Comment on "The Quadruple Bonding in C2 Reproduces the Properties of the Molecule"

δ-Bonding and Spin-Orbit Coupling Make SrAg4Sb2 a Topological Insulator

Bonding interactions and spin-orbit coupling in the topological insulator SrAg4Sb2 are investigated using DFT with orbital projection analysis. Ag-Ag delta bonding is a key ingredient in the topological insulating state because the4 d x y + 4 d x 2 - y 2 ${4d_{xy} + 4d_{x^2 - y^2 } }$ delta antibonding band forms a band inversion with the 5 s sigma bonding band. Spin-orbit coupling is required to lift d orbital degeneracies and lower the antibonding band enough to create the band inversion. These bonding effects are enabled by a longer-than-covalent Ag-Ag distance in the crystal lattice, which might be a structural characteristic of other transition metal based topological insulators. A simplified model of the topological bands is constructed to capture the essence of the topological insulating state in a way that may be engineered in other materials.

Decoding energy decomposition analysis: Machine-learned Insights on the impact of the density functional on the bonding analysis

The concept of chemical bonding is a crucial aspect of chemistry that aids in understanding the complexity and reactivity of molecules and materials. However, the interpretation of chemical bonds can be hindered by the choice of the theoretical approach and the specific method utilized. This study aims to investigate the effect of choosing different density functionals on the interpretation of bonding achieved through energy decomposition analysis (EDA). To achieve this goal, a data set was created, representing four bonding groups and various combinations of functionals and dispersion correction schemes. The calculations showed significant variation among the different functionals for the EDA terms, with the dispersion correction terms exhibiting the highest variability. More information was extracted by using machine learning in combination with dimensionality reduction on the data set. Results indicate that, despite the differences in the EDA terms obtained from different functionals, the functional has the least significant impact, suggesting minimal influence on the bonding interpretation.

Mimicking the C2 molecule: M2B2 and M3B2+ clusters (M = Li, Na) and the reactivity of the N-heterocyclic carbene bound Li2B2 complex

C2 has attracted considerable attention from the scientific community for its debatable bonding situation. Herein, we show that the global minima of M2B2 and M3B2+ (M = Li, Na) possess similar covalent bonding patterns to C2. Because of strong charge transfer from M2/M3 to B2 dimer, they can be better described as [M2]2+[B2]2- and [M3]3+[B2]2- salt complexes with the B22- core surrounded perpendicularly by two and three M+ atoms, respectively. The energy decomposition analyses in combination with the natural orbital for chemical valence theory give four bonding components in C2, M2B2, and M3B2+ clusters. However, the fourth component does not arise from a bonding interaction but from polarization/hybridization. Considering the effect of Pauli repulsion in σ-space, the attractive covalent interaction in these molecules mainly comes from the two π-bonds. We further presented stable N-heterocyclic carbene (NHC) and triphenylphosphine (PPh3) ligands bound Li2B2(NHC)2 and Li2B2(PPh3)2 complexes. A comparative study of reactivity towards L = CO2, CO, and N2 between Li2B2(NHC)2 and B2(NHC)2 is also performed. L-Li2B2(NHC)2 is highly stable against L dissociation at room temperature for L = CO2 and CO, and the stability is markedly higher than that in L-B2(NHC)2. The larger B2→L π-backdonation in L-Li2B2(NHC)2 also makes L more activated than in L-B2(NHC)2.

Dative quadruple bonds between d10 transition metals and beryllium in BeM(PMe3 )2 and BeM(CO)2 (M = Ni, Pd, and Pt) complexes: Transition metal fragments as six-electron donor and two-electron acceptor

The structure, chemical bonding, and reactivity of neutral 16 valence electrons (VE) transition metal complexes of beryllium, BeM(PMe₃ )₂ (1M-Be) and BeM(CO)₂ (2M-Be, M = Ni, Pd, and Pt) were studied. The molecular orbital and EDA-NOCV analysis suggest dative quadruple bonds between the transition metal and beryllium, viz., one Be→M σ bond, one Be←M σ bond, and two Be←M π bonds. The strength of these bonding interactions varies based on the ligands coordinated to the transition metal. The Be←M σ bond is stronger than the Be→M σ bond when the ligand is PMe_3, whereas the reverse order is observed when the ligand is CO. This is attributed to the higher π acceptor strength of CO as compared to PMe₃ . Since these complexes have M-Be dative quadruple bonds, the beryllium center is susceptible to ambiphilic reactivity, as indicated by high proton and hydride affinity values.

