Latent harmony in dicarbon between VB and MO theories through orthogonal hybridization of 3σ(g) and 2σ(u)

Besides the classic double bond scheme, several novel schemes have been proposed to describe the nature of the chemical bond in dicarbon (C(2)), including a quadruple bond and a singlet diradical state. The results from a symmetry-broken CASSCF(8,8)/aug-cc-pVTZ study present a harmony between MO and VB theories, based on the orthogonal hybridization of the 3σ(g) and 2σ(u) orbitals together with the other six pristine valence orbitals. This scheme achieves the same bonding energy, R(C–C), ω(e) and one electron density as that from the eight pristine valence orbitals. A quadruple bond scheme, identical to Prof. Shaik's result from VB theory, is achieved with the 4(th) bond energy in the range of 12.8–27.6 kcal mol(–1). Meanwhile, the weight of a singlet open-shell configuration is the highest among all the possible configurations.