Vibrational anharmonicity effects in electronic tunneling through molecular bridges

Effects of anharmonic bridge vibrations on electronic tunneling in donor-bridge-acceptor complexes are studied using a model of anharmonic bridge vibration coupled nonlinearly to an electronic degree of freedom. An anharmonicity parameter is introduced, enabling to reproduce the standard harmonic model with linear coupling as a limiting case. The frequency of electronic tunneling oscillations between the donor and acceptor sites is shown to be sensitive to the nuclear anharmonicity, where stretching and compression modes have an opposite effect on the electronic frequency. This phenomenon, that cannot be accounted for within the harmonic approximation, is analyzed and explained.     

Electron tunneling through sensitizer wires bound to proteins

We report a quantitative theoretical analysis of long-range electron transfer through sensitizer wires bound in the active-site channel of cytochrome P450cam. Each sensitizer wire consists of a substrate group with high binding affinity for the enzyme active site connected to a ruthenium-diimine through a bridging aliphatic or aromatic chain. Experiments have revealed a dramatic dependence of electron transfer rates on the chemical composition of both the bridging group and the substrate. Using combined molecular dynamics simulations and electronic coupling calculations, we show that electron tunneling through perfluorinated aromatic bridges is promoted by enhanced superexchange coupling through virtual reduced states. In contrast, electron flow through aliphatic bridges occurs by hole-mediated superexchange. We have found that a small number of wire conformations with strong donor–acceptor couplings can account for the observed electron tunneling rates for sensitizer wires terminated with either ethylbenzene or adamantane. In these instances, the rate is dependent not only on electronic coupling of the donor and acceptor but also on the nuclear motion of the sensitizer wire, necessitating the calculation of average rates over the course of a molecular dynamics simulation. These calculations along with related recent findings have made it possible to analyze the results of many other sensitizer-wire experiments that in turn point to new directions in our attempts to observe reactive intermediates in the catalytic cycles of P450 and other heme enzymes.     

Electron transfer processes in scanning tunneling spectroscopy through small supported particles

Mechanism of the staircase like I–V curve observed recently in scanning tunneling spectroscopy (STS) of a metal fine particle supported on an oxide covered substrate is clarified based on theoretical simulations. It is discussed how the step structures are influenced by the coupling of the fine particle charge to the remaining degrees of freedom, such as induced charge in the surrounding medium. Relation between the characteristic features of single electron tunneling (SET) and the STS of micro-clusters is discussed     

Electron transfer through molecular bridges between reducible pentakis(thiophenyl)benzene subunits

"Dimers" 3, 4 and 7, which consist of two reducible pentakis(thiophenyl)benzene subunits linked by different molecular structures, have been synthesised as model compounds for reducible molecular-wire-type synthons to represent differences in the electron-transfer ability as a function of the bridging structure. The bridging units consist of para-divinylbenzene in 3, bis-hydrazone in 4 and diacetylene in 7. Their ability to transfer electrons from one reducible subunit to the other was investigated by electrochemical and spectroelectrochemical methods and, in the case of 4 and 7, the solid-state structures support the experimental findings. The para-divinylbenzene bridge in 3 was found to completely isolate the reducible structures (Class I system). In contrast, the diacetylene bridge in 7 electronically connects the two reducible structures (Class III system) and, thus, demonstrates its potential application as a "molecular wire". The bis-hydrazone-linked compound 4 displayed only a low level of electronic connection between the subunits and was only observed in the spectroelectrochemical investigation.     

Electron tunneling in proteins program

We developed a unique integrated software package (called Electron Tunneling in Proteins Program or ETP) which provides an environment with different capabilities such as tunneling current calculation, semi‐empirical quantum mechanical calculation, and molecular modeling simulation for calculation and analysis of electron transfer reactions in proteins. ETP program is developed as a cross‐platform client‐server program in which all the different calculations are conducted at the server side while only the client terminal displays the resulting calculation outputs in the different supported representations. ETP program is integrated with a set of well‐known computational software packages including Gaussian, BALLVIEW, Dowser, pKip, and APBS. In addition, ETP program supports various visualization methods for the tunneling calculation results that assist in a more comprehensive understanding of the tunneling process. © 2016 Wiley Periodicals, Inc.     

Electron tunneling dynamics in anharmonic bath

Tunneling transition probability for a particle interacting with an anharmonic bath is found in a time-dependent Hartree approximation. The general expression is presented in terms of medium Keldysh functions that are assumed to be known. Furthermore, the transition probability is calculated in the noninteracting-blip approximation where the rate constant does not exhibit an activation dependence at high temperatures. The reorganization energy E(r) and the renormalized reaction heat epsilon are expressed in terms of the correlation matrix for a solvent and internal modes in both quantum and classical regimes. It is shown that E(r) and epsilon are temperature dependent.     

