  The molecule-like structure of the C isotopes (A=12, 14, 16) is investigated
using a microscopic $\alpha+\alpha+\alpha+n+n+\cdot \cdot \cdot$ model. The
valence neutrons are classified based on the molecular-orbit (MO) model, and
both $\pi$-orbit and $\sigma$-orbit are introduced around three
$\alpha$-clusters. The valence neutrons which occupy the $\pi$-orbit increase
the binding energy and stabilize the linear-chain of 3$\alpha$ against the
breathing-like break-up. However, $^{14}$C with the $\pi$-orbit does not show
clear energy minimum against the bending-like path. The combination of the
valence neutrons in the $\pi$- and the $\sigma$-orbit is promising to stabilize
the linear-chain state against the breathing- and bending- modes, and it is
found that the excited states of $^{16}$C with the
$(3/2^-_\pi)^2(1/2^-_\sigma)^2$ configuration for the four valence neutrons is
one of the most promising candidates for such structure.
