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  • 1
    Electronic Resource
    Electronic Resource
    Effects of excitation migration and translational diffusion in the luminescence quenching dynamics (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 815-827 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Luminescence decay in the presence of quencher is considered theoretically. Combined effects of molecular diffusion and excitation migration among energy-donors are treated within a unified framework. A set of general kinetic equations for describing the luminescence quenching dynamics is derived from a hierarchical system of many-body Smoluchowski equations for the reactant molecule distribution functions. Numerical and approximate analytic solutions to these equations for a simple model system show that the effective diffusion coefficient of donors upon a quencher can be considerably larger than the simple sum of translational diffusion coefficient and excitation-migration diffusion coefficient estimated for a system of fixed donor molecules. This finding is in accordance with a recent experimental result of Pandey et al. Another important finding is that the excitation migration diffusion coefficient should be proportional to the donor concentration C0D in the large C0D limit when the donor molecules are extremely mobile, while it varies with (C0D)4/3 for a system of immobile donors as is known. It is also shown that some well-known previous theories are incorrect at least in the fast excitation migration limit. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.469196
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  • 2
    Electronic Resource
    Electronic Resource
    Path integral centroid variables and the formulation of their exact real time dynamics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 2357-2370 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A formalism is presented in this paper which, for the first time, establishes the theoretical basis for the quantum time evolution of path integral centroid variables and also provides clear motivation for using these variables to study condensed phase quantum dynamics. The equilibrium centroid distribution is first shown to be a well-defined distribution function which is specific to the canonical density operator. A quantum mechanical quasi-density operator (QDO) is associated with each value of the distribution so that, upon application of the standard quantum mechanical formalism, the QDO can be used to provide a rigorous definition of both static and dynamical centroid variables. Various properties of the dynamical centroid variables are derived, including the perspective that the centroid constraint on the imaginary time paths introduces a nonstationarity in the equilibrium ensemble which, in turn, can be shown to yield information on the correlations of spontaneous fluctuations. The analytic solution for the harmonic oscillator and a numerical solution for a double well system are provided which illustrate the various aspects of the theory. The theory contained herein provides the basis for a derivation of Centroid Molecular Dynamics, as well as the systematic improvements of that theory. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479514
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  • 3
    Electronic Resource
    Electronic Resource
    A derivation of centroid molecular dynamics and other approximate time evolution methods for path integral centroid variables (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 2371-2384 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Several methods to approximately evolve path integral centroid variables in real time are presented in this paper, the first of which, the centroid molecular dynamics (CMD) method, is recast into the new formalism of the preceding paper and thereby derived. The approximations involved in the CMD method are thus fully characterized by mathematical derivations. Additional new approaches are also presented: centroid Hamiltonian dynamics (CHD), linearized quantum dynamics (LQD), and a perturbative correction of the LQD method (PT-LQD). The CHD method is shown to be a variation of the CMD method which conserves the approximate time dependent centroid Hamiltonian. The LQD method amounts to a linear approximation for the quantum Liouville equation, while the PT-LQD method includes a perturbative correction to the LQD method. All of these approaches are then tested for the equilibrium position correlation functions of three different one-dimensional nondissipative model systems, and it is shown that certain quantum effects are accounted for by all of them, while others, such as the long time coherence characteristic of low-dimensional nondissipative systems, are not. The CMD method is found to be consistently better than the LQD method, while the PT-LQD method improves the latter and is better than the CMD method in most cases. The CHD method gives results complementary to those of the CMD method. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479515
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  • 4
    Electronic Resource
    Electronic Resource
    Response to "Comment on ‘Simple reversible molecular dynamics algorithms for Nosé–Hoover chain dynamics' " [J. Chem. Phys. 110, 3623 (1999)] (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 3626-3628 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The purpose of Nosé–Hoover chain (NHC) dynamics at constant (N,V,T) is canonical distribution sampling, and this sampling is shown to be insensitive to fluctuations in the conserved quasi-Hamiltonian. For anharmonic potentials, it is also shown that the quasi-Hamiltonian conservation properties of the reversible algorithms developed by Martyna and Tuckerman degrade significantly. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478232
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  • 5
    Electronic Resource
    Electronic Resource
    Lithium impurity recombination in solid para-hydrogen: A path integral quantum transition state theory study (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 4098-4106 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The recombination of two lithium atoms trapped in one-vacancy defect sites of solid para-hydrogen at 4 K and zero external pressure is studied as a quantum activated process. The quantum activation free energy is calculated using path integral quantum transition state theory along with the method of path integral molecular dynamics simulation. The equilibrium volume of the system is determined by a constant pressure method that scales the sides of the rectangular simulation box. At a fixed equilibrium volume of the system, a constraint dynamics path integral simulation is then employed to determine the quantum path centroid free energy barrier along the reaction coordinate, which is taken to be the relative Li–Li separation. The two lithium atoms begin to recombine at a distance of approximately twice the lattice spacing, and the height of the barrier relative to the metastable well is 78±10 K. The rate of the intrinsic recombination step is estimated to be 1.3×103 s−1 at 4 K. It is found that the lithium nuclei exhibit significant tunneling behavior over their classical limit. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475807
