Site-directed electronic tunneling in a dissipative molecular environment

The ability to control electronic tunneling in complex molecular networks of multiple donor/acceptor sites is studied theoretically. Our past analysis, demonstrating the phenomenon of site-directed transport, was limited to the coherent tunneling regime. In this work we consider electronic coupling to a dissipative molecular environment including the effect of decoherence. The nuclear modes are classified into two categories. The first kind corresponds to the internal molecular modes, which are coupled to the electronic propagation along the molecular bridges. The second kind corresponds to the external solvent modes, which are coupled to the electronic transport between different segments of the molecular network. The electronic dynamics is simulated within the effective single electron picture in the framework of the tight binding approximation. The nuclear degrees of freedom are represented as harmonic modes and the electronic-nuclear coupling is treated within the time-dependent Redfield approximation. Our results demonstrate that site-directed tunneling prevails in the presence of dissipation, provided that the decoherence time is longer than the time period for tunneling oscillations (e.g., at low temperatures). Moreover, it is demonstrated that the strength of electronic coupling to the external nuclear modes (the solvent reorganization energy) controls the coherent intramolecular tunneling dynamics at short times and may be utilized for the experimental control of site-directed tunneling in a complex network.     

Contact effects on electronic transport in donor-bridge-acceptor complexes interacting with a thermal bath

A model for electron transfer in donor-bridge-acceptor complexes with electronic coupling to nuclear bridge modes is studied using the Redfield formulation. We demonstrate that the transport mechanism through the molecular bridge is controlled by the location of the electronic-nuclear coupling term along the bridge. As the electronic-nuclear coupling term is shifted from the donor/acceptor-bridge contact sites into the bridge, the mechanism changes from kinetic transport (incoherent, thermally activated, and bridge-length independent) to coherent tunneling oscillations. This study joins earlier works aiming to explore the factors which control the mechanism of electronic transport through molecular bridges and molecular wires.     

Promotion of deep tunneling through molecular barriers by electronic-nuclear coupling

Deep electronic tunneling through molecular barriers in donor-bridge-acceptor complexes is studied using an analytically solvable model. The effective tunneling matrix element is formulated as a sum over vibronic tunneling pathways. For a symmetric system the frequency of tunneling oscillations is shown to increase with the strength of electronic-nuclear coupling at the bridge, the number of electronic-nuclear coupling sites, or the frequency of a bridge vibration. Acceleration by several orders of magnitude is demonstrated within the range of realistic molecular parameters.     

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.     

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.     

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).     

Semiclassical treatment of thermally activated electron transfer in the inverted region under the fast dielectric relaxation

The previously formulated semiclassical theory (Zhao, Liang, and Nakamura, J. Phys. Chem. A 2006, 110, 8204) is used to study electron transfer in the Marcus inverted case by considering multidimensional potential energy surfaces of donor and acceptor. The Zhu-Nakamura formulas of nonadiabatic transition in the case of Landau-Zener type are incorporated into the approach. The theory properly takes into account the nonadiabatic transition coupled with the nuclear tunneling and can cover the whole range from weak to strong coupling regime uniformly under the assumption of fast solvent relaxation. The numerical calculations are performed for the 12-dimensional model of shifted harmonic oscillators and demonstrate that the reaction rate with respect to the electronic coupling shows a maximum, confirming the adiabatic suppression in the strong coupling limit. The adiabatic suppression is dramatically reduced by the effect of nuclear tunneling compared to the case that the Landau-Zener formula is used. The possible extension and applications to the case of the slow solvent dynamics are discussed.     

Electronic transport through molecular junctions with nonrigid molecule-leads coupling

The Landauer-type formulation of current through a molecular junction with electronic-nuclear coupling introduced by Troisi et al. [J. Chem. Phys. 118, 6072 (2003)] is generalized to account for the dependence of the molecule-leads coupling terms on the nuclear coordinates. Although this electronic-nuclear coupling is external to the molecule there is no need to extend the molecular subspace when projection operators are employed for calculations of the current through the junction. A test case of a conductor with vibrating contacts to the leads is studied numerically. It is demonstrated that contact vibrations lead to inelastic contributions to the current and to characteristic features in the I-V curve and its derivatives, similar to the ones observed for internal (molecular) electronic-nuclear coupling.     

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.     

