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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-a-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.

Density functional theory and ab initio calculations indicate that nucleophiles can significantly reduce enthalpic barriers to methane C-H bond activation. Valence bond analysis suggests the formation of a two-center three-electron bond as the origin for the catalytic nucleophile effect. A predictive model for methane activation catalysis follows, which suggests that strongly electron-attracting and electron-rich radicals, together with both a negatively charged and strongly electron-donating outer sphere nucleophile, result in the lowest reaction barriers. It is corroborated by the sensitivity of the calculated C-H activation barriers to the external nucleophile and to continuum solvent polarity. More generally, from the present studies, one may propose proteins with hydrophobic active sites, available strong nucleophiles, and hydrogen bond donors as attractive targets for engineering novel methane functionalizing enzymes.

International audience; In a recent publication in this journal, Laplaza, Contreras-Garcia, Fuster, Volatron and Chaquin [1] (LCFVC) report an application of the Dynamical Orbital Forces (DOF) method, [2] which was used by the authors to challenge the presence of an inverted central CC bond in [1.1.1]propellane (1 in Scheme 1), which was suggested long ago by Jackson and Allen, [3] then by Feller and Davidson, [4] and recently given theoretical support on the basis of ab initio valence bond calculations. [5] In this comment, we highlights several severe failures and shortcomings of the DOF method, which as we show makes it an inappropriate tool forcharacterizing the CC inverted bond in [1.1.1]propellane.

A general approach to hybridization, without imposing orthogonality of the hybrids of the central atom, is formulated. It is shown that the overlapping hybrids follow the rules of electronegativity of the central atom, and they increase with the increase of electronegativity (e.g. NH 4 + > CH 4 > BH 4 − ). For a given electronegativity, the hybrid-hybrid overlap decreases as the number of equivalent bonds increases (e.g., CH 4 3 + , CH 2 2+ ). Having the hybrid-hybrid overlap enables us to deduce the promotion energy invested by the various atoms to form the molecule; the larger the overlap the smaller the degree of hybridization, and the lesser is the promotion energy needed from the central atom to achieve maximum bonding. The approach is applied to the dicarbon molecule, C 2 . It is shown that after taking into account the promotion energy (∼46 kcal mol −1 per C), C 2 exhibits a quadruple bond.

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!

We analyze the properties of 15 3-electron bonds, which include σ-3-electron-bonds, such as dihalide radical anions and di-noble gas radical cations, π-3-electron-bonds as in hydrazine radical cations, and doubly-π-(3e)-bonded species such as O2, FeO+, S2, etc. The primary analytical tool is the breathing-orbital valence-bond (BOVB) method, which enables us to quantify the charge shift resonance energy (RECS) of the three electrons, and the bond dissociation energies (De). BOVB is tested reliable against MRCI calculations. Our findings show that in all 3-electron bonds, none of the VB structures have by themselves any bonding. In fact, in each VB structure, the three electrons maintain Pauli repulsion, while the entire bonding energy arises from resonance due to the charge shift between the two or more constituent VB structures. Hence, 3e-bonds are charge shift bonds (CSBs). The CSB character is probed by calculating the Laplacian (L) of the 3e-bond. Thus, much like the CSBs in electron-pair bonds, such a...

International audience; Ozone and its sulfur-substituted isomers are studied by means of the Breathing Orbital Valence Bond ab initio method, with the objective of estimating their controversial diradical characters. The calculated weights of the various VB structures and their individual diabatic energies are found to be consistent with each other. All 1,3-dipoles can be described in terms of three major VB structures, one diradical and two zwitterionic ones, out of the six structures, forming a complete basis. Ozone has a rather large diradical character, estimated to 44%–49%. SOO and SOS are even more diradicalar, whereas SSO and especially OSO are better described as closed-shell zwitterions. Moreover, the description of 1,3-dipoles, in terms of the three major structures, yields VB weights in full agreement with simple chemical wisdom, i.e., a diradical weight of 33% when the three structures are quasi-degenerate, and a smaller (larger) value when the diradical structure is higher (lower) in energy than the zwitterionic ones. Therefore, the VB-calculated weight of the diradical structure of a molecule qualifies itself as a quantitative measure of diradical character, and not only as an indicator of tendencies. Other definitions of the diradical character, based on molecular orbital/configuration interaction methods, are discussed.

International audience; The nature of the single bond in the three isoelectronic coinage metal dimers Cu2, Ag2 and Au2 is investigated by means of the ab initio Breathing Orbital Valence Bond (BOVB) method, which allows one to calculate the respective contributions of the covalent and ionic structures to the total wave function, as well as the resonance energy arising from their mixing. It is shown that the BOVB method at its highest level provides bond dissociation energies in very good agreement with reference CCSD(T) values for the three dimers. It is also found that the covalent/ionic resonance energy is important in all three cases, contributing to 40-50% to the total bonding energy, thus qualifying the bonds in Cu2 and Au2 as quasi-charge-shift bonds, and that of Ag2 as a borderline case in-between classical covalent bond and charge-shift one. These results are further confirmed by analyses of the wave functions in terms of the Atoms-in-Molecule theory, which show that the Laplacian of the density at the bond critical point is large and positive in all three cases, which classifies the three bonds as charge-shift bonds within this theory.

