Critical analysis of a variational method used to describe the molecular electron transport

TL;DR

This paper critically examines a variational method for molecular electron transport, demonstrating its failure to accurately predict conductance and showing that it yields unphysical results when generalized.

Contribution

The paper provides a rigorous critique of a variational approach based on boundary constraints, revealing fundamental flaws in its application to electron transport.

Findings

The variational method cannot correctly describe zero-bias conductance.

General constraints lead to unphysical zero conductance results.

The approach is fundamentally defective for transport calculations.

Abstract

In a recent paper [I.\ B\^aldea and H.\ K\"oppel, \prb {\bf 78}, 115315 (2008)], we showed that a variational approach [P.\ Delaney and J.\ C.\ Greer, \prl {\bf 93}, 036805 (2004)] proposed to compute the electron transport through molecules, which is based on boundary constraints of the Wigner function, is unable to correctly describe the zero-bias conductance of the simplest uncorrelated and correlated systems. In the present paper, we extend our previous analysis of the linear response limit of that approach, by considering, instead of the Wigner function, general constraints. We demonstrate that, if, as usual in transport theories, the quasi-particle distributions in electrodes are constrained, this method yields the completely unphysical result that the zero-bias conductance vanishes. Therefore, we conclude that the variational approach itself is defective.