Valence-bond studies of AH2 molecules

Minimal Slater basis set calculations are reported for H₂S. The calculations used both natural and hybrid atomic orbitals. The calculations were performed at H-S-H bond angles of 90 °, 92.2 ° and 95 °. The results are compared with similar calculations on H₂O and with calculations using the molecular orbital approximation. The only definite trend found in going from H₂O to H₂S is that the importance of the SH⁺H^– structure decreases. Changes in the relative importance of covalent and ionic structures depend upon which measure of importance is used. Calculations using a set of orthogonal hybrid orbitals again find the hybrid orbitals exhibiting non-perfect following behaviour with the hybrids remaining at about the equilibrium bond angle. Localized molecular orbitals were found to move in the opposite direction to the change in the H-S-H bond angle.     

Valence bond and molecular orbital studies of the A-F bond lengths in some AFn type molecules and their fluorinated cations

The results of ab initio MP2(full)/cc-pVTZ and DFT MPW1PW91/cc-pVTZ molecular orbital calculations of the bond lengths are reported for non-hypercoordinate and hypercoordinate systems of the general type AF_n^q+, with q≥0 and A = N, P, O, S and Cl. They show that except for OF₄²⁺ the bond lengths decrease as the cationic character increases. Increased-valence structures are used to provide valence bond (VB) rationalizations for the bond length shortenings. In these valence bond structures, the degree of multiple bonding increases as the cationic character increases.     

Valence bond studies of the D2h isomer of O4: An interim report

Single-zeta and π-electron double-zeta basis sets are used to examine some theories of the origin of the stability of the D_2h isomer of O₄, using ab initio valence-bond procedures. With these basis sets, resonance between covalent-type (i.e., O₂ ·· O₂) valence-bond structures does not lead to a stabilization of the dimer relative to the separated monomers. When basis sets of the same size are used to construct wave functions for covalent and ionic structures, covalent-ionic resonance (i.e., O₂ ·· O₂ ↔ O₂⁺ ·· O₂⁻ ↔ O₂⁻ ·· O₂⁺) is also unable to stabilize the dimer. Without consideration of the basis-set superposition error, stability is obtained when the size of the AO basis is increased for the dimer relative to the monomer, either via the basis for the ionic structures or by the inclusion of midbond functions. Brief consideration is given to an increased-valence structure for the dimer. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 547–555, 1997     

Valence bond theory for chemical dynamics

This essay provides a perspective on several issues in valence bond theory: the physical significance of semilocal bonding orbitals, the capability of valence bond concepts to explain systems with multireferences character, the use of valence bond theory to provide analytical representations of potential energy surfaces for chemical dynamics by the method of semiempirical valence bond potential energy surfaces (an early example of specific reaction parameters), by multiconfiguration molecular mechanics, by the combined valence bond-molecular mechanics method, and by the use of valence bond states as coupled diabatic states for describing electronically nonadiabatic processes (photochemistry). The essay includes both ab initio and semiempirical approaches.     

Valence bond study of hyperfine interactions and structure of Kr2F

A semi-empirical valence bond method for calculating isotropic and anisotropic hyperfine interaction constants in diatomic halogen anions and noble gas monohalides has been extended to the linear triatomic KrFKr. Comparison with the experimental values yields estimates for the KrF bond distance and the electron charge distribution in Kr₂F.     

Valence shell calculations on polyatomic molecules

Dipole moments and charge distributions for twenty molecules of widely different types have been calculated using (a) the CNDO/2 method and (b) a CNDO/2D method in which the orbitals from the CNDO/2 method are deorthogonalized by a Löwdin transformation and are then used to calculate the dipole moments in a rigorous manner. A statistical analysis of the results for the dipole moments calculated by the CNDO/2D method shows that they are in very slightly better agreement with experiment than those from the CNDO/2 method. The net charge distributions from the CNDO/2D method follow more closely the trends of ab initio calculations than do the CNDO/2 net charges.

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Zusammenfassung Dipolmomente und Ladungsdichten von Molekülen unterschiedlichen Typs wurden mittels des CNDO/2- und CNDO/2D-Verfahrens (d. i. mit delokalisierten Löwdin-Orbitalen als AO's) berechnet. Eine statistische Analyse zeigt, daß die Resultate der zweiten Methode etwas besser als die der ersten den experimentellen Ergebnissen folgen. Das Analoge gilt für die Nettoladungsverteilungen in bezug auf die Trends bei ab initio-Rechnungen.