A core-shell strategy for constructing a single-molecule junction

Understanding the effects of intermolecular interactions on the charge-transport properties of metal/molecule/metal junctions is an important step towards using individual molecules as building blocks for electronic devices. This work reports a systematic electron-transport investigation on a series of "core-shell"-structured oligo(phenylene ethynylene) (Gn-OPE) molecular wires. By using dendrimers of different generations as insulating "shells", the intermolecular π-π interactions between the OPE "cores" can be precisely controlled in single-component monolayers. Three techniques are used to evaluate the electron-transport properties of the Au/Gn-OPE/Au molecular junctions, including crossed-wire junction, scanning tunneling spectroscopy (STS), and scanning tunneling microscope (STM) break-junction techniques. The STM break-junction measurement reveals that the electron-transport pathways are strongly affected by the size of the side groups. When the side groups are small, electron transport could occur through three pathways, including through single-molecule junctions, double-molecule junctions, and molecular bridges between adjacent molecules formed by aromatic π-π coupling. The dendrimer shells effectively prohibit the π-π coupling effect, but at the same time, very large dendrimer side groups may hinder the formation of Au-S bonds. A first-generation dendrimer acts as an optimal shell that only allows electron transport through the single-molecule junction pathway, and forbids the other undesired pathways. It is demonstrated that the dendrimer-based core-shell strategy allows the single-molecule conductance to be probed in a homogenous monolayer without the influence of intermolecular π-π interactions.     

Simulation of environmental effects on coherent quantum dynamics in many-body systems

In this paper we describe an application of the trajectory-based semiclassical Liouville method for modeling coherent molecular dynamics on multiple electronic surfaces to the treatment of the evolution and decay of quantum electronic coherence in many-body systems. We consider a model representing the coherent evolution of quantum wave packets on two excited electronic surfaces of a diatomic molecule in the gas phase and in rare gas solvent environments, ranging from small clusters to a cryogenic solid. For the gas phase system, the semiclassical trajectory method is shown to reproduce the evolution of the electronic-nuclear coherence nearly quantitatively. The dynamics of decoherence are then investigated for the solvated systems using the semiclassical approach. It is found that, although solvation in general leads to more rapid and extensive loss of quantum coherence, the details of the coupled system-bath dynamics are important, and in some cases the environment can preserve or even enhance quantum coherence beyond that seen in the isolated system.     

Model study of coherent quantum dynamics of hole states in functionalized semiconductor nanostructures

Functionalization of semiconductor nanocrystals can be achieved by anchoring organic ligands to the surface dangling bonds. The resulting surface complexes often introduce electronic states in the semiconductor band gap. These interband states sensitize the host material for photoabsorption at frequencies characteristic of the molecular adsorbates, leading to the well-known process of photoexcitation and subsequent femtosecond interfacial electron transfer. This paper investigates the relaxation dynamics of hole states, energetically localized deep in the semiconductor band gap, after the ultrafast electron-hole pair separation due to interfacial electron transfer. Mixed quantum-classical methods, based on mean-field nuclear dynamics approximated by ab initio density functional theory molecular dynamics simulations, reveal superexchange hole tunneling between adjacent adsorbate molecules in a model study of functionalized TiO2-anatase nanostructures. It is shown that electronic coherences can persist for hundreds of picoseconds under cryogenic and vacuum conditions, despite the partial intrinsic decoherence induced by thermal ionic motion, providing results of broad theoretical and experimental interest.     

Use of U-shaped donor-bridge-acceptor molecules to study electron tunneling through nonbonded contacts

A systematic determination of electronic coupling matrix elements in U-shaped molecules is demonstrated. The unique architecture of these systems allows for the determination of the electronic coupling through a pendant molecular moiety that resides between the donor and acceptor groups; this moiety quantifies the efficiency of electron tunneling through nonbonded contacts. Experimental electron-transfer rate constants and reaction free energies are used to calibrate a molecular-based model that describes the solvation energy. This approach makes it possible to experimentally determine electronic couplings and compare them with computational values.     

