  We have implemented the linear response approximation of a method proposed to
compute the electron transport through correlated molecules based on the
time-independent Wigner function [P. Delaney and J. C. Greer, \prl {\bf 93},
36805 (2004)]. The results thus obtained for the zero-bias conductance through
quantum dot both without and with correlations demonstrate that this method is
either quantitatively nor qualitatively able to provide a correct physical
escription of the electric transport through nanosystems. We present an
analysis indicating that the failure is due to the manner of imposing the
boundary conditions, and that it cannot be simply remedied.
