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

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

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

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

Mechanoelectric Response of Single-Crystal Rubrene from Ab Initio Molecular Dynamics

A robust understanding of the mechanoelectric response of organic semiconductors is crucial for the development of materials for flexible electronics. In particular, the prospect of using external mechanical strain to induce a controlled modulation in the charge mobility of the material is appealing. Here we develop an accurate computational protocol for the prediction of the mechanical strain dependence of charge mobility. Ab initio molecular dynamics simulations with a van der Waals density functional are carried out to quantify the off-diagonal electronic disorder in the system as a function of strain by the explicit calculation of the thermal distributions of electronic coupling matrix elements. The approach is applied to a representative molecular organic semiconductor, single-crystal rubrene. We find that charge mobility along the high-mobility direction a⃗ increases with compressive strain, as one might expect. However, the increase is larger when compressive strain is applied in the perpendicular direction than in the parallel direction with respect to a⃗, in agreement with experimental reports. We show that this seemingly counterintuitive result is a consequence of a significantly greater suppression of electronic coupling fluctuations in the range of 50-150 cm-1, when strain is applied in the perpendicular direction. Thus our study highlights the importance of considering off-diagonal electron-phonon coupling in understanding the mechanoelectric response of organic semiconducting crystals. The computational approach developed here is well suited for the accurate prediction of strain-charge mobility relations and should provide a useful tool for the emerging field of molecular strain engineering

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

Ultrathin porphyrin and tetra-indole covalent organic frameworks for organic electronics applications

The electronic and charge transport properties of porphyrin and tetra-indole porphyrinoid single layer covalent organic frameworks (COFs) are investigated by means of density functional theory calculations. Ultrathin diacetylene-linked COFs based on oxidized tetra-indole cores are narrow gap 2D semiconductors, featuring a pronounced anisotropic electronic band structure due to the combination of dispersive and flat band characteristics, while registering high room temperature charge carrier mobilities. The capability of bandgap and charge carrier localization tuning via the careful selection of fourfold porphyrin and porphyrinoid cores and twofold articulated linkers is demonstrated, with the majority of systems exhibiting electronic gap values between 1.75 eV and 2.3 eV. Tetra-indoles are also capable of forming stable monolayers via non-articulated core fusing, resulting in 2D morphologies with extended π-conjugation and semi-metallic behavior

Polaronic structure of excess electrons and holes for a series of bulk iron oxides

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