Dynamics of charge transfer: rate processes formulated with nonequilibrium Green's functions

Bias-Polarity-Dependent Direct and Inverted Marcus Charge Transport Affecting Rectification in a Redox-Active Molecular Junction

This paper describes the transition from the normal to inverted Marcus region in solid-state tunnel junctions consisting of self-assembled monolayers of benzotetrathiafulvalene (BTTF), and how this transition determines the performance of a molecular diode. Temperature-dependent normalized differential conductance analyses indicate the participation of the HOMO (highest occupied molecular orbital) at large negative bias, which follows typical thermally activated hopping behavior associated with the normal Marcus regime. In contrast, hopping involving the HOMO dominates the mechanism of charge transport at positive bias, yet it is nearly activationless indicating the junction operates in the inverted Marcus region. Thus, within the same junction it is possible to switch between Marcus and inverted Marcus regimes by changing the bias polarity. Consequently, the current only decreases with decreasing temperature at negative bias when hopping is "frozen out," but not at positive bias resulting in a 30-fold increase in the molecular rectification efficiency. These results indicate that the charge transport in the inverted Marcus region is readily accessible in junctions with redox molecules in the weak coupling regime and control over different hopping regimes can be used to improve junction performance.

Functional Redox-Active Molecular Tunnel Junctions

Redox-active molecular junctions have attracted considerable attention because redox-active molecules provide accessible energy levels enabling electronic function at the molecular length scales, such as, rectification, conductance switching, or molecular transistors. Unlike charge transfer in wet electrochemical environments, it is still challenging to understand how redox-processes proceed in solid-state molecular junctions which lack counterions and solvent molecules to stabilize the charge on the molecules. In this minireview, we first introduce molecular junctions based on redox-active molecules and discuss their properties from both a chemistry and nanoelectronics point of view, and then discuss briefly the mechanisms of charge transport in solid-state redox-junctions followed by examples where redox-molecules generate new electronic function. We conclude with challenges that need to be addressed and interesting future directions from a chemical engineering and molecular design perspectives.

Wiedemann-Franz Law for Molecular Hopping Transport

The Wiedemann-Franz (WF) law is a fundamental result in solid-state physics that relates the thermal and electrical conductivity of a metal. It is derived from the predominant transport mechanism in metals: the motion of quasi-free charge-carrying particles. Here, an equivalent WF relationship is developed for molecular systems in which charge carriers are moving not as free particles but instead hop between redox sites. We derive a concise analytical relationship between the electrical and thermal conductivity generated by electron hopping in molecular systems and find that the linear temperature dependence of their ratio as expressed in the standard WF law is replaced by a linear dependence on the nuclear reorganization energy associated with the electron hopping process. The robustness of the molecular WF relation is confirmed by examining the conductance properties of a paradigmatic molecular junction. This result opens a new way to analyze conductivity in molecular systems, with possible applications advancing the design of molecular technologies that derive their function from electrical and/or thermal conductance.

Corresponding Orbitals Derived from Periodic Bloch States for Electron Transfer Calculations of Transition Metal Oxides

An approach for modeling electron transfer in solids and at surfaces of iron-(oxyhydr)oxides and other redox active solids has been developed for electronic structure methods (i.e., plane-wave density functional theory) capable of performing calculations with periodic cells and large system sizes efficiently while at the same time being accurate enough to be used in the estimation of the electron-transfer coupling matrix element, V _AB, and the electron transfer transmission factor, κ_el. This method is an extension of the valence bond theory electron transfer method for molecules and clusters implemented by Dupuis and others and used extensively by Rosso and co-workers in which scaled corresponding orbitals derived from the Bloch states are used to calculate the off-diagonal matrix elements H _AB and S _AB. A key development of the present work is the formulation of algorithms to improve the accuracy of the integration of the exact exchange integral in periodic boundary conditions. This method is demonstrated on model systems for electron small polaron transfer in iron-(oxyhydr)oxides, including bare Fe²⁺-Fe³⁺ ions, and in [Fe³⁺(OH₂)₂ (OH^-)₂)] _nⁿ⁺ chains representing the common edge-sharing Fe octahedral motif in these materials.

Spatial Factors for Triplet Fusion Reaction of Singlet Oxygen Photosensitization

First-principles quantum-chemical description of photosensitized singlet oxygen generation kinetics is challenging because of the intrinsic complexity of the underlying triplet fusion process in a floppy molecular complex with open-shell character. With a quantum-chemical kinetic model specifically tailored to deal with this problem, the reaction rates are investigated as a function of intermolecular incidence direction, orientation, and distance between O₂ and the photosensitizer. The adopted photosensitizer, 6-azo-2-thiothymine, combines practical interest and prototypical variability. The study quantitatively determined maximum singlet oxygen generation rates for 15 incidence/orientation directions, showing that they span 5 orders of magnitude between the largest and the smallest rate. Such information may provide a hands-on guideline for the experimental molecular design of new photosensitizers as well as further higher-level theoretical research.

