Comprehending the quadruple bonding conundrum in C₂ from excited state potential energy curves

The question of quadruple bonding in C₂ has emerged as a hot button issue, with opinions sharply divided between the practitioners of Valence Bond (VB) and Molecular Orbital (MO) theory. Here, we have systematically studied the Potential Energy Curves (PECs) of low lying high spin sigma states of C₂, N₂, Be₂ and HC[triple bond, length as m-dash]CH using several MO based techniques such as CASSCF, RASSCF and MRCI. The analyses of the PECs for the ²Σ_g/u (with 2S + 1 = 1, 3, 5, 7, 9) states of C₂ and comparisons with those of relevant dimers and the respective wavefunctions were conducted. We contend that unlike in the case of N₂ and HC[triple bond, length as m-dash]CH, the presence of a deep minimum in the ⁷Σ⁺ state of C₂ and CN⁺ suggests a latent quadruple bonding nature in these two dimers. Our investigations reveal that the number of bonds in the ground state can be determined for 2^nd row dimers by figuring out at what value of spin symmetry a purely dissociative PEC is obtained. For N₂ and HC[triple bond, length as m-dash]CH the purely dissociative PEC appears for the septet spin symmetry as compared to that for the nonet in C₂. This is indicative of a higher number of bonds between the two 2^nd row atoms in C₂ as compared to those of N₂ and HC[triple bond, length as m-dash]CH. Hence, we have struck a reconciliatory note between the MO and VB approaches. The evidence provided by us can be experimentally verified, thus providing the window so that the narrative can move beyond theoretical conjectures.