Is There a Quadruple Bond in C2?

The strongest dative bond in main-group compounds. Theoretical study of OAeF- (Ae = Be-Ba)

Quantum chemical calculations of the anions OAeF- (Ae = Be-Ba) have been carried out using ab initio methods at the CCSD(T)/def2-TZVPP level and density functional theory employing BP86 with various basis sets. The equilibrium structures have linear geometries for Ae = Be and Mg but they are strongly bent for Ae = Sr and Ba while the calcium species has a quasi-linear structure with a very low bending potential. The calculated bond dissociation energies suggest a record-high BDE of De = 144.08 kcal mol-1 for OBeF- at the CCSD(T)/def2-TZVPP level, which is the strongest BDE for a dative bond that has been found so far. The BDE of the heavier homologues have a continuously decreasing order for Ae with Be > Mg (113.01 kcal mol-1) > Ca (84.06 kcal mol-1) > Sr (72.06 kcal mol-1) > Ba (60.00 kcal mol-1). The calculation of the charge distribution reveals a significant charge donation OAe ← F- with a declining sequence for the heavier atoms Ae. The oxygen atom in OAeF- carries always a higher partial charge than the fluorine atom, which contradicts the standard electronegativities of the atoms. The surprising partial charges are explained with the bonding situation of the atoms in the actual electronic structure. The bonding analysis of the OAe-F- bonds using the EDA-NOCV method shows that the bonds have much more electrostatic character than the Ae-F- bonds in the diatomic anions. This finding is supported by the results of the LED partitioning approach. The dative interactions have three major and one minor component. The assignment of a quadruple bond for the heavier species with Ae = Ca, Sr, Ba is not reasonable. The driving force for the bent geometries is the accumulation of electronic charge in the lone-pair region at the Ae atoms, which enhances the electrostatic attraction with the other atoms. An adequate description of the bonding situation is given by the formula O--Ae+ ← F-.

Multiple Bonding in AeN- (Ae=Ca, Sr, Ba)

Quantum chemical calculations using ab initio methods at the MRCI+Q(8,9)/def2-QZVPPD and CCSD(T)/def2-QZVPPD levels as well as using density functional theory are reported for the diatomic molecules AeN- (Ae=Ca, Sr, Ba). The anions CaN- and SrN- have electronic triplet (3Π) ground states with nearly identical bond dissociation energies De ~57 kcal/mol calculated at the MRCI+Q(8,9)/def2-QZVPPD level. In contrast, the heavier homologue BaN- has a singlet (1Σ+) ground state, which is only 1.1 kcal/mol below the triplet (3Σ-) state. The computed bond dissociation energy of (1Σ+) BaN- is 68.4 kcal/mol. The calculations at the CCSD(T)-full/def2-QZVPPD and BP86-D3(BJ)/def2-QZVPPD levels are in reasonable agreement with the MRCI+Q(8,9)/def2-QZVPPD data, except for the singlet (1Σ+) state, which has a large multireference character. The calculated atomic partial charges given by the CM5, Voronoi and Hirshfeld methods suggest small to medium-sized Ae←N- charge donation for most electronic states. In contrast, the NBO method predicts for all species medium to large Ae→N- electronic charge donation, which is due to the neglect of the (n)p AOs of Ae atoms as genuine valence orbitals. Neither the bond orders nor the bond lengths correlate with the bond dissociation energies. The EDA-NOCV calculations show that the heavier alkaline earth atoms Ca, Sr, Ba use their (n)s and (n-1)d orbitals for covalent bonding.

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.

Analysis of chemical bonding of the ground and low-lying states of Mo2 and of Mo2Clx complexes, x = 2 - 10

In the present study, we perform accurate calculations via multireference configuration interaction and coupled cluster methodologies on the dimolybdenum molecule in conjunction with complete series of correlation and weighted core correlation consistent basis sets up to quintuple size. The bonding, dissociation energies, and spectroscopic parameters of the seven states that correlate to the ground state products are calculated. The ground state has a sextuple chemical bond and each of the calculated excited state has one less bond than the previous one. The calculated values for the ground(X1Σg+ ) state of Mo2 have been extrapolated to the complete basis set limits. Our final values, re=1.9324 Å and De(D0)=4.502{plus minus}0.007(4.471{plus minus}0.009) eV, are in excellent agreement with the experimental values of re=1.929, 1.938(9) Å and D0=4.476(10) eV. The Mo2 in 13Σg+ state is a weakly bound dimer, forming 5s...5pz bonds, with De=0.120 eV at re=3.53 Å. All calculated excited states (except 13Σg+) have a highly multireference character (C0=0.25-0.55). The ordering of the molecular bonding orbitals changes as the spin is increased from quintet to septet state. The quite low bond dissociation energy of the ground state is due to the splitting of the molecular bonding orbitals in two groups differing in energy by ~3 eV. Finally, the bond breaking of Mo2, as the multiplicity of spin is increased, is analyzed in parallel with the Mo-Mo bond breaking in a series of Mo2Clx complexes when x is increased. Physical insight into the nature of the sextuple bond and its low dissociation energy is provided.

