The Nature of the Fourth Bond in the Ground State of C2: The Quadruple Bond Conundrum

Does, or doesn’t C₂ break the glass ceiling of triple bonding? This work provides an overview on the bonding conundrum in C₂ and on the recent discussions regarding our proposal that it possesses a quadruple bond. As such, we focus herein on the main point of contention, the 4th bond of C₂, and discuss the main views. We present new data and an overview of the nature of the 4th bond—its proposed antiferromagnetically coupled nature, its strength, and a derivation of its bond energy from experimentally based thermochemical data. We address the bond‐order conundrum of C₂ arising from generalized VB (GVB) calculations by comparing it to HC?CH, and showing that the two molecules behave very similarly, and C₂ is in no way an exception. We analyse the root cause of the deviation of C₂ from the Badger Rule, and demonstrate that the reason for the smaller force constant (FC) of C₂ relative to HC?CH has nothing to do with the bond energies, or with the number of bonds in the two molecules. The FC is determined primarily by the bond length, which is set by the balance between the bond length preferences of the σ‐ versus π‐bonds in the two molecules. This interplay in the case of C₂ clearly shows the fingerprints of the 4th bond. Our discussion resolves the points of contention and shows that the arguments used to dismiss the quadruple bond nature of C₂ are not well founded.     

The Quadruple Bonding in C2 Reproduces the Properties of the Molecule

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 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!     

The Chemical Bond in C2

Quantum chemical calculations using the complete active space of the valence orbitals have been carried out for H_nCCH_n (n=0–3) and N₂. The quadratic force constants and the stretching potentials of H_nCCH_n have been calculated at the CASSCF/cc‐pVTZ level. The bond dissociation energies of the C?C bonds of C₂ and HC≡CH were computed using explicitly correlated CASPT2‐F12/cc‐pVTZ‐F12 wave functions. The bond dissociation energies and the force constants suggest that C₂ has a weaker C?C bond than acetylene. The analysis of the CASSCF wavefunctions in conjunction with the effective bond orders of the multiple bonds shows that there are four bonding components in C₂, while there are only three in acetylene and in N₂. The bonding components in C₂ consist of two weakly bonding σ bonds and two electron‐sharing π bonds. The bonding situation in C₂ can be described with the σ bonds in Be₂ that are enforced by two π bonds. There is no single Lewis structure that adequately depicts the bonding situation in C₂. The assignment of quadruple bonding in C₂ is misleading, because the bond is weaker than the triple bond in HC≡CH.     

C2 in a Box: Determining Its Intrinsic Bond Strength for the X1Σg+ Ground State

The intrinsic bond strength of C₂ in its ¹Σ_g⁺ ground state is determined from its stretching force constant utilizing MR‐CISD+Q(8,8), MR‐AQCC(8,8), and single‐determinant coupled cluster calculations with triple and quadruple excitations. By referencing the CC stretching force constant to its local counterparts of ethane, ethylene, and acetylene, an intrinsic bond strength half way between that of a double bond and a triple bond is obtained. Diabatic MR‐CISD+Q results do not change this. Confinement of C₂ and suitable reference molecules in a noble gas cage leads to compression, polarization, and charge transfer effects, which are quantified by the local CC stretching force constants and differences of correlated electron densities. These results are in line with two π bonds and a partial σ bond. Bond orders and bond dissociation energies of small hydrocarbons do not support quadruple bonding in C₂.     

Comment on “The electron‐pair origin of anti‐aromaticity: Spectroscopic manifestations”

In the article by Zilberg and Haas, “The Electron‐Pair Origin of Anti‐aromaticity: Spectroscopic Manifestations,” the relative sign of the two Kekulé valence bond functions, R and L, in conjugated cyclic hydrocarbons was discussed. It was proposed that in the ground‐state wave function of aromatic compounds, the two functions contribute with like sign, while in the ground state of anti‐aromatic compounds, the two functions contribute with opposite sign. In this Comment, it is shown that the two functions enter with like sign also into the ground‐state wave function of anti‐aromatic compounds. Furthermore, it was argued that resonance tends to (de)stabilize a symmetric ground‐state geometry in case of the (anti‐)aromatic compounds. The expression derived by Zilberg and Haas for the stabilization energy shows an unusual dependence on the ring size and distortion coordinate. An alternative formula is derived for the stabilization energy, in which the energy depends quadratically on the distortion coordinate. Without further numerical calculations, it is not possible to predict whether this term will (de)stabilize a symmetric geometry of the ground state of (anti‐)aromatic molecules. Rather, we are led to believe that the influence of term in question on the geometric stability may be small, thus not providing the main reason for the geometric distortion of anti‐aromatic compounds. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Stoichiometric Valence and Structural Valence—Two Different Sides of the Same Coin: “Bonding Power”

Two valencies instead of one! Stoichiometric valence and structural valence are two distinct properties of atoms. The former, ^stoichV, is derived from the composition of a compound and has integer values; the latter, ^structV, depends on the structure of a compound and has non‐integer values. The scheme shows a representation of valence states of antimony and oxidation of Sb^III to Sb^V, as a function of the eccentricity parameter Φ _i.

