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  • Atomic, Molecular and Optical Physics  (32)
  • Reaction paths  (4)
  • potential surfaces  (3)
  • 1
    Digitale Medien
    Digitale Medien
    Catchment region partitioning of energy hypersurfaces, I (1981)
    Springer
    Theoretical chemistry accounts 58 (1981), S. 309-330 
    Details
    ISSN: 1432-2234
    Schlagwort(e): Catchment regions ; Potential energy surfaces ; Reaction paths ; Chemical structure
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00553581
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  • 2
    Digitale Medien
    Digitale Medien
    Catchment region partitioning of energy hypersurfaces, I (1981)
    Springer
    Theoretical chemistry accounts 58 (1981), S. 309-330 
    Details
    ISSN: 1432-2234
    Schlagwort(e): Catchment regions ; Potential energy surfaces ; Reaction paths ; Chemical structure
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02426907
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  • 3
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Potential energy surfaces ; Reaction paths ; Transition states
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00554117
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  • 4
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Potential energy surfaces ; Reaction paths ; Transition states
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02404586
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  • 5
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Reaction mechanism ; group theory of reaction mechanism ; reaction topology ; potential surfaces ; reaction path ; synthesis planning
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00555021
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  • 6
    Digitale Medien
    Digitale Medien
    The topology of energy hypersurfaces IV. Generator sets for the fundamental group of reaction mechanisms and the complete set of reaction paths (1985)
    Springer
    Theoretical chemistry accounts 67 (1985), S. 91-113 
    Details
    ISSN: 1432-2234
    Schlagwort(e): Reaction mechanisms ; synthesis planning ; molecular design ; potential surfaces ; reaction path
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Abstract A countable set of distinguished fundamental reaction mechanisms on a potential surface serves as the set of generators for the fundamental group of reaction mechanisms. The effects of a change in the upper limit for energy on such groups are described with the aid of a lower semilattice, introduced into the family of all fundamental groups of reaction mechanisms, supported by the given potential energy surface. The algebraic structure of all reaction paths is described with the aid of groupoids and various subgroupoids and semigroups derived from them.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00547897
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  • 7
    Digitale Medien
    Digitale Medien
    The topology of energy hypersurfaces V. Potential-defying chemical species: a global analysis of vibrational stabilization and destabilization on potential energy hypersurfaces (1985)
    Springer
    Theoretical chemistry accounts 67 (1985), S. 115-136 
    Details
    ISSN: 1432-2234
    Schlagwort(e): Potential-defying chemical species ; vibrational stabilization ; potential surfaces ; zero-point energy ; tunneling
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Abstract Local and global topological criteria for the existence or non-existence of “potential defying” chemical species are investigated. The number and type of chemical structures which are not indicated by the qualitative features of potential surfaces and which owe their existence to an interplay of vibrational stabilization and destabilization in various domains of potential surfaces are related to topological invariants of compact manifolds. The topological analysis implies that potential defying species (including both stable and transition structures) never occur alone, but several of them occur simultaneously. Conditions are given for the minimum number of potential defying species of various types.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00547898
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  • 8
    Digitale Medien
    Digitale Medien
    Manifold theory of multidimensional potential surfaces (1981)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 20 (1981), S. 185-196 
    Details
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: Local coordinate systems are introduced into open sets of topological spaces, defined for the nuclear configuration space R of polyatomic nuclear systems. The open sets are directly related to common chemical concepts, such as chemical structure, reaction mechanism, and stability of reaction paths. A topological model of molecules and chemical reactions is a generalization of the geometrical model, and is particularly suitable to account for the nonrigid nature of chemical structures. The coordinate neighborhoods defined on R and on its submanifolds represent the extent and natural limits for partial analyses of multidimensional potential surfaces.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/qua.560200716
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  • 9
    Digitale Medien
    Digitale Medien
    A molecular geometry invariant property of energy level set boundaries in z space (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 24 (1983), S. 523-526 
    Details
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: Boundaries of electronic energy level sets in the nuclear charge space wZ can be parametrized as single valued functionals for any nuclear geometry of molecules, which property, combined with the general convexity of such level sets, leads to various electronic energy inequalities.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/qua.560240602
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  • 10
    Digitale Medien
    Digitale Medien
    Hyperspherical coordinate representation of potential surfaces of large molecules (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 267-272 
    Details
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: In a previous study an energy criterion has been applied for the simplification of the enumeration problem of various conformers of biomolecules. In the present note, the above energy criterion is combined with a spatial criterion that in general leads to a reduction in the size of those domains of biomolecule potential surfaces within which the search for chemically important conformers is warranted. The above model and the conformational domains of primary interest can be formulated in a hyperspherical representation. Advantages and disadvantages of representing biomolecule potential surfaces in terms of hyperspherical coordinates are discussed.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/qua.560260728
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