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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 2444-2450 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: "Agmon–Hopfield kinetics" refers to a first-order process whose rate depends on a control variable that changes with time by diffusion. We analyze the transition from short-time behavior, accurately described by the static approximation D=0, to long-time behavior, determined by competition between diffusion and the slow tail of the rate function. The analysis is asymptotic in D, increasing in accuracy as D→0. © 1997 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 111 (1999), S. 4886-4892 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Thermally activated escape over a high barrier fluctuating randomly in time is investigated for asymmetric flipping rates. By means of the Fokker–Planck approach approximate methods developed for symmetric noise are applied to calculate the relaxation eigenvector and ultimate relaxation rate for piecewise linear potentials in the Smoluchowski limit. The ranges of validity of these approaches are discussed. Furthermore, the exact result for weak thermal noise but arbitrary barrier flipping rates is derived and its dependence on the asymmetry studied in detail. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 5925-5932 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The short time dynamics of the semiclassical initial value separation are studied analytically for a one dimensional system. We find that at short times the approximation introduces spurious errors that depend on (h-dash-bar) and result from the anharmonic part of the potential. This is in contrast to classical mechanics which gives the first three initial time derivatives of a coordinate dependent operator exactly. Consideration of a model system shows, though, that the error introduced is not very large and that for times which are longer than a typical period of classical motion, semiclassical initial value representation propagation is superior to classical time propagation. © 2002 American Institute of 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 115 (2001), S. 4696-4707 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Coherent wave-packet dynamics on coupled electronic surfaces within a condensed–phase environment is studied. Based on a path integral approach, exact expressions for the case of a one-dimensional reaction coordinate in a donor–acceptor complex are derived. The path integrals over the electronic degree of freedom are further evaluated by applying the golden rule approximation. This procedure allows for an exact treatment of the coupling between solvent or residual molecular degrees of freedom and the reaction coordinate. A detailed picture of the intimate relation between dissipative wave-packet motion and electron transfer is gained also for lower temperatures, strong coupling and slow bath modes, where Redfield type of equations cannot be used. The electron transfer triggered by the coherent vibronic motion leads to a stepwise decay of the population in the donor state. On the acceptor surface the wave-packet dynamics displays a complex interference pattern. Further, it turns out that for a reaction coordinate fast compared to the environmental modes the electronic population dynamics is very sensitive to the initial correlations between bath and reactive mode. © 2001 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 104 (1996), S. 7526-7538 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a barrier potential with bound states that is exactly solvable and determine the eigenfunctions and eigenvalues of the Hamiltonian. The equilibrium density matrix of a particle moving at temperature T in this nonlinear barrier potential field is determined. The exact density matrix is compared with the result of the path integral approach in the semiclassical approximation. For opaque barriers the simple semiclassical approximation is found to be sufficient at high temperatures while at low temperatures the fluctuation paths may have a caustic depending on temperature and endpoints. Near the caustics the divergence of the simple semiclassical approximation of the density matrix is removed by a nonlinear fluctuation potential. For opaque barriers the improved semiclassical approximation is again in agreement with the exact result. In particular, bound states and the form of resonance states are described accurately by the semiclassical approach. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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