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 × 10 s. 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.

No abstract

No abstract

ABSTRACT:The interaction of water with metal oxide surfaces plays a crucial role in the catalytic and geochemical behavior of metal oxides. In a vast majority of studies, the interfacial structure is assumed to arise from a relatively static lowest energy configuration of atoms, even at room temperature. Using hematite (-Fe2O3) as a model oxide, we show through a direct comparison of in situ synchrotron X-ray scattering with density functional theorybased molecular dynamics (DFT-MD) simulations that the structure of the (11 ̅ 02) termination is dynamically stabilized by picosecond water exchange. Simulations show frequent exchanges between terminal aquo groups and adsorbed water in locations and with partial residence times consistent with experimentally determined atomic sites and fractional occupancies. Frequent water exchange occurs even for an ultrathin adsorbed water film persisting on the surface under a dry atmosphere. The resulting time-averaged interfacial structure consists of a ridged lateral arrangement of adsorbed water molecules hydrogen bonded to terminal aquo groups. Surface pKa prediction based on bond valence analysis suggests that water exchange will influence the proton transfer reactions underlying the acid/base reactivity at the interface. Our findings provide important new insights for understanding complex interfacial chemical processes at metal oxide-water interfaces.The interfaces between metal oxides and water are among the most important in nature and in emerging energy applications, with wide ranging impacts from photocatalytic water splitting [1][2][3][4] to the geochemical cycling of elements 5,6 . Key chemical processes such as adsorption, electron transfer, growth, and dissolution all depend principally on the atomic structure adopted at these interfaces. For example, dissolution and solute adsorption are regulated by the structure of interfacial water 7,8 . Surface acid/base chemistry 9,10 arises from the types and arrangement of terminal metal-coordinating aquo/hydroxyl groups 3,11-13 .At room temperature an interface is at dynamic equilibrium. In principle, the average interfacial structure depends on the interplay of relatively static atoms at the solid surface with relatively dynamic overlying water molecules. Simulations suggest that movement of overlying water molecules can play an essential role in stabilizing the interface and influencing its chemical behavior 14,15 . However, simulated [14][15][16][17] or spectroscopically probed 18 dynamics are seldom integrated with experimentally derived interface structure models to achieve comprehensive insight into interfacial structure 4 . To understand and predict chemical processes at dynamically active metal oxide-water interfaces, structure and dynamics must be considered as a unified whole.Accurate measurements of interface structure and water ordering rely on interface-sensitive synchrotron X-ray scattering methods 19 . The analysis of multiple crystal truncation rods (CTRs) provides a complete 3-dimensional interface mode...

The interface between transition-metal oxides and aqueous solutions plays an important role in biogeochemistry and photoelectrochemistry, but the atomistic structure is often elusive. Here we report on the surface geometry, solvation structure, and thermal fluctuations of the hydrogen bonding network at the hematite (001)-water interface as obtained from hybrid density functional theory-based molecular dynamics. We find that the protons terminating the surface form binary patterns by either pointing in-plane or out-of-plane. The patterns exist for about 1 ps and spontaneously interconvert in an ultrafast, solvent-driven process within 50 fs. This results in only about half of the terminating protons pointing toward the solvent and being acidic. The lifetimes of all hydrogen bonds formed at the interface are shorter than those in pure liquid water. The solvation structure reported herein forms the basis for a better fundamental understanding of electron transfer coupled to proton transfer reactions at this important interface.

Reaction barriers are a crucial ingredient for first principles based computational retro-synthesis efforts as well as for comprehensive reactivity assessments throughout chemical compound space. While extensive databases of experimental results exist, modern quantum machine learning applications require atomistic details which can only be obtained from quantum chemistry protocols. For competing E2 and S N 2 reaction channels we report 4,466 transition state and 143,200 reactant complex geometries and energies at MP2/6-311G(d) and single point DF-LCCSD/cc-pVTZ level of theory, respectively, covering the chemical compound space spanned by the substituents NO2, CN, CH3, and NH2 and early halogens (F, Cl, Br) and hydrogen as nucleophiles and early halogens as leaving groups. Reactants are chosen such that the activation energy of the competing E2 and S N 2 reactions are of comparable magnitude. The correct concerted motion for each of the one-step reactions has been validated for all transition states. We demonstrate how quantum machine learning models can support data set extension, and discuss the distribution of key internal coordinates of the transition states.

The computational prediction of atomistic structure is a long-standing problem in physics, chemistry, materials, and biology. Conventionally, force-fields or ab initio methods determine structure through energy minimization, which is either approximate or computationally demanding. This accuracy/cost trade-off prohibits the generation of synthetic big data sets accounting for chemical space with atomistic detail. Exploiting implicit correlations among relaxed structures in training data sets, our machine learning model Graph-To-Structure (G2S) generalizes across compound space in order to infer interatomic distances for out-of-sample compounds, effectively enabling the direct reconstruction of coordinates, and thereby bypassing the conventional energy optimization task. The numerical evidence collected includes 3D coordinate predictions for organic molecules, transition states, and crystalline solids. G2S improves systematically with training set size, reaching mean absolute interatomic distance prediction errors of less than 0.2 Å for less than eight thousand training structures — on par or better than conventional structure generators. Applicability tests of G2S include successful predictions for systems which typically require manual intervention, improved initial guesses for subsequent conventional ab initio based relaxation, and input generation for subsequent use of structure based quantum machine learning models.

The interplay of kinetics and thermodynamics governs reactive processes, and their control is key in synthesis efforts. While sophisticated numerical methods for studying equilibrium states have well advanced, quantitative predictions of kinetic behavior remain challenging. We introduce a reactant-to-barrier (R2B) machine learning model that rapidly and accurately infers activation energies and transition state geometries throughout the chemical compound space. R2B exhibits improving accuracy as training set sizes grow and requires as input solely the molecular graph of the reactant and the information of the reaction type. We provide numerical evidence for the applicability of R2B for two competing text-book reactions relevant to organic synthesis, E2 and S N 2, trained and tested on chemically diverse quantum data from the literature. After training on 1-1.8k examples, R2B predicts activation energies on average within less than 2.5 kcal/mol with respect to the coupled-cluster singles doubles reference within milliseconds. Principal component analysis of kernel matrices reveals the hierarchy of the multiple scales underpinning reactivity in chemical space: Nucleophiles and leaving groups, substituents, and pairwise substituent combinations correspond to systematic lowering of eigenvalues. Analysis of R2B based predictions of ∼11.5k E2 and S N 2 barriers in the gas-phase for previously undocumented reactants indicates that on average, E2 is favored in 75% of all cases and that S N 2 becomes likely for chlorine as nucleophile/leaving group and for substituents consisting of hydrogen or electron-withdrawing groups. Experimental reaction design from first principles is enabled due to R2B, which is demonstrated by the construction of decision trees. Numerical R2B based results for interatomic distances and angles of reactant and transition state geometries suggest that Hammond's postulate is applicable to S N 2, but not to E2.