Diabatic valence-hole states in the C$_2$ molecule: "Putting Humpty Dumpty together again"
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$_2$ ($^{1}Π_g$, $^{3}Π_g$, $^{1}Σ_u^+$, and $^{3}Σ_u^+$). The key concept of our model is the existence of two "valence-hole" configurations, $2σ_g^22σ_u^11π_{u}^33σ_g^2$ for $^{1,3}Π_g$ states and $2σ_g^22σ_u^11π_{u}^43σ_g^1$ for $^{1,3}Σ_u^+$ states that derive from $3σ_g\leftarrow2σ_u$ 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$_2$.