A sequential formula for electronic coupling in long range bridge-assisted electron transfer: Formulation of theory and application to alkanethiol monolayers

A recursion relation is formulated for the Green's function for calculating the effective electron coupling in bridge-assisted electronic transfer systems, within the framework of the tight-binding Hamiltonian. The recursion expression relates the Green's function of a chain bridge to that of the bridge that is one unit less. It is applicable regardless of the number of orbitals per unit. This method is applied to the system of a ferrocenylcarboxy-terminated alkanethiol on the Au(111) surface. At larger numbers of bridge units, the effective coupling strength shows an exponential decay as the number of methylene(–CH2–) units increases. This sequential formalism shows numerical stability even for a very long chain bridge and, since it uses only small matrices, requires much less computer time for the calculation. Identical bridge units are not a requirement, and so the method can be applied to more complicated systems

Linear response in theory of electron transfer reactions as an alternative to the molecular harmonic oscillator model

The effect of solvent fluctuations on the rate of electron transfer reactions is considered using linear response theory and a second-order cumulant expansion. An expression is obtained for the rate constant in terms of the dielectric response function of the solvent. It is shown thereby that this expression, which is usually derived using a molecular harmonic oscillator ("spin-boson") model, is valid not only for approximately harmonic systems such as solids but also for strongly molecularly anharmonic systems such as polar solvents. The derivation is a relatively simple alternative to one based on quantum field theoretic techniques. The effect of system inhomogeneity due to the presence of the solute molecule is also now included. An expression is given generalizing to frequency space and quantum mechanically the analogue of an electrostatic result relating the reorganization free energy to the free energy difference of two hypothetical systems [J. Chem. Phys. 39, 1734 (1963)]. The latter expression has been useful in adapting specific electrostatic models in the literature to electron transfer problems, and the present extension can be expected to have a similar utility

Building a regional forecasting model utilizing long-term relationships and short-term indicators

Economic indicators ; Forecasting ; Regional economics

A method for monitoring the variability in nuclear absorption characteristics of aviation fuels

A technique for monitoring variability in the nuclear absorption characteristics of aviation fuels has been developed. It is based on a highly collimated low energy gamma radiation source and a sodium iodide counter. The source and the counter assembly are separated by a geometrically well-defined test fuel cell. A computer program for determining the mass attenuation coefficient of the test fuel sample, based on the data acquired for a preset counting period, has been developed and tested on several types of aviation fuel