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Résumé Les moments dipolaires et les distributions de charge pour vingt molécules de types divers ont été calculés par: a) la méthode CNDO/2; b) une méthode CNDO/2D où les orbitales de CNDO/2 sont déorthogonalisées par une transformation de Löwdin. Une analyse statistique montre que les moments dipolaires calculés par CNDO/2D sont légèrement en meilleur accord avec l'expérience que ceux calculés par CNDO/2. Les distributions de charge de CNDO/2D sont plus ressemblantes à celles de calculs ab-initio que ne le sont les distributions de CNDO/2.

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This work represents part of the Ph.D. Dissertation submitted to the University of Virginia by D. D. S. and was supported by Grants No. 1-F01-GM41986-01 from the National Institutes of Health, Bethesda, Maryland, U.S.A., and No. AF-AFOSR-1184-67 from the Air Force Directorate of Scientific Research.

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NASA Research Trainee.     

Valence bond theoretical study for chemical reactivity

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Valence bond functions for the hydrogen molecule

Valence bond wavefunctions were constructed for H₂. Use of Slater exponents resulted in very slow convergence to the ground state energy. Convergence was improved by optimizing exponents which were found to increase as the principal quantum number n. However, this gave problems of linear dependence since optimum orbitals were strikingly similar for all n. The best function without angular correlation contained 27 terms constructed from 1s, 3s, 2p ₀, 3d ₀, 4f ₀, and 5g ₀ orbitals and gave an energy of –1.1594a.u. The best function with angular correlation gave E=-1.1656 a.u.

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Zusammenfassung Für das H₂-Molekül werden Wellenfunktionen nach der Valenzstrukturmethode konstruiert. Die Benutzung von Exponenten nach Slater führt zu einer sehr langsamen Konvergenz zur Grundzustandsenergie. Die Konvergenz wurde durch Optimierung der Exponenten verbessert, wobei diese mit der Hauptquantenzahl ansteigen. Dabei ergab sich jedoch das Problem linearer Abhängigkeit der Funktionen, da die optimalen Orbitale sehr ähnlich für alle n waren. Die beste Funktion ohne Winkelkorrelation enthielt 27 Terme, die aus den Orbitalen 1s, 3s, 2p ₀, 3d ₀, 4f ₀ und 5g ₀ konstruiert waren, und ergab eine Energie von –1,1594A.E. Die beste Funktion mit Winkelkorrelation ergab E=–1,1656 A.E.

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Résumé Des fonctions d'onde de liaison de valence sont construites pour H₂. L'emploi d'exposants de Slater entraîne une très faible convergence vers l'énergie de l'état fondamental. La convergence a été améliorée par optimisation des exposants qui croissent comme le nombre quantique principal n. Cependant, ceci crée des problèmes de dépendance linéaire car les orbitales optimales sont étonnement similaires pour tous les n. La meilleure fonction sans corrélation angulaire contient 27 termes construits à partir d'orbitales 1s, 3s, 2p ₀,3d ₀,4f ₀ et 5g ₀ et donne une énergie de –1,1594 u.a. La meilleure fonction avec corrélation angulaire donne E= –1,1656 u.a.

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Presented in part at the Symposium on Molecular Structure and Spectroscopy, The Ohio State University, Sept., 1968.

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N.I.H. Predoctoral Fellow 1964–1967.     

Valence bond treatment of systems involving orbital degeneracy

A semiempirical valence-bond treatment including polar structures has been developed. Explicit formulas are given for the calculation of energy matrix elements and of charge and spin densities. The method has been applied to benzyl and allyl radicals and to butadiene.

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Zusammenfassung Es wurde ein semiempirisches Valence-Bond-Verfahren einschlie\lich Polar-Strukturen ent-wickelt. Explizite Formeln werden für die Berechnung von Energiematrixelementen und für die Ladungs- und Spin-Dichte angegeben. Die Methode wurde auf das Benzyl- und das Allyl-Radikal und auf Butadien angewendet.

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Résumé On a dévelopé un traitment semi-empirique de la méthode des orbitals de valence avec inclusion des structures polaires. On donne des formules explicitées pour le calcul des éléments matriciels de l'énergie et des densités de charge et de spin. On a appliqué la méthode aux radicaux benzylique et allylique et à la molecule du butadiène.

     

Valence bond treatment of systems involving orbital degeneracy

Ground and excited electronic states of the allyl cation and anion, the butadiene radical cation and anion, and of the pentadienyl cation and anion have been calculated by a semiempirical valence bond method. The results of such calculations are in essential agreement with the known properties of such systems. A comparison of the results of the valence bond treatment with those expected on the basis of the qualitative resonance theory yields serious discrepancies which show up the limitations inherent in the latter formalism.