The block-localized wave function (BLW) method can derive the energetic, geometrical, and spectral changes with the deactivation of electron delocalization, and thus provide a unique way to elucidate the origin of improper, blueshifting hydrogen bonds versus proper, redshifting hydrogen bonds. A detailed analysis of the interactions of F(3)CH with NH(3) and OH(2) shows that blueshifting is a long-range phenomenon. Since among the various energy components contributing to hydrogen bonds, only the electrostatic interaction has long-range characteristics, we conclude that the contraction and blueshifting of a hydrogen bond is largely caused by electrostatic interactions. On the other hand, lengthening and redshifting is primarily due to the short-range n(Y)→σ*(X-H) hyperconjugation. The competition between these two opposing factors determines the final frequency change direction, for example, redshifting in F(3)CH⋅⋅⋅NH(3) and blueshifting in F(3)CH⋅⋅⋅OH(2). This mechanism works well in the series F(n)Cl(3)-n CH⋅⋅⋅Y (n=0-3, Y=NH(3), OH(2), SH(2)) and other systems. One exception is the complex of water and benzene. We observe the lengthening and redshifting of the O-H bond of water even with the electron transfer between benzene and water completely quenched. A distance-dependent analysis for this system reveals that the long-range electrostatic interaction is again responsible for the initial lengthening and redshifting.

The charge-shift bonding (CSB) concept was originally discovered through valence bond (VB) calculations. Later, CSB was found to have signatures in atoms-in-molecules and electron-localization-function and in experimental electron density measurements. However, the CSB concept has never been derived from a molecular orbital (MO)-based theory. We now provide a proof of principle that an MO-based approach enables one to derive the CSB family alongside the distinctly different classical family of covalent bonds. In this bridging energy decomposition analysis, the covalent-ionic resonance energy, RECS, of a bond is extracted by cloning an MO-based purely covalent reference state, which is a constrained two-configuration wave function. The energy gap between this reference state and the variational TCSCF ground state yields numerical values for RECS, which correlate with the values obtained at the VBSCF level. This simple MO-based method, which only takes care of static electron correlation, is already sufficient for distinguishing the classical covalent or polar-covalent bonds from charge-shift bonds. The equivalence of the VB and MO-based methods is further demonstrated when both methods are augmented by dynamic correlation. Thus, it is shown from both MO and VB perspectives that the bonding in the CSB family does not arise from electron correlation. Considering that the existence of the CSB family is associated also with quite a few experimental observations that we already reviewed ( Shaik , S. , Danovich , D. , Wu , W. , and Hiberty , P. C. Nat. Chem. , 2009 , 1 , 443 - 449 ), the new bonding concept has passed by now two stringent tests. This derivation, on the one hand, supports the new concept and on the other, it creates bridges between the two main theories of electronic structure.

Does, or doesn't C2 break the glass ceiling of triple bonding? This work provides an overview on the bonding conundrum in C2 and on the recent discussions regarding our proposal that it possesses a quadruple bond. As such, we focus herein on the main point of contention, the 4th bond of C2, and discuss the main views. We present new data and an overview of the nature of the 4th bond--its proposed antiferromagnetically coupled nature, its strength, and a derivation of its bond energy from experimentally based thermochemical data. We address the bond-order conundrum of C2 arising from generalized VB (GVB) calculations by comparing it to HC≡CH, and showing that the two molecules behave very similarly, and C2 is in no way an exception. We analyse the root cause of the deviation of C2 from the Badger Rule, and demonstrate that the reason for the smaller force constant (FC) of C2 relative to HC≡CH has nothing to do with the bond energies, or with the number of bonds in the two molecules. The FC is determined primarily by the bond length, which is set by the balance between the bond length preferences of the σ- versus π-bonds in the two molecules. This interplay in the case of C2 clearly shows the fingerprints of the 4th bond. Our discussion resolves the points of contention and shows that the arguments used to dismiss the quadruple bond nature of C2 are not well founded.

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.

International audience; So as to clarify some inconsistencies between some values reported in the title paper and some former results on the C2 moleculepreviously published by some of us, we wish to complete Table 2 in the title paper with footnotes b and c. The conclusions of the paperare unchanged.

National Natural Science Foundation of China[20873106]; Ministry of Science and Technology[2011CB808504]; Israel Science Foundation[ISF 53/09]

We describe herein a valence bond (VB) study of 27 triply bonded molecules of the general type X≡Y, where X and Y are main element atoms/fragments from groups 13-15 in the periodic table. The following conclusions were derived from the computational data: (a) Single π-bond and double π-bond energies for the entire set correlate with the "molecular electronegativity", which is the sum of the X and Y electronegativites for X≡Y. The correlation with the molecular electronegativity establishes a simple rule of periodicity: π-bonding strength generally increases from left to right in a period and decreases down a column in the periodic table. (b) The σ frame invariably prefers trans bending, while π-bonding gets destabilized and opposes the trans distortion. In HC≡CH, the π-bonding destabilization overrides the propensity of the σ frame to distort, while in the higher row molecules, the σ frame wins out and establishes trans-bent molecules with 2(1)/2 bonds, in accord with recent experimental evidence based on solid state (29)Si NMR of the Sekiguchi compound. Thus, in the trans-bent molecules "less bonds pay more". (c) All of the π bonds show significant bonding contributions from the resonance energy due to covalent-ionic mixing. This quantity is shown to correlate linearly with the corresponding "molecular electronegativity" and to reflect the mechanism required to satisfy the equilibrium condition for the bond. The π bonds for molecules possessing high molecular electronegativity are charge-shift bonds, wherein bonding is dominated by the resonance energy of the covalent and ionic forms, rather than by either form by itself.

