Analytic solutions to resonant and non-resonant through-bridge electronic coupling

Abstract

In a molecular electronic device, a key parameter of interest is the electronic coupling linking the various functional units (e.g. organic molecules/fragments, inorganic complexes, nano-electrodes). In practical applications, rate constants for specific electron-transfer processes can easily be evaluated considering all interactions within the system; often, exponential decreases in rate constants with increasing separation between functional units (bridge length) is found, and there is now considerable interest in finding systems with much slower, non-exponential decreases. The simple Hamiltonian model, first introduced in 1961 by McConnell, is qualitatively descriptive of most electron transfer processes and, with the aid of numerous analytical approximations, predicts an exponential bridge-length dependence. However, the range of validity of the approximations used is small and exponential falloff is known to be much more general and robust. We investigate the analytical solution recently obtained by Evenson and Karplus for various aspects of the problem and find that the most serious approximations used in analysing the McConnell Hamiltonian modify the value of the exponent rather than introduce non-exponentiality. Hence, we introduce some simple improved rate laws appropriate to both the exponential and non-exponential regimes. Also, the analysis is extended to consider important systems bridged by and/or bonds, in which the bridge band structure is more complex: similar rate laws are found to apply, and indeed all results obtained are expected to be generally descriptive.

A dark excited state of fluorescent protein chromophores, considered as Brooker dyes

“…The postulate is required because the bare interaction of the rings is insufficient to explain the first optical transition. [22] Additional effective interaction through the intermediate structures accounts for the additional splitting.…”

Controlling electron exchange in molecular assemblies

“…Even so, Marcus theory is extremely useful for designing molecular systems from first principles and there have been many studies over the past few years to determine how k ET depends on the chemical composition of the donor-acceptor dyad and especially on the role of the spacer unit [32]. The crucial factor is the coupling element and the rational design of advanced molecular dyads requires an improved knowledge of how to control V DA at the molecular level [33].…”

“…That a bridge rarely functions as a single electronic entity [33,37] is an additional complication. Conventional metallic wires have a well-defined resistivity that increases in proportion to their length.…”

“…The particular aspect of the spacer geometry that concerns us here is a gross change in structure that might be used as the basis for an off-on switch and we have focused our attention on the torsion angle between adjacent phenylene rings. Theoretical calculations have indicated that the overall electronic resistivity of an electronic conduit depends on how well molecular orbitals on adjacent subunits overlap to form a continuous medium [33,27]. This is certainly true in the case of a 4,4 -biphenyl unit where the angle between the two phenyl rings will influence the extent of electron delocalisation.…”

“The molecules and methods of chemical, biochemical, and nanoscale electron transfer”

“…He continued quantum chemical studies on molecular properties [17], including Stark electronic and vibrational effects [18,19] as well as photoelectron spectroscopy [20]. In the area of electron transfer he studied inter alia basic rate formalisms [21], long range bridged electron transfer [22,23], soliton theory [24], photosynthetic reaction-centre structure and function [25], and applications of Stark spectroscopy to properties of mixed-valence systems [26]. His interests drew him naturally towards Molecular Electronics, and to basic work on conductivity of molecular 'wires', switches and logic assemblies [27].…”