The Nature of the Polar Covalent Bond

Quantum chemical calculations using density functional theory are reported for the diatomic molecules LiF, BeO, and BN. The nature of the interatomic interactions is analyzed with the EDA-NOCV method, and the results are critically discussed and compared with data from QTAIM, NBO and Mayer approaches. Polar bonds, like nonpolar bonds, are caused by the interference of wave functions, which lead to an accumulation of electronic charge in the bonding region. Polar bonds generally have a larger percentage of electrostatic bonding to the total attraction, but nonpolar bonds may also possess large contributions from Coulombic interaction. The term "ionic contribution" refers to VB structures and is misleading because it refers to separate fragments with negligible overlap that occur only in the solid state and in solution, not in a molecule. The EDA-NOCV method gives detailed information about the individual orbital contributions, which can nicely be identified by visual inspection of the associated deformation densities. It is very important, particularly for polar bonds to distinguish between the interatomic interactions of the final dissociation products after bond rupture and the interactions between the fragments in the eventually formed bond.

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.

Probing the Nature of the Transition-Metal-Boron Bonds and Novel Aromaticity in Small Metal-Doped Boron Clusters Using Photoelectron Spectroscopy

Photoelectron spectroscopy combined with quantum chemistry has been a powerful approach to elucidate the structures and bonding of size-selected boron clusters (B_n^-), revealing a prevalent planar world that laid the foundation for borophenes. Investigations of metal-doped boron clusters not only lead to novel structures but also provide important information about the metal-boron bonds that are critical to understanding the properties of boride materials. The current review focuses on recent advances in transition-metal-doped boron clusters, including the discoveries of metal-boron multiple bonds and metal-doped novel aromatic boron clusters. The study of the RhB^- and RhB₂O^- clusters led to the discovery of the first quadruple bond between boron and a transition-metal atom, whereas a metal-boron triple bond was found in ReB₂O^- and IrB₂O^-. The ReB₄^- cluster was shown to be the first metallaborocycle with Möbius aromaticity, and the planar ReB₆^- cluster was found to exhibit aromaticity analogous to metallabenzenes. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.

The Valence-Bond (VB) Model and Its Intimate Relationship to the Symmetric or Permutation Group

VB and molecular orbital (MO) models are normally distinguished by the fact the first looks at molecules as a collection of atoms held together by chemical bonds while the latter adopts the view that each molecule should be regarded as an independent entity built up of electrons and nuclei and characterized by its molecular structure. Nevertheless, there is a much more fundamental difference between these two models which is only revealed when the symmetries of the many-electron Hamiltonian are fully taken into account: while the VB and MO wave functions exhibit the point-group symmetry, whenever present in the many-electron Hamiltonian, only VB wave functions exhibit the permutation symmetry, which is always present in the many-electron Hamiltonian. Practically all the conflicts among the practitioners of the two models can be traced down to the lack of permutation symmetry in the MO wave functions. Moreover, when examined from the permutation group perspective, it becomes clear that the concepts introduced by Pauling to deal with molecules can be equally applied to the study of the atomic structure. In other words, as strange as it may sound, VB can be extended to the study of atoms and, therefore, is a much more general model than MO.

Substituent Effects on the Quantum Interference of Two-Center One-Electron Bonds: [B2X6]- (X = H, F, Cl, CN, OH, CH3, and OCH3)

The interference energy analysis (IEA) provided by the generalized product function energy partitioning (GPF-EP) method was applied to investigate the influence of the neighboring atoms on the nature of the two-center one-electron (2c1e) bonds in the anion dimers of BX₃ species (X = H, F, Cl, CN, OH, CH₃, and OCH₃). The species were studied at the GVB-PP(6/12).SC(1,2)/6-31**G++ level of calculation. The IEA has revealed that there is a balance between two main factors determining the chemical stability of the species. Quantum interference acts as the sole stabilizing effect in the formation of the chemical bonds, particularly as the result of the drop in kinetic energy, and the electronegativity of the substituent has a direct influence on the magnitude of this effect. The quasi-classical energy is responsible for the destabilizing factors, mainly the group bulkiness, and the "electron-withdrawing" effect in the case of the cyano group.