The use of valence bond (VB) theory as a general and wide-ranging qualitative matrix of ideas and predictions is highlighted. Applications are demonstrated for chemical reactivity, properties of polyradicals, excited states, and chemical bonding. Highlighted subtopics include estimations of reaction barriers from simple properties of reactants and products; predictions of stable intermediates in organic, inorganic, and organometallic reactions; and predictions of reaction stereoselectivity. Additional coverage includes a pictorial model for ground and excited states of polyenes and polyradicals, predictions of Hund's rule violations, spin density polarizations and shifts, and a bonding rule in excited states of conjugated molecules. Discussion of new bonding ideas shows the far-reaching prospects of qualitative VB theory. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 18-29 DOI: 10.1002/wcms.7

Valence bond (VB) theory describes a conjugated system by a set of electron-localized Lewis resonance structures. VB assumes that the magnitude of the intramolecular electron delocalization can be measured in terms of a resonance energy (RE), taken to be the energy difference between the real conjugated system (delocalized) and the corresponding most stable virtual resonance structure (localized). Proper RE estimates within VB theory require both delocalized and localized states to be defined at the same theoretical level, and the definition of the localized state to closely correspond to the intuitive picture of the corresponding VB structure. In contrast, the VB-delocal and VB-local computational approaches adopted by Zielinski, et al. [preceding paper in this issue] used definitions for either the delocalized or the localized states which, in our view, depart from the intuitive chemical picture. Consequently, their RE estimates are much lower than seemingly appropriate experimental evaluations with which they strongly disagree. Very large basis sets approaching completeness blur the boundaries among resonance structures and result in “basis set artifact” problems within any variant of VB theory. However, block-localized wavefunction (BLW) computations with mid-size basis sets not only exhibit insignificant variations with theoretical levels, but the resulting RE estimates also are justified by comparisons with those employing experimental data and MO computations. We stress that RE differs from the aromatic stabilization energy (ASE). The RE measures the total stabilization of an aromatic system, whereas ASE measures only the part of the RE that exceeds that of appropriate conjugated (but non-aromatic) reference molecules.

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.

thisrule has been extended and generalized to other eliminationreactions; for example, involving leaving groups other thanhalogens. The rule is valid for acid-catalyzed E1 reactions aswell as base-induced E2 reactions, provided neither the basenortheb substituentsaretoobulky.Thus,inEquation (1),theformation of both (Z)- and (E)-but-2-enes is preferred overthat of but-1-ene upon the elimination of water.

The conventional resonance model describes carbonyls, imines, and thiocarbonyls, as well as their protonated analogues, by a superposition of two valence bond structures. Ab initio Breathing-Orbital Valence Bond computations on formaldehyde, formimine, and thioformaldehyde as well as their protonated forms are performed to directly quantify the weights of their valence bond structures. Following a gas phase study that showed that protonation significantly increases the weight of the carbenic form relative to the π polar-covalent bonded form (Braida, et al., Org Lett, 2008, 10, 1951), the present work estimates the influence of a polar protic solvent, modelized by water. Solvation effects are modeled explicitly by performing VB calculations on supersystems made of the organic substrate surrounded by four water molecules. It is shown that protonation significantly increases the polarity of the CX π bond in all three cases (X = O, NH, S) in solvated phase, in line with the known acceleration of nucleophilic additions on these compounds by acidic catalysis. Moreover, solvation significantly enhances the polarity of the CX π bond in the protonated forms of formaldehyde and thioformaldehyde, but has practically no effect on the CX π bond of protonated formimine. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

The electronic structures of the three lowest-lying states of NF are investigated by means of modern valence bond (VB) methods such as the VB self-consistent field (VBSCF), breathing orbital VB (BOVB), and VB configuration interaction (VBCI) methods. The wave functions for the three states are expressed in terms of 9-12 VB structures, which can be further condensed into three or four classical Lewis structures, whose weights are quantitatively estimated. Despite the compactness of the wave functions, the BOVB and VBCI methods reproduce the spectroscopic properties and dipole moments of the three states well, in good agreement with previous computational studies and experimental values. By analogy to the isoelectronic O(2) molecule, the ground state (3)Sigma(-) possesses both a sigma bond and 3-electron pi bonds. However, here the polar sigma bond contributes the most to the overall bonding. It is augmented by a fractional (19%) contribution of three-electron pi bonding that arises from pi charge transfer from fluorine to nitrogen. In the singlet (1)Delta and (1)Sigma(+) excited states the pi-bonding component is classically covalent, and it contributes 28% and 37% to the overall bonding picture for the two states, respectively. The resonance energies are calculated and reveal that pi bonding contributes at least 24, 35 and 42 kcal mol(-1) to the total bonding energies of the (3)Sigma(-), (1)Delta and (1)Sigma(+) states, respectively. Some unusual properties of the NF molecule, like the equilibrium distance shortening and bonding energy increasing upon excitation, the counterintuitive values of the dipole moments and the reversal of the dipole moments as the bond is stretched, are interpreted in the light of the simple valence bond picture. The overall polarity of the molecule is very small in the ground state, and is opposite to the relative electronegativity of N vs F in the singlet excited states. The values of the dipole moments in the three states are quantitatively accounted for by the calculated weights of the VB structures.

