C₂ in a Box: Determining Its Intrinsic Bond Strength for the X¹Σ_g⁺ Ground State

Abstract

The intrinsic bond strength of C2 in its (1)Σg(+) 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.

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

“…The theoretical estimates for the carbon isotropic magnetic shieldings in dicarbon obtained using the CASSCF (8,8)-GIAO, CCSD(T)-GIAO and CCSDT-GIAO methods are in good agreement, within the ca. 224-227 ppm range, but the HF-GIAO and MP2-GIAO results are considerably higher (see Table 1).…”

“…In fact, it is debatable whether thebond model should be preferred over the alternative "bent" bond model which, in spin-coupled calculations, yields a lower-energy wavefunction for ethyne. [31] On a side note, Foster-Boys localizations [32] of the active space orbitals from the full-valence CASSCF (8,8)/cc-pVQZ and CASSCF(10,10)/cc-pVQZ wavefunctions for dicarbon and ethyne, respectively, carried out using GAUSSIAN09, [18] produce rather similar sets of localized orbitals consistent with the "bent" bond model.…”

“…All CASSCF-GIAO calculations were carried out using the MCSCF-GIAO (multiconfigurational SCF with GIAOs) methodology described in references [15,16] and implemented in the Dalton program package. [17] For comparison purposes, similar contour plots for the total electron density, .r/, in C 2 and C 2 H 2 , were drawn from the respective CASSCF (8,8)/cc-pVQZ and CASSCF(10,10)/cc-pVQZ data obtained using GAUSSIAN09. [18] In order to study the method and basis set dependence of the off-nucleus shielding tensors in C 2 and C 2 H 2 , the changes in .r/ along the respective molecular axes were examined using several additional levels of theory: MP2-GIAO (second order Møller-Plesset perturbation theory with GIAOs), in combination with the standard cc-pVQZ, cc-pV5Z and cc-pV6Z basis sets, as well as CCSD(T)-GIAO (coupledcluster with GIAOs including all single and double excitations, and a perturbative estimate of the connected triples) and CCSDT-GIAO (CC with GIAOs including all single, double and triple excitations), both with the standard cc-pVQZ basis.…”

“…[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.…”

Eliminating symmetry problems in electronegativity equalization and correcting self‐interaction errors in conceptual DFT

“…The C 2 bond is still subject to intriguing debates . According to Cooper et al “the enhanced contributions from triplet coupling in C 2 contribute to the difficulty of describing the electronic structure of this system in terms of conventional bonding models that feature a whole number of two‐center two‐electron bonds.” The assessment of VPEq appears hampered, because the valency is somewhere between 2 ≤ V ≤ 4.…”