Valence Bond Approach Research Articles

Frustrated magnetism and resonating valence bond physics in two-dimensional kagome-like magnets

We explore the phase diagram and the low-energy physics of three Heisenberg antiferromagnets which, like the kagome lattice, are networks of corner-sharing triangles but contain two sets of inequivalent short-distance resonance loops. We use a combination of exact diagonalization, analytical strong-coupling theories, and resonating valence bond approaches, and scan through the ratio of the two inequivalent exchange couplings. In one limit, the lattices effectively become bipartite, while at the opposite limit heavily frustrated nets emerge. In between, competing tunneling processes result in short-ranged spin correlations, a manifold of low-lying singlets (which can be understood as localized bound states of magnetic excitations), and the stabilization of valence bond crystals with resonating building blocks.

Non-orthogonal and orthogonal valence bond wavefunctions in the hydrogen molecule: the diabatic view

The ability of the valence bond (VB) approach to describe a molecular system in ‘chemical terms’ finds its theoretical justification in the fact that the VB wavefunctions are supposed to be diabatic, i.e. with a well-defined nature, not depending on the nuclear geometry. The intimate nature of the VB wavefunctions is here analysed by computing the non-adiabatic coupling for the simple, paradigmatic case of the hydrogen (H2) molecule. This analysis reveals that the neutral and ionic VB wavefunctions cannot be considered as diabatic states, given that they present a large non-adiabatic coupling. The diabatic states, obtained by a suitable transformation of the VB wavefunctions, are found to be the wavefunctions of the orthogonal VB (OVB) approach, which therefore gains a legitimacy in the analysis of the composition of the adiabatic wavefunctions. Such an analysis has some bearing on the description of the nature of the chemical bond in H2: the neutral structure gives a dissociative curve and the bond is due to the stabilisation brought by the ionic structure that mixes together with the neutral structure in the ground state wavefunction at short internuclear distances. The ability of the (at first glance) neutral VB wavefunction based on the 1s orbitals to describe in a compact way the ground state (and therefore the chemical bond) is ascribed to an almost optimal mixing in this wavefunction of the diabatic neutral and ionic states at all internuclear distances.

Elucidation of the Forces Governing the Stereochemistry of Biphenyl

AbstractBiphenyl prefers a twisted conformation rather than a planar or perpendicular structure. Although conjugation (stabilization) and steric repulsion (destabilization) coexist in the planar structure, both would be relieved in the perpendicular structure in which an alternative stabilizing interaction, namely hyperconjugation, dominates. It has been assumed that the twisted conformer results from a balance of the attractive and repulsive forces. By using the block‐localized wavefunction (BLW) method, which is an ab initio valence bond (VB) approach, we have quantified the stabilization (conjugation and hyperconjugation) and destabilization (steric repulsion) energy changes as a function of the twist angle, and demonstrated that the minimum equilibrium structure indeed is a result of the coupling of these two conflicting forces. At the B3LYP/TZVPP level of theory, the BLW computations showed that the π‐conjugation effect contributes to the stability of the planar biphenyl by 46.4 kJ/mol, whereas the σ–π* hyperconjugation stabilization energy in the perpendicular structure is 36.4 kJ/mol. However, we note that there is also a weak σ–σ* hyperconjugative interaction between the two phenyl rings in the planar structure, which is estimated to stabilize the planar structure by an additional 6.6 kJ/mol. The overall steric effect was determined to be 17.1 kJ/mol, which is higher than the ethane rotational barrier (12 kJ/mol) and highlights the repulsion between the adjacent C–C bonds and the ortho‐hydrogen atoms in the planar biphenyl.

Ab initio nonorthogonal valence bond methods

AbstractModern classical valence bond (VB) methods provide clear interpretation and chemical insights by employing covalent and ionic VB structures explicitly. This review focuses on a methodical development of current modern classical VB methods. As a basic method of the classical VB theory, the VB self‐consistent field (VBSCF) method provides a compact wave function, mainly containing static correlation. On the basis of the VBSCF method, the development of classical VB methods can be divided into two aspects—one focuses on improvement of computational accuracy, such as the breathing orbital VB (BOVB), VB configuration interaction (VBCI), and VB second‐order perturbation theory (VBPT2) methods; the other focuses on extending VB approaches to molecules and reactions in solvated or biological environments, including the VB polarizable continuum model (VBPCM), VB solvation model (VBSM), VB effective fragment potential (VBEFP), and VB/molecular mechanics (VB/MM) methods. These improved methods have the advantage of VB theory and provide intuitive chemical insights into medium‐sized chemical problems. Finally, the further development of modern classical VB methods is briefly discussed.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

