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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 1470-1480 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider an interconnection between the oscillator (spin-boson) model of the continuum outer-sphere electron transfer (ET) reaction and its stochastic dynamical description in terms of generalized Langevin equation (GLE) for longitudinal polarization. The oscillator Hamiltonian derived from the GLE can be reduced to its conventional spin-boson form in the limit of the infinite frequency of the primary polarization mode, called solvaton coordinate. In the framework of the Golden Rule approximation the ET rate expressions of both (solvaton and spin-boson) theories are exactly the same. This is shown without invoking a condition of the infinite solvaton frequency. A hypothesis concerned with a physical nature of bath oscillators is suggested. These modes, embodying dielectric friction effects within the GLE description, are associated with transverse polarization waves of a continuum medium. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 1607-1618 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Polyexponential kinetical behavior typical for condensed phase reactions in highly viscous media is studied on a simple example of one-dimensional diffusion equation with a sink modeling a chemical conversion of reactants. The corresponding polyexponential regime is demonstrated to have a thorough analogy with the quasiclassical approximation of one-dimensional quantum mechanics and a relevant approximation for the Green's function is developed. The asymptotic short- and long-time kinetics are examined at the analytical level. Contrary to the frozen medium approximation according to which the slow diffusion motion of the medium is entirely ignored, the present quasiclassical model is fit for a qualitative description of the total time interval covering the reaction events from the initial moment up to the ultimate steady-state monoexponential evolution. The range of validity of the quasiclassical approach is discussed. Numerical tests expose some peculiarities of the present treatment for equilibrium and nonequilibrium initial distributions. The work presents a qualitative development of the theory of nonexponential kinetics pioneered by papers of Agmon and Hopfield, Sumi and Marcus, and Nadler and Marcus. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 97 (1993), S. 3270-3277 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 3734-3746 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Born–Kirkwood–Onsager (BKO) model of solvation, where a solute molecule is positioned inside a cavity cut into a solvent, which is considered as a dielectric continuum, is studied within the bounds of nonlocal electrostatics. The nonlocal cavity model is explicitly formulated and the corresponding nonlocal Poisson equation is reduced to an integral equation describing the behavior of the charge density induced in the medium. It is found that the presence of a cavity does not create singularities in the total electrostatic potential and its normal derivatives. Such singularities appear only in the local limit and are completely dissipated by nonlocal effects. The Born case of a spherical cavity with a point charge at its centre is investigated in detail. The corresponding one-dimensional integral Poisson equation is solved numerically and values for the solvation energy are determined. Several tests of this approach are presented: (a) We show that our integral equation reduces in the local limit to the chief equation of the local BKO theory. (b) We provide certain approximations which enable us to obtain the solution corresponding to the preceding nonlocal treatment of Dogonadze and Kornyshev (DK). (c) We make a comparison with the results of molecular solvation theory (mean spherical approximation), as applied to the calculation of solvation energies of spherical ions. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 2848-2848 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 1103-1114 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A local continuum solvation theory, exactly treating electrostatic matching conditions on the boundary of a cavity occupied by a solute particle, is extended to cover time-dependent solvation phenomena. The corresponding integral equation is solved with a complex-valued frequency-dependent dielectric function cursive-epsilon(ω), resulting in a complex-valued ω-dependent reaction field. The inverse Fourier transform then produces the real-valued solvation energy, presented in the form of a time correlation function (TCF). We applied this technique to describe the solvation TCF for a benzophenone anion in Debye (acetonitrile) and two-mode Debye (dimethylformamide) solvents. For the Debye solvent the TCF is described by two exponential components, for the two-mode Debye solvent, by three. The overall dynamics in each case is longer than that given by the simple continuum model. We also consider a steady-state kinetic regime and the corresponding rate constant for adiabatic electron-transfer reactions. Here the boundary effect introduced within a frequency-dependent theory generates only a small effect in comparison with calculations made within the static continuum model. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 6083-6094 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The dynamical model of tunneling interlevel transitions is extended to describe the kinetics of H-atom transfer in real reactions proceeding in the condensed phase. The reaction mechanism includes an explicit consideration of three modes; the high-frequency reactive motion of the H atom, the low-frequency intermolecular promotion mode, and an intramolecular mode which changes significantly during the reaction and is associated with the hybridization geometry changes of the reaction center. The rate constant expression is derived in terms of the standard technique of the theory of radiationless transitions. Its high- and moderate-temperature analysis reproduces the results obtained earlier in the framework of the Golden Rule approach. Peculiarities of the present theory are revealed beyond this temperature range. A remarkable low-temperature threshold effect causes steep temperature trends in the reaction rate which are likely to account for some recent kinetic experiments. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 6072-6082 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We study how the quantization of energy levels affects the deep tunneling rate expression for a double-well system immersed in a harmonic bath. The model of tunneling transitions implies that the energy of a tunneling system is not conserved during a transition because its interaction with the environment is explicitly taken into account. The Golden Rule approach invoked usually cannot be directly applied for such a model. We consider its modification in which the expression for the rate constant depends symmetrically on spectral line shapes of energy levels in both reactant and product wells. The derivation is based on the Breit–Wigner resonance expansion of a dynamical transition probability which is extended on condensed phase systems and averaged at the next stage over fluctuations of the energy levels promoted by system/environment interactions. Test computations for a one-dimensional model case demonstrate novel features inherent to this approach which are clearly revealed in the low-temperature kinetic regime. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 13 (1969), S. 409-420 
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Für die Behandlung der Nicht-Orthogonalität von Atomfunktionen und die Korrelation der π-Elektronen wird eine Näherungsmethode vorgeschlagen, bei der die Pariser-Parr-Pople-(PPP)-Methode als nullte Näherung in einer Störungsrechnung verwendet wird. Die Formel für den Grundzustand von π-Systemen ist für die Beschreibung einiger Effekte geeignet, die in der PPP-Beschreibung nicht berücksichtigt werden. Insbesondere wird gezeigt, wie solche intermolekularen Phänomene wie Abstoßung infolge Austausch und Dispersions-Wechselwirkung bei der MO-Methode berücksichtigt werden können. Die Energie des Grundzustandes von π-Elektronensystemen wird mit und ohne Berücksichtigung der π-Elektronenkorrelation berechnet. Wenn für die Atomfunktionen die Nicht-Orthogonalität berücksichtigt wird, so können die experimentellen Werte dieser Energie mit Hilfe eines „spektroskopischen“ Satzes von Standardparametern erhalten werden. Vermutlich ist es möglich, im Rahmen dieser Methode, die spektroskopischen, thermochemischen und kinetischen Daten einheitlich und konsistent zu beschreiben.
