Interference, fluctuation, and alternation of electron tunneling in protein media. 1. Two tunneling routes in photosynthetic reaction center alternate due to thermal fluctuation of protein conformation

Electron tunneling routes for the electron transfer from the bacteriopheophytin anion to the primary quinone in the bacterial photosynthetic reaction center of Rhodobactor sphaeroides are investigated by a combined method of molecular dynamics simulations for the protein conformation fluctuation and quantum chemical calculations for the electronic states of the donor, acceptor, and protein medium. The analysis of the tunneling route is made by mapping interatomic electron tunneling currents for each protein conformation. We found that there are two dominant routes mainly passing through Trp(M252) (Trp route) or mainly passing through Met(M218) (Met route). Actual electron tunneling pathways alternate between the two routes, depending on the protein conformation which varies with time. When either the Trp route or the Met route dominates, the electron tunneling matrix element /T(DA)/ becomes large. When both the Trp route and the Met route dominate, /T(DA)/ becomes very small due to the destructive interference of the electron tunneling currents between the two routes. We found that a linear relationship exists between the value of /T(DA)/ and the inverse of the degree of destructive interference Q for a wide range of values (ca. 3-10(3) for Q). A similar relationship was also found previously for electron transfer in ruthenium-modified azurins, suggesting that this relationship holds true in general. From these results, we are led to the conclusion that /T(DA)/ cannot exceed a maximum value at Q = 1, even if much variation of /T(DA)/ happens due to the fluctuation of protein conformation. We also conclude that the property of the electron transfer alternates between constructive and destructive interference, due to the fluctuation of protein conformation. It is impossible to keep a system in either constructive or destructive interference because thermal fluctuation of protein conformation takes place.     

On the electron transfer through Geobacter sulfurreducens PilA protein

Geobacter sulfurreducens pili composed of the Type IV pili structural peptide PilA have been implicated as efficient electronic conductors. Though investigated experimentally, no detailed theoretical studies have been performed to date that provide quantitative estimation of the transmission spectrum, electron transfer (ET) paths, efficiency of current generation, and other factors needed for understanding possible mechanisms of conductivity. In the present work, we calculate from first principles the possibilities of electron tunneling through 3 PilA fragments which structure was identified recently by NMR. The results indicate that positively charged amino acids, arginines and lysines form electrostatic traps in the middle of the peptide preventing ET at low bias voltages (<～6 V). At higher biases the traps are filled with electrons making possible sequential electron tunneling through the central part of the protein. In addition, leucines and phenylalanines form ET loops facilitating electron stabilization within the protein and sequential ET. Our results indicate that ET through the PilA protein cannot occur by coherent ET, but suggest a sequential (incoherent) mechanism. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1706–1717     

Anomalous temperature-isotope dependence in proton-coupled electron transfer

Motivated by the experiments of Hodgkiss et al. [J. Phys. Chem. (submitted)] on electron transfer (ET) through a H-bonding interface, we present a new theoretical model for proton-coupled electron transfer (PCET) in the condensed phase, that does not involve real proton transfer. These experiments, which directly probe the joint T-isotope effects in coupled charge transfer reactions, show anomalous T dependence in k(H)k(D), where k(H) and k(D) are the ET rates through the H-bonding interface with H-bonded protons and deuterons, respectively. We address the anomalous T dependence of the k(H)k(D) in our model by attributing the modulation of the electron tunneling dynamics to bath-induced fluctuations in the proton coordinate, so that the mechanism for coupled charge transfer might be better termed vibrationally assisted ET rather than PCET. We argue that such a mechanism may be relevant to understanding traditional PCET processes, i.e., those in which protons undergo a transfer from donor to acceptor during the course of ET, provided there is an appropriate time scale separating both coupled charge transfers. Likewise, it may also be useful in understanding long-range ET in proteins, where tunneling pathways between redox cofactors often pass through H-bonded amino acid residues, or other systems with sufficiently decoupled proton and electron donating functionalities.     