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Zusammenfassung Der Grundzustand und die elektronisch angeregten Zustände der folgenden Systeme wurden mittels einer semiempirischen Valence-Bond-Methode berechnet: Allyl Kation und Anion, Butadien Radikal Kation und Anion, Pentadienyl Kation und Anion. Die Ergebnisse stehen in vernünftiger Übereinstimmung mit den bekannten experimentellen Daten. Ein Vergleich der Resultate, die mittels der Valence-Bond-Methode erhalten werden, mit jenen, die man aufgrund der qualitativen Resonanz-Theorie erwarten würde, ergibt wesentliche Unterschiede, die auf die Grenzen hinweisen, die dem letztgenannten Formalismus eigen sind.

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Résumé L'état fondamental et les états électroniques excités du cation et de l'anion allyl, du cation radical et de l'anion radical du butadiène et du cation et de l'anion pentadiényl ont été calculés par la méthode semiempirique valence bond. Les résultats de ces calculs correspondent raisonnablement aux données expérimentales connues pour ces systèmes. Une comparaison des résultats théoriques avec les prédictions de la théorie de résonance donne des différences qui démontrent les limites de ce formalisme qualitatif.

     

Valence bond description for structures of O3, SO2 and NO

A modern valence bond approach, namely bonded tableau unitary group approach, is applied to ozone, sulphur dioxide and nitrite systems, respectively. It is shown that the biradical structure is in the primary position in describing the molecular structure of ozone. Thus three instead of two resonance structures are needed to describe the ground state of ozone. The case of sulphur dioxide is similar to that of ozone. It is found that, however, for the nitrite anion four resonance structures are needed.     

Valence bond corrected single reference coupled cluster approach

Summary An extension of the single reference coupled cluster method truncated to 1- and 2-body cluster components (CCSD) to quasidegenerate systems, where 3-and 4-body connected cluster components play an important role, is proposed. The basic idea is to extract the information concerning the 3- and 4-body clusters from some independent source, similarly as was implicitly done in the so-called ACPQ or ACC(S)D methods, and correct accordingly the absolute term in the CCSD equations. As a source of these approximate 3- and 4-body clusters, simple valence bond (VB) type wave functions are employed, since they are capable of describing electronic structure of various molecular systems for a wide range of nuclear conformations including their dissociation. The cluster analysis of these VB wave functions, that provides the desired information concerning the connected 3- and 4-body cluster components, is outlined and the explicit form of required correction terms to the CCSD equations is given.     

Ab initio studies of chemical equilibria. Equilibria containing first row hydrides AH2, AH3, and AH4 and their positive ions

Equilibrium constants were calculated for fourteen simple reactions involving AH₂, AH₃, and AH₄ first row hydrides and their positive ions. Except for the “experimental” correlation energies used, the theoretical approach is entirely non-empirical in character. The results suggest that if the correlation effects were accounted for in a more sophisticated way, most of the calculated equilibrium constants would be more reliable than the available experimental data.     

Physical nature of the chemical bond II. Valence atomic orbital and energy partitioning studies of linear nitriles

The valence atomic orbitals (VAO 's) of several linear nitriles are determined using non-empirical SCF –LCAO –MO wave functions expanded in a minimal (CN^?, HCN, FCN, C₂N₂), double-zeta (CN^?, HCN), or double-zeta + polarization (HCN) basis of Slater atomic orbitals (AO 's). The molecular energy of each system (except the double-zeta + polarization HCN system) is partitioned according to the procedure of Ruedenberg to obtain numerical values of nitrile C and N atomic and C?N bond components of the energy. In addition, the nitrile results are compared with minimal AO basis results obtained previously by other authors for homonuclear diatomics, diatomic hydrides and H₂O. The numerical data are used to test the internal self-consistency of the various definitions entering the partitioning method, i.e. whether or not analogous quantities assume similar values in chemically similar situations. The analysis of nitrile SCF –MO wave functions in terms of the set of VAO 's characteristic of the system under consideration is shown to be a promising approach to the problem of extracting useful information from the wave functions. In general, numerical results for the nitrile systems studied are fairly consistent with the concepts on which the partitioning method is based: promotion, quasi-classical interaction, sharing penetration, sharing interference and charge transfer. However, the VAO expansions for several energy components need to be investigated further and possibly revised.