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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 7621-7629 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper we investigate a new approach to reduced dimensionality descriptions of quantum mechanical systems resident in a bath. We study physical situations in which the coupling between the system and the bath is slowly varying. Our method involves an operator expansion of the Feynman propagator following the Zassenhaus theorem. From this general expansion we are able to derive an especially simple special case in which the coupling is a slowly varying function of the position operators of the system and the bath. From the approximate propagator after tracing over bath degrees, we are able to derive a short time propagator which yields both a form for efficient numerical calculation and an effective Schrödinger equation for the evolution of the system under the average influence of the bath. This theory is then applied to tunneling rearrangement in mixed crystals of benzoic acid. We find that independent of potential energy perturbations, dynamic system bath couplings increase the rate of tunneling. A central goal of this type of approach is to model the increasingly complex experimental data for large (often biological) systems.
    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 115 (2001), S. 4670-4675 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In an earlier paper we developed a collective motion description of atomic liquids, by expressing the quantum Hamiltonian in terms of rotated components of the density Fourier transform, which allowed the treatment of potential interaction terms without approximations. In the present paper, we further explore the physical content of our formalism and we show how it can be used for calculations in a real system. © 2001 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 113 (2000), S. 7437-7445 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper presents a new approach to the study of quantum dynamics in condensed phases. The methodology is comprised of two main components. First, a formally exact method is described which allows the description of the liquid as a collection of coupled (through kinetic and potential coupling) harmonic modes. The modes are related to the Fourier modes of the component particle densities. Once the modes have been defined, a canonical transformation from the standard classical interparticle Hamilton function describes a new Hamilton function, which is exactly equivalent and defined on these harmonic coordinates. The final step in this section is the transformation of this Hamilton function into a quantum Hamiltonian operator. The second step in the process is the derivation of a new quantum mechanical evolution operator which is exact and allows the correction from a reference evolution operator, which is formed by adiabatic evolution on an approximate potential. A particular approximate potential which we suggest will be useful, is the collection of harmonic modes given in the Zwanzig Hamiltonian, weighted by the spectral density. Application of the reference interaction propagator methodology can then correct the approximate adiabatic evolution operator based on the approximate potential to the exact Hamiltonian of Fourier modes described above. A test problem of a double well nonlinearly coupled to a harmonic oscillator shows that the methodology obtains rapid numerical convergence. The paper closes with a description of how the methodology would be applied to a many-dimensional (hundreds of degrees of freedom) picture of reaction in a condensed phase. © 2000 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 114 (2001), S. 2910-2918 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A computational method to discover the existence of vibrations (promoting vibrations) symmetrically coupled to the reaction coordinate is presented in the context of chemical reactions in condensed phases. Using the Zwanzig Hamiltonian as a theoretical model and molecular dynamics simulations of a model, linear triatomic in a Lennard–Jones liquid, it is shown that such a coupled motion leaves a unique signature on the spectral density computed from the autocorrelated force on the reaction coordinate. The spectral density is shown to have a peak at the effective frequency of the promoting vibration whose height increases with the reaction coordinate and vanishes at the transition state. © 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 100 (1994), S. 8795-8801 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper we report new developments in the expansion and partial resummation of the evolution operator. Higher order resummations allow derivation of an effective one-dimensional potential which accurately represents quantum dynamics for even strongly coupled low-frequency modes. This allows a system bath approximation which can accurately reproduce multidimensional quantum mechanics. In addition the formulation presented in this paper should prove significantly easier to extend to many-body problems than previous formulations we have derived. The accuracy of the method for even highly nonadiabatic applications, and the ease of implementation suggests that this approach will be useful in the calculation of the quantum dynamics of many dimensional systems.
    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 103 (1995), S. 7277-7286 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper we report quantum calculations of the survival probability in linear hydrocarbon chains. We have performed both adiabatic gauge transform calculations and calculations that include corrections beyond the adiabatic approximation. We have managed to perform intermediate steps of the calculations analytically. We require the initial basis set expansion and final summations to be performed numerically. The corrections beyond the adiabatic approximation are shown to be small for this system for multiple time step calculations and large for single time step calculations. We have proved an identity that allows the extension of the calculations for HC2 to longer chains at little computational cost. In particular, we have proved that the quantum solution for any linear hydrocarbon chain can be obtained from the solution of a problem with 3 degrees of freedom. We have performed multi-step adiabatic calculations for HC2 and HC6 that converge at up to 35–40 fs. We have devised a simple diagrammatic scheme that summarizes our method in a very compact form. Finally, we propose an alternative strategy of calculation that might lead to very fast solutions of the quantum dynamics of this system. © 1995 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 101 (1994), S. 10436-10441 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper describes the application of our recently derived infinite order evolution operator expansion and resummation technique to the problem of vibrational energy redistribution in molecules. For a standard mass tensor coupled model of a linear hydrocarbon we show how the resummation technique allows the derivation of an approximate evolution operator that in a single time step accurately reproduces vibrational dynamics for over 25 fs in hydrocarbons. This single time evolution operator can be calculated efficiently enough so that long time dynamics with multiple time steps seem to now be within reach. In addition, the structure of the theory is such that longer chain hydrocarbons can be efficiently "built up'' from shorter chain molecules. The theory starts with an adiabatic approximation which describes coupled vibrational degrees of freedom by uncoupled but guage shifted evolution operators. A modified version of this adiabatic approximation shows promise for application to molecules of a size too large to be handled exactly. © 1994 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 108 (1998), S. 3620-3625 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In the gas phase, tunneling reaction rates can be significantly enhanced if the reaction coordinate is symmetrically coupled to a harmonic oscillation, as has been emphasized by Benderskii and co-workers [Adv. Chem. Phys. 88, 1 (1994)]. This is due to the fact that the symmetric coupling leads to modulation of the barrier height. Similar effects have been observed in reactions in model condensed phase studies, as in the Hamiltonians that have been studied by Borgis and Hynes [J. Chem. Phys. 94, 3619 (1991)] and Suarez and Silbey [J. Chem. Phys. 94, 4809 (1991)]. All of these works assume that tunneling proceeds from the ground state. In this paper, we use the exponential resummation technique that we used in our recent work on the quantum Kramers problem, to study the case when there can be excitations to higher states and activated transmission over a barrier. We present a general methodology to exactly include direct coupling between the reaction coordinate and the symmetrically coupled promoting vibration and find that the rate of reactions in condensed phases is enhanced as in the case of tunneling from the ground state. This effect, however, is strongly modulated by loss of coherence induced by the condensed phase environment. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 2424-2429 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper further investigates quantum activated rate theory from the viewpoint of quantum evolution operators. It is shown that a new adiabatic separation of the quantum system-bath Hamiltonian can, in a single time step, account for quantum turnover behavior at moderate temperatures, and it is also shown how this turnover exponentially vanishes at low temperatures. It is further shown that incorporation of nonadiabatic (interaction representation form) corrections produces quantitatively accurate results at low temperatures, thus extending the applicability of the interaction representation form of nonadiabatic corrections to adiabatic evolution operators. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 6871-6879 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This article presents a derivation of the rate of reaction in the quantum activated rate problem. In this problem, one studies the rate of a chemical reaction when the reaction is placed in a dissipative bath. Our derivation defines the rate in terms of the flux autocorrelation function and proceeds via the recently developed interaction representation for nonadiabatic corrections to adiabatic evolution operators. This methodology is an infinite order resummation of nonadiabatic corrections to evolution operators. The approach produces an analytic expression which yields accurate results over a range of temperatures, viscosities and system parameters through the Kramers turnover region. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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