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  • 11
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 15 (1969), S. 174-180 
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Ein Modell für die Reaktion CH 3 . +CH2=CH2 wird untersucht, einschließlich der Änderung der Hybridisation des Reaktionszentrums. Die Wechselwirkungsenergie wird in zwei Teile zerlegt. Der erste Teil ist eine Stabilisationsenergie — der Beitrag, der der Delokalisierung des π-Elektrons (einschließlich Hybridisationseffekte) entspricht. Der zweite Teil ist eine Austauschabstoßung, die von allen Valenzelektronen der drei Kohlenstoffatome herrührt. Korrellationskorrekturen werden berücksichtigt. Eine Fläche der potentiellen Energie wird konstruiert mit einem Sattelpunktswert, der dicht an der experimentellen Aktivierungsenergie liegt. Die verwendeten Näherungsmethoden werden diskutiert. Die vorgeführte Methode ist eine Verallgemeinerung der Methode der Reaktivitätsindices aus der Theorie der chemischen Reaktivität. Sie kann als eine Rechtfertigung dieser mehr empirischen Näherung angesehen werden.
    Abstract: Résumé Etude d'un modèle pour la réaction CH 3 . +CH2=CH2 où l'on tient compte du changement d'hybridation du centre réactif. L'énergie d'interaction est divisée en deux termes. Le premier est une énergie de stabilisation; c'est la contribution dela délocalisation des électrons π (effets d'hybridation compris). Il est calculé par la méthode PPP. Le second terme est une répulsion d'échange dûe à tous les électrons de valence des trois atomes de carbone. Les corrections de corrélation sont introduites. Une surface d'énergie potentielle est construite; elle fournit une valeur de l'énergie d'activation proche de celle obtenue expérimentalement. Les approximations utilisées sont discutées. La méthode proposée est une généralisation de celles des indices de réactivité. On peut la considérer comme justifiant cette approche plus empirique.
    Notes: Abstract A model for the reaction CH 3 . +CH2=CH2 is studied including the hybridization change of the reaction center. The interaction energy is devided into two parts. The first is a stabilization energy — the contribution due to the π-electron delocalization (including the hybridization effects). It is computed by the PPP method. The second part is an exchange repulsion due to all valence electrons of the three carbon atoms. Correlation corrections are considered. A potential energy surface is constructed, giving a saddle point value close to the experimental activation energy. A discussion is given of the approximations involved. The method suggested is a generalization of the reactivity indices method of the theory of chemical reactivity. It can be regarded as a justification of this more empirical approach.
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 72 (1987), S. 63-67 
    ISSN: 1432-2234
    Keywords: Potential energy surfaces ; Branching points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The chemically interesting potential energy surfaces (PES) are considered on which the conditions underlying application of structural stability principle and Morse inequalities are violated. The possibility of treatment of singular branching points on a PES slope in terms of intrinsic reaction curves (IRC) is discussed.
    Type of Medium: Electronic Resource
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  • 13
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 23-45 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In order to treat the interaction energy of two molecules a standard Rayleigh-Schrödinger perturbation theory is developed. The Hartree-Fock functions of the separated molecules are used as one particle basis functions, the initial set of states being truncated and non-orthogonal. The non-orthogonality is included into the Hamiltonian by orthogonalization of the basis set. The unperturbed Hamiltonian is chosen so that it possesses the correct symmetry properties with respect to the electron permutations between different molecules. The procedure of this kind automatically results in the appearance of charge transfer states.A graphical technique is elaborated which is a modified version of the Feynman-Goldstone technique and provides a convenient representation of the interaction energy contributions of any order. As an example the first- and the second-order diagrams are considered.A correct expression for the dispersion energy is obtained which differs by a factor from that of the theory using a nonsymmetrical zero approximation.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 14
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 17 (1980), S. 399-413 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An attempt is made to refine the physical background underlying qualitative quantum-chemical concepts that are an essential component of the modern theory of chemical reactivity. The energy of electron delocalization in a transition state (stabilization energy, SE) is used as a measure of chemical reactivity. Using Coulson's integral representation for bond order matrix enables one to present the Woodward-Hoffmann rules and the effects of conjugated substitutents as theorems for a Hückel SE in alternant systems. A part of the results are extended to heteroatomic systems. The validity of the present treatment is discussed in terms of the SCF PPP theory.