Spin-Coupled Theory for ‘N Electrons in M Orbitals’ Active Spaces

Spin-coupled (SC) theory, an ab initio valence bond (VB) approach which uses a compact and an easy-to-interpret single-orbital product wave function comparable in quality to a ‘N in N’ complete-active-space self-consistent field [CASSCF(N,N)] construction, is extended to ‘N in M’ (N ≠ M) active spaces. The SC(N,M) wave function retains the essential features of the original SC model: It involves just the products of nonorthogonal orbitals covering all distributions of N electrons between M orbitals in which as few orbitals as possible, |N – M|, are doubly occupied (for N > M) or missing (for N < M) and all other orbitals are singly occupied; each of these products is combined with a flexible spin function which allows any mode of coupling of the spins of the orbitals within the product. The SC(N,M) wave function remains much more compact than a CASSCF(N,M) construction; for example, the SC(6,7) wave function includes 35 configuration state functions (CSFs) as opposed to the 490 CSFs in the CASSCF case. The essential features of the SC(N,M) method are illustrated through a SC(6,5) calculation on the cyclopentadienyl anion, C5H5(–), and a SC(6,7) calculation on the tropylium cation, C7H7(+). The SC(6,5) and SC(6,7) wave functions for C5H5(–) and C7H7(+) are shown to provide remarkably clear modern VB models for the electronic structures of these aromatic cyclic ions which closely resemble the well-known SC model of benzene and yet recover almost all of the correlation energy included in the corresponding CASSCF(6,5) and CASSCF(6,7) wave functions: over 97% in the case of C5H5(–) and over 95% in the case of C7H7(+).

Resonance and Aromaticity: An Ab Initio Valence Bond Approach

Resonance energy is one of the criteria to measure aromaticity. The effect of the use of different orbital models is investigated in the calculated resonance energies of cyclic conjugated hydrocarbons within the framework of the ab initio Valence Bond Self-Consistent Field (VBSCF) method. The VB wave function for each system was constructed using a linear combination of the VB structures (spin functions), which closely resemble the Kekulé valence structures, and two types of orbitals, that is, strictly atomic (local) and delocalized atomic (delocal) p-orbitals, were used to describe the π-system. It is found that the Pauling-Wheland's resonance energy with nonorthogonal structures decreases, while the same with orthogonalized structures and the total mean resonance energy (the sum of the weighted off-diagonal contributions in the Hamiltonian matrix of orthogonalized structures) increase when delocal orbitals are used as compared to local p-orbitals. Analysis of the interactions between the different structures of a system shows that the resonance in the 6π electrons conjugated circuits have the largest contributions to the resonance energy. The VBSCF calculations also show that the extra stability of phenanthrene, a kinked benzenoid, as compared to its linear counterpart, anthracene, is a consequence of the resonance in the π-system rather than the H-H interaction in the bay region as suggested previously. Finally, the empirical parameters for the resonance interactions between different 4n+2 or 4n π electrons conjugated circuits, used in Randić's conjugated circuits theory or Herdon's semi-emprical VB approach, are quantified. These parameters have to be scaled by the structure coefficients (weights) of the contributing structures.

The origins and later developments of molecular orbital theory

AbstractHund in 1926 speculated on the assignment of quantum numbers for the electronic states of diatomic molecules, basing his assignments on the correlation between the diatomic states and those of the united atom limit. Mulliken, who had earlier considered the problem of this assignment using old quantum theory, followed Hund in 1927, in the new quantum theory, correlating the states of a diatomic molecule from the united to the separated atoms. In 1932, he introduced the term orbital for the one‐electron states of an atom or molecule. He was the first to seriously explore the orbitals of polyatomic molecules (1932). Burrau in 1927 made the first successful attempt to solve the Schrodinger's equation for H, and Condon (1927) assigned two electrons to Burrau's orbital to obtain an estimate of the binding energy of H2. Lennard‐Jones (LJ) (1929) introduced the linear combination of atomic orbital model, and following the aufbau principle showed that this explained the paramagnetism of O2. Slater (1929) wrote many‐electron wave functions as determinants of spin‐orbitals, and LJ (1949) showed that with this formulation molecular orbitals (MOs) could be transformed into bond‐localized functions; this provided the link to the valence bond approach and the traditional view of the chemical bond. Huckel (1930) was the first to develop a semiempirical MO model for π‐electron hydrocarbons, and this was later extended by others for all‐electron wave functions. Boys (1950) saw the implication of Gaussian functions for calculating the electron repulsion integrals needed for ab initio calculations, and a later approach by Kohn and coworkers (1964 and 1965) produced a density functional MO theory in which electron repulsion is calculated from the whole electron density. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Classical Valence Bond Approach by Modern Methods