The recently developed (L. Song, W. Wu, Q. Zhang, S. Shaik, J. Phys. Chem. A 2004, 108, 6017-6024) valence bond method coupled to a polarized continuum model (VBPCM) is applied to the Menshutkin reaction, NH 3 +CH 3 Cl→CH 3 NH 3 + +Cl - , in the gas phase and in aqueous solution. The computed barriers and reaction energies at the level of the breathing orbital VB method (P. C. Hiberty, J. P. Flament, E. Noizet, Chem. Phys. Lett. 1992, 189, 259), BOVB and VBPCM//BOVB, are comparable to CCSD(T) and CCSD(T)//PCM results and to experimental values in solution. The gas-phase reaction is endothermic and leads to an ion-pair complex via a late transition state. By contrast, the reaction in the aqueous phase is exothermic and leads to separate solvated ions as reaction products, via an early transition state. The VB calculations provide also the reactivity parameters needed to apply the valence bond state correlation diagram method, VBSCD (S. Shaik, A. Shurki, Angew. Chem. Int. Ed. 1999, 38, 586). It is shown that the reactivity parameters along with their semi-empirical derivations provide together a satisfactory qualitative and quantitative account of the barriers.

The low-lying isomers of the P6 species are investigated at various levels of calculations, ranging from MP2/6-31G(d) to CCSD(T) in triple-zeta basis set involving polarization functions up to f. In addition to the five possible normal-valent isomers, which obey the octet rules, several other conformations are found to be stationary points on the potential energy surface. Among the five normal-valent isomers, the benzvalene structure is found to be the most stable one, in agreement with former studies. The benzene-like D6h planar hexagon is the least stable one, lying 32.3 kcal/mol over benzvalene, and spontaneously distorts to a less symmetrical, nonplanar six-membered ring. Above the benzvalene structure, and lying, respectively, 5.8 and 15.8 kcal/mol higher, the two lowest lying isomers are the prismane and the chair-like forms. This latter conformation, which does not obey the octet rule, exhibits two one-electron PP hemibonds and can be considered as a generic model for a new category of heterobenzene analogs, among which is the recently discovered dimer of diphosphirenyl radical. © 2007 Wiley Periodicals, Inc. Heteroatom Chem 18:129–134, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20324

This study uses valence bond (VB) theory to analyze in detail the previously established finding that alongside the two classical bond families of covalent and ionic bonds, which describe the electron-pair bond, there exists a distinct class of charge-shift bonds (CS-bonds) in which the fluctuation of the electron pair density plays a dominant role. Such bonds are characterized by weak binding, or even a repulsive, covalent component, and by a large covalent-ionic resonance energy RE(cs) that is responsible for the major part, or even for the totality, of the bonding energy. In the present work, the nature of CS-bonding and its fundamental mechanisms are analyzed in detail by means of a VB study of some typical homonuclear bonds (H-H, H3C-CH3, H2N-NH2, HO-OH, F-F, and Cl-Cl), ranging from classical-covalent to fully charge-shift bonds. It is shown that CS-bonding is characterized by a covalent dissociation curve with a shallow minimum situated at long interatomic distances, or even a fully repulsive covalent curve. As the atoms that are involved in the bond are taken from left to right or from bottom to top of the periodic table, the weakening effect of the adjacent bonds or lone pairs increases, while at the same time the reduced resonance integral, that couples the covalent and ionic forms, increases. As a consequence, the weakening of the covalent interaction is gradually compensated by a strengthening of CS-bonding. The large RE(cs) quantity of CS-bonds is shown to be an outcome of the mechanism necessary to establish equilibrium and optimum bonding during bond formation. It is shown that the shrinkage of the orbitals in the covalent structure lowers the potential energy, V, but excessively raises the kinetic energy, T, thereby tipping the virial ratio off-balance. Subsequent addition of the ionic structures lowers T while having a lesser effect on V, thus restoring the requisite virial ratio (T/-V = 1/2). Generalizing to typically classical covalent bonds, like H-H or C-C bonds, the mechanism by which the virial ratio is obeyed during bond formation is primarily orbital shrinkage, and therefore the charge-shift resonance energy has only a small corrective effect. On the other hand, for bonds bearing adjacent lone pairs and/or involving electronegative atoms, like F-F or Cl-Cl, the formation of the bond corresponds to a large increase of kinetic energy, which must be compensated for by a large participation or covalent-ionic mixing.

The ab initio VB study for the electronic structure of the C2 molecule in the ground state is presented in this work. VB calculations involving 78 chemically relevant VB structures can predict the bonding energy of C2 quite well. Sequentially, a VBCIS calculation provides spectroscopic parameters that are very close to full CI calculated values in the same basis set. Furthermore, the analysis of the bonding scheme shows that a triply bonded structure is the major one in terms of weights, and the lowest in energy at the equilibrium distance. The second structure in terms of weights is an ethylene-like structure, displaying a σ + π double bond. The structure with two suspended π bonds but no σ bond contributes only marginally to the ground state. This ordering of weights for the VB structures describing the C2 molecule is shown to be consistent with the shape of the molecular orbitals and with the multireference character of the ground state. With the triply bonded bonding scheme, the natures of the π and σ bonds are investigated, and then the corresponding "in situ" bond strengths are estimated. The contribution of the covalent-ionic resonance energy to π and σ bonding is revealed and discussed.

