New Perspective on Electron Transfer through Molecules

Abstract

Motivated by experiments which display unusual length and temperature effects for electron transfer in the nanometer length regime, we propose a new approach for describing long-range electron transfer (ET) processes through molecules. We posit that the electron reorganization in the molecules (e.g., the electronic polarization of a macromolecule or organic film by an applied electric potential, or the injected charge generating a dipole moment) should be included in the description. We numerically solve a one-dimensional model for the electron transport, which includes electron-electron interactions explicitly, and we show that it generates a power law distance dependence for electron transport similar to that observed in experiments. The model does not include vibrations explicitly and should be consistent with the weak temperature dependences observed experimentally. This approach emphasizes the need to treat the electronic changes in the molecule(s) more explicitly to understand the behavior.

Figure 1

A scheme of the proposed model. (A) The unperturbed neutral system in which the charge is distributed evenly. The positive charged ions are presented schematically as blue spheres while the valence electrons are presented in orange. (B) Upon applying an electric field, either by electrodes or by exciting a donor species at one end of the system, the electrons are rearranged to form a dipole moment. As a result, there is a deficiency of negative charge at the positive pole (right side) and an excess of negative charge at the negative pole (left end). (C) Electron charge density is injected into the positive pole from the donor/electrode, and then an electron is ejected out from the negative pole.

Figure 2

Scheme of the model used in the simulations. The electronic levels (ε_m, U_m) in the molecule are separated by tunneling barriers (which is accounted for by a coupling parameter t₀). The molecule is mounted between metallic leads with coupling strengths Γ^L, Γ^R between which a voltage bias (V) is applied. Note that this schematic illustration represents the configuration and does not necessarily represent that actual physical setup; e.g., the site energies are not necessarily the same.

Figure 3

Panel a shows the charge distribution on the sites at a voltage bias of 3 V and Γ^L/R = 1 eV (inset shows the corresponding data for Γ^L/R = 0.1 eV), and panel c shows the current–voltage characteristics for a chain containing 16 sites, with intersite couplings of t₀ = 1 meV (green), 5 meV (blue), 10 meV (red), and 50 meV (black). Panel b shows the nonequilibrium charge distribution as a function of the voltage bias for a 5 meV coupling. Panel d shows the length dependence of the charge current at a voltage bias of 3 V for t₀ = 1 meV (green), 5 meV (blue), 10 meV (red), and 50 meV (black) (inset shows a close up at low currents). The data sets are fit by y(x)= Ae^–Bx + C/x, where A = 0.29, B = 0.81, and C = 0.22. Other parameters are ε_m = −0.1 eV; U_m = 0.5 eV; m = 1, 2, ..., 16; and T = 300 K.

Figure 4

Panel a shows the molecular charge distribution (blue) and charge current (red) at the dc voltage bias 2 V and an instantaneous pulse of 1 V at 5 × 10^–14 s. Panel b shows the deviation of electron population from the mean value, resolved in time and space for a chain containing 16 sites with intersite couplings of t₀ = 10 meV. Other parameters are ε_m = −0.1 eV; U_m = 0.5 eV; m = 1, 2, ..., 16; Γ = 1 eV; and T = 300 K.