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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 63 (1983), S. 9-33 
    ISSN: 1432-2234
    Keywords: Potential energy surfaces ; Computer-aided synthesis design ; Quantum chemical synthesis design ; Reaction mechanism ; Reaction networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract By introducing equivalence classes of critical points of potential energy hypersurfaces a unique topological space, Reaction Topology (3N E, T C ) is defined over an Euclidean nuclear configuration space 3N E for a system of N nuclei and k electrons. Relations between the topological concepts of molecular structure and reaction mechanism are analyzed. Topological equivalences between Euclidean and Riemannian representations of nuclear configuration spaces are exploited for the analysis of quantum mechanical reaction networks of all possible chemical reactions over the given potential energy hypersurface.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 67 (1985), S. 43-61 
    ISSN: 1432-2234
    Keywords: Reaction mechanism ; group theory of reaction mechanism ; reaction topology ; potential surfaces ; reaction path ; synthesis planning
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The family of all possible reaction mechanisms on a potential surface has an algebraic structure with potential applications in quantum chemical molecular design and synthesis planning. Transformation properties and equivalence relations of reaction paths on potential energy hypersurfaces lead to a topological definition of reaction mechanisms. The family of all fundamental reaction mechanisms on the hypersurface has a group structure,the fundamental group of an appropriately defined topological space. Isomorphism and homomorphism relations between fundamental groups of reaction mechanisms are used to characterize the chemically important topological properties of various subsets of a hypersurface, or those of different excited state hypersurfaces.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 62 (1982), S. 133-161 
    ISSN: 1432-2234
    Keywords: Reaction topology ; Potential energy surfaces ; Reaction path ; Chemical structure ; Reaction mechanism
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Some of the basic notions of chemistry, associated with an energy function of several variables, are shown to be of topological character. Properties of potential energy hypersurfaces, structural relations, models for interconversion processes and transformations between such models suggest a topological theory (reaction topology) for the analysis of potential energy hypersurfaces. By introducing appropriate topologies into the nuclear configuration spaceR and equivalent topologies on the energy hypersurfaceE, rigorous definitions are given for fundamental chemical concepts such asmolecular structure andreaction mechanism. These definitions are based on the properties of the expectation value of energy, a quantum mechanical observable. Topologies based on curvature, structural and energetic relations of the energy hypersurface are proposed for a theoretical interpretation of molecular processes.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 59 (1980), S. 321-332 
    ISSN: 1432-2234
    Keywords: Electronic energy ; Potential energy surfaces ; Isoelectronic molecules ; Upper and lower bounds for energy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Within the Born-Oppenheimer approximation an inequality relation is derived between points of electronic energy hypersurfaces of pairs of isoelectronic molecules. The inequality is directly applicable to point pairs fulfilling a symmetry criterion for the nuclear frameworks and it may be extended to coordinate domains on both hypersurfaces. The result is applied to special examples of conformational problems, dissociation reactions and impurity —vacancy centres in solid clusters.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 59 (1981), S. 321-332 
    ISSN: 1432-2234
    Keywords: Electronic energy ; Potential energy surfaces ; Isoelectronic molecules ; Upper and lower bounds for energy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Within the Born-Oppenheimer approximation an inequality relation is derived between points of electronic energy hypersurfaces of pairs of isoelectronic molecules. The inequality is directly applicable to point pairs fulfilling a symmetry criterion for the nuclear frameworks and it may be extended to coordinate domains on both hypersurfaces. The result is applied to special examples of conformational problems, dissociation reactions and impurity —vacancy centres in solid clusters.
    Type of Medium: Electronic Resource
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