An Excursion from Normal to Inverted C?C Bonds Shows a Clear Demarcation between Covalent and Charge‐Shift C?C Bonds

What is the nature of the C? C bond? Valence bond and electron density computations of 16 C? C bonds show two families of bonds that flesh out as a phase diagram. One family, involving ethane, cyclopropane and so forth, is typified by covalent C? C bonding wherein covalent spin‐pairing accounts for most of the bond energy. The second family includes the inverted bridgehead bonds of small propellanes, where the bond is neither covalent nor ionic, but owes its existence to the resonance stabilization between the respective structures; hence a charge‐shift (CS) bond. The dual family also emerges from calculated and experimental electron density properties. Covalent C? C bonds are characterized by negative Laplacians of the density, whereas CS‐bonds display small or positive Laplacians. The positive Laplacian defines a region suffering from neighbouring repulsive interactions, which is precisely the case in the inverted bonding region. Such regions are rich in kinetic energy, and indeed the energy‐density analysis reveals that CS‐bonds are richer in kinetic energy than the covalent C? C bonds. The large covalent–ionic resonance energy is precisely the mechanism that lowers the kinetic energy in the bonding region and restores equilibrium bonding. Thus, different degrees of repulsive strain create two bonding families of the same chemical bond made from a single atomic constituent. It is further shown that the idea of repulsive strain is portable and can predict the properties of propellanes of various sizes and different wing substituents. Experimentally (M. Messerschmidt, S. Scheins, L. Bruberth, M. Patzel, G. Szeimies, C. Paulman, P. Luger, Angew. Chem. 2005 , 117, 3993–3997; Angew. Chem. Int. Ed. 2005 , 44, 3925–3928), the C? C bond families are beautifully represented in [1.1.1]propellane, where the inverted C? C is a CS‐bond, while the wings are made from covalent C? C bonds. What other manifestations can we expect from CS‐bonds? Answers from experiment have the potential of recharting the mental map of chemical bonding.     

Charge‐Shift Bonding: A New and Unique Form of Bonding

Charge‐shift bonds (CSBs) constitute a new class of bonds different than covalent/polar‐covalent and ionic bonds. Bonding in CSBs does not arise from either the covalent or the ionic structures of the bond, but rather from the resonance interaction between the structures. This Essay describes the reasons why the CSB family was overlooked by valence‐bond pioneers and then demonstrates that the unique status of CSBs is not theory‐dependent. Thus, valence bond (VB), molecular orbital (MO), and energy decomposition analysis (EDA), as well as a variety of electron density theories all show the distinction of CSBs vis‐à‐vis covalent and ionic bonds. Furthermore, the covalent–ionic resonance energy can be quantified from experiment, and hence has the same essential status as resonance energies of organic molecules, e.g., benzene. The Essay ends by arguing that CSBs are a distinct family of bonding, with a potential to bring about a Renaissance in the mental map of the chemical bond, and to contribute to productive chemical diversity.     

When Is a Bond Broken? The Polarizability Perspective.

The question of when a chemical bond can be said to be broken is of fundamental chemical interest but has not been widely studied. Herein we propose that the maxima of static polarizability along bond dissociation coordinates naturally define cutoff points for bond rupture, as they represent the onset of localization of shared electron density into constituent fragments. Examples of computed polarizability maxima over the course of bond cleavage in main-group and transition metal compounds are provided, across covalent, dative and charge-shift bonds. The behavior along reaction paths is also considered. Overall, the static polarizability is found to be a sensitive reporter of electronic structure reorganization associated with bond stretching, and thus can serve as a metric for describing bond cleavage (or diagnose the absence of a chemical bond).     