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  • 6
    Electronic Resource
    Electronic Resource
    A relationship between centroid dynamics and path integral quantum transition state theory (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 8747-8757 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The theory of Feynman path centroid dynamics is applied to the calculation of quantum barrier crossing rates. The formulation starts from the exact definition of the quantum survival probability of the reactant state, and the reaction rate is then defined as the steady-state limit of the decay rate of the survival probability. A formulation is given in terms of exact centroid dynamics. Then, based on an approximation for the initial reactant state and the centroid molecular dynamics (CMD) approximation for the dynamics, a new approximate rate expression is obtained which is equal to the path integral quantum transition state theory (PI-QTST) expression multiplied by a transmission factor of order unity. This factor varies with the choice of the dividing surface in the low temperature limit, but it is invariant to that choice at higher temperatures. It is then shown that the PI-QTST rate expression results from the quadratic barrier approximation for the calculation of the transmission factor only. The potential to use the new rate expression as an improved version of the PI-QTST is also tested for model systems. For certain choices of the dividing surface, it is shown that the new reaction rate expression results in improvement over the PI-QTST results. The overall formulation also yields a better understanding of the barrier crossing dynamics viewed from the centroid perspective and the rigorous origin of the PI-QTST formula. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481490
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  • 7
    Electronic Resource
    Electronic Resource
    Simple reversible molecular dynamics algorithms for Nosé–Hoover chain dynamics (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 9514-9526 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Reversible algorithms for Nosé–Hoover chain (NHC) dynamics are developed by simple extensions of Verlet-type algorithms: leap frog, position Verlet, and velocity Verlet. Tests for a model one dimensional harmonic oscillator show that they generate proper canonical distributions and are stable even with a large time step. Using these algorithms, the effects of the Nosé mass and chain length are examined. For a chain length of two, the sampling efficiency is much more sensitive to the Nosé mass than for a longer chain of length four. This indicates that the chain length in general should be longer than two. The noniterative nature of the algorithms allows them to be easily adapted for constraint dynamics. For the most general case where multiple NHC's are coupled to a system with constraints, a correction of the first Nosé acceleration is required, which is derived from the continuity equation on a constrained hypersurface of the phase space. Tests for model systems of two and three coupled harmonic oscillators with one normal mode constrained show that these algorithms, in combination with the corrected dynamical equations, sample the canonical distributions for the unconstrained degrees of freedom. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475247
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  • 8
    Electronic Resource
    Electronic Resource
    A Feynman path centroid dynamics approach for the computation of time correlation functions involving nonlinear operators (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 919-929 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The centroid dynamics formalism is extended to the calculation of time correlation functions of nonlinear operators. It is shown that centroid correlation functions can be related to quantum mechanical ones via higher order Kubo-type transforms. A key step is the construction of the correlation functions from a mixed classical/semiclassical centroid representation of the operators. A general methodology is developed to relate these Kubo-type transforms to the desired quantum correlation functions. The approach is tested using a one-dimensional anharmonic potential for which the 〈x2x2(t)〉 and the 〈x3x3(t)〉 correlation functions are computed. Applications of this new approach are also outlined. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481872
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  • 9
    Electronic Resource
    Electronic Resource
    Feynman path centroid dynamics for Fermi–Dirac statistics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 5303-5305 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this communication the centroid molecular dynamics (CMD) method is tested for systems of fermions using a modified version of the expression for the fermion Feynman path centroid density derived in a recent publication [J. Chem. Phys. 110, 3647 (1999)]. The method is applied to a model system consisting of two noninteracting fermions in an anharmonic potential well and the position autocorrelation function is computed. The exact fermion position autocorrelation function exhibits a longer period of oscillation when compared to the bosonic case. This shift is due to the anharmonic nature of the given potential function where the level spacing decreases with the increase of energy. The CMD results agree very well with the exact quantum mechanical results for this example. This indicates, along with the previous results on a boson system, that quantum statistics can in principle be incorporated into the CMD method without any degradation of the accuracy of the approximation. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479789
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  • 10
    Electronic Resource
    Electronic Resource
    Fourth-order quantum master equation and its Markovian bath limit (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 2705-2717 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Fourth-order quantum master equations (FQMEs) are derived in both time nonlocal and local forms for a general system Hamiltonian, with new detailed expressions for the fourth-order kernel, where the bath correlation functions are explicitly decoupled from the system superoperators. Further simplifications can be made for the model of linearly coupled harmonic oscillator bath. Consideration of the high temperature Ohmic bath limit leads to a general Markovian FQME with compact forms of time independent superoperators. Two examples of this equation are then considered. For the system of a quantum particle in a continuous potential field, the equation reduces to a known form of the quantum Fokker–Planck equation, except for a fourth-order potential renormalization term that can be neglected only in the weak system-bath interaction regime. For a two-level system with off-diagonal coupling to the bath, fourth-order corrections do not alter the relaxation characteristics of the second-order equation and introduce additional coherence terms in the equations for the off-diagonal elements. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1445105
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