Theories of the chemical bond and its true nature

Two different models for chemical bond were developed almost simultaneously after the Schrödinger formulation of quantum theory. These are known as the valence bond (VB) and molecular orbital (MO) theories. Initially chemists preferred the VB theory and ignored the MO theory. Now the VB theory is almost dropped out of currency. The context of discovery and Linus Pauling’s overpowering influence gave the VB theory its initial advantage. The current universal acceptance of the MO theory is due to its ability to provide direct interpretation of many different types of experiments now being pursued. In current research both localized bonds and delocalized charge distributions play important roles and the MO theory has been successful in giving a good account of both.     

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

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

经典价键理论的从头算计算方法

价键理论是两大现代化学键理论之一,广泛应用于化学键本质和化学反应机理的研究。由于计算困难,价键理论应用局限于定性的讨论而无法有效地开展从头计算研究。现代经典价键理论在经典价键理论的理论基础上,引入合理有效的计算方法,提高了价键计算的效率。本文回顾近年来经典价键理论从头算方法在提高计算精度和拓展研究范围方面的发展,并简要展望价键理论方法的发展趋势。     

Myth and Reality in the Attitude toward Valence‐Bond (VB) Theory: Are Its ‘Failures’ Real?

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.     

Heats of atomization of some conjugated molecules containing nitrogen or oxygen by a novel semiempirical method

Heats of atomization for a range of conjugated molecules containing nitrogen or oxygen are calculated by a semiempirical method that combines some features of both the MO and VB theories. The π ground state of each conjugated molecule is represented as a linear combination of Kekulé structures. Unlike in the VB theory, each Kekulé structure is a determinant containing bond orbitals. Here experimental heats of atomization are reproduced approximately as well as by the more sophisticated SCF –MO approach. The use of this method is, however, much simpler since it amounts to a single diagonalization of a matrix of the order equal to the number of Kekulé structures only.     

The dipole moment of LiH(X1Σ+): Spin-coupled valence-bond study

The spin-coupled VB theory is applied to the dipole moment function μ(R) of LiH(X¹Σ⁺). A series of calculations is reported (1, 78, 127 and 188 spatial configurations) which demonstrates the rapid convergence of this property onto that given by accurate MO CI wavefunctions. The binding is essentially due to the exchange interaction between a heavily deformed Li valence orbital and an almost unchanged H(1s) function. The observed deformation of the Li(2s) orbital is due largely to acquisition of H(1s) character, and not to hydridisation.     

Molecular orbital resonance theory: A new approach to the treatment of quantum chemical problems

An alternative approach to the treatment of the quantum chemical problems combining both, the MO and VB theory, is proposed. This approach retains the concept of resonance from the VB method, but it treats each particular bond in the MO sense. The method is illustrated with a few examples. Relative stabilities of benzene, pentalene and cyclobutadiene are derived. A Hückel (4m + 2) rule is derived for the annulenes. The charge polarisation in the case of the pentalene molecule is explained. A distortion of the pentalene molecule is considered and it is shown that within this approach the distortion depends on the charge polarisation.     

Natural Bond Orbital Study on the Nature of Binding in the H2 Molecule

We use the natural bond orbital (NBO) method to decompose a MO wavefunction into the intuitive valence bond (VB) structures. At least two natural orbital type MO are required to describe the essential binding of the H₂ molecule at all inter nuclear distances. At first the MO wavefunction is transformed into an unrestricted Hartree-Fock wave-function consisted of non-orthogonal localized orbitals u' and v', and then the NBO method is used to decompose u' and v' into the physical meaningful orthogonal localized orbitals. Our results show that the orbitals u' and v' are decomposed into an atomic and an overlap parts. The latter part gives rise to the conventional ionic structure in the VB picture.     

The ground and excited states of polyenyl radicals C2n-1H2n + 1 (n = 2-13): a valence bond study.

The semiempirical valence bond (VB) method, VBDFT(s), is applied to the ground states and the covalent excited states of polyenyl radicals C2n - 1H2n + 1 (n = 2-13). The method uses a single scalable parameter with a value that carries over from the study of the covalent excited states of polyenes (W. Wu, D. Danovich, A. Shurki, S. Shaik, J. Phys. Chem. A, 2000, 104, 8744). Whenever comparison is possible, the VB excitation energies are found to be in good accord with sophisticated molecular orbital (MO)-based methods like CASPT2. The symmetry-adapted Rumer structures are used to discuss the state-symmetry and VB constitution of the ground and excited states, and the expansion to VB determinants is used to gain insight on spin density patterns. The theory helps to understand in a coherent and lucid manner the properties of polyenyl radicals, such as the makeup of the various states, their geometries and energies, and the distribution of the unpaired electrons (the neutral solitons).     

