A hypervalent pentacoordinate boron compound with an N-B-N three-center four-electron bond

For the purpose of synthesizing and characterizing hypervalent boron compounds with strong hypervalent interaction, we have prepared a boron compound with a tridentate ligand bearing two pyrimidine rings as nitrogen donors. X-ray analysis and molecular orbital calculations suggested that the boron compound was of hypervalent pentacoordinate structure with an N-B-N hypervalent bond. Thus, we have prepared the first hypervalent second row element compound with apical N coordination. A breakdown of energy contributions by DFT calculations revealed that the N-B-N bond energy of the pentacoordinate state ground state (13) was 2.8 kcal mol(-1). Implications were that the conjugation energy difference of 6.6 kcal mol(-1) (14.2-7.6 kcal mol(-1)) with the tetracoordinate state was a crucial factor for shifting stability toward the pentacoordinate structure.     

Multicenter bonding and the structure of electron-rich molecules. Model of three-center four-electron bonding reconsidered

The concept of three-center four-electron (3c-4e) bonding, which has often been invoked in attempts to interpret the electronic structure of electron-rich molecules, is scrutinized using various methodologies, including generalized population analysis and the analysis of the so-called domain-averaged Fermi holes. Results for representative examples show clearly how manifestations of the 3c-4e model can depend critically on the quality of the wave function being analyzed. In general, the existence of 3c-4e bonding tends to be most compatible with the analysis of wave functions of lower quality; enhancements to the flexibility of the basis and/or the inclusion of electron correlation can lead to dramatic changes, such that the 3c-4e scheme transforms into a pattern of two more or less normal, albeit often very polar, two-center two-electron bonds.     

Symmetry of three-center,four-electron bonds

Three-center, four-electron bonds provide unusually strong interactions; however, their nature remains ununderstood. Investigations of the strength, symmetry and the covalent versus electrostatic character of three-center hydrogen bonds have vastly contributed to the understanding of chemical bonding, whereas the assessments of the analogous three-center halogen, chalcogen, tetrel and metallic -type long bonding are still lagging behind. Herein, we disclose the X-ray crystallographic, NMR spectroscopic and computational investigation of three-center, four-electron [D–X–D]⁺ bonding for a variety of cations (X⁺ = H⁺, Li⁺, Na⁺, F⁺, Cl⁺, Br⁺, I⁺, Ag⁺ and Au⁺) using a benchmark bidentate model system. Formation of a three-center bond, [D–X–D]⁺ is accompanied by an at least 30% shortening of the D–X bonds. We introduce a numerical index that correlates symmetry to the ionic size and the electron affinity of the central cation, X⁺. Providing an improved understanding of the fundamental factors determining bond symmetry on a comprehensive level is expected to facilitate future developments and applications of secondary bonding and hypervalent chemistry.

The factors determining the symmetry and the fundamental nature of the three-center, four-electron bonds are assessed.     

A valence bond study of the oxygen molecule

Ab initio valence bond calculations are performed for the three lowest states of the oxygen molecule (³Σ⁻_g, ¹Δ_g, and ¹Σ⁺_g). One objective of the present study was to make a contribution to previous valence bond discussions about the oxygen “double” bond. Further, we study the origin of a small barrier in the potential energy surface of the ground state. Two compact models are employed to maintain the clear picture that can be offered by the valence bond method. The first model has only the Rumer structures that are essential for bonding and a proper dissociation. The second model, in addition, has structures which represent excited atoms. These prove to be important for the dissociation energies. For both models, the orbitals are fully optimized. The spectroscopic data obtained are significantly better than are the (few) valence bond results on O₂ that have been published and have the quality of multiconfiguration self-consistent field calculations in which the same valence space is used. The “hump” in the potential energy surface of the ground state is shown to arise from a spin recoupling. The free atoms correspond to a spin coupling that is incapable of describing the formation of bonds. Only at short distances, an alternative spin coupling provides bonding and the repulsive curve is converted into an attractive one. Our results on this subject support a valence bond explanation previously given by McWeeny [R. McWeeny, Int. J. Quantum Chem. Symp. 24 , 733 (1990)]. © 1996 John Wiley & Sons, Inc.     

