Kinetics of trifurcated electron flow in the decaheme bacterial proteins MtrC and MtrF.

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 [Formula: see text]-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.

Cysteine Linkages Accelerate Electron Flow through Tetra-Heme Protein STC.

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 a higher degree, the pathway model of biological ET partly capture the predicted rate enhancements, our study highlights the importance of the atomistic and chemical nature of the tunneling medium at short biological tunneling distances. Cysteine linkages are likely to enhance electron flow also in the larger deca-heme proteins MtrC and MtrF, where heme-heme motifs with sub-optimal edge-to-edge distances are used to shuttle electrons in multiple directions.

Electronic couplings for molecular charge transfer: benchmarking CDFT, FODFT and FODFTB against high-level ab initio calculations. II.

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.

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.

In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated π-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.

Ultrafast Estimation of Electronic Couplings for Electron Transfer between π-Conjugated Organic Molecules.

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.

On the Inapplicability of Electron-Hopping Models for the Organic Semiconductor Phenyl-C61-butyric Acid Methyl Ester (PCBM).

Phenyl-C61-butyric acid methyl ester (PCBM) is one of the most popular semiconductors in organic photovoltaic cells, but the electron-transport mechanism in the microcrystalline domains of this material as well as its preferred packing structure remain unclear. Here we use density functional theory to calculate electronic-coupling matrix elements, reorganization energies, and activation energies for available experimental and model crystal structures. We find that the picture of an excess electron hopping from one fullerene to another does not apply for any of the crystalline phases, rendering traditional rate equations inappropriate. We also find that the cohesive energy increases in the order body-centered-cubic < hexagonal < simple cubic < monoclinic < triclinic, independently of the type of dispersion correction used. Our results indicate that the coupled electron-ion dynamics needs to be solved explicitly to obtain a realistic description of charge transfer in this material.