    Type of Medium: Electronic Resource
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  • 15
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 19 (1981), S. 611-635 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A direct method for calculating resonant states in reactive scattering is suggested, permitting us to obtain the characteristics of multichannel resonances (partial width amplitudes). The method is based on the construction of a Laurent expansion of the scattering matrix S(∊ -iΓ/2) in the complex plane. The position of the poles of the S matrix are derived by solving the dynamical problem with complex energy values. The residue at the pole gives all the information concerning the partial widths. The method is applied to a linear triatomic reactive scattering problem. The properties of the resonant states in the H + H2 system are calculated as an example. Two broad resonances are found which have not been reported in previous calculations. The interference of overlapping resonances is shown to have a profound effect on the energy dependence of the transition probabilities.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 16
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We suggest the explicit transformation of the parametrized atomic φ-basis semiempirical Hamiltonian to the Löwdin λ basis. A nontrivial problem then arises concerning the transformation of the four-index electron interaction matrix Γ, for which parametrization is given in the φ basis, whereas the NDO approximation is introduced in the λ basis. The main result is that under the CNDO assumption the two-index Coulomb matrix can be transformed independently of other integrals of Γ. The explicit form of the transformation between the Coulomb matrix γ of parameters given in the φ basis and the Coulomb matrix λγ in the λ basis is found. The λγ calculated by this method differs only slightly from the result of the exact complicated four-index transformation. On the other hand the elements of γ and λγ may differ by several eV when overlap is significant.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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  • 17
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 555-574 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A self-consistent perturbation theory is derived in the framework of Roothaan's MOLCAO procedure for closed shell systems. Contrary to previous investigations which have considered only one particle perturbations, two particle perturbation operators are considered. Expressions for the first-order density matrix and first- and second-order energy corrections are obtained. A diagram formulation of the complete perturbation expansion is presented.The results are applied to the treatment of the intermolecular interaction problem. The interaction energy is represented as a sum of several contributions: Coulomb, exchange, resonance, polarization and exchange repulsion. A semi-empirical version of the theory is suggested which explicitly involves all the physically significant energy terms and may be useful for the investigation of complex systems.
    Type of Medium: Electronic Resource
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  • 18
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 467-489 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A variational calculation of the interaction between two H2 molecules using minimal basis set of 1s functions is performed to check the efficiency of various versions of the perturbation theory for intermolecular interactions. The matrix procedure starting with the zero-order Hamiltonian which is symmetric with respect to intermolecular electron permutations shows better convergence than the procedures using nonsymmetric zero approximations. This conclusion follows from the calculations of ground state and four lowest excited states for three geometric configurations of the H4 system. The behaviour of the potential curves is interpreted in terms of symmetric perturbation theory. The various contributions to the interaction energy are considered in detail. The importance of charge transfer states for the description of the intermediate range of intermolecular separations is specially emphasized.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 19
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We have analyzed two approaches to reproduce the resonance expansion of the scattering matrix appropriate for the calculation of molecular resonance states. The first is based on the resonance theory of Siegert-Humblet-Rosenfeld (SHR) and the second on the Fano-Feshbach formalism. The direct method of calculating the resonance expansion characteristics, devised on the basis of the SHR theory, makes it possible to obtain the energies and partial widths (detailed decay rate constants) of resonances. The Fano-Feshbach formalism, on the other hand, elucidates the resonance state as a concept and facilitates the interpretation of calculation results. The use of computational methods is illustrated by the study of the decay of a model triatomic system and of gas-phase nucleophilic substitution reactions. Used in the latter case is the division of all degrees of freedom of the reacting system into the adiabatic and dynamic ones along with an algorithm of inclusion of the restricted dynamical treatment in the calculation of reaction rate constants.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 20
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Chemical Kinetics 11 (1979), S. 853-865 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A procedure is suggested to estimate the positions of a transition state (TS) along the reaction coordinate in reaction series involving several radical reactions. It is based on the dependence between experimental activation energies U± and heat effects Q. Taking into account the shift of a TS position, the following relation between these quantities is obtained: U± -; U0± = A (Q - Q0)2 + B(Q - Q0). The subscript 0 indicates the standard reference reaction. For three series, namely, the hydrogen abstraction from hydrocarbon substrates by radicals CH3·, CF·3, and Br·, the bond lengths characterizing the TS reaction center are evaluated. The TS positions appear to vary significantly in the reaction series, which accounts for significant changes in the experimentally observed activation volumes. The derivation of the Hammond rule and the range of its validity for the series with polar and steric substituent effects are discussed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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