Ultrafast electron dynamics at ice-metal interfaces: competition between heterogeneous electron transfer and solvation

Microscopic insight into heterogeneous electron transfer requires an understanding of the participating donor and acceptor states and of their respective interaction. In the regime of strong electronic coupling, two limits have been discussed where either the states overlap directly or the states are separated by a potential barrier. In both situations, the transfer probability is determined by the magnitude of the wave function overlap, whereby in the case of the potential barrier, its width and height are rate limiting. In our study, we observe a dynamical crossover between these two regimes by investigating the electron-transfer dynamics of localized, solvated electrons at ice-metal interfaces. Employing femtosecond time-resolved two-photon photoelectron spectroscopy, we analyze the population dynamics of excess electrons in the ice layer, which experience the competing processes of transfer to the metal electrode and energetic stabilization in the ice by molecular reorientation. Comparing the dynamics of D(2)O on Cu(111) and Ru(001), we observe an early regime at t < 300 fs, where the transfer time is determined by wave-function overlap with the metal and a second regime (t > 300 fs), where the transfer proceeds nearly independent of the substrate. The assignment of these two regimes to the established mechanisms of electron transfer is backed by an empirical model calculation that reproduces the experimental data in an excellent manner.     

Electronic coupling in electron transfer and the influence of nuclear modes: theoretical and computational probes

Long-range electronic coupling of local donor and acceptor sites is formulated in the context of thermal and optical electron transfer and then illustrated with examples based on electronic structure calculations. The relationship of the calculated results to available experimental kinetic and optical data is discussed in detail. The influence of nuclear modes on the magnitude of the coupling (i.e., departures from the Condon approximation) is investigated in terms of both discrete molecular modes and solvent modes, and a general expression is presented for the modulation of the superexchange tunneling gap by motion along the electron transfer reaction coordinate. AcknowledgementsThe author is grateful to R.J. Cave and M. Rust for making available molecular coordinates for acridinium derivatives, and to R.J. Cave for several valuable discussions. This work was supported by the Division of Chemical Sciences, US Department of Energy, under grant DE-AC02-98CH10886.     

Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.     

Using meta conjugation to enhance charge separation versus charge recombination in phenylacetylene donor-bridge-acceptor complexes

A pair of donor-bridge-acceptor electron-transfer complexes, with a carbazole donor and a naphthalimide acceptor connected by either a para- or meta-conjugated phenylacetylene bridge, are synthesized and studied using time-resolved and steady-state spectroscopy. These experiments show that the charge separation times, which depend on the coupling of the donor and acceptor through the excited bridge moiety, are similar for the two molecules (Meta and Para). The charge recombination time, however, is a factor of 10 slower for Meta than for Para. These results are related to changes in the electronic coupling of the bridge depending on its electronic state, and show that meta-conjugated bridges provide a possible motif for the design of asymmetric molecular wires.     

SERS and tunneling spectroscopy investigation of iron-protoporphyrin IX adsorbed on a silver tip

Iron-protoporphyrin IX adsorbed on a scanning tunneling microscopy silver tip is investigated by combining surface enhancement Raman (SERS) and tunneling spectroscopies down to single molecule regime. Both the Raman signals and the tunneling current intensity reveal fast switching between the iron oxidation states and present analogous, significant fluctuations in time. The results point out the occurrence of a strong electronic coupling between the molecule and the metal, and may contribute to elucidate the dynamical phenomena at the molecule-metal interface, deserving some nanotechnological interest.     

Interplay between barrier width and height in electron tunneling: photoinduced electron transfer in porphyrin-based donor-bridge-acceptor systems

The rate of electron tunneling in molecular donor-bridge-acceptor (D-B-A) systems is determined both by the tunneling barrier width and height, that is, both by the distance between the donor and acceptor as well as by the energy gap between the donor and bridge moieties. These factors are therefore important to control when designing functional electron transfer systems, such as constructs for photovoltaics, artificial photosynthesis, and molecular scale electronics. In this paper we have investigated a set of D-B-A systems in which the distance and the energy difference between the donor and bridge states (DeltaEDB) are systematically varied. Zinc(II) and gold(III) porphyrins were chosen as electron donor and acceptor because of their suitable driving force for photoinduced electron transfer (-0.9 eV in butyronitrile) and well-characterized photophysics. We have previously shown, in accordance with the superexchange mechanism for electron transfer, that the electron transfer rate is proportional to the inverse of DeltaEDB in a series of zinc/gold porphyrin D-B-A systems with bridges of constant edge to edge distance (19.6 A) and varying DeltaEDB (3900-17 600 cm(-1)). Here, we use the same donor and acceptor but the bridge is shortened or extended giving a set of oligo-p-phenyleneethynylene bridges (OPE) with four different edge to edge distances ranging from 12.7 to 33.4 A. These two sets of D-B-A systems-ZnP-RB-AuP+ and ZnP-nB-AuP+-have one bridge in common, and hence, for the first time both the distance and DeltaEDB dependence of electron transfer can be studied simultaneously in a systematic way.