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  • 1
    Electronic Resource
    Electronic Resource
    Reactive domains of energy hypersurfaces and the stability of minimum energy reaction paths (1980)
    Springer
    Theoretical chemistry accounts 54 (1980), S. 95-111 
    Details
    ISSN: 1432-2234
    Keywords: Potential energy surfaces ; Reaction paths ; Transition states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Special properties of the Riemannian metric for energy hypersurfaces, defined within the framework of the Born-Oppenheimer approximation, are utilized in devising a partitioning scheme for domains of nuclear coordinates. The chemically important coordinate domains are distinguished from domains of lesser importance by their curvature properties. Conditions are derived for the stability of minimum energy reaction paths, and the effects of instability regions are investigated. Instability domains along minimum energy paths may allow small vibrational perturbations to alter the outcome of the chemical reaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02404586
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  • 2
    Electronic Resource
    Electronic Resource
    Catchment region partitioning of energy hypersurfaces, I (1981)
    Springer
    Theoretical chemistry accounts 58 (1981), S. 309-330 
    Details
    ISSN: 1432-2234
    Keywords: Catchment regions ; Potential energy surfaces ; Reaction paths ; Chemical structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The space of internal coordinates of a molecular system is partitioned into catchment regions of various critical points of the energy hypersurface. The partitioning is based on an ordering of steepest descent paths into equivalence classes. The properties of these catchment regions and their boundaries are analyzed and the concepts of chemical structure, reaction path and reaction mechanism are discussed within the framework of the Born-Oppenheimer and energy hypersurface approximations. Relations between catchment regions and the chemically important reactive domains of energy hypersurfaces, as well as models for “branching” of reaction mechanisms, caused by instability domainsD μ, μ ≥ 1, are investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00553581
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  • 3
    Electronic Resource
    Electronic Resource
    Catchment region partitioning of energy hypersurfaces, I (1981)
    Springer
    Theoretical chemistry accounts 58 (1981), S. 309-330 
    Details
    ISSN: 1432-2234
    Keywords: Catchment regions ; Potential energy surfaces ; Reaction paths ; Chemical structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The space of internal coordinates of a molecular system is partitioned into catchment regions of various critical points of the energy hypersurface. The partitioning is based on an ordering of steepest descent paths into equivalence classes. The properties of these catchment regions and their boundaries are analyzed and the concepts of chemical structure, reaction path and reaction mechanism are discussed within the framework of the Born-Oppenheimer and energy hypersurface approximations. Relations between catchment regions and the chemically important reactive domains of energy hypersurfaces, as well as models for “branching” of reaction mechanisms, caused by instability domainsD μ, μ ≥ 1, are investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02426907
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  • 4
    Electronic Resource
    Electronic Resource
    Topology of energy hypersurfaces (1982)
    Springer
    Theoretical chemistry accounts 62 (1982), S. 133-161 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF00581478
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  • 5
    Electronic Resource
    Electronic Resource
    The topology of energy hypersurfaces II. Reaction topology in euclidean spaces (1983)
    Springer
    Theoretical chemistry accounts 63 (1983), S. 9-33 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF00549152
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  • 6
    Electronic Resource
    Electronic Resource
    Reactive domains of energy hypersurfaces and the stability of minimum energy reaction paths (1980)
    Springer
    Theoretical chemistry accounts 54 (1980), S. 95-111 
    Details
    ISSN: 1432-2234
    Keywords: Potential energy surfaces ; Reaction paths ; Transition states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Special properties of the Riemannian metric for energy hypersurfaces, defined within the framework of the Born-Oppenheimer approximation, are utilized in devising a partitioning scheme for domains of nuclear coordinates. The chemically important coordinate domains are distinguished from domains of lesser importance by their curvature properties. Conditions are derived for the stability of minimum energy reaction paths, and the effects of instability regions are investigated. Instability domains along minimum energy paths may allow small vibrational perturbations to alter the outcome of the chemical reaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00554117
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  • 7
    Electronic Resource
    Electronic Resource
    The topology of energy hypersurfaces III. The fundamental group of reaction mechanisms on potential energy hypersurfaces (1985)
    Springer
    Theoretical chemistry accounts 67 (1985), S. 43-61 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00555021
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