  Recent experiment found a quantum length dependence of oligothiophene
molecule conductance at low bias [Xu et al., nano Lett. \textbf{5}, 1491
(2005)], the long molecule has large conductance. By means of a
first-principles method we obtain both the quantum length dependence of
conductance at low bias and the classical length dependence of conductance at
high bias region for oligothiophene. In between there is an oscillated
conductance behavior. The transport behaviors are determined by the distinct
electronic structures of the molecular compounds. The various conductance
length dependence may appear for the organic compounds. Our further
investigation finds that the classical conductance length dependence in
polyphenanthrene dithiolates and another unusual conductance length dependence
in polyacene ditholates: the quantum length dependence of conductance is at the
high bias and the classical length dependence of conductance is at the low
bias.