The nature of the multicenter, long bond in ditetracyanoethylene dianion complex [TCNE]2(2-) is elucidated using high level ab initio Valence Bond (VB) theory coupled with Quantum Monte Carlo (QMC) methods. This dimer is the prototype of the general family of pancake-bonded dimers with large interplanar separations. Quantitative results obtained with a compact wave function in terms of only six VB structures match the reference CCSD(T) bonding energies. Analysis of the VB wave function shows that the weights of the VB structures are not compatible with a covalent bond between the π* orbitals of the fragments. On the other hand, these weights are consistent with a simple picture in terms of two resonating bonding schemes, one displaying a pair of interfragment three-electron σ bonds and the other displaying intrafragment three-electron π bonds. This simple picture explains at once (1) the long interfragment bond length, which is independent of the countercations but typical of three-electron (3-e) CC σ bonds, (2) the interfragment orbital overlaps which are very close to the theoretical optimal overlap of 1/6 for a 3-e σ bond, and (3) the unusual importance of dynamic correlation, which is precisely the main bonding component of 3-e bonds. Moreover, it is shown that the [TCNE]2(2-) system is topologically equivalent to the square C4H4(2-) dianion, a well-established aromatic system. To better understand the role of the cyano substituents, the unsubstituted diethylenic Na(+)2[C2H4]2(2-) complex is studied and shown to be only metastable and topologically equivalent to a rectangular C4H4(2-) dianion, devoid of aromaticity.

International audience; An original procedure is proposed, based on valence bond theory, to calculate accurate dissociation energies for multiply bonded molecules, while always dealing with extremely compact wave functions involving three valence bond structures at most. The procedure consists of dividing the bond-breaking into sequential steps, thus breaking one by one the separate components of the multiple bond. By using the breathing-orbital valence bond method (Hiberty and Shaik, 2002), it is ensured that both static and dynamic differential electron correlations are taken into account in each step. The procedure is illustrated for typical examples of multiply bonded molecules, N2, C2 and CO. The so-calculated total dissociation energies are at par with accurate calculations by state-of-the-art standard methods in the same basis set. The procedure also allows one to get some deep insight into the properties of the individual bonds that constitute the multiple bond. A so-called quasi-classical state is defined, in which the electrons of the bond under study have only one spin arrangement pattern, αβ, thus disabling the exchange of the two spin arrangements that is necessary for a covalent bonding interaction to take place. Taking this quasi-classical state as a non-bonded reference, one may estimate the “in-situ bonding energy” of an individual bond, as calculated at the molecular equilibrium geometry and in the presence of the other electrons. The procedure may also be used to assess the preferred bond length of an individual bond, which is shown to amount to 1.33 Å for the σ bond of N2, while the π bonds get stronger and stronger as the interatomic distance is shortened. Another application is the calculation of the resonance energy arising from the mixing of the ionic components of an individual bond to its covalent component, and the comparison of this resonance energy with the in-situ bonding energy. This shows that the σ bond of N2 and C2 is a classical covalent bond. On the other hand, the π bonds have a substantial resonance energy that put them close to the category of charge-shift bonds.

We discuss here the modern valence bond (VB) description of the electron-pair bond vis-a-vis the Lewis–Pauling model and show that along the two classical families of covalent and ionic bonds, there exists a family of charge-shift bonds (CSBs) in which the “resonance fluctuation” of the electron-pair density plays a dominant role. A bridge is created between the VB description of bonding and three other approaches to the problem: the electron localization function (ELF), atoms-in-molecules (AIM), and molecular orbital (MO)-based theories. In VB theory, CSB manifests by repulsive or weakly bonded covalent state and large covalent–ionic resonance energy, RE CS. In ELF, it shows up by a depleted basin population with fluctuations and in AIM by a positive Laplacian. CSB is derivable also from MO-based theory. As such, CSB is shown to be a fundamental mechanism that satisfies the equilibrium condition of bonding, namely, the virial ratio of the kinetic and potential energy contributions to the bond energy. The chapter defines the atomic propensity for CSB and outlines its territory: Atoms (fragments) that are prone to CSB are compact electronegative and/or lone-pair-rich species. As such, the territory of CSB transcends considerations of static charge distribution, and it involves (a) homopolar bonds of heteroatoms with zero static ionicity, (b) heteropolar σ- and π-bonds of the electronegative and/or electron-pair-rich elements among themselves and to other atoms (e.g., the higher metalloids, Si, Ge, Sn, etc.), and (c) electron-rich hypercoordinate molecules. Several experimental manifestations of charge-shift bonding are discussed.

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.

This paper deals with a cen- tral paradigm of chemistry, the elec- tron-pair bond. Valence bond (VB) theory and electron-localization func- tion (ELF) calculations of 21 single bonds demonstrate that along the two classical bond families of covalent and ionic bonds, there exists a class of charge-shift bonds (CS bonds) in which the fluctuation of the electron pair den- sity plays a dominant role. In VB theory, CS bonding manifests by way of a large covalent-ionic resonance energy, RECS, and in ELF by a depleted basin population with large variances (fluctuations). CS bonding is shown to be a fundamental mechanism that is necessary to satisfy the equilibrium condition, namely the virial ratio of the kinetic and potential energy contribu- tions to the bond energy. The paper de- fines the atomic propensity and territo- ry for CS bonding: Atoms (fragments) that are prone to CS bonding are com- pact electronegative and/or lone-pair- rich species. As such, the territory of CS bonding transcends considerations of static charge distribution, and in- volves: a) homopolar bonds of heteroa- toms with zero static ionicity, b) heter- opolar s and p bonds of the electro- negative and/or electron-pair-rich ele- ments among themselves and to other atoms (e.g., the higher metalloids, Si, Ge, Sn, etc), c) all hypercoordinate molecules. Several experimental mani- festations of charge-shift bonding are discussed, such as depleted bonding density, the rarity of ionic chemistry of silicon in condensed phases, and the high barriers of halogen-transfer reac- tions as compared to hydrogen-trans- fers.

