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  • 1
    Electronic Resource
    Electronic Resource
    The topology of catchment regions of potential energy hypersurfaces (1999)
    Springer
    Theoretical chemistry accounts 102 (1999), S. 279-284 
    Details
    ISSN: 1432-2234
    Keywords: Key words: Catchment regions ; Potential energy surfaces ; Molecular conformation analysis ; Fundamental group of reaction mechanisms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. A simple proof is presented for a fundamental topological property of catchment regions of potential energy hypersurfaces: each catchment region C(λ,i), representing a chemical species and its conformational range on the potential energy hypersurface, is simply k-connected for each dimension k=1,2,…3N−6−λ, where λ is the index of the catchment region. The consequences of this property on the structure of the fundamental group of reaction mechanisms (the one-dimensional homotopy group of reaction paths) is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002140050499
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  • 2
    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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  • 3
    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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  • 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
    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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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Quantum chemical reaction networks, reaction graphs and the structure of potential energy hypersurfaces (1982)
    Springer
    Theoretical chemistry accounts 60 (1982), S. 409-428 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF00548695
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  • 8
    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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  • 9
    Electronic Resource
    Electronic Resource
    Electronic energy inequalities for isoelectronic molecular systems (1980)
    Springer
    Theoretical chemistry accounts 59 (1980), S. 321-332 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF00553391
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  • 10
    Electronic Resource
    Electronic Resource
    Electronic energy inequalities for isoelectronic molecular systems (1981)
    Springer
    Theoretical chemistry accounts 59 (1981), S. 321-332 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF02402397
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