Electron deficient bridges involving silylenes: a theoretical study

Ab initio and density functional studies show that silylenes can form complexes with BH(3) and the resultant complexes possess 3c-2e bridges. The complexation energy for the formation of the these H-bridged structures is in the range of 18-46 kcal/mol. The characteristics of the electron deficient bridges depend on the substituents attached to the silylenes. With an increase in the pi-donating capacity of the substituents, the exothermicity of complex formation gets reduced but the kinetic stability of the H-bridged structures increase. The natural bond orbital analysis shows that all the H-bridged structures are associated with sigma(B-H)-->ppi(Si) second-order delocalization, which is responsible for the origin of the 3c-2e bonds. The complexation energies of the silylene-BH(3) complexes have been shown to have a correlation to the singlet-triplet energy gaps of silylenes.     

Dynamical tunneling through a chaotic region

It is shown that a non-vibrating diatomic molecule (i.e. a rigid rotor) in the presence of a strong laser field changes its hindered rotational motion (which on the average is in resonance with the oscillating time dependent field) from anti-clockwise to clockwise (hindered) rotational motion. This transition is classically forbidden and is another example of a quantum mechanical tunneling phenomenon occurring due to the time-reversal symmetry of the Hamiltonian. Classically, the two stable rotational modes are separated by an extended chaotic region in phase space. The Husimi representation of the quasienergy states of the time-periodic quantum system enables us to localize wave packets inside the classical stability islands. The effect of the field and the molecular parameters on the perioid of this oscillation is obtained from the quasienergy splittings without the need to carry out long time dependent computations. An analytical analysis of the dynamical tunneling using an extended version of the (t,t) formalism recently developed (J. Chem. Phys.99, 4590 (1993)) is in remarkable agreement with the numerical results.Member of the Minerva center of non-linear physics of complex systems at the Technion     

Electron tunneling through molecular media: a density functional study of Au/Dithiol/Au systems.

We report a density functional theory study of the electronic properties of n-alkanedithiols (CnS2, with n=4, 8 and 12) sandwiched between two Au(111) infinite slab electrodes. We investigate the influence of the distance between the two electrodes and of the molecular chain length, tilt angle, and coverage on the local density of states (LDOS) at the Fermi energy (E(f)). We find that the (small) value of the LDOS at Ef near the center of the molecular wires--a quantity that is related to the tunneling current--is mainly determined by the length n of the alkane chains: it originates from the tails of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) which are broadened by the interaction with the electrodes, and decays exponentially with the length of the molecular wire. This opens a nonresonance tunneling channel for charge transport at small bias voltages. While the length of the hydrocarbon chain appears to be the determining factor, the tilt angle of the molecular wires with respect to the electrode surfaces, and therefore the distance between these, has a small influence on the LDOS at the center of the molecule, while the effect of coverage can be ignored. The picture which emerges from these calculations is totally consistent with a through-bond tunneling mechanism.     

Electrochemically induced electron transfer through molecular bridges

In this Opinion, we address some of the most important results obtained electrochemically in the area of intramolecular electron transfer (ET). The focus is on freely diffusing molecular systems in which a donor D and an acceptor A are separated by a well-defined bridge B (D-B-A systems). B can be a saturated spacer, a delocalized bridge, or the more complex peptide backbones. As to the acceptors, the selected examples encompass species that can be charged reversibly but a special emphasis is on ETs associated with the concerted cleavage of a sigma bond (dissociative ETs). Our goal is to showcase the essential background, the most appropriate electrochemical tools and methodologies, and a series of selected examples where molecular electrochemistry has provided invaluable information on the mechanisms of intramolecular ET and electronic communication through bridges.     

Importance of covalence,conformational effects and tunneling-barrier heights for long-range electron transfer: Insights from dyads with oligo-p-phenylene,oligo-p-xylene and oligo-p-dimethoxybenzene bridges

