  We investigate the electronic origin of the bending stiffness of conducting
molecules. It is found that the bending stiffness associated with electronic
motion, which we refer to as electro-stiffness, $\kappa_{e}$, is governed by
the molecular orbital overlap $t$ and the gap width $u$ between HOMO and LUMO
levels, and behaves as $\kappa_{e}\sim t^{2}/\sqrt{u^2+t^{2}}$. To study the
effect of doping, we analyze the electron filling-fraction dependence on
$\kappa_{e}$ and show that doped molecules are more flexible. In addition, to
estimate the contribution of $\kappa_{e}$ to the total stiffness, we consider
molecules under a voltage bias, and study the length contraction ratio as a
function of the voltage. The molecules are shown to be contracted or dilated,
with $\kappa_{e}$ increasing nonlinearly with the applied bias.