Quadruple chemical bonding in the diatomic anions TcN- , RuC- , RhB- , and PdBe. J Comput Chem 2021;42:1126-1137. [PMID: 33851470 DOI: 10.1002/jcc.26527]

Quadruple bonding is uncommon for main group elements and the identification of species forming such bonds is remarkably interesting particularly in diatomic anions for which there is a lack of information. Here, it is found that the MX^- anions, TcN^- , RuC^- , RhB^- , and PdBe^- , present quadruple bonding, as do the corresponding MX neutrals, even though a different type of σ² bond is involved in ∑⁺ states of neutral and anions. Specifically, the ground states (X² Δ or X² ∑⁺ ) of the four anions and their first excited states (A² ∑⁺ or A² Δ) of TcN^- , RuC^- , and RhB^- present quadruple bonds consisting of two σ and two π bonds: (4d_z2  - 2p_z )² , 5p_z ⁰  ← 2s² , (4d_xz  - 2p_x )² , and (4d_yz  - 2p_y )² . Bond lengths, dissociation energies, spectroscopic data and electron affinities were calculated via high-level multireference and coupled-cluster methodology using the aug-cc-pV5Z_X (-PP)_M basis set. Strong bonding results in short bond lengths ranging from 1.602 (TcN^- ) to 1.944 (PdBe^- ) Å. Adiabatic (diabatic) binding energies reach up to 139 (184) kcal/mol. Electron affinities (EA) were calculated at 1.368 (TcN), 1.242 (RuC), 0.873 (RhB), 0.743 (PdBe) eV. Only for RhB has EA been measured experimentally at 0.961 eV, in good agreement with the value reported here.

Comprehending the quadruple bonding conundrum in C2 from excited state potential energy curves

The question of quadruple bonding in C₂ has emerged as a hot button issue, with opinions sharply divided between the practitioners of Valence Bond (VB) and Molecular Orbital (MO) theory.

The question of quadruple bonding in C₂ has emerged as a hot button issue, with opinions sharply divided between the practitioners of Valence Bond (VB) and Molecular Orbital (MO) theory. Here, we have systematically studied the Potential Energy Curves (PECs) of low lying high spin sigma states of C₂, N₂, Be₂ and HC Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> CH using several MO based techniques such as CASSCF, RASSCF and MRCI. The analyses of the PECs for the ^2S+1Σ_g/u (with 2S + 1 = 1, 3, 5, 7, 9) states of C₂ and comparisons with those of relevant dimers and the respective wavefunctions were conducted. We contend that unlike in the case of N₂ and HC Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> CH, the presence of a deep minimum in the ⁷Σ⁺ state of C₂ and CN⁺ suggests a latent quadruple bonding nature in these two dimers. Our investigations reveal that the number of bonds in the ground state can be determined for 2^nd row dimers by figuring out at what value of spin symmetry a purely dissociative PEC is obtained. For N₂ and HC Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> CH the purely dissociative PEC appears for the septet spin symmetry as compared to that for the nonet in C₂. This is indicative of a higher number of bonds between the two 2^nd row atoms in C₂ as compared to those of N₂ and HC Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> CH. Hence, we have struck a reconciliatory note between the MO and VB approaches. The evidence provided by us can be experimentally verified, thus providing the window so that the narrative can move beyond theoretical conjectures.

Observation of Four-Fold Boron-Metal Bonds in RhB(BO-) and RhB

The maximum bond order between two main-group atoms was known to be three. However, it has been suggested recently that there is quadruple bonding in C₂ and analogous eight-valence electron species. While the quadruple bond in C₂ has aroused some debates, an interesting question is: are main-group elements capable of forming quadruple bonds? Here we use photoelectron spectroscopy and computational chemistry to probe the electronic structure and chemical bonding in RhB₂O^- and RhB^- and show that the boron atom engages in quadruple bonding with rhodium in RhB(BO)^- and neutral RhB. The quadruple bonds consist of two π-bonds formed between the Rh 4d_xz/4d_yz and B 2p_x/2p_y orbitals and two σ-bonds between the Rh 4d_z² and B 2s/2p_z orbitals. To confirm the quadruple bond in RhB, we also investigate the linear Rh≡B-H⁺ species and find a triple bond between Rh and B, which has a longer bond length, lower stretching frequency, and smaller bond dissociation energy in comparison with that of the Rh≣B quadruple bond in RhB.

