The Quadruple Bonding in C₂ Reproduces the Properties of the Molecule

Abstract

Ever since Lewis depicted the triple bond for acetylene, triple bonding has been considered as the highest limit of multiple bonding for main elements. Here we show that C2 is bonded by a quadruple bond that can be distinctly characterized by valence-bond (VB) calculations. We demonstrate that the quadruply-bonded structure determines the key observables of the molecule, and accounts by itself for about 90% of the molecule's bond dissociation energy, and for its bond lengths and its force constant. The quadruply-bonded structure is made of two strong π bonds, one strong σ bond and a weaker fourth σ-type bond, the bond strength of which is estimated as 17-21 kcal mol(-1). Alternative VB structures with double bonds; either two π bonds or one π bond and one σ bond lie at 129.5 and 106.1 kcal mol(-1), respectively, above the quadruply-bonded structure, and they collapse to the latter structure given freedom to improve their double bonding by dative σ bonding. The usefulness of the quadruply-bonded model is underscored by "predicting" the properties of the (3)Σ+u state. C2's very high reactivity is rooted in its fourth weak bond. Thus, carbon and first-row main elements are open to quadruple bonding!

Why Does C2 Cause so Many Problems?

“…We wantt op oint out that the core of the controversy is not the number of bonds but the strengtho ft he total s bonding in C 2 ,w hich is suggestedb ys everalg roups to be much weaker than in acetylene. On page S23 of the Supporting Information [1] one finds as ketch of the two determinants Det1 and Det2 that describe the coupling between two carbon atomsi nt he 3 Ps tate (Det1) and the 5 Ss tate (Det2), which agreesw ith our descriptionso fY QC(1) and Y QC(2) in Figure 1. There are contradictings tatements and missingi nformation which make the numerical resulta nd the conclusion questionable.…”

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The title publication by Shaik et al [1] on the chemical bonding in C 2 is an important contributiont ou nderstand the origin of the conflicting views about the strengtho ft he interatomic interactions in dicarbon which are presented in their paper and in the publications of other groups using av ariety of methods. They calculate the in-situ strengtho ft he s bonding D 2s in-situ from the energyd ifference between Y 2s and Y QC .T his is shown in Figure 1w hich is adapted from Scheme 4o fS haik et al [1] Figure1as hows the quasiclassical state Y QC(1) that is depicted as Y QC in their Scheme 4. The results come from valence bond (VB) calculations, which give bond dissociation energies and bond lengths that are in good agreement with experimental data and with the results of the other methods.

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“…There are contradictings tatements and missingi nformation which make the numerical resulta nd the conclusion questionable. This makes us wonder aboutt he choice of averaged energies of Y QC(1) (Det1) and Y QC(2) (Det2) for estimating the strengtho ft he s bonds in the VB calculations of Shaik et al [1] It would be helpful to know the individual values of D 2sin-situ (1) and D 2s in-situ (2) with respect to Y QC(1) (Det1) and Y QC(2) (Det2)a sr eference states. They calculate the in-situ strengtho ft he s bonding D 2s in-situ from the energyd ifference between Y 2s and Y QC .T his is shown in Figure 1w hich is adapted from Scheme 4o fS haik et al [1] Figure1as hows the quasiclassical state Y QC(1) that is depicted as Y QC in their Scheme 4.…”

Magnetic Shielding Studies of C2 and C2H2 Support Higher than Triple Bond Multiplicity in C2

“…[1][2][3][4][5][6][7][8][9][10][11] According to Shaik et al, [1][2][3][4] in its X 1 † C g ground state C 2 features a quadruple bond comprised of two bonds and two bonds. However, despite its higher multiplicity, this quadruple bond is weaker than the triple carbon-carbon bond in ground-state ethyne, C 2 H 2 , which has a higher force constant and a shorter bond length.…”

Bonding in B 2 and B 2 + : Insights from full configuration interaction and valence bond studies

“…The description of bonding in small molecules remains a challenge: although for simple diatomic molecules chemical bonding seems clear, the situation in C 2 showed that it can still lead to surprises [1][2][3][4][5][6][7]. Several theoretical studies, at various levels of theory, have been devoted to describe the chemical bonding in the C 2 molecule.…”