Why is the bond multiplicity in C2 so elusive?

Dynamical electron correlation and the chemical bond. III. Covalent bonds in the A2 molecules (A = C-F)

For most molecules the spin-coupled generalized valence bond (SCGVB) wavefunction accounts for the effects of non-dynamical electron correlation. The remaining errors in the prediction of molecular properties and the outcomes of molecular processes are then solely due to dynamical electron correlation. In this article we extend our previous studies of the effects of dynamical electron correlation on the potential energy curves and spectroscopic constants of the AH and AF (A = B-F) molecules to the homonuclear diatomic molecules, A2 (A = C-F). At large R the magnitude of ΔEDEC(R), the correlation energy of the molecule relative to that in the atoms, increases nearly exponentially with decreasing R, just as we found in the AH and AF molecules. But, as R continues to decrease the rate of increase in the magnitude of ΔEDEC(R) slows, eventually leading to a minimum for C2-O2. Examination of the SCGVB wavefunction for the N2 molecule around the minimum in ΔEDEC(R) did not reveal a clear cause for this puzzling behavior. As before, the changes in ΔEDEC(R) around Re were found to have an uneven effect on the spectroscopic constants of the A2 molecules.

Spin-Coupled Generalized Valence Bond Theory: New Perspectves on the Electronic Structure of Molecules and Chemical Bonds

Spin-Coupled Generalized Valence Bond (SCGVB) theory provides the foundation for a comprehensive theory of the electronic structure of molecules. SCGVB theory offers a compelling orbital description of the electronic structure of molecules as well as an efficient and effective zero-order wave function for calculations striving for quantitative predictions of molecular structures, energetics, and other properties. The orbitals in the SCGVB wave function are usually semilocalized, and for most molecules, they can be interpreted using concepts familiar to all chemists (hybrid orbitals, localized bond pairs, lone pairs, etc.). SCGVB theory also provides new perspectives on the nature of the bonds in molecules such as C₂, Be₂ and SF₄/SF₆. SCGVB theory contributes unparalleled insights into the underlying cause of the first-row anomaly in inorganic chemistry as well as the electronic structure of organic molecules and the electronic mechanisms of organic reactions. The SCGVB wave function accounts for nondynamical correlation effects and, thus, corrects the most serious deficiency in molecular orbital (RHF) wave functions. Dynamical correlation effects, which are critical for quantitative predictions, can be taken into account using the SCGVB wave function as the zero-order wave function for multireference configuration interaction or coupled cluster calculations.

Orbital Hybridization in Modern Valence Bond Wave Functions: Methane, Ethylene, and Acetylene

The concept of hybrid orbitals is one of the key theoretical concepts used by chemists to explain the structures and other properties of molecules. Recent work found that the hybrid orbitals from modern ab initio valence bond wave functions differ significantly from traditional hybrid orbitals. We report a detailed analysis of the orbitals of methane, ethylene, and acetylene from spin-coupled generalized valence bond (SCGVB) wave functions, a variationally optimized valence bond wave function that places no constraints on the orbitals and spin function. The carbon-centered orbitals in the SCGVB wave functions are found to be 2s-2p hybrid orbitals largely localized on the carbon atom and pointed directly at the hydrogen atoms to which they are bonded. However, the SCGVB orbitals for methane, ethylene, and acetylene differ markedly from the sp³, sp², and sp hybrid orbitals traditionally associated with these molecules. It is now clear that the orbitals in modern valence bond wave functions do not follow the hybridization rules of traditional valence bond theory. These findings imply that, in modern valence bond theories, other factors are responsible for the structures and properties of molecules that are traditionally attributed to orbital hybridization.

The dicarbon bonding puzzle viewed with photoelectron imaging

Bonding in the ground state of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}$$\end{document}2 is still a matter of controversy, as reasonable arguments may be made for a dicarbon bond order of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3$$\end{document}3, or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4$$\end{document}4. Here we report on photoelectron spectra of the C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}^{-}$$\end{document}2− anion, measured at a range of wavelengths using a high-resolution photoelectron imaging spectrometer, which reveal both the ground \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X}^{1}{\Sigma}_{\mathrm{g}}^{+}$$\end{document}X1Σg+ and first-excited \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a}^{3}{\Pi}_{{\mathrm{u}}}$$\end{document}a3Πu electronic states. These measurements yield electron angular anisotropies that identify the character of two orbitals: the diffuse detachment orbital of the anion and the highest occupied molecular orbital of the neutral. This work indicates that electron detachment occurs from predominantly \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s$$\end{document}s-like (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3{\sigma}_{\mathrm{g}}$$\end{document}3σg) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}p-like (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1{\pi }_{{\mathrm{u}}}$$\end{document}1πu) orbitals, respectively, which is inconsistent with the predictions required for the high bond-order models of strongly \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$sp$$\end{document}sp-mixed orbitals. This result suggests that the dominant contribution to the dicarbon bonding involves a double-bonded configuration, with 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi$$\end{document}π bonds and no accompanying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document}σ bond.

In spite of its apparent simplicity, the dicarbon molecule has a bonding structure which is matter of debate. Here the authors measure high-resolution spectra of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{C}}}_{2}$$\end{document}C2 anion by photoelectron imaging, revealing a bonding configuration dominated by a double \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi$$\end{document}π bond, with no accompanying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document}σ bond.