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.

One-electron bonds are not "half-bonds"

Despite the success of the molecular orbital (MO) and valence-bond (VB) models to describe the electronic structure and properties of molecules, neither MO nor VB provides an explanation for the nature of the chemical bond. The first to address this problem was Ruedenberg, who showed that chemical bonds result from quantum interference. He developed a method to calculate the interference contribution to the total electronic energy and density and applied it to molecules containing typical two-centre two-electron (2c-2e) covalent bonds. To test the generality of Ruedenberg's hypothesis, we developed a powerful Interference Energy Analysis (IEA) method to calculate the interference contributions of individual chemical bonds to the total energy of diatomic and polyatomic molecules, and showed that any two-electron bond, despite its polarity, results from quantum interference. Nevertheless, many stable molecules are experimentally known whose chemical structures clearly indicate the existence of two-centre one-electron bonds (2c-1e). Therefore, the question remains if quantum interference will be the dominant effect for these systems. This work describes the extension of the IEA for treating two-centre one-electron bonds, making use of a Generalised Product Function (GPF) built from spin coupled wave functions of N electrons in M orbitals, SC(N,M). Several diatomic and polyatomic molecules were analysed and whenever possible the results were compared with the analogous case of a two-electron bond. The results indicate that interference is the dominant effect for the one-electron bonds, which reinforces the role of quantum interference as the central element in chemical bonding theory.

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.

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.

Solving the Schrödinger equation of atoms and molecules: Chemical-formula theory, free-complement chemical-formula theory, and intermediate variational theory

Chemistry is governed by the principle of quantum mechanics as expressed by the Schrödinger equation (SE) and Dirac equation (DE). The exact general theory for solving these fundamental equations is therefore a key for formulating accurately predictive theory in chemical science. The free-complement (FC) theory for solving the SE of atoms and molecules proposed by one of the authors is such a general theory. On the other hand, the working theory most widely used in chemistry is the chemical formula that refers to the molecular structural formula and chemical reaction formula, collectively. There, the central concepts are the local atomic concept, transferability, and from-atoms-to-molecule concept. Since the chemical formula is the most successful working theory in chemistry ever existed, we formulate our FC theory to have the structure reflecting the chemical formula. Our basic postulate is that as far as the SE is the principle of chemistry, its solutions for chemistry should have the structure that can be related to the chemical formulas. So, in this paper, we first formulate a theory that designs the wave function to reflect the structure of the chemical formula. We call this theory chemical formula theory (CFT). In the CFT, we place the valence ground and excited states of each atom at each position of the chemical formula of the molecule and let them interact using their free valences to form the ground and excited states of the molecule. The principle there is the variational principle so that the ground and excited states obtained satisfy the orthogonality and Hamiltonian-orthogonality relations. Then, we formulate the exact FC theory starting from the initial functions produced by the CFT. This FC theory is referred to as free-complement chemical-formula theory (FC-CFT), which is expected to describe efficiently the solution of the SE by the above reason. The FC-CFT wave function is modified from that of CFT. Since this modification is done by the exact SE, its analysis may give some insights to chemists that assist their chemistry. Thus, this theory would be not only exact but also conceptually useful. Furthermore, the intermediate theory between CFT and FC-CFT would also be useful. There, we use only integratable functions and apply the variational principle so that we refer to this theory as FC-CFT-variational (FC-CFT-V). It is an advanced theory of CFT. Since the variational method is straightforward and powerful, we can do extensive chemical studies in a reasonable accuracy. After finishing such studies, if we still need an exact level of solutions, we add the remaining functions of the FC-CFT and perform the exact calculations. Furthermore, when we deal with large and even giant molecules, the inter-exchange (iExg) theory for the antisymmetry rule introduced previously leads to a large simplification. There, the inter-exchanges between distant electron pairs fade away so that only Coulombic interactions survive. Further in giant systems, even an electrostatic description becomes possible. Then, the FC-CFT for exactly solving the SE would behave essentially to order N for large and giant molecular systems, though the pre-factor should be very large and must be minimized.

