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  • 1
    Electronic Resource
    Electronic Resource
    A random network model for water (1981)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 85 (1981), S. 1108-1119 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j150609a009
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  • 2
    Electronic Resource
    Electronic Resource
    The time-local Fokker–Planck equation (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 2526-2535 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A time-local Fokker–Planck equation (TLFPE) is derived which accounts for memory effects in stochastic problems. This is expected to provide a computationally efficient method of modeling the phase space evolution of such systems by simple (local time) Langevin equations with Markovian fluctuating forces that are characterized by time-dependent moments; it is this explicit time dependence that describes the memory effects. The TLFPE is derived from the probability theory of non-Markovian systems as a generalization of Chandrasekar's derivation of the Fokker–Planck equation (FPE) from the Chapman–Kolmogarov equation for Markovian systems. In this article it is applied to free particle diffusion and barrier crossing problems, and is shown to give rise to physically realistic results. Further, the form of the TLFPE suggests that the conditions required for systems to exhibit Markovian behavior are less restrictive than the Brownian criterion of separation of time scales between the fluctuating forces and the momentum response of the system. Rather, a sufficient condition is that the time-dependent moments of the TLFPE reach plateau values before the time scale of the phenomenon of interest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457944
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  • 3
    Electronic Resource
    Electronic Resource
    Recombination of electron–ion pairs for arbitrary mean free path (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 2666-2671 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A theory is developed of the dependence of the steady-state electron–ion pair recombination rate constant on the electron mean free path. The problem, in classical mechanics, is reduced to the stochastic dynamics of the electron in the one-dimensional effective potential V˜(R)=−kTRc/R −2kT ln R. Rc is the Onsager length Ze2/4πεkT. For a large mean free path λ, the recombination rate is determined by energy relaxation of electrons which cross the transition state of V˜(R) at RT=Rc/2, whereas for small λ the Debye result for spatial diffusion-controlled recombination is obtained. The theory gives the dependence of the rate in the crossover regime where λ is comparable to Rc. The results are in good agreement with experiment and Monte Carlo simulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455964
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  • 4
    Electronic Resource
    Electronic Resource
    Reaction dynamics on a fluctuating potential (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 5695-5703 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The steady state rate constant for passage over a fluctuating potential barrier is derived from the Fokker–Planck equation using the stable states picture. The time scale of fluctuations in barrier height and position do not influence the reactive frequency; however, the reactive frequency does depend upon the time scale of fluctuations in the barrier curvature. If these are fast relative to [ω2m+(ξ/2)2]1/2, where ωm is the mean barrier frequency and ξ is the friction for motion along the reaction coordinate, then the crossing takes place on the potential of mean force. If the barrier fluctuations are slow on the same time scale, then the rate is an average over that for the distribution of barriers. In both of these limits the form of the Kramers solutions is recovered, whereas in the intermediate case, the rate also depends explicitly on the relaxation time scale of the fluctuations. A physically reasonable model for the decay of fluctuations in the potential is proposed and used to obtain an analytic expression for the rate that covers the range between these two limits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455579
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  • 5
    Electronic Resource
    Electronic Resource
    An atom–atom encounter model of energy transfer from polyatomic molecules (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 6795-6803 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The atom–atom encounter model for collisional energy transfer by monatomic colliders previously developed for diatomics [M.G. Sceats, Chem. Phys. Lett. 151, 281 (1988)] is extended to polyatomic molecules. For small molecules, such as triatomics, the density of states is sufficiently low at high energies that the result can be enumerated for each state. For large polyatomics a statistical approach based on either microcanonical or effective canonical distributions can be used when independent degrees of freedom are assumed. An effective anharmonicity at high energy is incorporated by inclusion of diagonal terms for these independent degrees of freedom. The primary feature of the model is that it accounts for kinematic effects, such as momentum transfer efficiency and the adiabatic nature of collisions, which are not accounted for in ergodic theories of energy transfer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457349
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  • 6
    Electronic Resource