Two σ- and two π-dative quadruple bonds between the s-block element and transition metal in [BeM(CO)4; M = Fe - Os]

We report the chemical bonding and reactivity of the first example of neutral 18 valence electron transition metal complexes of beryllium, [BeM(CO)₄; M = Fe - Os], in trigonal bipyramidal coordination geometry, where the bonding between the transition metal and the s-block element beryllium (M-Be) can be best described by dative quadruple bonds. In contrast to the conventional multiple bonding pattern, the quadruple bonds comprise two σ-bonds and two π-bonds, viz., one Be → M σ-bond, one M → Be σ-bond, and two M → Be π-bonds. Since the M-Be quadruple bonds are described by dative interactions, the Be centre shows ambiphilic character as indicated by the high proton and hydride affinity values.

From the gas phase to the solid state: The chemical bonding in the superheavy element flerovium

As early as 1975, Pitzer suggested that copernicium, flerovium and oganesson are volatile substances behaving noble-gas like because of their closed-shell configurations and accompanying relativistic effects. It is, however, precarious to predict the chemical bonding and physical behavior of a solid by knowledge of the atomic or molecular properties only. Copernicium and oganesson have been analyzed very recently by our group. Both are predicted to be semi-conductors and volatile substances with rather low melting and boiling points, which may justify a comparison with the noble gas elements. Here we study closed-shell flerovium in detail to predict solid-state properties including the melting point from a decomposition of the total energy into many-body forces derived from relativistic coupled-cluster and from density functional theory. The convergence of such a decomposition for flerovium is critically analyzed, and the problem of using density functional theory is highlighted. We predict that flerovium is in many ways not behaving like a typical noble gas element despite its closed-shell 7$p_{1/2}^2$ configuration and resulting weak interactions. Unlike for the noble gases, the many-body expansion in terms of the interaction energy is not converging smoothly. This makes the accurate prediction of phase transitions very difficult. Nevertheless, a first prediction by Monte-Carlo simulation estimates the melting point at $284\pm 50$ K. Furthermore, calculations for the electronic band gap suggests that flerovium is a semi-conductor similar to copernicium

Bonding analysis of the C2 precursor Me3E–C2–I(Ph)FBF3 (E = C, Si, Ge)

A series of possible precursors for generating C2 with the general formula Me3E–C2–I(Ph)FBF3 [E = C (1), Si (2), and Ge (3)] has been theoretically investigated using quantum chemical calculations. The equilibrium geometries of all species show a linear E–C2–I+ backbone. The inspection of the electronic structure of the Me3E–C2 bond by energy decomposition analysis coupled with the natural orbital for chemical valence (EDA-NOCV) method suggests a combination of electron sharing C–C σ-bond and v weak π-dative bond between Me3C and C2 fragments in the doublet state for species 1 (E = C). For species 2 (Si) and 3 (Ge), the analysis reveals σ-dative Me3E–C2 bonds (E = Si, Ge; Me3E←C2) resulting from the interaction of singly charged (Me3E)+ and (C2–IPh(BF4))− fragments in their singlet states. The C2–I bond is diagnosed as an electron sharing σ-bond in all three species, 1, 2 and 3.