Proton-coupled electron transfer in molecular electrocatalysis: theoretical methods and design principles

Molecular electrocatalysts play an essential role in a wide range of energy conversion processes. The objective of electrocatalyst design is to maximize the turnover frequency and minimize the overpotential for the overall catalytic cycle. Typically, the catalytic cycle is dominated by key proton-coupled electron transfer (PCET) processes comprised of sequential or concerted electron and proton transfer steps. Theoretical methods have been developed to investigate the mechanisms, thermodynamics, and kinetics of PCET processes in electrocatalytic cycles. Electronic structure methods can be used to calculate the reduction potentials and pKa's and to generate thermodynamic schemes, free energy reaction pathways, and Pourbaix diagrams, which indicate the most stable species under certain conditions. These types of calculations have assisted in identifying the thermodynamically favorable mechanisms under specified experimental conditions, such as acid strength and overpotential. Such calculations have also revealed linear correlations among the thermodynamic properties, which can be used to predict the impact of modifying the ligands, substituents, or metal centers. The thermodynamic properties can be tuned with electron-withdrawing or electron-donating substituents. Ligand modification can exploit the role of noninnocent ligands. For example, ligand protonation typically decreases the overpotential. Calculations of rate constants for electron and proton transfer, as well as concerted PCET, have assisted in identifying the kinetically favorable mechanisms under specified conditions. The concerted PCET mechanism is thought to lower the overpotential required for catalysis by avoiding high-energy intermediates. Rate constant calculations have revealed that the concerted mechanism involving intramolecular proton transfer will be favored by designing more flexible ligands that facilitate the proton donor-acceptor motion while also maintaining a sufficiently short equilibrium proton donor-acceptor distance. Overall, theoretical methods have assisted in the interpretation of experimental data and the design of more effective molecular electrocatalysts.

Breaking the simple proportionality between molecular conductances and charge transfer rates

A theoretical framework is presented to describe and to understand the observed relationship between molecular conductances and charge transfer rates across molecular bridges as a function of length, structure, and charge transfer mechanism. The approach uses a reduced density matrix formulation with a phenomenological treatment of system–bath couplings to describe charge transfer kinetics and a Green's function based Landauer–Buttiker method to describe steady-state currents. Application of the framework is independent of the transport regime and includes bath-induced decoherence effects. This model shows that the relationship between molecular conductances and charge transfer rates follows a power-law. The nonlinear rate–conductance relationship is shown to arise from differences in the charge transport barrier heights and from differences in environmental decoherence rates for the two experiments. This model explains otherwise puzzling correlations between molecular conductances and electrochemical kinetics.

Single molecule logical devices

After almost 40 years of development, molecular electronics has given birth to many exciting ideas that range from molecular wires to molecular qubit-based quantum computers. This chapter reviews our efforts to answer a simple question: how smart can a single molecule be? In our case a molecule able to perform a simple Boolean function is a child prodigy. Following the Aviram and Ratner approach, these molecules are inserted between several conducting electrodes. The electronic conduction of the resulting molecular junction is extremely sensitive to the chemical nature of the molecule. Therefore designing this latter correctly allows the implementation of a given function inside the molecular junction. Throughout the chapter different approaches are reviewed, from hybrid devices to quantum molecular logic gates. We particularly stress that one can implement an entire logic circuit in a single molecule, using either classical-like intramolecular connections, or a deformation of the molecular orbitals induced by a conformational change of the molecule. These approaches are radically different from the hybrid-device approach, where several molecules are connected together to build the circuit.

Ghost transmission: How large basis sets can make electron transport calculations worse

The Landauer approach has proven to be an invaluable tool for calculating the electron transport properties of single molecules, especially when combined with a nonequilibrium Green's function approach and Kohn-Sham density functional theory. However, when using large nonorthogonal atom-centered basis sets, such as those common in quantum chemistry, one can find erroneous results if the Landauer approach is applied blindly. In fact, basis sets of triple-zeta quality or higher sometimes result in an artificially high transmission and possibly even qualitatively wrong conclusions regarding chemical trends. In these cases, transport persists when molecular atoms are replaced by basis functions alone ("ghost atoms"). The occurrence of such ghost transmission is correlated with low-energy virtual molecular orbitals of the central subsystem and may be interpreted as a biased and thus inaccurate description of vacuum transmission. An approximate practical correction scheme is to calculate the ghost transmission and subtract it from the full transmission. As a further consequence of this study, it is recommended that sensitive molecules be used for parameter studies, in particular those whose transmission functions show antiresonance features such as benzene-based systems connected to the electrodes in meta positions and other low-conducting systems such as alkanes and silanes.