistent with a role as redox shuttle that facilitates extracellular respiration

Detailed balance, internal consistency, and energy conservation in fragment orbital- based surface hopping

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

Methemoglobin formation in mutant hemoglobin α chains: electron transfer parameters and rates

Hemoglobin-mediated transport of dioxygen (O2) critically depends on the stability of the reduced (Fe2+) form of the heme cofactors. Some protein mutations stabilize the oxidized (Fe3+) 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 (Fe3+) state (in particular, the Hb Miyagi variant with K61E mutation). Solvent reorganization (λsolv 73–96%) makes major contributions to reorganization free energy, whereas protein reorganization (λprot) accounts for 27–30% except for the Miyagi and J-Buda variants (λprot ∼4%). Analysis of heme-solvent H-bonding interactions among variants provide insights into the role of Lys61 residue in stabilizing the Fe2+ state. Semiclassical Marcus ET theory-based calculations predict experimental kET 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

FOB-SH: Fragment orbital-based surface hopping for charge carrier transport in organic and biological molecules and materials

We introduce a fragment orbital-based fewest switches surface hopping method, FOB-SH, designed to efficiently simulate charge carrier transport in strongly fluctuating condensed phase systems such as organic semiconductors and biomolecules. The charge carrier wavefunction is expanded and the electronic Hamiltonian constructed in a set of singly occupied molecular orbitals of the molecular sites that mediate the charge transfer. Diagonal elements of the electronic Hamiltonian (site energies) are obtained from a force field, whereas the off-diagonal or electronic coupling matrix elements are obtained using our recently developed analytic overlap method. We derive a general expression for the exact forces on the adiabatic ground and excited electronic state surfaces from the nuclear gradients of the charge localized electronic states. Applications to electron hole transfer in a model ethylene dimer and through a chain of ten model ethylenes validate our implementation and demonstrate its computational efficiency. On the larger system, we calculate the qualitative behaviour of charge mobility with change in temperature T for different regimes of the intermolecular electronic coupling. For small couplings, FOB-SH predicts a crossover from a thermally activated regime at low temperatures to a band-like transport regime at higher temperatures. For higher electronic couplings, the thermally activated regime disappears and the mobility decreases according to a power law. This is interpreted by a gradual loss in probability for resonance between the sites as the temperature increases. The polaron hopping model solved for the same system gives a qualitatively different result and underestimates the mobility decay at higher temperatures. Taken together, the FOB-SH methodology introduced here shows promise for a realistic investigation of charge carrier transport in complex organic, aqueous, and biological systems