Conceptual density functional theory for electron transfer and transport in mesoscopic systems

Abstract

Molecular and supramolecular systems are essentially mesoscopic in character. The electron self-exchange, in the case of energy fluctuations, or electron transfer/transport, in the case of the presence of an externally driven electrochemical potential, between mesoscopic sites is energetically driven in such a manner where the electrochemical capacitance (C) is fundamental. Thus, the electron transfer/transport through channels connecting two distinct energetic (ΔE) and spatially separated mesoscopic sites is capacitively modulated. Remarkably, the relationship between the quantum conductance (G) and the standard electrochemical rate constant (k), which is indispensable to understanding the physical and chemical characteristics governing electron exchange in molecular scale systems, was revealed to be related to C, that is, C = G/k. Accordingly, C is the proportional missing term that controls the electron transfer/transport in mesoscopic systems in a wide-range, and equally it can be understood from first principles density functional quantum mechanical approaches. Indeed the differences in energy between states is calculated (or experimentally accessed) throughout the electrochemical capacitance as ΔE = β/C, and thus constitutes the driving force for G and/or k, where β is only a proportional constant that includes the square of the unit electron charge times the square of the number of electron particles interchanged.

Common Principles of Molecular Electronics and Nanoscale Electrochemistry

“…In the presence of an electrolyte, the associated potential of the gate is screened by the environment, which is illustrated by solvent molecules now surrounding the electrochemical capacitance, C μ̅ , instead of C μ . Thus, C μ̅ now replaces C μ as the series association of ionic (double-layer as a typical exemplar) and quantum capacitors , (see more details below), thus constituting the missing physical structure of interest to interpret the time-dependent (or the time-scale) response of molecular electronics ,− (attended in an electrolyte environment) and molecular electrochemistry. , When an electrolyte is present, the electrical field screening is a critical aspect , because the solvent chemical environment is essential to dictate the electron dynamics, according to electron transfer models. , …”

“…The latter is the case where the charge of the mesoscopic (or molecular) scale capacitance is embedded in an electrolyte environment, like that depicted in Figure b . This obviously corresponds to the time-scale of the electrochemical reaction conforming to a single electron transfer such as , where k is the well-known electron transfer rate constant. Equation is validated in ref and thus represents the quantum RC circuit model for electrochemistry at room temperature.…”

“…Figure b shows, as exemplified in the 11-ferrocenyl-undecanethiol monolayer assembled on gold electrodes, how the Gaussian shape obtained experimentally from impedance measurements thus spreads with the dielectric environment, complying with eq . Note that the electronic DOS (Figure b) associated with eq (right side) is not the nuclear Franck–Condon weighted DOS (the left side has been developed semiclassically). , Both DOS functions affect the electron transfer rate; however, from a detailed quantum statistical mechanics standpoint, it is not completely understood how they are fundamentally correlated, an issue to be evaluated in greater detail elsewhere.…”

“…We are now interested in pointing out that “wires” made of molecules can connect the electrochemical capacitive resonant switchers (for instance, ferrocene) to the electrode (see Figure a); these molecular wires (sometimes called molecular nanowires) act as the bridge whereby electrons can be transmitted or transported along the molecular electronic structure by hopping, enabling transport over larger distances. , DNA strands are used as nanowires (with length ∼7 nm) and the propensity they acquire to transmit or transport charge can be evaluated by using the dynamics of a quantum electrochemical RC circuit, as introduced above, by simply applying the C μ̅ = G / k relationship . Regardless of whether the process is tunneling or hopping, the C μ̅ = G / k relationship may be attended and the influence of the electronic structure is achieved implicitly by C μ̅ (and the contained DOS shape).…”

Redox Capacitive Assaying of C-Reactive Protein at a Peptide Supported Aptamer Interface

“…In recent years, there has been a growing interest in the development of optimized interfaces capable of supporting the detection of clinically relevant analytes, especially those translatable to rapid low cost analyses. − Derived immunosensors ,− (which translate a biological biomarker recognition into a measurable signal) have been based on a variety of electrochemical techniques, such as voltammetry, amperometry, , and electrochemical impedance spectroscopy (EIS). − EIS is a natively spectroscopic and highly sensitive method within which interfacial charge transfer resistance R ct is most commonly assessed as a reporter of analyte recognition. , Recently we introduced electrochemical impedance-derived capacitive spectroscopy ,− as a label-free, reagentless method of mapping the change in interfacial redox capacitance ( C r ) as a transducer, omitting the need for a solution phase redox-probe. ,− The partition of mobile electrons between an electrode and a surface tethered chargeable (redox or quantum) species generates a spectroscopically resolvable capacitance. We have shown that this interfacial signal is fundamentally quantum mechanical in nature − and that the charging signature is highly sensitive to changes in local environment. ,, When incorporated into a redox addressable molecular film capable of selectively binding an analyte, C r can (where the binding site is in close proximity) become a sensitive function of target concentration. To date, such interfaces have been created by covalent immobilization of bioreceptors within a mixed self-assembled monolayer (SAM), one film component being redox active, the second serving as a receptor anchor. ,, …”