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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 60 (1981), S. 97-110 
    ISSN: 1432-2234
    Keywords: Reaction topology ; Potential surfaces ; Reaction mechanisms ; Critical points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Topologies are introduced into the nuclear configuration space R of molecular systems, based upon equipotential contour hypersurfaces on the otential energy hypersurface E. Critical level topologies T fc and T fc′, based upon the number and distribution of various critical points of E, are of particular importance, since they represent convenient yet rigorous mathematical models for relations between elementary reaction mechanisms, and for relations between open sets of nuclear geometries which are classically accessible at a given total energy.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 60 (1982), S. 409-428 
    ISSN: 1432-2234
    Keywords: Potential energy surfaces ; Reaction topology ; Reaction graphs ; Reaction networks ; Reaction path
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Global properties of the Born-Oppenheimer energy expectation value functional, defined over the nuclear configuration space R, are analyzed. Quantum chemical reaction graphs and reaction networks are defined in terms of intersection graphs of connected sets of nuclear geometries, representing various chemical structures. The set of all possible reaction mechanisms on the given energy hypersurface and the associated activation energy conditions are analyzed using reachability matrices defined over digraphs D s(λ) and D s(λ, E).
    Type of Medium: Electronic Resource
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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 73 (1988), S. 221-228 
    ISSN: 1432-2234
    Keywords: Potential surfaces ; Conformation analysis ; Reaction topology ; Multicenter interactions ; Symmetry ; Periodicity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Symmetry and periodicity of potential energy surfaces of chemical reactions and conformational changes are determined by the symmetry properties of the nuclear frameworks of all possible nuclear configurations of the given overall stoichiometry. For example, a mirror plane of a nuclear configuration implies a mirror plane of the potential surface (or that of the potential energy hypersurface in higher dimensions), and a local rotational symmetry of substituents implies a translational symmetry, that is, periodicity of the potential surface, if the latter is defined in terms of the usual bond length/bond angle internal coordinates. Such symmetry relations on potential surfaces are rather trivial consequences of molecular symmetry properties; however, when taken collectively for entire domains of nuclear configurations, they lead to nontrivial conclusions. Whereas symmetry properties and energy contents of individual conformations can be studied locally within limited domains of the potential surface, a global analysis of the potential surface may reveal significantly more. In this note, some consequences of the above approach are explored, and a simple test is proposed for the detection and evaluation of the importance of multicenter interactions in conformers related to one another by bond rotations.
    Type of Medium: Electronic Resource
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