ADVERTISEMENT RETURN TO ISSUEPREVReviewClassical Valence Bond Approach by Modern MethodsWei Wu*†, Peifeng Su†, Sason Shaik*‡, and Philippe C. Hiberty*§View Author Information† The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China‡ Institute of Chemistry and The Lise Meitner-Minerva Center for Computational Quantum Chemistry, The Hebrew University, Jerusalem 91904, Israel§ Laboratoire de Chimie Physique, Groupe de Chimie Théorique, CNRS UMR 8000, Université de Paris-Sud, 91405 Orsay Cédex, FranceE-mail: [email protected] (W.W.); [email protected] (S.S.); [email protected] (P.C.H.). Phone: +86-5922182825 (W.W.); +972-26585909 (S.S.); +33-169156175 (P.C.H.). Fax: +86-5922184708 (W.W.); +972-26584680 (S.S.); +33-0169154447 (P.C.H.).Cite this: Chem. Rev. 2011, 111, 11, 7557–7593Publication Date (Web):August 18, 2011Publication History Received20 July 2010Published online18 August 2011Published inissue 9 November 2011https://doi.org/10.1021/cr100228rCopyright © 2011 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views4991Altmetric-Citations198LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit Read OnlinePDF (5 MB) Get e-AlertsSUBJECTS:Chemical calculations,Chemical structure,Energy,Molecules,Wave function Get e-Alerts

Heisenberg’s chemical legacy: resonance and the chemical bond

Heisenberg’s explanation of how two coupled oscillators exchange energy represented a dramatic success for his new matrix mechanics. As matrix mechanics transmuted into wave mechanics, resulting in what Heisenberg himself described as “…an extraordinary broadening and enrichment of the formalism of the quantum theory”, the term resonance also experienced a corresponding evolution. Heitler and London’s seminal application of wave mechanics to explain the quantum origins of the covalent bond, combined with Pauling’s characterization of the effect, introduced resonance into the chemical lexicon. As the Valence Bond approach gave way to a soon-to-be dominant Molecular Orbital method, our understanding of the term resonance, as it might apply to our understanding the chemical bond, has also changed.

The empirical valence bond model: theory and applications

AbstractRecent years have seen an explosion in computer power, allowing for the examination of ever more challenging problems. For instance, a recent simulation study, which was the first of its kind, was able to actually explore the dynamical nature of enzyme catalysis on a millisecond timescale (Pisliakov AV, Cao J, Kamerlin SCL, Warshel A. Proc Natl Acad Sci U S A 2009, 106:17359.), something that as recently as a year or two ago would have been considered impossible. However, the questions that need addressing are nevertheless very complex, and experimental approaches can unfortunately often be inconclusive (Åqvist J, Kolmodin K, Florián J, Warshel A, Chem Biol 1999, 6:R71.) in answering them. Therefore, it is essential to have an approach that is both reliable and able to capture complex systems in order to resolve long‐standing controversies [particularly with regards to questions such as the origin of enzyme catalysis, where the relevant energy contributions cannot be separated without some computational models (Warshel A, Sharma PK, Kato M, Xiang Y, Liu H, Olsson MHM, Chem Rev 2006, 106:3210.)]. Herein, we will present the empirical valence bond (EVB) approach, which, at present, is arguably the most powerful tool for examining chemical reactivity in the condensed phase. We will illustrate the effectiveness of the EVB method when evaluating, for instance, catalytic effects and demonstrate that it is currently the optimal tool for elucidating challenging problems such as understanding the catalytic power of enzymes. Finally, the increasing appreciation of this approach can maybe best illustrated not only by its proliferation but also by attempts to capture its basic chemistry under a different name, as will be discussed in this work. © 2011 John Wiley &amp; Sons, Ltd. WIREs Comput Mol Sci 2011 1 30–45 DOI: 10.1002/wcms.10This article is categorized under: Electronic Structure Theory &gt; Combined QM/MM Methods

