ANALYTIC SOLUTIONS TO RESONANT AND NONRESONANT THROUGH-BRIDGE ELECTRONIC COUPLING

In a molecular electronic device, a key parameter of interest is the e lectronic coupling linking the various functional units (e.g. organic molecules/fragments, inorganic complexes, nano-electrodes). In practic al applications, rate constants for specific electron-transfer process es can easily be evaluated considering all interactions within the sys tem; often, exponential decreases in rate constants with increasing se paration 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 tr ansfer processes and, with the aid of numerous analytical approximatio ns, predicts an exponential bridge-length dependence. However, the ran ge of validity of the approximations used is small and exponential fal loff is known to be much more general and robust. We investigate the a nalytical solution recently obtained by Evenson and Karplus for variou s aspects of the problem and find that the most serious approximations used in analysing the McConnell Hamiltonian modify the value of the e xponent 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 i mportant systems bridged by sigma and/or pi 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 descript ive.