  Recent experiments by Venkatamaran {\em et al.} [Nature (London) {\bf 442},
904 (2006)] on a series of molecular wires with varying chemical compositions,
revealed a linear dependence of the conductance on $\mathrm{cos}^2\theta$,
where $\theta$ is the angle of twist between neighboring aromatic rings. To
investigate whether or not this dependence has a more general applicability, we
present a first principles theoretical study of the transport properties of
this family of molecules as a function of the chemical composition,
conformation and the contact atom and geometry. If the Fermi energy
$E_\mathrm{F}$ lies within the HOMO-LUMO gap, then we reproduce the above
experimental results. More generally, however, if $E_\mathrm{F}$ is located
within either the LUMO or HOMO states, the presence of resonances destroys the
linear dependence of the conductance on $\mathrm{cos}^2\theta$ and gives rise
to non-monotonic behaviour associated with the level structure of the different
molecules. Our results suggest that the above experiments provide a novel
method for extracting spectroscopic information about molecules contacted to
electrodes.