Electron delocalization and bond formation under the ELF framework

A first approach to the relationship between the electron localization function (ELF) and electronic delocalization upon bond formation is provided. We show from first principles the ability of ELF at the bond critical points to act as an index of the electron reorganization involved in chemical bonding. Simultaneously, this index, that we shall call ELF delocalization index (EDI), constitutes a good measure of electron delocalization. We will show how the core of ELF is proportional to the Wiberg index under the valence bond approach. This relationship will be exploited for some representative examples where EDI is able to identify the stages of bond formation. Furthermore, a maximum in EDI along this process has been found to correlate with the molecular equilibrium configuration, allowing for a formulation of a “maximal localization principle” for the stable structure of covalent compounds in terms of ELF.

A comparison of approaches to estimate the resonance energy

We discuss Ab Initio approaches to calculate the energy lowering (stabilisation) due to aromaticity. We compare the valence bond method and the block-localised wave function approaches to calculate the resonance energy. We conclude that the valence bond approach employs a Pauling–Wheland resonance energy and that the block-localised approach employs a delocalisation criterion. The latter is shown to be more basis set dependent in a series of illustrative calculations.

ChemInform Abstract: Aromaticity and Tautomerism in Porphyrins and Porphyrinoids

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

The EVB as a quantitative tool for formulating simulations and analyzing biological and chemical reactions.

Recent years have seen dramatic improvements in computer power, allowing ever more challenging problems to be approached. In light of this, it is imperative to have a quantitative model for examining chemical reactivity, both in the condensed phase and in solution, as well as to accurately quantify physical organic chemistry (particularly as experimental approaches can often be inconclusive). Similarly, computational approaches allow for great progress in studying enzyme catalysis, as they allow for the separation of the relevant energy contributions to catalysis. Due to the complexity of the problems that need addressing, there is a need for an approach that can combine reliability with an ability to capture complex systems in order to resolve long-standing controversies in a unique way. Herein, we will demonstrate that the empirical valence bond (EVB) approach provides a powerful way to connect the classical concepts of physical organic chemistry to the actual energies of enzymatic reactions by means of computation. Additionally, we will discuss the proliferation of this approach, as well as attempts to capture its basic chemistry and repackage it under different names. We believe that the EVB approach is the most powerful tool that is currently available for studies of chemical processes in the condensed phase in general and enzymes in particular, particularly when trying to explore the different proposals about the origin of the catalytic power of enzymes.

Electrostatic Contribution to the Transition States Binding Free Energy Using Simplified Coarse Grained Model

Simplified coarse-grained (CG) models (of the type originally developed by Levitt and Warshel (1)) can provide an effective way of evaluating the free energies of explicit protein models (2). Here we use such a reference potential strategy in evaluating the transition state electrostatic binding free energies calculations, which are essential for the rational enzyme design. The method is examined and demonstrated in studies of the effects of mutation on the transition state binding free energies of the esterase catalytic substrates (p-nitrophenyl acetate, 1-and 2-naphthyl acetates) of human carbonic anhydrase II (hCAII) and dienelactone hydrolase (DLH). These have been computed using empirical valence bond (EVB) approach in MOLARIS program (3) with and without the use of the CG model as a reference potential. The calculated electrostatic contributions to the transition state binding free energies reproduce the experimental trends (4, 5). This indicates that the method should provide a powerful tool for exploring the esterase activities of hCAII and DLH for understanding the promiscuity of these enzymes.(1) Levitt, M. and Warshel, A., Nature, 1975, vol. 253, no. 5495, pp. 694-698.(2) Messer, M. M., Roca, M., Chu, Z. T., Vicatos, S., Vardi-Kilshtain, A. and Warshel, A., Proteins, 2009, in press.(3) Lee, F. S., Chu, Z. T. and Warshel, A., J. Comp. Chem., 1993, vol. 14 p. 161.(4) Gould, S. M. and Tawfik, D. S., Biochemistry, 2005, vol. 44, no. 14, pp. 5444-5452.(5) Kim, H.-K., Liu, J.-W., Carr, P.D., Ollis, D.L., Acta Cryst., 2005, vol. D61, pp. 920-031.