This review reports on our recent studies of phototriggered charge transfer in rigid rod-like donor-bridge-acceptor molecules in liquid solution as well as between randomly dispersed electron donors and acceptors in frozen organic glasses. Investigation of the distance dependence of the rates of these reactions provides detailed insight into the various factors that govern long-range charge transfer efficiencies. The importance of covalence can be probed by a comparison of charge tunneling through a frozen toluene matrix to tunneling across an oligo-p-xylene bridge. The distance decay constants for these two processes are β = 1.26 Å^?1 and β = 0.52 Å^?1, respectively, indicating that charge tunneling across a covalent xylene–xylene contact is ～2 orders of magnitude more efficient than that across a noncovalent toluene–toluene contact. Conformational effects were investigated by comparing hole tunneling across oligo-p-xylene and oligo-p-phenylene bridges. The latter are significantly more π-conjugated and mediate long-range hole tunneling with β = 0.21 Å^?1 between a ruthenium–phenothiazine donor–acceptor couple. Quantitative analysis indicates that in this particular instance, tunneling across a phenylene–phenylene contact is roughly 50 times more efficient than tunneling across a xylene–xylene contact. The use of oligo-p-dimethoxybenzene wires instead of the structurally very similar oligo-p-xylene bridges was found to lead to a strong acceleration of long-range hole transfer rates: The 23.5-Å charge transfer step across four xylene units occurs within 20 μs, but the charge transfer over the same distance across four dimethoxybenzene units takes only 17 ns. This is attributed to a tunneling-barrier effect that is caused by a large difference in oxidation potentials between the two types of bridges.     

Theory of electron transmission through atom bridges

The transmission eigenchannels of A1 and Na atom bridges formed between jellium electrodes are investigated by a first-principles calculation. A transparent view on electronic transport in atom-size structures is provided by the decomposition of electronic states into eigenchannels. In particular we show how LDOS and current density resolved into eigenchannels reflect the spatial nature of atomic orbitals of the atoms composing the nanostructures. On the other hand, the eigenchannel DOS has already for the straight three-Al-atom bridge a 1D band character. From this we conclude that the transport through the single A1 atom in this case mainly has a 1D character (channel) in contrast to a 0D resonant tunneling (dot) character. The effect of the bending of the bridge shape is significant for the A1 bridges, but not for the Na bridges.     

Electron tunneling in single crystals of Pseudomonas aeruginosa azurins.

Rates of reduction of Os(III), Ru(III), and Re(I) by Cu(I) in His83-modified Pseudomonas aeruginosa azurins (M-Cu distance approximately 17 A) have been measured in single crystals, where protein conformation and surface solvation are precisely defined by high-resolution X-ray structure determinations: 1.7(8) x 10(6) s(-1) (298 K), 1.8(8) x 10(6) s(-1) (140 K), [Ru(bpy)2(im)(3+)-]; 3.0(15) x 10(6) s(-1) (298 K), [Ru(tpy)(bpy)(3+)-]; 3.0(15) x 10(6) s(-1) (298 K), [Ru(tpy)(phen)(3+)-]; 9.0(50) x 10(2) s(-1) (298 K), [Os(bpy)2(im)(3+)-]; 4.4(20) x 10(6) s(-1) (298 K), [Re(CO)3(phen)(+)] (bpy = 2,2'-bipyridine; im = imidazole; tpy = 2,2':6',2' '-terpyridine; phen = 1,10-phenanthroline). The time constants for electron tunneling in crystals are roughly the same as those measured in solution, indicating very similar protein structures in the two states. High-resolution structures of the oxidized (1.5 A) and reduced (1.4 A) states of Ru(II)(tpy)(phen)(His83)Az establish that very small changes in copper coordination accompany reduction but reveal a shorter axial interaction between copper and the Gly45 peptide carbonyl oxygen [2.6 A for Cu(II)] than had been recognized previously. Although Ru(bpy)2(im)(His83)Az is less solvated in the crystal, the reorganization energy for Cu(I) --> Ru(III) electron transfer falls in the range (0.6-0.8 eV) determined experimentally for the reaction in solution. Our work suggests that outer-sphere protein reorganization is the dominant activation component required for electron tunneling.     

SiO2 units networking through ionic liquid-like bridges

Hybrid organic–inorganic silica-based materials containing bridging ionic liquid-like entities were prepared, from 1,3-di(3-trimethoxysilylpropyl)-imidazolium iodide and tetraethoxysilane. The final material is characterized by a high thermal stability. TEM micrographs of the obtained hybrid material allow its comparison with silica nanoparticles bridged through ionic liquid-like links. Correspondence: Marie-Alexandra Neouze, Institute for Materials Chemistry, Vienna University of Technology, Getreidemarkt 9/165, 1060 Vienna, Austria.     

Rapid proton-coupled electron-transfer of hydroquinone through phenylenevinylene bridges

We describe the synthesis of two oligo(phenylene vinylene)s (OPVs) with a hydroquinone moiety and a thiol anchor group: 4-(2',5'-dihydroxystyryl)benzyl thioacetate and 4-[4'-(2' ',5' '-dihydroxystyryl)styryl]benzyl thioacetate. Monolayers on gold of these molecules were examined by electrochemical techniques to determine the electron transfer kinetics of the hydroquinone functionality (H2Q) through these delocalized tethers ("molecular wires") as a function of pH. Between pH 4 and 9, rate constants were ca. 100-fold faster than for the same H2Q functionality confined to the surface via alkane tethers. Also, in this same pH range rate constants were independent of the length of the OPV bridge. These new electroactive molecules in which the hydroquinone functionality is wired to the gold surface by means of OPV tethers should be useful platforms for constructing bioelectronic devices such as biosensors, biofuel cells, and biophotovoltaic cells with a fast response time.     