    Electronic Resource
    Collisional energy transfer from highly vibrationally excited triatomic molecules (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 6804-6812 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The atom–atom encounter model developed in the accompanying paper [M. G. Sceats, J. Chem. Phys. 91, 0000 (1989)] is applied to the collisional deactivation of highly vibrationally excited triatomic molecules CS2 and SO2 by the monatomic colliders He, Ne, Ar, Kr, and Xe at 300 K. The molecular inputs are a crude normal mode analysis, vibrational frequencies and effective anharmonicities, while the collisional inputs are parameters of the atom–atom potentials. The results for CS2 are compared with the simulations of Bruehl and Schatz and the experiments of Dove, Hippler, and Troe, while those for SO2 are compared with the simulations of Schranz and Troe and the experimental results of Heymann, Hippler, and Troe. Excellent agreement is found with experiment, and the superlinear energy dependence of the average energy transfer is attributed to anharmonicity of the triatomic molecule.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457350
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  • 7
    Electronic Resource
    Electronic Resource
    Bimolecular reactions on surfaces. Theory for arbitrary mean free path and interaction potential (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 5489-5495 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The bimolecular reaction rate of molecules constrained to a surface is obtained in a simple form. The solution applies for any central force potential and for arbitrary mean free path, giving in the limit of high friction the solution to the diffusion equation with its logarithmic dependence on surface density and in the limit of low friction the result of canonical variational transition state theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454560
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  • 8
    Electronic Resource
    Electronic Resource
    Polymer cyclization and ring opening kinetics. I. Theory (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 4526-4534 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A model of the initial kinetics of cyclization and ring opening of a polymer is developed using a generalized Langevin approach. The model reduces the complex problem to a simpler one of evaluating the dynamics of passage over a transition state in the one-dimensional effective potential of mean force deduced from a superposition of the end-segment binding potential and the end-segment distribution function for unreactive end segments. The model accounts not only for the short range binding, but also for the long range excluded volume and hydrodynamic interactions. It is shown how the initial rates of the theory, and the steady state of cyclization rate of Wilemski–Fixman–Doi theory combine to give the cyclization kinetics over the entire time domain. Expressions for the evolution of the yields of cyclized and linear polymers have been obtained. These include the fluorescence decay times for use in experiments which use such probes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453760
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  • 9
    Electronic Resource
    Electronic Resource
    The Hamiltonian formulation of configurationally constrained bimolecular kinetics: A test against simulations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 4111-4117 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Hamiltonian-based model developed by the authors [N. J. Cotes and M. G. Sceats, J. Chem. Phys. 89, 2816 (1988)] for bimolecular reactions which exhibit severe configurational restrictions, such as orientational requirements for reaction at surface sites, provides an analytical expression for the reaction rate which involves the evaluation of the potential of mean force along the radial coordinate that describes the binding. The expression for the reaction rate is evaluated for the case of a charged molecule interacting with a binding site on a dipolar particle. The results of the model are compared with the multidimensional Brownian-dynamics simulations of Northrup et al. [J. Chem. Phys. 84, 5536 (1986)] and excellent agreement is obtained in the diffusion limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456840
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  • 10
    Electronic Resource
    Electronic Resource
    Bimolecular reactions with a reactive site on a spherical particle: A Hamiltonian formulation (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 2816-2821 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A formulation is presented for the bimolecular reaction rate between a small reactant molecule A in bulk with a reactive site B on the surface of a large particle E. The approach allows a direct comparison of this rate with that between A and B in bulk. The direct interaction potential between A and B is modeled by a central force potential VAB(R) which is assumed to be unchanged upon binding of B. The reaction rate is evaluated by reduction of the problem to a one-dimensional barrier crossing problem on the effective potential V˜(R)=V(R)−kT ln[ f (R)], where the entropic term accounts for the constraints of binding on the surface. The solution applies for arbitrary mean free path, and its limits are applicable to reactions in solutions (diffusion regime) and in gas phase (free molecule regime).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454984
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