H2XP…SHY复合物中磷键与硫键的理论研究

用从头算量子化学方法MP2 与CCSD(T)研究了H₂XP和SHY (X, Y=H, F, Cl, Br)分子的P与S之间形成的磷键X―P…S与硫键Y―S…P的本质与规律以及取代基X与Y对成键的影响. 计算结果表明, 硫键比磷键强, 连接在Lewis 酸上的取代基的电负性增大导致形成的磷键或硫键增强, 键能增大, 对单体的结构和性质的影响也增大; 而连接在Lewis 碱上的取代基效应则相反. 硫键键能为8.37-23.45 kJ·mol^-1, 最强的硫键结构是Y 电负性最大而X 电负性最小的HFS…PH₃, CCSD(T)计算的键能是16.04 kJ·mol^-1; 磷键键能为7.54-14.65 kJ·mol^-1, 最强的磷键结构是X 电负性最大而Y 电负性最小的H₂FP…SH₂, CCSD(T)计算的键能是12.52 kJ·mol^-1. 对磷键与硫键能量贡献较大的是交换与静电作用. 分子间超共轭lp(S)-σ^*(PX)与lp(P)-σ^*(SY)对磷键与硫键的形成起着重要作用, 它导致单体的极化, 其中硫键的极化效应较大, 从而有一定的共价特征.     

Heterolytic bond dissociation in water: why is it so easy for C4H9Cl but not for C3H9SiCl?

The recently developed (Song, L.; Wu, W.; Zhang, Q.; Shaik, S. J. Phys. Chem. A 2004, 108, 6017-6024) valence bond method coupled to a polarized continuum model (VBPCM) is used to address the long standing conundrum of the heterolytic dissociation of the C-Cl and Si-Cl bonds, respectively, in tertiary-butyl chloride and trimethylsilyl chloride in condensed phases. The method is used here to compare the bond dissociation in the gas phase and in aqueous solution. In addition to the ground state reaction profile, VB theory also provides the energies of the purely covalent and purely ionic VB structures as a function of the reaction coordinate. Accordingly, the C-Cl and Si-Cl bonds are shown to be of different natures. In the gas phase, the resonance energy arising from covalent-ionic mixing at equilibrium geometry amounts to 42 kcal/mol for tertiary-butyl chloride, whereas the same quantity for trimethylsilyl chloride is significantly higher at 62 kcal/mol. With such a high value, the root cause of the Si-Cl bonding is the covalent-ionic resonance energy, and this bond belongs to the category of charge-shift bonds (Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D.; Hiberty, P. C. Chem.- Eur. J. 2005, 11, 6358). This difference between the C-Cl and Si-Cl bonds carries over to the solvated phase and impacts the heterolytic cleavages of the two bonds. For both molecules, solvation lowers the ionic curve below the covalent one, and hence the bond dissociation in the solvent generates the two ions, Me3E+ Cl- (E = C, Si). In both cases, the root cause of the barrier is the loss of the covalent-ionic resonance energy. In the heterolysis reaction of Si-Cl, the covalent-ionic resonance energy remains large and fully contributes to the dissociation energy, thereby leading to a high barrier for heterolytic cleavage, and thus prohibiting the generation of ions. By contrast, the covalent-ionic resonance energy is smaller for the C-Cl bond and only partially contributes to the barrier for heterolysis, which is consequently small, leading readily to ions that are commonly observed in the classical SN1 mechanism. Thus, the reluctance of R3Si-X molecules to undergo heterolysis in condensed phases and more generally the rarity of free silicenium ions under these conditions are experimental manifestations of the charge-shift character of the Si-Cl bond.     

Barriers of hydrogen abstraction vs halogen exchange: an experimental manifestation of charge-shift bonding

