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

Abstract

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 Au͑111͒ surface. At larger numbers of bridge units, the effective coupling strength shows an exponential decay as the number of methylene͑-CH 2 -͒ 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.

Scanning Tunneling Spectroscopy of Insulating Self-Assembled Monolayers on Au(111)

“…Calculations based on this formalism have been widely used to describe the molecular conductance of a number of organic structures based on their conductance spectra. 28,29,32,34,[36][37][38][39][40] It is important to note that molecules with similar chemical structures can give rise to completely different conductances if the transmission function is modulated by extrinsic factors such as differences in chemical bonding at the substrate-molecule interface, as has been predicted theoretically. 37,41 Three factors are critical in determining molecular conductance: T(E,V) itself, which in principle can be derived from the energy levels of a molecule adsorbed onto the substrate, the alignment of the chemical potentials µ t and µ s with respect to the molecular energy levels, and knowledge of the spatial variation of the electrostatic potential.…”

Photoelectrochemical Generation of Electronically Conducting Polymer-Based Hybrid Junctions on Modified Si(111) Surfaces

“…Indeed, for covalently attached molecules, hole tunneling through σ-bonded alkyl chains has been found to be more efficient than electron tunneling. 15 In fact, the values of the structure-dependent attenuation factor 16,17 suggest that this process is as efficient as electron tunneling through π-conjugated systems. In contrast, the presence of a silicon oxide layer between the silicon surface and the alkyl chain would inhibit hole tunneling.…”

The initial and final states of electron and energy transfer processes: Diabatization as motivated by system-solvent interactions

“…For this reason, many electron-transfer theorists have preferred to avoid calculating diabatic states altogether, choosing instead to extract the electronic couplings necessary for predicting electron transfer rates using indirect methods that do not make explicit reference to diabatic states. [36][37][38][39][40][41][42][43] Nevertheless, because the physical meaning of diabatic states in condensed environments is paramount, it is worthwhile and useful to construct approximate system diabatic states even if these computed states are not unique. Ideally, a diabatization algorithm applicable to electron and energy transfer in condensed environments should…”