Solvation of H3O+ by phenol: hydrogen bonding vs pi complexation

Ab initio calculations at the second-order M?ller-Plesset perturbation theoretic level have been carried out to study the solvation of protonated water by phenol molecules. The results show that in addition to classical O-H...O hydrogen bonds, C-H...O, pi...H-O, and pi...H-C bonds are also formed, thus stabilizing the H3O+(C(6)H(5)OH)3 complex.     

Wheland intermediates: an ab initio valence bond study

The traditional resonance model for electrophilic attacks on substituted aromatic rings is revisited using high level valence bond (VB) calculations. A large π-donation is found in the X = NH(2) case and a weaker one for the X = Cl case, not only for ortho and para isomers but also for the meta case, which can be explained by considering five (not three) fundamental VB structures. No substantial π-effect is found in the X = NO(2) case, generally viewed as π-attractive.     

The role of three-center/four-electron bonds in superelectrophilic dirhodium carbene and nitrene catalytic intermediates

Three-center/four-electron (3c/4e) bonds are important bonding motifs that dictate the electronic structure, and thereby the reactivity, of metal-metal bonded carbene and nitrene intermediate complexes that are crucial to the dirhodium-catalyzed functionalization of hydrocarbons. In this Perspective article, general features of the 3c/4e bond are presented and discussed in comparison to two-center/two-electron (2c/2e) bonds. Specifically, 3c/4e bonding interactions lead to longer distances between the atoms involved and measurably weaker bonds. Additionally, excited states derived from the 3c/4e bonding manifold are lower in energy than those derived from a 2c/2e manifold, signifying a greater degree of reactivity in the former case. Three coterminous 3c/4e Ru-Ru-N bonds are present in metal-metal/metal-ligand multiply bonded diruthenium terminal nitrido compounds. This bonding situation results in an unusual superelectrophilic character of the nitride nitrogen atom, exemplified by its insertion into aryl C-H bonds via an electrophilic aromatic substitution mechanism. The key catalytic intermediates in dirhodium-catalyzed C-H functionalization reactions, dirhodium carbene and dirhodium nitrene complexes, may also be described as superelectrophilic by virtue of 3c/4e Rh-Rh-C(or N) σ and π bonds. These 3c/4e bonding interactions set apart dirhodium carbene and nitrene intermediates from other, less electrophilic, carbene or nitrene species.     

A variational biorthogonal valence bond method

The details of a simple and efficient scheme for performing variational biorthogonal valence bond calculations are presented. A variational bound on the energy functional is obtained through the use of a complete configuration expansion in a well-chosen subset of orbitals. The resultant wave functions are clearly dominated by the covalent (spin-coupled) structures, with a negligible contribution from ionic structures. The orbitals obtained compare favorably with overlap enhanced atomic orbitals obtained by other valence bond approaches. The method is illustrated by calculations on water and dioxygen difluoride. © 1994 by John Wiley & Sons, Inc.     

Stability and bonding of disilyne and its isomers: A generalized valence bond-effective potential study

We have employed an effective potential and a single-zeta basis in SCF–MO computations to estimate the relative stability of linear disilyne HSiSiH and five isomeric structures defined in earlier all-electron ab initio SCF–MO computations. The effect of electron correlation has been estimated by generalized valence-bond (GVB ) computations for the five valence electron pairs of these structures. All our computations indicate that linear disilyne is the least stable structure and that H₂SiSi, the silicon analog of vinylidene carbene, is the most stable structure. In these structures silicon occurs in divalent and tetravalent states. The nature of silicon bonding in these valence states is illustrated by contour diagrams of the GVB orbital pairs.     

Protons in supercritical water: a multistate empirical valence bond study

Molecular dynamics simulations have been performed to analyze microscopic details related to aqueous solvation of excess protons along the supercritical T = 673 K isotherm, spanning a density interval from a typical liquid down to vapor environments. The simulation methodology relies on a multistate empirical valence bond Hamiltonian model that includes a proton translocation mechanism. Our results predict a gradual stabilization of the solvated Eigen cation [H(3)O.(H(2)O)(3)](+) at lower densities, in detriment of the symmetric Zundel dimer [H.(H(2)O)(2)](+). At all densities, the average solvation structure in the close vicinity of the hydronium is characterized by three hydrogen bond acceptor water molecules and presents minor changes in the solute water distances. Characteristic times for the proton translocation jumps have been computed using population relaxation time correlation functions. Compared to room temperature results, the rates at high densities are 4 times faster and become progressively slower in steamlike environments. Diffusion coefficients for the excess proton have also been computed. In agreement with conductometric data, our results show that contributions from the Grotthus mechanism to the overall proton transport diminish at lower densities and predict that in steamlike environments, the proton diffusion is almost 1 order of magnitude slower than that for pure water. Spectroscopic information for the solvated proton is accordant to the gradual prevalence of proton localization in Eigen-like structures at lower densities.     