    Abstract: Résumé On propose une méthode approchée pour traiter la non orthogonalité des fonctions atomiques et la corrélation des électrons π au moyen de la théorie des perturbations utilisant l'approximation de la méthode de Pariser-Parr-Pople comme ordre zéro. La formule obtenue pour l'énergie du fondamental permet de décrire un certain nombre d'effets dont la théorie PPP ne peut rendre compte. En particulier on montre comment certains phénomènes intermoléculaires comme la répulsion d'échange et la dispersion peuvent être pris en considération. L'énergie de l'état fondamental des systèmes d'électrons π est calculée avec et sans corrélation. Si la non orthogonalité des fonctions d'onde atomiques est incluse, les valeurs expérimentales de ces énergies peuvent être décrites en utilisant un ensemble «spectroscopique» de paramètres standards. Dans le cadre de cette méthode il est probablement possible de décrire simultanément les propriétés spectroscopiques, thermochimiques et cinétiques.
    Notes: Abstract An approximate method is proposed for treating the non-orthogonality of atomic functions and correlation of π-electrons by means of perturbation theory and Pariser-Parr-Pople (PPP) method as a zero approximation. The formula derived for the ground state energy of π-systems is suitable to describe a number of effects, which the PPP theory, in principle, cannot account for. In particular, it is shown how such intermolecular phenomena like exchange repulsion and dispersion interaction can be accounted for in MO method. The ground state energies of π-electron systems are calculated with and without an account of π-electron correlation. If for the atomic functions non-orthogonality is taken into consideration the experimental values of these energies can be described using a “spectroscopic” set of standard calculation parameters. Probably, within the framework of this method, it is possible to describe simultaneously and consistently the spectroscopic, thermochemical and kinetic data.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 15 (1969), S. 174-180 
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Ein Modell für die Reaktion CH 3 . +CH2=CH2 wird untersucht, einschließlich der Änderung der Hybridisation des Reaktionszentrums. Die Wechselwirkungsenergie wird in zwei Teile zerlegt. Der erste Teil ist eine Stabilisationsenergie — der Beitrag, der der Delokalisierung des π-Elektrons (einschließlich Hybridisationseffekte) entspricht. Der zweite Teil ist eine Austauschabstoßung, die von allen Valenzelektronen der drei Kohlenstoffatome herrührt. Korrellationskorrekturen werden berücksichtigt. Eine Fläche der potentiellen Energie wird konstruiert mit einem Sattelpunktswert, der dicht an der experimentellen Aktivierungsenergie liegt. Die verwendeten Näherungsmethoden werden diskutiert. Die vorgeführte Methode ist eine Verallgemeinerung der Methode der Reaktivitätsindices aus der Theorie der chemischen Reaktivität. Sie kann als eine Rechtfertigung dieser mehr empirischen Näherung angesehen werden.
    Abstract: Résumé Etude d'un modèle pour la réaction CH 3 . +CH2=CH2 où l'on tient compte du changement d'hybridation du centre réactif. L'énergie d'interaction est divisée en deux termes. Le premier est une énergie de stabilisation; c'est la contribution dela délocalisation des électrons π (effets d'hybridation compris). Il est calculé par la méthode PPP. Le second terme est une répulsion d'échange dûe à tous les électrons de valence des trois atomes de carbone. Les corrections de corrélation sont introduites. Une surface d'énergie potentielle est construite; elle fournit une valeur de l'énergie d'activation proche de celle obtenue expérimentalement. Les approximations utilisées sont discutées. La méthode proposée est une généralisation de celles des indices de réactivité. On peut la considérer comme justifiant cette approche plus empirique.
    Notes: Abstract A model for the reaction CH 3 . +CH2=CH2 is studied including the hybridization change of the reaction center. The interaction energy is devided into two parts. The first is a stabilization energy — the contribution due to the π-electron delocalization (including the hybridization effects). It is computed by the PPP method. The second part is an exchange repulsion due to all valence electrons of the three carbon atoms. Correlation corrections are considered. A potential energy surface is constructed, giving a saddle point value close to the experimental activation energy. A discussion is given of the approximations involved. The method suggested is a generalization of the reactivity indices method of the theory of chemical reactivity. It can be regarded as a justification of this more empirical approach.
    Type of Medium: Electronic Resource
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