The paper reviews briefly the various computational strategies, which have been devised by different groups to probe the symmetrizing vs distortive propensities of the π-bonding species of polyenes. All methods point to the same conclusion that the π-bonding components of benzene, allyl, aromatic annulenes and related species have intrinsic distortive tendencies; these species maintain bond-equalized geometries due to the symmetrizing driving force of the corresponding σ frames. Some frequently asked questions, that deal with the compatibility of the π-distortivity scenario with the greater body of experimental data regarding aromatic stability and π-delocalization, are addressed. Many of these questions are immediately answered, once the notion is accepted that delocalized π-systems possess a duality: their π-component is distortive and at the same time resonance stabilized relative to the localized structure with the same geometry. The notion of distortive π-electronic components of polyenes is shown to find a natural place in the wider context of a unified model of electronic delocalization that is valid for both conjugated π- and σ-electronic systems.

Ab inito computational experiments are used to decompose the total resistance energies for allylic species and benzene, towards localizing Kekulean distortions, into their σ and π components. While the σ component is always symmetrizing, and responsible for the identical C–C bond lengths of these molecules, the π components are distortive along a Kekulean distortion. As such, the π components must be viewed as unstable electronic species that are forced by the σ frame to adopt a regular rather than bond-alternated geometry. The distortivity of the π components of conjugated molecules is shown to be consistent with a valence bond model for delocalization that is equally valid for isoelectronic species of the σ as well as π varieties. This property unifies the π components of benzene and allylic species with their σ electronic analogs: hydrogen chains, rings and transition states of organic chemical reactions. The π distortivity has some observable consequences. For example, upon excitation of benzene and other aromatic molecules from the ground to the 1B2u excited states, such that π resonance is disrupted, the low frequency of the b2uvibrational mode of the ground states undergoes up-shift (exaltation) in the excited states. Another consequence is that benzene derivatives that possess strong bond localization in the ground states attain almost uniform C–C bond lengths in the 1B2u-like excited states. As argued, the traditional view that considers π electronic systems to have intrinsic stability, leads to a number of disturbing paradoxes. By contrast, the distortivity of π electronic component removes all the paradoxes and unifies σ and π electronic systems into a single coherent picture of electronic delocalization and resonance-stabilization.

Quantum mechanics has provided chemistry with two general theories, valence bond (VB) theory and molecular orbital (MO) theory. The two theories were developed at about the same time, but quickly diverged into rival schools that have competed, sometimes fervently, on charting the mental map and epistemology of chemistry. Three practitioners of MO and VB theory talk - fighting a little, trying to understand - of the past and present of these two approaches to describing bonding in molecules.

A cost-effective general procedure is proposed to calculate the electron affinities of covalent linkages, which can attach an electron to create a three-electron bond. The procedure is based on a thermodynamic cycle, of which each step is calculated by a method that is specific to it. In the present work, the first step, the dissociation of a two-electron bond, is studied at the MP4 level with a correction for basis set effects, which is calculated at the MP2 level, and an empirical correlation correction that is routinely used in the Gaussian-2 scheme. Experimental data or density functional theory can be used for the second step, while the third step, the formation of a three-electron bond, is studied at the MP2 level in large basis set. ZPE corrections are included in steps 1 and 3. The method is applied to some alkyl-substituted disulfides and yields results that are in good agreement with reference values when available. Some ways to make the procedure even more economical and applicable to large molecules are discussed.

According to common wisdom propagated in textbooks and papers, valence-bond (VB) theory fails and makes predictions in contradiction with experiment. Four iconic ‘failures’ are: a) the wrong prediction of the ground state of the O2 molecule, b) the failure to predict the properties of cyclobutadiene (CBD) viz. those of benzene, c) the failure to predict the aromaticity/anti-aromaticity of molecular ions like C5H and C5H, C3H and C3H, C7H and C7H, etc; and d) the failure to predict that, e.g., CH4 has two different ionization potentials. This paper analyzes the origins of these ‘failures’ and shows that two of them (stated in a and d) are myths of unclear origins, while the other two originate in misuse of an oversimplified version of VB theory, i.e., simple resonance theory that merely enumerate resonance structures. It is demonstrated that, in each case, a properly used VB theory at a simple and portable level leads to correct predictions, as successful as those made by use of molecular-orbital (MO) theory. This notion of VB ‘failure’, which is traced back to the VB-MO rivalry, in the early days of quantum chemistry, should now be considered obsolete, unwarranted, and counterproductive. A modern chemist should know that there are two ways of describing electronic structure, which are not two contrasting theories, but rather two representations or two guises of the same reality. Their capabilities and insights into chemical problems are complementary, and the exclusion of any one of them undermines the intellectual heritage of chemistry.