Orbital electronegativity and analytical representation of atom valence state energy

An analytical representation of atom valence state energy (E(n_j), j = 1,…?4; E(n_j) is a nonlinear function of orbital occupancy numbers n_j) is proposed and explicitly derived for H? Ar; the values of electronegativity calculated based on E(n_j) agree within truncation error with those of Hinze and Jaffe. However, in our representation, orbital electronegativity χ and hardness parameters η of a given orbital always include nonlinear contributions from other orbitals, hence accounting for their influence on χ and η. An atomic charge calculation procedure based on E(n_j) is also described and shown to perform well.     

Estimation of electronegativity values of elements in different valence states

The electronegativities of 82 elements in different valence states and with the most common coordination numbers have been quantitatively calculated on the basis of an effective ionic potential defined by the ionization energy and ionic radius. It is found that for a given cation, the electronegativity increases with increasing oxidation state and decreases with increasing coordination number. For the transition-metal cations, the electronegativity of the low-spin state is higher than that of the high-spin state. The ligand field stabilization, the first filling of p orbitals, the transition-metal contraction, and especially the lanthanide contraction are well-reflected by the relative values of our proposed electronegativity. This new scale is useful for us to estimate some quantities (e.g., the Lewis acid strength for the main group elements and the hydration free energy for the first transition series) and predict the structure and property of materials.     

A second quantized formulation of valence bond theory

Valence bond theory is formulated in terms of second quantized operators and is related to the theory of the unitary group of spin-free orbital transformations. The construction of Weyl basis states, the evaluation of matrix elements, and the application to a linked-diagram valence bond perturbation theory are all discussed.     

Electron-rich three-center bonding: role of s,p interactions across the p-block

This paper analyzes the importance of s,p mixing-a necessary addition to the simplest Rundle-Pimentel picture-and periodic and group trends in electron-rich three-center bonding. Our analysis proceeds through a detailed quantum chemical study of the stability of electron-rich three-center bonding in triatomic 22-valence electron anions. To provide interpretations, a perturbational molecular orbital (MO) analysis of s,p mixing is carried out. This analysis of the orbitals and the overlap populations is then tested by density functional calculations for a number of linear trihalides, trichalcogenides, and tripnictides. The most important effect of s,p mixing on the in-line bonding is in destabilization of the 3sigma(g) orbital and is determined by the overlap between the s orbital of the central atom and the p orbital of the terminal atom. Further destabilization arises from the repulsion of p(pi) lone pairs. Both of these antibonding effects increase with increasing negative charge of the system. The stability of isoelectronic X(3) systems thus decreases when moving from right to left in the periodic table. Interesting group trends are discerned; for instance, for the electron-rich tripnictides, the ability to accommodate a hypervalent electron count is the largest in the middle rather at the end of the group. Particularly strong s,p mixing can reverse the bonding/antibonding character of MOs: thus MO 2sigma(u) that is responsible for bonding for trihalides and trichalcogenides is actually antibonding in N(3)(7)(-).     

A new approach to the relationship between bond energy and electronegativity

The familiar equation whereby Pauling related heteronuclear bond energies D_A–B to the electronegativity difference Δχ (=∣χ_A − χ_B∣) and the homonuclear bond energies D_A–A and D_B–B has been the subject of critical scrutiny for at least half a century. A modification to this equation that combines the concepts of electronegativity and hardness/softness can be rewritten in terms of two quantities x and y, both having absolute significance. Both homo- and heteronuclear bond energies can be rationalised from these new equations. The quantities x are linearly related to Pauling electronegativities, while y appears to be a measure of an atom’s intrinsic bonding potential, related to size and availability of valence orbitals.