Interference, fluctuation, and alternation of electron tunneling in protein media. 2. Non-condon theory for the energy gap dependence of electron transfer rate

Developing the quantum transition rate theory of Prezhdo and Rossky (J. Chem. Phys. 1997, 107, 5863), we produced a new non-Condon theory of the rate of electron transfer (ET) which happens through a protein medium with conformational fluctuation. The new theory is expressed by a convolution form of the power spectrum for the autocorrelation function of the electronic tunneling matrix element T(DA)(t) with quantum correction and the ordinary Franck-Condon factor. The new theory satisfies the detailed balance condition for the forward and backward ET rates. The ET rate formula is divided into two terms of elastic and inelastic tunneling mechanisms on the mathematical basis. The present theory is applied to the ET from Bph(-) to Q(A) in the reaction center of Rhodobacter sphaeroides. Numerical calculations of T(DA)(t) were made by a combined method of molecular dynamics simulations and quantum chemistry calculations. We showed that the normalized autocorrelation function of T(DA)(t) is almost expressed by exponential forms. The calculated energy gap law of the ET rate is nearly Marcus' parabola in most of the normal region and around the maximum region, but it does not decay substantially in the inverted region, which is called the anomalous inverted region. We also showed that the energy gap law at the high uphill energy gap in the normal region is elevated considerably from the Marcus' parabola, which is called the anomalous normal region. Those anomalous energy gap laws are due to the inelastic tunneling mechanism which works actively at the energy gap far from zero. We presented an empirical formula for easily calculating the non-Condon ET rate, which is usable by many researchers. We provided experimental evidence for the anomalous inverted region which was basically reproduced by the present theory. The present theory was extensively compared with the previous non-Condon theories.     

Long-distance electron tunneling in proteins

Long-distance tunneling is the major mechanism of electron transfer (ET) in proteins. For a number of years, a major question has been whether specific electron tunneling pathways exist. This question is still debated in the literature, because the pathways are not observed directly, and interpretation of experimental results on ET rates involves ambiguities. The extremely small tunneling interactions are difficult to calculate accurately. Recently, there has been remarkable progress in the area; however, some problems still remain unresolved. The accurate prediction of the absolute rates of long-distance ET reactions and other biological charge-transfer reactions is a particularly pressing issue. The current theoretical calculations indicate that the specific paths do exist in static protein structures. However, the protein motions can result in significant averaging of the spatial tunneling patterns, and it is not clear how accurately subtle quantum interference effects are described by the present theories. The key to resolving these issues is to perform accurate, first-principles calculations of electron tunneling that include the dynamics of the protein. This paper reviews some of theoretical issues of electron tunneling dynamics in inhomogeneous organic media.     

Long-range interfacial electron transfer and electrocatalysis of molecular scale <Emphasis Type="Italic">Prussian</Emphasis> Blue nanoparticles linked to Au(111)-electrode surfaces by different chemical contacting groups

We have explored interfacial electrochemical electron transfer (ET) and electrocatalysis of 5–6 nm Prussian Blue nanoparticles (PBNPs) immobilized on Au(111)-electrode surfaces via molecular wiring with variable-length, and differently functionalized thiol-based self-assembled molecular monolayers (SAMs). The SAMs contain positively (?NH₃ ⁺) or negatively charged (–COO–) terminal group, as well an electrostatically neutral hydrophobic terminal group (–CH₃). The surface microscopic structures of the immobilized PBNPs were characterized by high-resolution atomic force microscopy (AFM) directly in aqueous electrolyte solution under the same conditions as for electrochemical measurements. The PBNPs displayed fast and reversible interfacial ET on all the surfaces, notably in multi-ET steps as reflected in narrow voltammetric peaks. The ET kinetics can be controlled by adjusting the length of the SAM forming linker molecules. The interfacial ET rate constants were found to depend exponentially on the ET distance for distances longer than a few methylene groups in the chain, with decay factors (β) of 0.9, 1.1, and 1.3 per CH₂, for SAMs terminated by ?NH₃ ⁺,–COO–, and–CH₃, respectively. This feature suggests, first that the interfacial ET processes follow a tunneling mechanism, resembling that of metalloproteins in a similar assembly. Secondly, the electronic contact of the SAM terminal groups that anchor non-covalently the PBNP are crucial as reported for other types of molecular junctions. Highly efficient PBNP electrocatalysis of H₂O₂ reduction was also observed for the three linker groups, and the electrocatalytic mechanisms analyzed.     

