Self-consistent-field study of conduction through conjugated molecules

Abstract

Current-voltage $(I-V)$ characteristics of individual molecules connected by metallic leads are studied theoretically. Using the Pariser-Parr-Pople quantum chemical method to model the molecule enables us to include electron-electron interactions in the Hartree approximation. The self-consistent-field method is used to calculate charging together with other properties for the total system under bias. Thereafter the Landauer formula is used to calculate the current from the transmission amplitudes. The most important parameter to understand charging is the position of the chemical potentials of the leads in relation to the molecular levels. At finite bias, the main part of the potential drop is located at the molecule-lead junctions. Also, the potential of the molecule is shown to partially follow the chemical potential closest to the highest occupied molecular orbital (HOMO). Therefore, the resonant tunneling steps in the $I-V$ curves are smoothed giving a $I-V$ resembling a “Coulomb-gap.” However, the charge of the molecule is not quantized since the molecule is small with quite strong interactions with the leads. The calculations predict an increase in the current at the bias corresponding to the energy gap of the molecule irrespective of the metals used in the leads. When the bias is increased further, charge is redistributed from the HOMO level to the lowest unoccupied molecular orbital of the molecule. This gives a step in the $I-V$ curves and a corresponding change in the potential profile over the molecule. Calculations were mainly performed on polyene molecules. Molecules asymmetrically coupled to the leads model the $I-V$ curves for molecules contacted by a scanning tunneling microscopy tip. $I-V$ curves for pentapyrrole and another molecule that show negative differential conductance are also analyzed. The charging of these two systems depends on the shape of the molecular wave functions.