CmHm (m= 4, 6, 8) species are analyzed in Dmh and D(1/2)mh geometries by means of valence bond (VB) calculations. The fundamental factors that distinguish aromatic and antiaromatic modes of electron delocalization are elucidated by analysis of the mixing between the covalent-state and ionic structures that distribute the electrons in all possible modes available in the cycle. The major difference found is that, by contrast to the aromatic species where all the ionic structures mix into the covalent state, in the antiaromatic species the set of diagonal-ionic structures is excluded from mixing with the covalent-state, owing to its fundamental symmetry features. This exclusion of covalent–ionic mixing is expressed at the most fundamental building blocks of the wavefunction; the spin-alternant state. The spin-alternant state is a resonance hybrid of the two spin-alternant determinants. This resonance hybrid will support a collective motion of the pπ-electrons around the perimeter of the ring only if ionic structures can mix to mediate the electronic flow. It is shown that in aromatic species all the ionic structures mix and sustain a continuous electronic flow around the ring perimeter. By contrast, owing to the exclusion of the diagonal-ionic structures in antiaromatic compounds, the electronic flow in antiaromatic species is interrupted. Symmetry and angular momentum analyses of the ground state in the presence of an external magnetic field show that the properties of the spin-alternant state can qualitatively describe the magnetic properties of the two classes. The continuous flow of π-electrons mediated by the ionic structures of aromatic species is responsible for the enhanced diamagnetism of these species. By contrast, paramagnetic π-ring current in antiaromatic species becomes possible only in the presence of the magnetic field that allows the mixing of the otherwise excluded ionic structures. Copyright © 2003 John Wiley & Sons, Ltd.

At variance with some opinions recently published as a commentary in this Journal, we show that the arguments used against the hybrid atomic orbital model are fundamentally wrong. In fact, the hybrid atomic orbital model correctly describes electron density and molecular properties in full agreement with experiment. The usefulness of this model is emphasized, and hints are suggested to teach it to students in the framework of the molecular orbital theory.

This account describes the breathing-orbital valence bond (BOVB) method, a modern valence bond method that incorporates differential dynamic correlation associated with the bond making and breaking of a chemical event. The method aims to combine the properties of interpretability and compactness of the classical valence bond method with good accuracy of the energetics. The domain of applicability of the BOVB method is mainly for problems that require interpretation of an electronic wave function in terms of Lewis structures. The method generates all the covalent and ionic Lewis structures that are relevant to the electronic state, and represents each of them by a single valence bond configuration state function. A balanced description of the different Lewis structures is then ensured by allowing each configuration to have its specific set of orbitals during the optimization process. In this framework, the dynamic correlation associated with the breaking or forming of a bond is viewed as the instantaneous adaptation of the orbitals to the electron fluctuation inherent to the bond; hence, the “breathing orbital” characterization. Applications of the BOVB method to a variety of problems are described, for example, two-electron bonds, odd-electron bonds, bonds to transition metals, resonance energies, and diabatic surfaces. In all these applications, the method is shown to provide bonding energies that compare well to accurately calculated or experimental values, despite the extreme compactness of the wave functions.

Breathing orbital valence bond (BOVB) computations (Hiberty, P. C.; Humbel, S.; Byrman, C. P.; van Lenthe, J. H. J. Chem. Phys. 1994, 101, 5969) are used to obtain nonidentity barriers for hydrogen transfer reactions between X and X‘ groups, X ≠ X‘ = CH3, SiH3, GeH3, SnH3, PbH3. Modeling of these barriers by means of VB state correlation diagrams (Shaik, S.; Shurki, A. Angew. Chem., Int. Ed. Engl. 1999, 38, 586) leads to a simple expression for the barrier (eq 29) as an interplay of an intrinsic term and the reaction driving force. The equation predicts barrier heights that are compatible with the BOVB computed barrier heights. Its comparison with the Marcus equation shows similarities and differences.

The effects of methyl substitution on the geometries and bonding energies of a systematic series of three-electron-bonded radical cations of the type [H(n)X...XH(n)](+), covering all possible symmetrical three-electron bonds that may take place between atoms of the second and third rows of the periodic table, have been investigated at the level of Møller-Plesset perturbation theory. Methyl substitution leads to significant weakening and lengthening of the X...X bond when X is a second-row atom. The effects increase with the number of substitutions and are more and more important in the series X = N, O, F. By contrast, methyl substitution leaves the bonding energies between third-row atoms practically unchanged but leads to a surprising bond shortening in the S...S and P...P cases. These seemingly contradictory effects are rationalized through a qualitative analysis based on an elementary molecular orbital description of three-electron bonding.

Some typical hypervalent molecules, SF4 , PF5 , and ClF3 , as well as precursors SF ((4) Σ(-) state) and SF2 ((3) B1 state), are studied by means of the breathing-orbital valence bond (BOVB) method, chosen for its capability of combining compactness with accuracy of energetics. A unique feature of this study is that for the first time, the method used to gain insight into the bonding modes is the same as that used to calculate the bonding energies, so as to guarantee that the qualitative picture obtained captures the essential physics of the bonding system. The (4) Σ(-) state of SF is shown to be bonded by a three-electron σ bond assisted by strong π back-donation of dynamic nature. The linear (3) B1 state of SF2 , as well as the ground states of SF4 , PF5 and ClF3 , are described in terms of four VB structures that all have significant weights in the range 0.17-0.31, with exceptionally large resonance energies arising from their mixing. It is concluded that the bonding mode of these hypervalent species and isoelectronic ones complies with Coulson's version of the Rundle-Pimentel model, but assisted by charge-shift bonding. The conditions for hypervalence to occur are stated.