This paper shows that the differences between the barriers of the halogen exchange reactions, in the H + XH systems, and the hydrogen abstraction reactions, in the X + HX systems (X = F, Cl, Br), measure the covalent-ionic resonance energies of the corresponding X-H bonds. These processes are investigated using CCSD(T) calculations as well as the breathing-orbital valence bond (BOVB) method. Thus, the VB analysis shows that (i) at the level of covalent structures the barriers are the same for the two series and (ii) the higher barriers for halogen exchange processes originate solely from the less efficient mixing of the ionic structures into the respective covalent structures. The barrier differences, in the HXH vs XHX series, which decrease as X is varied from F to I, can be estimated as one-quarter of the covalent-ionic resonance energy of the H-X bond. The largest difference (22 kcal/mol) is calculated for X = F in accord with the finding that the H-F bond possesses the largest covalent-ionic resonance energy, 87 kcal/mol, which constitutes the major part of the bonding energy. The H-F bond belongs to the class of "charge-shift" bonds (Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D. L.; Hiberty, P. C. Chem. Eur. J. 2005, 21, 6358), which are all typified by dominant covalent-ionic resonance energies. Since the barrier difference between the two series is an experimental measure of the resonance energy quantity, in the particular case of X = F, the unusually high barrier for the fluorine exchange reaction emerges as an experimental manifestation of charge-shift bonding.     

Probing the weakest bond and the cleavage of p‐chlorobenzaldehyde diperoxide energetic molecule via quantum chemical calculations and theoretical charge density analysis

A high‐level ab initio Hartree‐Fock/Møller‐Plesset 2 and density functional theory quantum chemical calculations were performed on p‐chlorobenzaldehyde diperoxide energetic molecule to understand its bond topological, electrostatic, and energetic properties. The optimized molecular geometry for the basis set 6‐311G** exhibit chair diperoxide ring and planar aromatic side rings. Although the diperoxide ring bear same type of side rings, surprisingly, both the rings are almost perpendicular to each other, and the dihedral angle is 96.1°. The MP2 method predicts the O? O bond distance as ～1.466 Å. The charge density calculation reveals that the C? C bonds of chlorobenzaldehyde ring have rich electron density and the value is ～2.14 e Å^?3. The maximum electron density of the O? O bonds does not lie along the internuclear axes; in view of this, a feeble density is noticed in the ring plane. The high negative values of laplacian of C? C bonds (approximately ?22.4 e Å^?5) indicate the solidarity of these bonds, whereas it is found too small (approximately ?1.8 e Å^?5 for MP2 calculation) in O? O bonds that shows the existence of high degree of bond charge depletion. The energy density in all the C? C bonds are found to be uniform. A high electronegative potential region is found at the diperoxide ring which is expected to be a nucleophilic attack area. Among the bonds, the O? O bond charge is highly depleted and it also has high bond kinetic energy density; in consequence of this, the molecular cleavage is expected to happen across these bonds when the material expose to any external stimuli such as heat or pressure treatment. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Charge-Shift Bonding: A New and Unique Form of Bonding

Charge-shift bonds (CSBs) constitute a new class of bonds different than covalent/polar-covalent and ionic bonds. Bonding in CSBs does not arise from either the covalent or the ionic structures of the bond, but rather from the resonance interaction between the structures. This Essay describes the reasons why the CSB family was overlooked by valence-bond pioneers and then demonstrates that the unique status of CSBs is not theory-dependent. Thus, valence bond (VB), molecular orbital (MO), and energy decomposition analysis (EDA), as well as a variety of electron density theories all show the distinction of CSBs vis-à-vis covalent and ionic bonds. Furthermore, the covalent–ionic resonance energy can be quantified from experiment, and hence has the same essential status as resonance energies of organic molecules, e.g., benzene. The Essay ends by arguing that CSBs are a distinct family of bonding, with a potential to bring about a Renaissance in the mental map of the chemical bond, and to contribute to productive chemical diversity.     

The nature of the N?O bond in amine oxides

Despite the ubiquitous presence of amine oxides in chemistry, there is no consensus about the nature of the N O bond in these compounds. In this work, we have used electron density analysis to investigate the nature of this bond in substituted amine oxides, R₃NO, and have compared it with the nature of the N O bond in hydroxylamines, R₂NOR, and model molecules that have well-established chemical bond character. The results showed that the N O bond length and relative stability are proportional to the inductive effect of the substituents. Quantum chemical topology, natural bond orbitals (NBO), and natural resonance theory (NRT) analyses indicated that the N O bond is polar covalent in all the studied amine oxides, but the ionic contribution is different. NBO and NRT analyses revealed that molecules with more electronegative substituents have strongly delocalized N O and N R bonds, whereas molecules with electropositive substituents have localized bonds.     