Bond orders of the diatomic molecules

Bond order quantifies the number of electrons dressed-exchanged between two atoms in a material and is important for understanding many chemical properties. Diatomic molecules are the smallest molecules possessing chemical bonds and play key roles in atmospheric chemistry, biochemistry, lab chemistry, and chemical manufacturing. Here we quantum-mechanically calculate bond orders for 288 diatomic molecules and ions. For homodiatomics, we show bond orders correlate to bond energies for elements within the same chemical group. We quantify and discuss how semicore electrons weaken bond orders for elements having diffuse semicore electrons. Lots of chemistry is effected by this. We introduce a first-principles method to represent orbital-independent bond order as a sum of orbital-dependent bond order components. This bond order component analysis (BOCA) applies to any spin-orbitals that are unitary transformations of the natural spin-orbitals, with or without periodic boundary conditions, and to non-magnetic and (collinear or non-collinear) magnetic materials. We use this BOCA to study all period 2 homodiatomics plus Mo2, Cr2, ClO, ClO-, and Mo2(acetate)4. Using Manz's bond order equation with DDEC6 partitioning, the Mo-Mo bond order was 4.12 in Mo2 and 1.46 in Mo2(acetate)4 with a sum of bond orders for each Mo atom of ∼4. Our study informs both chemistry research and education. As a learning aid, we introduce an analogy between bond orders in materials and message transmission in computer networks. We also introduce the first working quantitative heuristic model for all period 2 homodiatomic bond orders. This heuristic model incorporates s-p mixing to give heuristic bond orders of ¾ (Be2), 1¾ (B2), 2¾ (C2), and whole number bond orders for the remaining period 2 homodiatomics.

On the metastability of doubly charged homonuclear diatomics

Generalized valence bond (GVB) and spin-coupled (SC) calculations were used in conjunction with the generalized product function energy partitioning (GPF-EP) method to describe the origin of metastability in doubly charged homonuclear dications. A model to describe the formation of metastable potential wells based on interference and quasi-classical effects is presented. The GPF-EP picture of dications is the result of polarization-aided strong covalent bonding surpassing Coulomb electrostatic repulsion. Important differences in the quasi-classical density profiles of He₂²⁺ and Ne₂²⁺ reveal the underlying mechanism that could lead to bound or unbound states. Finally, the nature of the chemical bond of N₂²⁺, O₂²⁺, and F₂²⁺ is described. The results suggest that the ground states of the mentioned dications are bounded and that the depth of the potential wells of these exotic species is related to the interference effect, in the same way as in previously studied neutral molecules.

Is There a Quadruple Bond in C2?

The chemical structure of the ground state of C2 has been the subject of intense debate after the suggestion that the molecule could exhibit a "fourth" covalent bond. In this paper, we investigate this problem explicitly avoiding all the points of conflict from the previous papers to show that there is no quadruple bond in C2. The generalized product function energy partitioning (GPF-EP) method has been applied to calculate the interference energy (IE) that accounts for the formation of covalent bonds for each bond of the molecule. The IE analysis shows that for the standard σ and π bonds interference exhibits the expected behavior, while for the "fourth" bond interference is a destabilizing factor. To make sure this could not be attributed to a new kind of bond, we performed an equivalent analysis for the (3)Σ(-) excited state of C3 molecule in which similar "bonding" occurs between the two ending carbon atoms. We also show that the difference in force constants of C2 and acetylene can be rationalized in terms of the amount of charge density in the internuclear region by looking at the changes in the overlaps between orbitals along the bond axis.

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)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!

The Bond Order of C2 from a Strictly N-Representable Natural Orbital Energy Functional Perspective

The bond order of the ground electronic state of the carbon dimer has been analyzed in the light of natural orbital functional theory calculations carried out with an approximate, albeit strictly N-representable, energy functional. Three distinct solutions have been found from the Euler equations of the minimization of the energy functional with respect to the natural orbitals and their occupation numbers, which expand upon increasing values of the internuclear coordinate. In the close vicinity of the minimum energy region, two of the solutions compete around a discontinuity point. The former, corresponding to the absolute minimum energy, features two valence natural orbitals of each of the following symmetries, σ, σ*, π and π*, and has three bonding interactions and one antibonding interaction, which is very suggestive of a bond order large than two but smaller than three. The latter, features one σ-σ* linked pair of natural orbitals and three degenerate pseudo-bonding like orbitals, paired each with one triply degenerate pseudo-antibonding orbital, which points to a bond order larger than three. When correlation effects, other than Hartree-Fock for example, between the paired natural orbitals are accounted for, this second solution vanishes yielding a smooth continuous dissociation curve. Comparison of the vibrational energies and electron ionization energies, calculated on this curve, with their corresponding experimental marks, lend further support to a bond order for C2 intermediate between acetylene and ethylene.

The Chemical Bond in C2

Quantum chemical calculations using the complete active space of the valence orbitals have been carried out for Hn CCHn (n=0-3) and N2. The quadratic force constants and the stretching potentials of Hn CCHn 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 X(1)Σg(+) Ground State

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.