The Hitchhiker's Guide to the Wave Function∥

The electronic wave function of molecules is 3N-dimensional and inseparable in the coordinates of the N electrons. Whereas molecular orbitals are often invoked to visualize the electronic structure, they are nonunique, with the same 3N-dimensional wave function being represented by an infinite number of 3-D, one-electron functions (orbitals). Furthermore, multireference wave functions cannot be described by an antisymmetrized product of a single set of occupied orbitals. What is required is a way to visualize the full dimensionality of the wave function, including the effects of correlation, as a 3N-dimensional being would be able to do. In the past 5 years, we have been developing a way to analyze and visualize highly dimensional wave functions by focusing on the structure of the repeating unit demanded by fermionic behavior. This 3N-dimensional repeating unit, the wave function "tile", can be projected onto the three dimensions of each electron, in turn, to reveal the complete electronic structure. It is found that the tile reproduces canonical chemical motifs such as core-electrons, single bonds and lone pairs. Multiple bonds emerge as the "banana" bonds favored by Pauling. As a function of the reaction coordinate, electron motions are visualized that correspond to the curly arrow notation of organic chemists. Excited states can also be inspected. Analyzing a wave function in terms of fermionic tiling allows for insight not facilitated by the inspection of orbitals or configuration interaction vectors: The wave function tiles of resonance structures reveal that electron correlation in benzene pushes opposing spin electrons to occupy alternate Kekulé structures, and in C₂, the emerging structure supports the notion of a triply bonded structure with a weak, fourth bonding contribution.

Photodissociation of dicarbon: How nature breaks an unusual multiple bond

It has long been observed that the coma of a comet is often green while its tail is not. While the explanation for this must be that the molecules responsible for the green emission, C₂, are photodissociated, the mechanism was, until now, unknown. We have observed the photodissociation of C₂ in the laboratory for the first time and, in doing so, have determined its bond dissociation energy with unprecedented precision. Invoking the observed mechanism, the calculated lifetime of cometary C₂ is found to be consistent with astronomical observations.

The dicarbon molecule (C₂) is found in flames, comets, stars, and the diffuse interstellar medium. In comets, it is responsible for the green color of the coma, but it is not found in the tail. It has long been held to photodissociate in sunlight with a lifetime precluding observation in the tail, but the mechanism was not known. Here we directly observe photodissociation of C₂. From the speed of the recoiling carbon atoms, a bond dissociation energy of 602.804(29) kJ·mol−1 is determined, with an uncertainty comparable to its more experimentally accessible N₂ and O₂ counterparts. The value is within 0.03 kJ·mol⁻¹ of high-level quantum theory. This work shows that, to break the quadruple bond of C₂ using sunlight, the molecule must absorb two photons and undergo two “forbidden” transitions.

A Critical Look at Linus Pauling's Influence on the Understanding of Chemical Bonding

The influence of Linus Pauling on the understanding of chemical bonding is critically examined. Pauling deserves credit for presenting a connection between the quantum theoretical description of chemical bonding and Gilbert Lewis's classical bonding model of localized electron pair bonds for a wide range of chemistry. Using the concept of resonance that he introduced, he was able to present a consistent description of chemical bonding for molecules, metals, and ionic crystals which was used by many chemists and subsequently found its way into chemistry textbooks. However, his one-sided restriction to the valence bond method and his rejection of the molecular orbital approach hindered further development of chemical bonding theory for a while and his close association of the heuristic Lewis binding model with the quantum chemical VB approach led to misleading ideas until today.

Routes involving no free C2 in a DFT-computed mechanistic model for the reported room-temperature chemical synthesis of C2

Recent lively debates about the nature of the quadruple bonding in the diatomic species C2 have been heightened by recent suggestions of molecules in which carbon may be similarly bonded to other elements. The desirability of having methods for generating such species at ambient temperatures and in solution in order to study their properties may have been realized by a recent report of the first chemical synthesis of free C2 itself under mild conditions. The method involved unimolecular fragmentation of an alkynyl zwitterion 2 as generated from the precursor 1, resulting in production and then trapping of free C2 at ambient temperatures rather than the high temperature gas phase methods normally employed for C2 generation. Here, alternative mechanisms are proposed for this reaction based on DFT calculations involving bimolecular 1,1- or 1,2-iodobenzene displacement reactions from 2 directly by galvinoxyl radical, or hydride transfer from 9,10-dihydroanthracene to 2. These mechanisms result in the same trapped products as observed experimentally, but unlike that involving unimolecular generation of free C2, exhibit calculated free energy barriers commensurate with the reaction times observed at room temperatures. The relative energies of the transition states for 1,1 vs. 1,2 substitution provide a rationalisation for the observed isotopic substitution patterns. The same mechanism also provides an energetically facile path to polymeric synthesis of carbon rich species by extending the carbon chain attached to the iodonium group, eventually resulting in formation of amorphous carbon and discrete molecules such as C60.