Water-mediated electron transfer between protein redox centers

Recent experimental and theoretical investigations show that water molecules between or near redox partners can significantly affect their electron-transfer (ET) properties. Here we study the effects of intervening water molecules on the electron self-exchange reaction of azurin (Az), by performing a conformational sampling on the water medium and by using a newly developed ab initio method to calculate transfer integrals between molecular redox sites. We show that the insertion of water molecules at the interface between the copper active sites of Az dimers slightly increases the overall ET rate, while some favorable water conformations can considerably enhance the ET kinetics. These features are traced back to the interplay of two competing factors: the electrostatic interaction between the water and protein subsystems (mainly opposing the ET process for the water arrangements drawn from MD simulations) and the effectiveness of water in mediating ET coupling pathways. Such an interplay provides a physical basis for the found absence of correlation between the electronic couplings derived through ab initio electronic structure calculations and the related quantities obtained through the Empirical Pathways (EP) method. In fact, the latter does not account for electrostatic effects on the transfer integrals. Thus, we conclude that the water-mediated electron tunneling is not controlled by the geometry of a single physical pathway. We discuss the results in terms of the interplay between different ET pathways controlled by the conformational changes of one of the water molecules via its electrostatic influence. Finally, we examine the dynamical effects of the interfacial water and check the validity of the Condon approximation.     

Automatic retrosynthetic route planning using template-free models

Retrosynthetic route planning can be considered a rule-based reasoning procedure. The possibilities for each transformation are generated based on collected reaction rules, and then potential reaction routes are recommended by various optimization algorithms. Although there has been much progress in computer-assisted retrosynthetic route planning and reaction prediction, fully data-driven automatic retrosynthetic route planning remains challenging. Here we present a template-free approach that is independent of reaction templates, rules, or atom mapping, to implement automatic retrosynthetic route planning. We treated each reaction prediction task as a data-driven sequence-to-sequence problem using the multi-head attention-based Transformer architecture, which has demonstrated power in machine translation tasks. Using reactions from the United States patent literature, our end-to-end models naturally incorporate the global chemical environments of molecules and achieve remarkable performance in top-1 predictive accuracy (63.0%, with the reaction class provided) and top-1 molecular validity (99.6%) in one-step retrosynthetic tasks. Inspired by the success rate of the one-step reaction prediction, we further carried out iterative, multi-step retrosynthetic route planning for four case products, which was successful. We then constructed an automatic data-driven end-to-end retrosynthetic route planning system (AutoSynRoute) using Monte Carlo tree search with a heuristic scoring function. AutoSynRoute successfully reproduced published synthesis routes for the four case products. The end-to-end model for reaction task prediction can be easily extended to larger or customer-requested reaction databases. Our study presents an important step in realizing automatic retrosynthetic route planning.

Retrosynthetic pathway planning using a template-free model coupled with heuristic Monte Carlo tree search.     

Influence of end group and surface structure on the current-voltage characteristics of alkanethiol monolayers on Au(111)