Temperature dependence of electronic coupling through oligo-p-phenyleneethynylene bridges

A series of donor-bridge-acceptor (D-B-A) systems with varying donor-acceptor distances has been studied with respect to the temperature dependence of the triplet excitation energy transfer (TEET) rates. The donor and acceptor, zinc(II) and free-base porphyrin, respectively, were separated by oligo-p-phenyleneethynylene (OPE) bridges, where the number of phenyleneethynylene groups was varied between two and five, giving rise to edge-to-edge separations ranging between 12.7 and 33.4 A. The study was performed in 2-MTHF between room temperature and 80 K. It was found that the distance dependence was exponential, in line with the McConnell model, and the attenuation factor, beta, was temperature dependent. The experimentally determined temperature dependence of beta was evaluated by using a previously derived model for the conformational dependence of the electronic coupling based on results from extensive quantum chemical, DFT and time-dependent DFT (TD-DFT), calculations. Two regimes in the temperature interval could be identified: one high-temperature, low-viscosity regime, and one low-temperature, high-viscosity regime. In the first regime, the temperature dependence of beta was, according to the model, well described by a Boltzmann conformational distribution. In the latter, the molecular motions that govern the electronic coupling are slowed down to the same order of magnitude as the TEET rates. This, in effect, leads to a distortion of the conformational distribution. In the high-temperature regime the model could reproduce the temperature dependence of beta, and the extracted rotational barrier between two neighboring phenyl units of the bridge structure, E(i)=1.1 kJ mol(-1), was in line with previous experimental and theoretical studies. After inclusion of parameters that take the viscosity of the medium into account, successful modeling of the experimentally observed temperature dependence of the distance dependence was achieved over the whole temperature interval.     

Electron and energy transfer in donor-acceptor systems with conjugated molecular bridges

Electron and energy transfer reactions in covalently connected donor-bridge-acceptor assemblies are strongly dependent, not only on the donor-acceptor distance, but also on the electronic structure of the bridge. In this article we describe some well characterised systems where the bridges are pi-conjugated chromophores, and where, specifically, the interplay between bridge length and energy plays an important role for the donor-acceptor electronic coupling. For any application that relies on the transport of electrons, for example molecule based solar cells or molecular scale electronics, it will be imperative to predict the electron transfer capabilities of different molecular structures. The potential difficulties with making such predictions and the lack of suitable models are also discussed.     

Site-directed electronic tunneling through a vibrating molecular network

The effect of electronic-nuclear coupling on electronic transport through a complex molecular network is studied. Electronic tunneling dynamics in a network of N donor/acceptor sites, connected by molecular bridges, is shown to be controlled by electronic-nuclear coupling at the bridges. Particularly, electronic coupling to an accepting nuclear mode at the contact site between the donor and the rest of the network is shown to affect the tunneling path selection to specific acceptors. In the "deep" tunneling regime, the network is mapped onto an N-level system using a recursive perturbation expansion, enabling analytical treatment of the electronic dynamics. The analytic formulation is applied for two model systems, demonstrating site-directed tunneling by electronic-nuclear coupling. Numerical simulations suggest that this phenomenon is not limited to the deep tunneling regime.     

Site-directed deep electronic tunneling through a molecular network

Electronic tunneling in a complex molecular network of N(>2) donor/acceptor sites, connected by molecular bridges, is analyzed. The "deep" tunneling dynamics is formulated using a recursive perturbation expansion, yielding a McConnell-type reduced N-level model Hamiltonian. Applications to models of molecular junctions demonstrate that the donor-bridge contact parameters can be tuned in order to control the tunneling dynamics and particularly to direct the tunneling pathway to either one of the various acceptors.     

Distance dependence of photoinduced electron transfer through non-conjugated bridges

Picosecond time-resolved emission studies of a series of molecules containing an electron donor-acceptor pair interconnected by a series of rigid non-conjugated bridges reveal the occurrence of very fast photoinduced intramolecular electron transfer. The length of the bridge was varied to provide donor-acceptor centre-to-centre separations ranging from 8.1 to 13.3 Å (edge-to-edge 5 to 10.2 Å). At centre-to-centre separations up to 10.7 Å the rate of photoinduced electron transfer exceeded 5×10¹⁰ s⁻¹ (τ<20 ps); at the largest separation, 13.3 Å, the rate was 1.47×10¹⁰ s⁻¹ (τ = 68 ps).