We show that when a molecular junction is under an external bias, its properties can not be uniquely determined by the total electron density in the same manner as the density functional theory (DFT) for ground state (GS) properties. In order to correctly incorporate bias-induced nonequilibrium effects, we present a dual mean field (DMF) approach. The key idea is that the total electron density together with the density of current-carrying electrons are sufficient to determine the properties of the system. Two mean fields, one for current-carrying electrons and the other one for equilibrium electrons can then be derived.By generalizing the Thomas-Fermi-Dirac (TFD) model to non-equilibrium cases, we analytically derived the DMF exchange energy density functional. We implemented the DMF approach into the computational package SIESTA to study non-equilibrium electron transport through molecular junctions. Calculations for a graphene nanoribbon (GNR) junction show that compared with the commonly used textit{ab initio} transport theory, the DMF approach could significantly reduce the electric current at low biases due to the non-equilibrium corrections to the mean field potential in the scattering region.
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