     

Reply to “Comment on the Comparative Use of the Electron Density and Its Laplacian”

In our reply to the preceding comment by Richard Bader we show that the statements of the author are not justified and that he contradicts his own previous work.     

Stereodynamics of Metal–Ligand Assembly: What Lies Beneath the “Simple” Spectral Signatures of C2‐Symmetric Chiral Chelates

A series of C₂‐symmetric chiral tetra‐dentate ligands were prepared by using [4,5]‐ or [5,6]‐pinene‐fused 2,2′‐bipyridyl units that are supported across a rigid arylene–ethynylene backbone. These conformationally pre‐organised chelates support stable 1:1 metal complexes, which were fully characterised by UV/Vis, fluorescence, circular dichroism (CD), and ¹H NMR spectroscopy. A careful inspection of the exciton‐coupled circular dichroism (ECCD) and ¹H NMR spectra of the reaction mixture in solution, however, revealed the evolution and decay of intermediate species en route to the final 1:1 metal–ligand adduct. Consistent with this model, mass spectrometric analysis revealed the presence of multiple metal complexes in solution at high ligand‐to‐metal ratios, which were essentially unobservable by UV/Vis or fluorescence spectroscopic techniques. Comparative studies with a bi‐dentate model system have fully established the functional role of the π‐conjugated ligand skeleton that dramatically enhances the thermodynamic stability of the 1:1 complex. In addition to serving as a useful spectroscopic handle to understand the otherwise “invisible” solution dynamics of this metal–ligand assembly process, temperature‐dependent changes in the proton resonances associated with the chiral ligands allowed us to determine the activation barrier (ΔG^≠) for the chirality switching between the thermodynamically stable but kinetically labile (P)‐ and (M)‐stereoisomers.     

The Nature of the UC Double Bond: Pushing the Stability of High‐Oxidation‐State Uranium Carbenes to the Limit

Treatment of [K(BIPM^MesH)] (BIPM^Mes={C(PPh₂NMes)₂}^2?; Mes=C₆H₂‐2,4,6‐Me₃) with [UCl₄(thf)₃] (1 equiv) afforded [U(BIPM^MesH)(Cl)₃(thf)] ( 1 ), which generated [U(BIPM^Mes)(Cl)₂(thf)₂] ( 2 ), following treatment with benzyl potassium. Attempts to oxidise 2 resulted in intractable mixtures, ligand scrambling to give [U(BIPM^Mes)₂] or the formation of [U(BIPM^MesH)(O)₂(Cl)(thf)] ( 3 ). The complex [U(BIPM^Dipp)(μ‐Cl)₄(Li)₂(OEt₂)(tmeda)] ( 4 ) (BIPM^Dipp={C(PPh₂NDipp)₂}^2?; Dipp=C₆H₃‐2,6‐iPr₂; tmeda=N,N,N′,N′‐tetramethylethylenediamine) was prepared from [Li₂(BIPM^Dipp)(tmeda)] and [UCl₄(thf)₃] and, following reflux in toluene, could be isolated as [U(BIPM^Dipp)(Cl)₂(thf)₂] ( 5 ). Treatment of 4 with iodine (0.5 equiv) afforded [U(BIPM^Dipp)(Cl)₂(μ‐Cl)₂(Li)(thf)₂] ( 6 ). Complex 6 resists oxidation, and treating 4 or 5 with N‐oxides gives [{U(BIPM^DippH)(O)₂‐ (μ‐Cl)₂Li(tmeda)] ( 7 ) and [{U(BIPM^DippH)(O)₂(μ‐Cl)}₂] ( 8 ). Treatment of 4 with tBuOLi (3 equiv) and I₂ (1 equiv) gives [U(BIPM^Dipp)(OtBu)₃(I)] ( 9 ), which represents an exceptionally rare example of a crystallographically authenticated uranium(VI)–carbon σ bond. Although 9 appears sterically saturated, it decomposes over time to give [U(BIPM^Dipp)(OtBu)₃]. Complex 4 reacts with PhCOtBu and Ph₂CO to form [U(BIPM^Dipp)(μ‐Cl)₄(Li)₂(tmeda)(OCPhtBu)] ( 10 ) and [U(BIPM^Dipp)(Cl)(μ‐Cl)₂(Li)(tmeda)(OCPh₂)] ( 11 ). In contrast, complex 5 does not react with PhCOtBu and Ph₂CO, which we attribute to steric blocking. However, complexes 5 and 6 react with PhCHO to afford (DippNPPh₂)₂C?C(H)Ph ( 12 ). Complex 9 does not react with PhCOtBu, Ph₂CO or PhCHO; this is attributed to steric blocking. Theoretical calculations have enabled a qualitative bracketing of the extent of covalency in early‐metal carbenes as a function of metal, oxidation state and the number of phosphanyl substituents, revealing modest covalent contributions to U?C double bonds.