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  • 1
    Electronic Resource
    Electronic Resource
    Extended hessian matrix along the reaction coordinate (1981)
    Springer
    Theoretical chemistry accounts 58 (1981), S. 301-308 
    Details
    ISSN: 1432-2234
    Keywords: Extended Hessian matrix ; Vibration theory ; Rigged Riemannian space ; Intrinsic reaction coordinate (IRC) approach
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract We shall prove by the coordinate-free covariant treatment that the vibrational frequency along the reaction coordinate is exactly given by the extended Hessian matrix in a rigged configuration space where the reaction coordinate is identified with a “straight line”. The diagonalization of the extended Hessian matrix is straightforward with no recourse to the prescribed procedure of eliminating the coupling matrix elements between the promoting mode of chemical reaction and the vibrational modes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02426906
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  • 2
    Electronic Resource
    Electronic Resource
    Differential geometry of chemically reacting systems (1978)
    Springer
    Theoretical chemistry accounts 49 (1978), S. 321-347 
    Details
    ISSN: 1432-2234
    Keywords: Reaction coordinate ; Intrinsic reaction coordinate (IRC) approach ; Chemically reacting systems, differential geometrical study of ∼
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract This paper is a detailed differential geometrical study of chemically reacting systems. In particular the following coordinate-free properties of chemically reacting systems are obtained: 1) the general solution of the intrinsic reaction coordinate (IRC) (henceforth referred to as meta-IRC), 2) “extended” definitions of the Hessian matrix and normal vibrations at any non-equilibrium point on the surface, and 3) clarification of the close connection between the geometry of meta-IRC and the geography of the surface at a transition point. The theory is elucidated using a model potential surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00552483
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  • 3
    Electronic Resource
    Electronic Resource
    Intrinsic dynamism in chemically reacting systems (1979)
    Springer
    Theoretical chemistry accounts 51 (1979), S. 189-206 
    Details
    ISSN: 1432-2234
    Keywords: Intrinsic dynamism ; Intrinsic reaction coordinate (IRC) approach ; Chemically reacting systems,cell structure of ∼ ; Stable limit theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The geometrical cell structure of the chemically reacting system is discussed. The boundary of the cell uniquely defines the dividing surface between the initial reactant side and the final product side. Introducing the concept of the intrinsic reaction time (IRT) and the accumulation time (AT) of reaction along the meta-IRC (intrinsic reaction coordinate), the intrinsic dynamism in the cell is discussed. Then, the stable limit theorems with respect to the intrinsic nature of the normal vibrations are derived. The theory is elucidated by using a model potential surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00572927
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  • 4
    Electronic Resource
    Electronic Resource
    Intrinsic field theory of chemical reactions (1979)
    Springer
    Theoretical chemistry accounts 51 (1979), S. 275-296 
    Details
    ISSN: 1432-2234
    Keywords: Intrinsic field theory ; Intrinsic reaction coordinate (IRC) approach ; Intrinsic principle of least action ; Geodesic law ; Structural stability ; Dynamical potential field
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract An intrinsic principle of least action is presented for the intrinsic dynamism of chemical reactions. Then, as the stationary trajectory, a meta-IRC (intrinsic reaction coordinate) draws a geodesic curve in a rigged Riemannian space. This establishes a geodesic law for the intrinsic dynamism. Moreover, a diagrammatic perturbation theory is formulated for the intrinsic dynamism, and a dynamical interaction between a chemically reacting system and a background system is investigated. Then, the structural stability of the system is discussed using a new concept of the dynamical potential field. An example is given in order to elucidate the present theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00548937
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  • 5
    Electronic Resource
    Electronic Resource
    Novel variational principles of chemical reaction (1980)
    Springer
    Theoretical chemistry accounts 57 (1980), S. 81-94 
    Details
    ISSN: 1432-2234
    Keywords: Minimum principle ; Intrinsic reaction coordinate (IRC) approach ; Geodesic law ; Intrinsic principle of least action
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Minimum principles of chemical reaction coordinates are established. IRC (intrinsic reaction coordinate) draws the path of minimum distance from reactant to product. The distance is measured in the rigged configuration Riemannian space whose metric is determined by the distribution of the adiabatic potential energy. Moreover, minimum property of the intrinsic principle of least action is established for the intrinsic dynamism of chemical reaction. Minimum principle of the path connecting intercell boundary with cell is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00547999
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  • 6
    Electronic Resource
    Electronic Resource
    Extended hessian matrix along the reaction coordinate (1981)
    Springer
    Theoretical chemistry accounts 58 (1981), S. 301-308 
    Details
    ISSN: 1432-2234
    Keywords: Extended Hessian matrix ; Vibration theory ; Rigged Riemannian space ; Intrinsic reaction coordinate (IRC) approach
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract We shall prove by the coordinate-free covariant treatment that the vibrational frequency along the reaction coordinate is exactly given by the extended Hessian matrix in a rigged configuration space where the reaction coordinate is identified with a “straight line”. The diagonalization of the extended Hessian matrix is straightforward with no recourse to the prescribed procedure of eliminating the coupling matrix elements between the promoting mode of chemical reaction and the vibrational modes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00553580
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