Density functional calculations of nanoscale conductance

TL;DR

This paper critically examines the use of density functional theory for nanoscale conductance calculations, identifying its limitations and proposing a new methodology based on time-dependent current density functional theory for improved accuracy.

Contribution

It provides a rigorous analysis of existing DFT methods for conductance and introduces an extended approach using time-dependent current density functional theory for finite bias scenarios.

Findings

Local and gradient-corrected approximations fail for weakly coupled molecules.

Standard DFT misses exchange-correlation corrections in the weak bias regime.

A new methodology based on an extension of time-dependent current DFT is proposed for finite bias calculations.

Abstract

Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. For finite bias, a new methodology for performing calculations can be rigorously derived using an extension of time-dependent current density functional theory from the Schroedinger equation to a Master equation.