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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
    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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  • 5
    Electronic Resource
    Electronic Resource
    The fundamental syntopy of quasi-symmetric systems: Geometric criteria and the underlying syntopy of a nuclear configuration space (1993)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 45 (1993), S. 177-187 
    Details
    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: Point symmetry is a discrete concept; A nuclear configuration for a given stoichiometry either has or has not a particular point symmetry. By contrast, both static and dynamic properties of actual molecules exhibit continuous features. Using the formalism of fuzzy-set theory, we had previously proposed the concept of syntopy as a continuous extension of the symmetry concept for quasi-symmetric systems: This was based on an energetic criterion taking into account the energy costs of nuclear rearrangements. This extension of symmetry was necessarily dependent on the considered electronic state: For a given geometric arrangement of the nuclei, the energy cost of some rearrangement is dependent on the actual potential surface, that is, on the electronic state, in the Born-Oppenheimer approximation. In the extension of the syntopy model reported in the present work, we consider a syntopy criterion that is common to all electronic states. The syntopy thus defined - called the fundamental syntopy of the reduced nuclear configuration space - is independent of the potential surface and of the electronic state: It is defined only in terms of a geometric condition, which makes it more appropriate to rationalize mesoscopic structures. This new syntopy model provides a connection between all possible syntopies generated by the various potential-energy surfaces supported by the considered family of atomic nuclei. © 1993 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560450205
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  • 6
    Electronic Resource
    Electronic Resource
    Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. I (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 53 (1995), S. 375-386 
    Details
    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: The present article develops a methodology and a unifying theorem to treat, on an equal footing, mathematical phenomena that were hitherto studied separately in each of the research fields of dynamical systems and quantum chemistry involving the spectral symmetry of alternant hydrocarbons. This article also serves as a foundation of a theoretical framework for the analysis of certain dynamical systems of chemical kinetic equations, which shall be made in the context of operator algebra in Parts II and III of this series of papers. © 1995 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560530404
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  • 7
    Electronic Resource
    Electronic Resource
    A topological analysis of molecular shape and structure (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 59 (1996), S. 379-390 
    Details
    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 a novel approach to molecular shape representation, molecular electronic density functions are treated as 3D hypersurfaces in a 4D Euclidean space, spanned by the three spatial coordinates and an electronic density threshold variable. The general objects resulting from this approach are topological spheres with handles, modeling the electron density. Based on this model, a new, simple representation of molecular topology of electron density is proposed, using a tree describing the evolution of topological spheres with handles as function of a varying density threshold. The vertices of the tree are characterized by nonnegative integers (the genea of the topological objects). This representation is compared to earlier, detailed 3D topological descriptions of molecular shape as well as to the more conventional molecular network (bond skeleton) representation. A variety of relevant topological equivalence relations of molecules are discussed and a new, global, molecular similarity measure is proposed. © 1996 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Representation of square-cell configurations in the complex plane: Tools for the characterization of molecular monolayers and cross sections of molecular surfaces (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 43 (1992), S. 375-392 
    Details
    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: Two numerical codes, a complex face vector F and a real face vector D are developed for the characterization of square-cell configurations (lattice animals), used for representing the shapes of molecular monolayers and cross sections of molecular surfaces. The real face vector D represents all the intrinsic properties, size, and shape of the lattice animal. The complex face vector F contains complete information about the size, the shape, and also the placement of the particular lattice animal with respect to the lattice. Based on the properties of the face vectors, a method is developed for the classification of similar animals into equivalence classes. The face vector method is proposed for an algorithmic, nonvisual computer analysis of similarity of shapes of molecular monolayers and planar domains of cross sections of molecular surfaces, approximated by lattice animals.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560430307
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  • 9
    Electronic Resource
    Electronic Resource
    Relations among functional groups within a stoichiometry: A nuclear configuration space approach (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 43 (1992), S. 647-658 
    Details
    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 general scheme is proposed for the study of the interrelations and transformations of flexible functional groups within the configuration space M of all possible chemical species of a fixed overall stoichiometry S. The methods presented provide a concise but sufficiently detailed description of the occurrence of various functional groups in different families of nuclear arrangements, as well as their transformations into one another during chemical reactions and conformational changes. The approach uses experimental information on the importance of various functional groups, topological criteria for the flexibility of these functional groups, and the fundamental pattern of distribution of configurational families within the nuclear configuration space. The resulting schemes have simple, easily programmable representations. © 1992 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560430504
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  • 10
    Electronic Resource
    Electronic Resource
    Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. II (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 53 (1995), S. 387-406 
    Details
    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: The methodology and theoretical framework of Part I of this series of articles have been further developed to the setting of the Banach algebra B(B), of all bounded operators acting on a Banach space B. Using the above setting B(B), certain dynamical systems of chemical kinetic equations are illustrated in conjunction with Part I and with the analysis of more general systems, some of which will be made in Part III of this series of articles. The main theorem and its auxiliary theorem in the present article elucidate in a unifying manner the structure and the underlying pattern of the spectral symmetry of linear operators (acting on Banach spaces and Hilbert spaces) that are investigated in each of the research fields of dynamical systems and quantum chemistry involving the spectral symmetry of alternant hydrocarbons. © 1995 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560530405
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