New insight into the electronic structure of iron(IV)‐oxo porphyrin compound I. A quantum chemical topological analysis

The electronic structure of iron‐oxo porphyrin π‐cation radical complex Por^·+Fe^IV?O (S? H) has been studied for doublet and quartet electronic states by means of two methods of the quantum chemical topology analysis: electron localization function (ELF) η(r) and electron density ρ(r). The formation of this complex leads to essential perturbation of the topological structure of the carbon–carbon bonds in porphyrin moiety. The double C?C bonds in the pyrrole anion subunits, represented by pair of bonding disynaptic basins V_i=1,2(C,C) in isolated porphyrin, are replaced by single attractor V(C,C)_i=1–20 after complexation with the Fe cation. The iron–nitrogen bonds are covalent dative bonds, N→Fe, described by the disynaptic bonding basins V(Fe,N)_i=1–4, where electron density is almost formed by the lone pairs of the N atoms. The nature of the iron–oxygen bond predicted by the ELF topological analysis, shows a main contribution of the electrostatic interaction, Fe^δ+···O^δ?, as long as no attractors between the C(Fe) and C(O) core basins were found, although there are common surfaces between the iron and oxygen basines and coupling between iron and oxygen lone pairs, that could be interpreted as a charge‐shift bond. The Fe? S bond, characterized by the disynaptic bonding basin V(Fe,S), is partially a dative bond with the lone pair donated from sulfur atom. The change of electronic state from the doublet (M = 2) to quartet (M = 4) leads to reorganization of spin polarization, which is observed only for the porphyrin skeleton (?0.43e to 0.50e) and S? H bond (?0.55e to 0.52e). © 2012 Wiley Periodicals, Inc.     

Observing the 3D Chemical Bond and its Energy Distribution in a Projected Space

Our curiosity-driven desire to “see” chemical bonds dates back at least one-hundred years, perhaps to antiquity. Sweeping improvements in the accuracy of measured and predicted electron charge densities, alongside our largely bondcentric understanding of molecules and materials, heighten this desire with means and significance. Here we present a method for analyzing chemical bonds and their energy distributions in a two-dimensional projected space called the condensed charge density. Bond “silhouettes” in the condensed charge density can be reverse-projected to reveal precise three-dimensional bonding regions we call bond bundles. We show that delocalized metallic bonds and organic covalent bonds alike can be objectively analyzed, the formation of bonds observed, and that the crystallographic structure of simple metals can be rationalized in terms of bond bundle structure. Our method also reproduces the expected results of organic chemistry, enabling the recontextualization of existing bond models from a charge density perspective.     

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!     

Chalcogenophilicity of mercury

Density-functional theory (DFT) calculations have been carried out to investigate the chalcogenophilicity of mercury (Hg) reported recently [J. Am. Chem. Soc. 2010, 132, 647-655]. Molecules of different sizes have been studied including ME, [M(EH)(4)](n), M(SH)(3)EH (M = Cd, Hg; E = S, Se, Te; n = 0, 2+) and [Tm(Y)]MEZ complexes (Tm = tris(2-mercapto-1-R-imidzolyl)hydroborato; Y = H, Me, Bu(t); M = Zn, Cd, Hg; E = S, Se, Te; Z = H, Ph). The bonding of Cd and Hg in their complexes depends on the oxidation state of the metal and nature of the ligands. More electronegative ligands form bonds of ionic type with Cd and Hg while less electronegative ligands form bonds that are more covalent. The Cd-ligand bond distances are shorter for the ionic type of bonding and longer for the covalent type of bonding than those of the corresponding Hg-ligand bonds. The variation of this Cd/Hg bonding is in accordance with the ionic and covalent radii of Cd and Hg. The experimentally observed (shorter) Hg-Se and Hg-Te bond distances in [Tm(Bu(t))]HgEPh (E = S, Se, Te) are due to the lower electronegativity of Se and Te, crystal packing, and the presence of a very bulky group. The bond dissociation energy (BDE) for Hg is the highest for Hg-S followed by Hg-Se and Hg-Te regardless of complex type.     