Conduction in graphenes

It is shown that, within the tight-binding approximation, Fermi-level ballistic conduction for a perimeter-connected graphene fragment follows a simple selection rule: the zero eigenvalues of the molecular graph and of its subgraph minus both contact vertices must be equal in number, as must those of the two subgraphs with single contact vertices deleted. In chemical terms, the new rule therefore involves counting nonbonding orbitals of four molecules. The rule is initially derived within the source and sink potential scattering framework, but has equivalent forms that unify the molecular-orbital and valence-bond approaches to conduction. It is shown that the new selection rule can be cast in terms of Kekule counts, bond orders, and frontier-orbital coefficients. In particular, for a Kekulean graphene, conduction pathways are shown to be ranked in efficiency by a (nonmonotonic) function of Pauling bond order between the contact vertices. Frontier-orbital analysis of conduction approximates this function. For a monoradical graphene, the analogous function is shown to depend on Pauling spin densities at contact vertices.

How Does Energized NCCCCCN Lose Carbon in the Gas Phase? A Joint Experimental and Theoretical Study

Neutral NCCCCCN may be prepared in a collision cell of a VG ZAB 2HF mass spectrometer by charge stripping of (NCCCCCN)(*-), formed in the ion source by the process NCCCCH(OEt)(CN) + HO(-) --> H(2)O + NCCCC(-)(OEt)(CN) --> (NCCCCCN)(*-) + EtO(*). A comparison of the neutralization/reionization ((-)NR(+)) and charge reversal ((-)CR(+)) spectra of (NCCCCCN)(*-) indicate that some neutrals NCCCCCN are energized and rearrange to an isomer which decomposes by loss of carbon. An ab initio study at the CCSD(T)/cc-pVTZ//B3LYP/6-311+G(3df) level of theory indicates that (i) triplet NCCCCCN is the ground state with a T/S energy gap of -14.9 kcal mol(-1); (ii) the structures of triplet and singlet NCCCCCN need to be described by molecular obital theory, and a simple valence bond approach cannot be used for this system; and (iii) there are several possible routes by which an energized neutral may lose carbon, but the major route involves the triplet nitrile to isonitrile rearrangement NCCCCCN --> CNCCCCN --> NCCCCN + C.

Valence bond approach for calculating bond energies of diatomic intermetallic compounds with multiple bonds and comparison with experiment

The experimental dissociation energies of 19 diatomic intermetallic molecules with multiple bonds are compared with the corresponding values calculated by a previously proposed empirical valence bond model. The limitations of the model are discussed. Apparent discrepancies between experimental and calculated values can be qualitatively accounted for by molecular orbital considerations.

Quantum theory of aromatic hydrocarbon carcinogenesis

Early history of the quantum-mechanical approach to the elucidation of the mechanisms of chemical carcinogenesis is presented in outline form. It is concluded that the K. L reactivity region theory still provides a good working hypothesis for theoretical evaluation. Experimental indices of carcinogenicity are then shown to correlate with a straightforward kinetic model that uses K, L-region Pauling bond orders as reactivity parameters. The bond order calculations are found to correlate precisely with SCF-LCAO-MO results, and are derived on the basis of a highly simplified valence-bond approach.

On the origin of the catalytic power of carboxypeptidase A and other metalloenzymes

Zinc metalloenzymes play a major role in key biological processes and carboxypeptidase-A (CPA) is a major prototype of such enzymes. The present work quantifies the energetics of the catalytic reaction of CPA and its mutants using the empirical valence bond (EVB) approach. The simulations allow us to quantify the origin of the catalytic power of this enzyme and to examine different mechanistic alternatives. The first step of the analysis used experimental information to determine the activation energy of each assumed mechanism of the reference reaction without the enzyme. The next step of the analysis involved EVB simulations of the reference reaction and then a calibration of the simulations by forcing them to reproduce the energetics of the reference reaction, in each assumed mechanism. The calibrated EVB was then used in systematic simulations of the catalytic reaction in the protein environment, without changing any parameter. The simulations reproduced the observed rate enhancement in two feasible general acid-general base mechanisms (GAGB-1 and GAGB-2), although the calculations with the GAGB-2 mechanism underestimated the catalytic effect in some treatments. We also reproduced the catalytic effect in the R127A mutant. The mutation calculations indicate that the GAGB-2 mechanism is significantly less likely than the GAGB-1 mechanism. It is also found, that the enzyme loses all its catalytic effect without the metal. This and earlier studies show that the catalytic effect of the metal is not some constant electrostatic effect, that can be assessed from gas phase studies, but a reflection of the dielectric effect of the specific environment.