Diabatic valence-hole states in the C$_2$ molecule: "Putting Humpty Dumpty together again"

TL;DR

This paper develops a multi-state diabatic model for the C$_2$ molecule, revealing the significant role of valence-hole configurations in its complex electronic structure and bonding, which has implications for understanding its spectroscopic and dynamic properties.

Contribution

It introduces a novel global diabatic model incorporating valence-hole configurations to clarify the electronic structure of C$_2$ across multiple symmetry states.

Findings

Valence-hole configurations dominate the lowest-energy states at equilibrium.

The model explains the profound impact of these configurations on C$_2$'s electronic structure.

The presence of valence-hole states influences the molecule's bonding and dynamics.

Abstract

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$_2$.