Topological insights into the nature of the halogen-carbon bonds in dimethylhalonium ylides and their cations

In this study the nature of the bonding in a series of dimethylhalonium ylides (fluoronium, chloronium, bromonium and iodonium) was analyzed by means of topological methodologies (AIM and ELF analysis), to document the changes in the nature of the C-X bonds (X = F, Cl, Br, I) upon the series. For the sake of comparison the same study was performed on the corresponding dimethylhalonium cations (XC 2H 6 (+)) and the XCH 3 series. The wave functions used for the topological analysis were obtained at B3LYP level using extended triple-zeta basis sets. The formation of the cationic XC 2H 6 (+) structures can be interpreted to arise from the interaction between the XCH 3 and CH 3 (+) moieties. The resultant structures can be explained in terms of the superposition of two electrostatically interacting and two dative mesomeric structures. The halogen-carbon bonds have all the characteristics of the charge-shift (CS) bonds. The analysis of the C-X bond in the XC 2H 5 series shows a progressive reinforcing of the CH 3X-CH 2 bond, from FC 2H 5 that can be considered as formed from two fragments, FCH 3 and CH 2, to IC 2H 5, in which the CH 3I-CH 2 bond has all the features of a multiple bond involving atoms bearing lone pairs. Particularly interesting is BrC 2H 5, in which a special type of bond (hybrid covalent-dative double bond) has been characterized. The energetic stability of the XC 2H 5 structures with respect to the dissociation into the XCH 2 + CH 3 and XCH 3 + CH 2 ground-state fragments was studied in detail.     

Electron localization function and electron localizability indicator applied to study the bonding in the peroxynitrous acid HOONO

The ground‐state electronic structure of peroxynitrous acid (HOONO) and its singlet biradicaloid form (HO ··· ONO) have been studied using topological analysis of the electron localization function (ELF), together with the electron localizability indicator (ELI‐D), at the DFT (B3LYP, M05, M052X, and M06), CCSD, and CASSCF levels. Three isomers of HOONO (cis‐cis, cis‐perp, and trans‐perp) have been considered. The results show that from all functionals applied, only B3LYP yields the correct geometrical structure. The ELF and ELI‐D‐topology of the O? O and central N? O bonds strongly depends on the wave function used for analysis. Calculations carried out at CAS (14,12)/aug‐cc‐pVTZ//CCSD(T)/aug‐cc‐pVTZ level reveal two bonds of the charge‐shift type: a protocovalent N? O bond with a basin population of 0.82–1.08e, and a more electron depleted O? O bond with a population of 0.66–0.71e. The most favorable dissociation channel (HOONO → HO + ONO) corresponds to breaking of the most electron‐deficient bond (O? O). In the case of cis‐ and trans‐HO ··· ONO, the ELF, ELI‐D, and electron density fields results demonstrate a closed‐shell O ··· O interaction. The α‐spin electrons are found mainly (0.64e) in the lone pairs of oxygen V_{i = 1,2} (O) from the OH group. The β‐spin electrons are delocalized over the ONO group, with the largest concentration (0.34e) on the lone pair of nitrogen V(N). © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

pi bonding in second and third row molecules: testing the strength of Linus's blanket

