Insight into spin-orbital interaction using MCSCF method: A special analysis of the ¹ Σ_g ⁺ electronic state in C₂ and...

The symmetry-broken wave function can transform the ¹ Σ_g ⁺ state of C₂ from the classic double bonding to the quadruple bonding, where the transformed wave functions of ϕ _L and ϕ _R are singly occupied by two opposite-spinning electrons. In this article, the effective bond order (EBO) contribution of the fourth bond in C₂ is assessed through the overlap integral between ϕ _L and ϕ _R , namely the value (0.60) is the EBO contribution of the fourth bond in the transformed scheme. Hence, the new EBO is 3.36, which is more equitable than the original EBO (2.15) in the traditional scheme. In addition, the singlet diradical character of the linear polyacetylenic C₄ and C₆ in the ¹ Σ_g ⁺ state is addressed for the first time. No spin-polarized bonding exists in other linear C_2n clusters, because the ionic interaction in the polyacetylenic ¹ Σ_g ⁺ state of C₄ is negligible. Moreover, the coupling energy between α and β single electrons in C₄ is only 4.0 kcal mol^-1 based on the electron spin-flip energy. © 2019 Wiley Periodicals, Inc.