Block-localized wavefunction (BLW) method at the density functional theory (DFT) level

The block-localized wavefunction (BLW) approach is an ab initio valence bond (VB) method incorporating the efficiency of molecular orbital (MO) theory. It can generate the wavefunction for a resonance structure or diabatic state self-consistently by partitioning the overall electrons and primitive orbitals into several subgroups and expanding each block-localized molecular orbital in only one subspace. Although block-localized molecular orbitals in the same subspace are constrained to be orthogonal (a feature of MO theory), orbitals between different subspaces are generally nonorthogonal (a feature of VB theory). The BLW method is particularly useful in the quantification of the electron delocalization (resonance) effect within a molecule and the charge-transfer effect between molecules. In this paper, we extend the BLW method to the density functional theory (DFT) level and implement the BLW-DFT method to the quantum mechanical software GAMESS. Test applications to the pi conjugation in the planar allyl radical and ions with the basis sets of 6-31G(d), 6-31+G(d), 6-311+G(d,p), and cc-pVTZ show that the basis set dependency is insignificant. In addition, the BLW-DFT method can also be used to elucidate the nature of intermolecular interactions. Examples of pi-cation interactions and solute-solvent interactions will be presented and discussed. By expressing each diabatic state with one BLW, the BLW method can be further used to study chemical reactions and electron-transfer processes whose potential energy surfaces are typically described by two or more diabatic states.     

The Nature of Chemical Bonds from PNOF5 Calculations

Natural orbital functional theory (NOFT) is used for the first time in the analysis of different types of chemical bonds. Concretely, the Piris natural orbital functional PNOF5 is used. It provides a localization scheme that yields an orbital picture which agrees very well with the empirical valence shell electron pair repulsion theory (VSEPR) and Bent’s rule, as well as with other theoretical pictures provided by valence bond (VB) or linear combination of atomic orbitals–molecular orbital (LCAO‐MO) methods. In this context, PNOF5 provides a novel tool for chemical bond analysis. In this work, PNOF5 is applied to selected molecules that have ionic, polar covalent, covalent, multiple (σ and π), 3c–2e, and 3c–4e bonds.     

Heats of atomization of conjugated hydrocarbons by a new semiempirical method

Heats of atomization of a range of conjugated hydrocarbons are calculated by a semiempirical method which combines characteristic features of the MO and the VB theory. The -ground state of each hydrocarbon is represented as a linear combination of Kekulé structures where, unlike the VB theory, each Kekulé structure is a determinant containing bond Orbitals. In this approach only the Hückel parameter has to be adjusted. Experimental heats of atomization are by this method reproduced approximately equally well as by the more sophisticated SCF-MO approach. The use of this method is however much simpler since it amounts to a single diagonalization of a matrix of the order equal to the number of Kekulé structures only.     

Theoretical study of the formation of acetylene from two CH fragments

The interaction between two CH radicals to form C₂H₂ is studied theoretically. The fragments are treated by MO theory but the interaction between them is described by VB theory. Thus reveals a sudden change in spin coupling at R_CC≈ 6 au from that characteristic of CH(²Π)-CH(²Π) to CH(⁴Σ^?)-CH(⁴Σ^?) and this is associated with a barrier in the potential energy surface≈ 0.33 eV in height.     

Ordering of Kekulé structures using nonadjacent numbers

Kekulé indices and conjugated circuits are computed for 36 Kekulé structures, together with two VB quantities associated with the corresponding factor graphs (previously called submolecules). These latter quantitites are nonadjacent numbers of Hosoya and the reciprocal of the connectivity indices of Randi?. It was found that the index of Hosoya successfully orders a set of Kekulé structures belonging to the same hydrocarbon in a parallel order as their Kekulé indices and branching indices. This substantiates the relation between VB and MO theories. A code is derived by summing contributions of nonadjacent numbers in all Kekulé stuctures of a hydrocarbon. The order of the resulting codes is found to be identical to the order of the molecular properties (resonance energies, π-energies, and eigenvalues) of the hydrocarbons.     

How to properly compute the resonance energy within the ab initio valence bond theory: a response to the ZHJVL paper

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.     

Orbital symmetry,orbital stability,and orbital pairing rules for organic reactions in the ground state

A generalization of the Hartree–Fock molecular orbital (MO) theory for treating diradical intermediates was explained pictorially by drawing molecular orbitals of diradical species such as ring-opened trimethylene. The generalized MO theory applied to elucidate electronic mechanisms of concerted, ionic, radical, and ion-radical reactions of organic reactants in the ground state. Generalized MO computations revealed the most essential characteristics of these reactions and mutal relationships between the worlds of Woodward–Hoffmann and Hughes–Ingold. Generalized MO studies supported our orbital symmetry, stability and pairing rules for concerted, ionic and radical reactions in the ground state, respectively. An extension of MO treatments to excited states reactions was briefly pointed out in relation to the density and spin correlation functions by the multireference CI wave functions.