We present density functional theory calculations of the electronic structure and tunneling characteristics of alkanethiolate monolayers on Au(111). We systematically analyze radical3 x radical3 full coverage monolayers of SC6H12X molecules with different terminal groups, X=CH3, NH2, SH, OH, COOH, OCH3, on defect-free ("perfect") Au(111). We also study the influence of the surface-molecule bonding structure by comparing the properties of monolayers of SC6H12CH3 molecules on the perfect surface and on Au(111) surfaces with vacancies or adatoms. The tunneling currents (I) through the adsorbed monolayers with a single chemical contact have been calculated within the Tersoff-Hamann approach for voltages between -1 and +1 V. Computed currents are found to depend linearly on V at low voltage, with typical values of approximately 60 and 150 pA/molecule at 0.2 and 0.5 V, respectively, in good agreement with several experimental data. Computed tunneling currents show also a significant dependence on both the terminal group X and the surface structure. In particular, in order of decreasing intensities, currents for the different end groups are NH2 approximately SH>CH3>OH>OCH3>COOH. The relationships between the tunneling current, the work function of the surface+SAM, and the lineup of the HOMO with respect to the Fermi energy of the metal surface are examined.     

Semiclassical treatments of electron transfer rate from weak to strong electronic coupling regime

Electron transfer (ET) rate is a fundamental parameter to characterize ET processes in physical, chemical, material and biologic sciences. It is affected by a number of quantum phenomena, such as nuclear tunneling, curve crossing, quantum interference, and the coupling to the environment. It is thus a challenge to accurately evaluate the ET rate since one has to incorporate both quantum effects and dissipation. In this review article, we present several semiclassical theories proposed in our group to cover the regime from weak to strong electronic coupling. Their applications to some concrete systems are also shown.     

Single electron transfer events and dynamical heterogeneity in the small protein azurin from Pseudomonas aeruginosa

Monitoring the fluorescence of single-dye-labeled azurin molecules, we observed the reaction of azurin with hexacyanoferrate under controlled redox potential yielding data on the timing of individual (forward and backward) electron transfer (ET) events. Change-point analysis of the time traces demonstrates significant fluctuations of ET rates and of mid-point potential E₀. These fluctuations are a signature of dynamical heterogeneity, here observed on a 14 kDa protein, the smallest to date. By correlating changes in forward and backward reaction rates we found that 6% of the observed change events could be explained by a change in midpoint potential, while for 25% a change of the donor–acceptor coupling could explain the data. The remaining 69% are driven by variations in complex association constants or structural changes that cause forward and back ET rates to vary independently. Thus, the observed spread in individual ET rates could be related in a unique way to variations in molecular parameters. The relevance for the understanding of metabolic processes is briefly discussed.

Observing electron transfer events in individual azurin molecules, we relate the spread in transfer rates in a unique way to variations in molecular parameters.     

Photoinduced electron transfer across linearly fused oligo-norbornyl structures

The rates of photoinduced electron transfer (ET) reactions across two oligo-norbornyl spacer groups (S), that is, structure 1 fused by two norbornadiene (NBD) units and structure 2 fused by three NBD units, are examined. Substituted naphthalene acted as an electron donor (D), whilst ethylene-1,2-dicarboxylate as an electron acceptor (A). ET rates were measured by fluorescence quenching experiments on these D-S-A dyads, and the results were correlated with reaction free energies according to the Marcus relationship. It was found that naphthalene with phenyl substituents showed relatively slower ET rates. The conformational flexibility of phenyl substituents may cause a hindrance on the electronic coupling between D and A. Another salient feature was the abnormally high quenching rates observed in nonpolar solvents such as cyclohexane, the results of which may be ascribed to a competing energy transfer process.     

“Broken-hearted” carbon bowl via electron shuttle reaction: energetics and electron coupling

Unprecedented one-step C C bond cleavage leading to opening of the buckybowl (π-bowl), that could provide access to carbon-rich structures with previously inaccessible topologies, is reported; highlighting the possibility to implement drastically different synthetic routes to π-bowls in contrast to conventional ones applied for polycyclic aromatic hydrocarbons. Through theoretical modeling, we evaluated the mechanistic pathways feasible for π-bowl planarization and factors that could affect such a transformation including strain and released energies. Through employment of Marcus theory, optical spectroscopy, and crystallographic analysis, we estimated the possibility of charge transfer and electron coupling between “open” corannulene and a strong electron acceptor such as 7,7,8,8-tetracyanoquinodimethane. Alternative to a one-pot solid-state corannulene “unzipping” route, we reported a nine-step solution-based approach for preparation of novel planar “open” corannulene-based derivatives in which electronic structures and photophysical profiles were estimated through the energies and isosurfaces of the frontier natural transition orbitals.