Isolable dicarbon stabilized by a single phosphine ligand

In contrast to naturally occurring F₂, O₂ and N₂, diatomic C₂ is an intriguing species that has only been observed indirectly in the gas phase, and because of its high reactivity has eluded isolation in the condensed phase. It has previously been stabilized in L→C₂←L compounds but the bonding situation of the central C₂ in this motif differs remarkably from that of free C₂. Here we have prepared and structurally characterized diatomic C₂ as a monoligated complex L→C₂ using a bulky phosphine ligand bearing two imidazolidin-2-iminato groups (L is (NHC^R=N)₂(CH₃)P, where NHC^R is an N-heterocyclic carbene). The compound is stable in solution at ambient temperature and has also been isolated in the solid state. Reactivity studies, in combination with quantum chemical analysis, suggest that the two carbon atoms of the L→C₂ complex both have carbene character. The complex underwent intermolecular C-H bond activation upon thermolysis and exhibited hydroalkoxylation-like reactivity with methanol.

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.

Insight into spin-orbital interaction using MCSCF method: A special analysis of the 1 Σg + electronic state in C2 and the linear polyacetylenic C4 and C6

The symmetry-broken wave function can transform the ¹ Σ_g ⁺ state of C₂ from the classic double bonding to the quadruple bonding, where the transformed wave functions of ϕ _L and ϕ _R are singly occupied by two opposite-spinning electrons. In this article, the effective bond order (EBO) contribution of the fourth bond in C₂ is assessed through the overlap integral between ϕ _L and ϕ _R , namely the value (0.60) is the EBO contribution of the fourth bond in the transformed scheme. Hence, the new EBO is 3.36, which is more equitable than the original EBO (2.15) in the traditional scheme. In addition, the singlet diradical character of the linear polyacetylenic C₄ and C₆ in the ¹ Σ_g ⁺ state is addressed for the first time. No spin-polarized bonding exists in other linear C_2n clusters, because the ionic interaction in the polyacetylenic ¹ Σ_g ⁺ state of C₄ is negligible. Moreover, the coupling energy between α and β single electrons in C₄ is only 4.0 kcal mol^-1 based on the electron spin-flip energy. © 2019 Wiley Periodicals, Inc.

EOM-CC guide to Fock-space travel: the C2 edition

Electronic structure calculations for C₂, C₂⁻, and C₂²⁻ using the CC/EOM-CC family of methods. Results illustrate that EOM-CCSD provides an attractive alternative to MR approaches.

Pleading for a Dual Molecular-Orbital/Valence-Bond Culture

Electron pairs through the looking glass might well discover that they can show two faces, one delocalized or the other localized, and that both are perfectly correct. Going back and forth between these two representations, according to which one is the most relevant and insightful for the case at hand, is easy and essential to get a complete understanding of electronic structure.

From quantum fragments to Lewis structures: electron counting in position space

From quantum atoms to electron counting the rs-AdNCP strategy: a Lewis structure through (nc,2e) functions.

A Response to a Comment by G. Frenking and M. Hermann on: "The Quadruple Bonding in C2 Reproduces the Properties of the Molecule"

In response to the comment by Frenking and Hermann on our work in this journal (Chem. Eur J. 2016, 22, 4116) it is is shown once again that C₂ has a quadruple bond with three strong bonds and one weaker exo-bond. All other bonding forms are less stable.