  Despite the long history of spectroscopic studies of the C$_2$ molecule,
fundamental questions about its chemical bonding are still being hotly debated.
The complex electronic structure of C$_2$ is a consequence of its dense
manifold of near-degenerate, low-lying electronic states. A global multi-state
diabatic model is proposed here to disentangle the numerous configuration
interactions within four symmetry manifolds of C$_2$ ($^{1}\Pi_g$, $^{3}\Pi_g$,
$^{1}\Sigma_u^+$, and $^{3}\Sigma_u^+$). The key concept of our model is the
existence of two "valence-hole" configurations,
$2\sigma_g^22\sigma_u^11\pi_{u}^33\sigma_g^2$ for $^{1,3}\Pi_g$ states and
$2\sigma_g^22\sigma_u^11\pi_{u}^43\sigma_g^1$ for $^{1,3}\Sigma_u^+$ states
that derive from $3\sigma_g\leftarrow2\sigma_u$ electron promotion. The
lowest-energy state from each of the four C$_2$ symmetry species is dominated
by this type of valence-hole configuration at its equilibrium internuclear
separation. As a result of their large binding energy (nominal bond order of 3)
and correlation with the 2s$^2$2p$^2$+2s2p$^3$ separated-atom configurations,
the presence of these valence-hole configurations has a profound impact on the
$global$ electronic structure and unimolecular dynamics of C$_2$.