An electron shuttle contributed to breaking corannulene''s heart through a unique one-step reductive C C bond cleavage in the traditionally robust π-bowl. The heartbreak did not stop there as “broken analogs” were developed through a solution-phase route.     

Low-temperature electronic transport through macromolecules and characteristics of intramolecular electron transfer

Long-distance electron transfer (ET) plays an important part in many biological processes. Also, fundamental understanding of ET processes could give grounds for designing miniaturized electronic devices. So far, experimental data on the ET mostly concern ET rates which characterize ET processes as a whole. Here, we develop a different approach which could provide more information about intrinsic characteristics of the long-range intramolecular ET. A starting point of the studies is an obvious resemblance between ET processes and electric transport through molecular wires placed between metallic contacts. Accordingly, the theory of electronic transport through molecular wires is applied to analyze characteristics of a long-range electron transfer through molecular bridges. Assuming a coherent electron tunneling to be a predominant mechanism of ET at low temperatures, it is shown that low-temperature current-voltage characteristics could exhibit a special structure, and the latter contains information concerning intrinsic features of the intramolecular ET. Using the Buttiker dephasing model within the scattering matrix formalism, we analyze the effect of dephasing on the electron transmission function and current-voltage curves.     

Coherence in electron transfer pathways

Central to the view of electron-transfer reactions is the idea that nuclear motion generates a transition state geometry at which the electron/hole amplitude propagates coherently from the electron donor to the electron acceptor. In the weakly coupled or nonadiabatic regime, the electron amplitude tunnels through an electronic barrier between the donor and acceptor. The structure of the barrier is determined by the covalent and noncovalent interactions of the bridge. Because the tunneling barrier depends on the nuclear coordinates of the reactants (and on the surrounding medium), the tunneling barrier is highly anisotropic, and it is useful to identify particular routes, or pathways, along which the transmission amplitude propagates. Moreover, when more than one such pathway exists, and the paths give rise to comparable transmission amplitude magnitudes, one may expect to observe quantum interferences among pathways if the propagation remains coherent. Given that the effective tunneling barrier height and width are affected by the nuclear positions, the modulation of the nuclear coordinates will lead to a modulation of the tunneling barrier and hence of the electron flow. For long distance electron transfer in biological and biomimetic systems, nuclear fluctuations, arising from flexible protein moieties and mobile water bridges, can become quite significant. We discuss experimental and theoretical results that explore the quantum interferences among coupling pathways in electron-transfer kinetics; we emphasize recent data and theories associated with the signatures of chirality and inelastic processes, which are manifested in the tunneling pathway coherence (or absence of coherence).     

Facile interfacial electron transfer through n-alkyl monolayers formed on silicon (111) surfaces

Electron transfer (ET) kinetics through alkyl monolayers, formed on n-type Si(111) surface by the direct reaction of alkylmagnesium bromide (n-C_nH_2n+1MgBr, n=2, 6, 10, and 15) with hydrogen-terminated Si(111), was investigated in acetonitrile (MeCN) with anthraquinone (AQ) as the electrochemical probe. Cyclic voltammetric measurements indicate that the ability of the monolayer to block interfacial electron transfer increases with increasing alkyl chain length. In particular, the voltammetric behavior changes from non-rectifying (i.e., chemically reversible redox couple), to rectifying (i.e., diode-like when the reverse wave is pushed into the gap) with increasing chain length. The dependence of the logarithm of the electron transfer rate constant as a function on the number of carbons in the alkyl chain is not consistent with electron tunneling through the full thickness of the film. In fact, the measured constant, 0.05 ± 0.03 per methylene, is much smaller than the well-established tunneling constant, ∼1.0/CH₂ in the closely packed alkanethiol monolayers on gold suggesting permeation of the AQ into the film.