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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 transportthrough molecules, which is based on boundary constraints of the Wignerfunction, is unable to correctly describe the zero-bias conductance of thesimplest uncorrelated and correlated systems. In the present paper, we extendour previous analysis of the linear response limit of that approach, byconsidering, instead of the Wigner function, general constraints. Wedemonstrate that, if, as usual in transport theories, the quasi-particledistributions in electrodes are constrained, this method yields the completelyunphysical result that the zero-bias conductance vanishes. Therefore, weconclude that the variational approach itself is defective.

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