Soliton, charge-density wave structure and band gaps in odd polyene and symmetrical polymethinecyanine (Brooker) ions and in t-polyacetylene: Implications for molecular electronics

Reimers, Jeffrey R.; Craw, J. S.; Hush, Noel S.

doi:10.1063/1.42664

Cited by 1 publication

(3 citation statements)

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“…The bridge-length dependence determined from equation (1) is shown in figure 2 for situations where x = 1.9 (inside the resonance region), 2.1 (just outside the resonance region) and 3.0 (somewhat distant from the resonance region) and α/β = 0.1. Shown are results for |H DA | obtained essentially exactly by evaluating k R [5], from Evenson and Karplus' [20] two-level weak-coupling approximation, equation ( 8), from our exponential-decay law, equation (11), and from McConnell's [13] exponentialdecay law, equation (4). Inside the resonance region, the results obtained from the two-level weak-coupling approximation mimic the exact results but show significant errors in the vicinity of the resonances [16].…”

Section: No Asymptotic Band Gapmentioning

confidence: 99%

“…[1,2]) and the design of molecular electronic devices (e.g. refs [3,4]). Our interest has lain in the development of models [5,6] applicable when fast, long-range electron transfer that does not necessarily decrease exponentially with increasing bridge length occurs, and the application of these models to chemical systems [4,[7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…refs [3,4]). Our interest has lain in the development of models [5,6] applicable when fast, long-range electron transfer that does not necessarily decrease exponentially with increasing bridge length occurs, and the application of these models to chemical systems [4,[7][8][9][10][11][12]. These models allow for large coupling between the donor or acceptor and the bridge, resonance between donor or acceptor and bridge energy levels, asymmetric systems, and explicit electronelectron or electron-phonon interactions.…”

Section: Introductionmentioning

confidence: 99%

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

Reimers¹,

Hush²

1996

Nanotechnology

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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.

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