International audience; The ground state and first singlet excited state of ethylene, so-called N and V states, respectively, are studied by means of modern valence bond methods. It is found that extremely compact wave functions, made of three VB structures for the N state and four structures for the V state, provide an N → V transition energy of 8.01 eV, in good agreement with experiment (7.88 eV for the N → V transition energy estimated from experiments). Further improvement to 7.96/7.93 eV is achieved at the variational and diffusion Monte Carlo (MC) levels, respectively, VMC/DMC, using a Jastrow factor coupled with the same compact VB wave function. Furthermore, the measure of the spatial extension of the V state wave function, 19.14 a02, is in the range of accepted values obtained by large-scale state-of-the-art molecular orbital-based methods. The σ response to the fluctuations of the π electrons in the V state, known to be a crucial feature of the V state, is taken into account using the breathing orbital valence bond method, which allows the VB structures to have different sets of orbitals. Further valence bond calculations in a larger space of configurations, involving explicit participation of the σ response, with 9 VB structures for the N state and 14 for the V state, confirm the results of the minimal structure set, yielding an N → V transition energy of 7.97 eV and a spatial extension of 19.16 a02 for the V state. Both types of valence bond calculations show that the V state of ethylene is not fully ionic as usually assumed, but involving also a symmetry-adapted combination of VB structures each with asymmetric covalent π bonds. The latter VB structures have cumulated weights of 18–26 % and stabilize the V state by about 0.9 eV. It is further shown that these latter VB structures, rather than the commonly considered zwitterionic ones, are the ones responsible for the spatial extension of the V state, known to be ca. 50 % larger than the V state.

Breathing orbital valence bond (BOVB) computations (Hiberty, P. C.; Humbel, S.; Archirel, P. J. Phys. Chem. 1994, 98, 11697) are used to obtain identity barriers for hydrogen transfer reactions between X groups, X = H, CH3, SiH3, GeH3, SnH3, and PbH3. Modeling of these barriers by means of VB state correlation diagrams (Shaik, S.; Shurki, A. Angew. Chem. 1999, 38, 586) lead to simple expressions for the barriers (eqs 21 and 22). These expressions show that the organizing quantity of the barriers is the singlet−triplet excitation energy (ΔEST) or bond energy (D) of the X−H bond that undergoes activation. The larger the ΔEST or D, the higher the identity barrier. These equations are successfully applied to deduce barriers for hydrogen transfers between electronegative groups, X = X‘ = F, Cl, Br, and I. The “polar effect” (Russell, G. A. In Free Radicals; Kochi, J. K., Ed.; Wiley: New York, 1973; Vol 1, p 293−298) is shown to be significant but virtually constant in the series. Thus, identity processes mask...

The manifestations of the symmetry-breaking artifact in three-electron-bonded systems have been investigated at several computational levels including second-order Moller–Plesset perturbation theory (MP2), coupled cluster (CC), and Bruckner-coupled cluster (B-CC) theories. The model systems, [HnX∴XHn]+(X=Ne, F, O, N, Ar, Cl, S, P; n=0–3) cover all types of three-electron bonds that can possibly take place between atoms of the second and third rows of the Periodic Table. The critical interatomic distance beyond which symmetry breaking begins to take place at the Hartree–Fock and Moller–Plesset levels are determined for each model system. Their magnitude are found to obey regular tendencies which are related to the compactness of the orbitals involved in the three-electron bonds. In all model systems, the onsets of symmetry-breaking at the MP2 level are greater or equal to the equilibrium bonding distance between the XHn fragments. The symmetry-breaking artifact results in severe discontinuities in the diss...

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 bonding distances, vibrational frequencies, and dissociation energies of a series of dihalogen radical anions, X∴Y- (X, Y = F, Cl, Br, I), held together by three-electron bonds, are calculated at the MP2 and MP4 levels and compared to the CCSD(T) level and to experimental values when available. In agreement with a qualitative model which is expressed in valence bond terms, it is found that Moller−Pesset calculations offer a good description of symmetrical homonuclear three-electron bonds by providing fairly accurate equilibrium bond lengths, stretching frequencies, and dissociation energies. By contrast, the Moller−Plesset method fails for some unsymmetrical systems, leading to largely erroneous equilibrium distances and stretching frequencies. The qualitative model predicts such errors to be related to an inaptitude of the UHF reference determinant to properly describe the sharing out of the charge between the two fragments. This inadequacy results in a set of optimized molecular orbitals that is poo...

The 24 valence isomers of diphosphinine, P2(C−H)4, have been investigated at an electron-correlated ab initio level and by density functional theory. In analogy with benzene, the three planar forms exhibit full aromaticity and are the most stable isomers on the potential surface. The next isomers, by order of stabilities, are the diphosphabenzvalenes, the Dewar diphosphabenzenes, the prismanes, and the diphosphabicyclopropenyls. They are distinctly less stable than the planar isomers, and their relative energies range from 23 all the way to 93 kcal/mol above the absolute minimum. Among the planar isomers, the most stable one is the (ortho) 1,2-diphosphabenzene, in apparent contradiction with the fact that this species has not been synthesized yet. Some lines of thought to resolve this apparent dilemma are proposed, and the relative reactivities of planar isomers are discussed in terms of their different diradical character. Strain energies are calculated for the nonplanar isomers and compared to those of ...

Charge-shift bonds form a distinct class of bonds where all or most of the bond energy is provided by the resonance energy between the covalent and ionic structures of the bond. This phenomenon is ...