Cn (n=2-4): current status

The major aspects of the C₂, C₃ and C₄ elemental carbon clusters are surveyed. For C₂, a brief analysis of its current status is presented. Regarding C₃, the most recent results obtained in our group are reviewed with emphasis on modelling its potential energy surface which is particularly complicated due to the presence of multiple conical intersections. As for C₄, the most stable isomeric forms of both triplet and singlet spin states and their possible interconversion pathways are examined afresh by means of accurate ab initio calculations. The main strategies for modelling the ground triplet C₄ potential are also discussed. Starting from a truncated cluster expansion and a previously reported DMBE form for C₃, an approximate four-body term is calibrated from the ab initio energies. The final six-dimensional global DMBE form so obtained reproduces all known topographical aspects while providing an accurate description of the C₄ linear-rhombic isomerization pathway. It is therefore commended for both spectroscopic and reaction dynamics studies.This article is part of the theme issue 'Modern theoretical chemistry'.

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.

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.

Trends in Strong Chemical Bonding in C2, CN, CN-, CO, N2, NO, NO+, and O2

The strong chemical bonds between C, N, and O play a central role in chemistry, and their formation and cleavage are critical steps in very many catalytic processes. The close-lying molecular orbital energies and large correlation effects pose a challenge to electronic structure calculations and have led to different bonding interpretations, most notably for C₂. One way to approach this problem is by strict benchmark comparison of related systems. This work reports reference electronic structures and computed bond dissociation enthalpies D₀ for C₂, CN, CN^-, CO, N₂, NO, NO⁺, O₂ and related systems C₂⁺ and C₂^- at chemical accuracy (∼1 kcal/mol or 4 kJ/mol) using CCSD(T)/aug-cc-pV5Z, with additional benchmarks of HF, MP2, CCSD, explicitly correlated F12 methods, and four density functionals. Very large correlation and basis set effects are responsible for up to 93% of total D₀. The order of the molecular orbitals 1π_u and 3σ_g changes, as seen in textbooks, depending on total and effective nuclear charge. Linear trends are observed in 2σ_u-2σ_g orbital splitting (R² = 0.91) and in D₀ of C₂, C₂^-, and C₂⁺ (R² = 0.99). The correlation component of D₀ of C₂ is by far the largest (∼93%) due to a poor HF description. Importantly, density functional theory fails massively in describing this series consistently in both limits of effective nuclear charge, and Hartree-Fock exchange or meta functionals do not remedy this 100 kJ/mol error, which should thus be addressed in future density functional developments as it affects very many studies involving cleavage or formation of these bonds.

Are One-Electron Bonds Any Different from Standard Two-Electron Covalent Bonds?

The nature of the chemical bond is perhaps the central subject in theoretical chemistry. Our understanding of the behavior of molecules developed amazingly in the last century, mostly with the rise of quantum mechanics (QM) and QM-based theories such as valence bond theory and molecular orbital theory. Such theories are very successful in describing molecular properties, but they are not able to explain the origin of the chemical bond. This problem was first analyzed in the 1960s by Ruedenberg, who showed that covalent bonds are the direct result of quantum interference between one-electron states. The generality of this result and its quantification were made possible through the recent development of the generalized product function energy partitioning (GPF-EP) method by our group, which allows the partitioning of the electronic density and energy into their interference and quasi-classical (noninterference) contributions. Furthermore, with GPF wave functions these effects can be analyzed separately for each bond of a molecule. This interference energy analysis has been applied to a large variety of molecules, including diatomics and polyatomics, molecules with single, double, and triple bonds, molecules with different degrees of polarity, linear or branched molecules, cyclic or acyclic molecules, conjugated molecules, and aromatics, in order to verify the role played by quantum interference. In all cases the conclusion is exactly the same: for each bond in each of the molecules considered, the main contribution to its stability comes from the interference term. Two-center one-electron (2c1e) bonds are the simplest kind of chemical bonds. Yet they are often viewed as odd or unconventional cases of bonding. Are they any different from conventional (2c2e) bonds? If so, what differences can we expect in the nature of (2c1e) bonds relative to electron-pair bonds? In this Account, we extend the GPF-EP method to describe bonds involving N electrons in M orbitals (N < M) and show its application to (2c1e) bonds. As examples we chose the molecules H₂⁺, H₃C·CH₃⁺, B₂H₄^-, [Cu·BH₃(PH₃)₃], and an alkali-metal cation dimer, and we evaluated the components of the electronic energy and density, which account for the formation of the bond, and compared the results with those for the respective analogous molecules exhibiting the "conventional" two-electron bond. In all cases, it was verified that interference is the dominant effect for the one-electron bonds. The GPF-EP results clearly indicate that molecules exhibiting (2c1e) bonds should not be considered as special systems, since one- and two-electron bonds result from quantum interference and therefore there is no conceptual difference between them. Moreover, these results show that quantum interference provides a way to unify the chemical bond concept.