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 HCCH using several MO based techniques such as CASSCF, RASSCF and MRCI. The analyses of the PECs for the ^2S+1Σ_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 HCCH, 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 HCCH 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 HCCH. 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.

中文翻译：

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从激发态势能曲线理解C2中的四重键合难题

C ₂中的四重键问题已成为热点问题，在价键 (VB) 和分子轨道 (MO) 理论的实践者之间意见分歧很大。在这里，我们使用 CASSCF、RASSCF 和 MRCI 等几种基于 MO 的技术系统地研究了 C ₂、N ₂、Be ₂和 HC CH的低位高自旋 σ 态的势能曲线 (PEC) 。_{C 2的}^{2 S +1} Σ _g/u（2 S + 1 = 1, 3, 5, 7, 9）状态的 PEC 分析并与相关二聚体和各自的波函数进行了比较。我们认为，与 N ₂和 HC CH 的情况不同，在C ₂和 CN ^+的7 Σ ⁺状态中存在深最小值表明这两个二聚体中存在潜在的四重键合性质。我们的研究表明，通过确定在什么自旋对称值下获得纯解离 PEC，可以确定第 2 行二聚体的基态键数^。对于 N ₂和 HC CH，与 C ₂中的九重对称相比，纯解离 PEC 出现在 septet 自旋对称中. 这表明与 N ₂和 HC CH相比，C _{2中的两个第 2}^{行原子之间的键数更高。}因此，我们在 MO 和 VB 方法之间达成了和解。我们提供的证据可以通过实验验证，从而提供窗口，使叙述可以超越理论猜想。