The flexibility of valence bond (VB) theory provides a new method of calculating pi-bond energies in the double-bonded species H(m)A=BH(n), where A, B = C, N, O, Si, P, S. This new method circumvents the problems usually associated with obtaining pi-bond strengths by targeting only the pi bond, while all other factors remain constant. In this manner, a clean separation between sigma- and pi effects can be achieved which highlights some expected trends in bond strength upon moving from left to right and up and down the Periodic Table. Intra-row pi bonds conform to the classic statement by Pauling [L. Pauling, The Natiure of the Chemical Bond, Cornell University Press, Ithaca, 1960, 3rd edition] regarding the relationship of heteronuclear bond strengths to their homonuclear constituents whereas inter-row pi bonds do not. This variance with Pauling's statement is shown to be due to the constraining effect of the underlying sigma bonds which prevents optimal p(pi)-p(pi) overlap. While Pauling's statement was based on the assumption that the resonance energy (RE) would be large for heteronuclear and small for homonuclear bonds, we have found large REs for all bonds studied herein; this leads to the conclusion that REs are dependent not only on the electronegativity difference but also the electronegativity sum of the constituent atoms. This situation where the bond is neither covalent nor ionic but originates in the covalent-ionic mixing has been termed charge shift (CS) bonding [S. Shaik, P. Maitre, G. Sini, P. C. Hiberty, J. Am. Chem. Soc. 1992, 114, 7861]. We have shown that CS bonding extends beyond single sigma bonds in first row molecules, thus supporting the idea that CS-bonding is a ubiquitous bonding form.     

The structure and chemical bonding in the N(2)-CuX and N(2)...XCu (X = F, Cl, Br) systems studied by means of the molecular orbital and Quantum Chemical Topology methods

Ab initio studies carried out at the MP2(full)/6-311+G(2df) and MP2(full)/aug-cc-pVTZ-PP computational levels reveals that dinitrogen (N(2)) and cuprous halides (CuX, X = F, Cl, Br) form three types of systems with the side-on and end-on coordination of N(2): N[triple bond]N-CuX (C(infinity v)), N(2)-CuX (C(2v)) stabilized by the donor-acceptor bonds and weak van der Waals complexes N(2)...XCu (C(2v)) with dominant dispersive forces. An electron density transfer between the N(2) and CuX depends on type of the N(2) coordination and a comparison of the NPA charges yields the [N[triple bond]N](delta+)-[CuX](delta-) and [N(2)](delta-)-[CuX](delta+) formula. According to the NBO analysis, the Cu-N coordinate bonds are governed by predominant LP(N2)-->sigma*(Cu-X) "2e-delocalization" in the most stable N[triple bond]N-CuX systems, meanwhile back donation LP(Cu)-->pi*(N-N) prevails in less stable N(2)-CuX molecules. A topological analysis of the electron density (AIM) presents single BCP between the Cu and N nuclei in the N[triple bond]N-CuX, two BCPs corresponding to two donor-acceptor Cu-N bonds in the N(2)-CuX and single BCP between electron density maximum of the N[triple bond]N bond and halogen nucleus in the van der Waals complexes N(2)...XCu. In all systems values of the Laplacian nabla(2)rho(r)(r(BCP)) are positive and they decrease following a trend of the complex stability i.e. N[triple bond]N-CuX (C(infinity v)) > N(2)-CuX (C(2v)) > N(2)...XCu (C(2v)). A topological analysis of the electron localization function (ELF) reveals strongly ionic bond in isolated CuF and a contribution of covalent character in the Cu-Cl and Cu-Br bonds. The donor-acceptor bonds Cu-N are characterized by bonding disynaptic basins V(Cu,N) with attractors localized at positions corresponding to slightly distorted lone pairs V(N) in isolated N(2). In the N[triple bond]N-CuX systems, there were no creation of any new bonding attractors in regions where classically the donor-acceptor bonds are expected and there is no sign of typical covalent bond Cu-N with the bonding pair. Calculations carried out for the N[triple bond]N-CuX reveal small polarization of the electron density in the N[triple bond]N bond, which is reflected by the bond polarity index being in range of 0.14 (F) to 0.11 (Cl).