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  • 1
    Electronic Resource
    Electronic Resource
    Order in chaos and the dynamics and kinetics of unimolecular conformational isomerization (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 3405-3425 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A high degree of structure and therefore order in chaos is found to exist in the detailed dynamical pathways to conformational isomerization. It is shown that this structure can be used to determine the probabilities associated with the dynamical pathways to reaction, trapping, and back reaction. An earlier publication described the mediation of the dynamics of 3-phospholene by phase space structures we called "reactive islands'' (RIS)21. In this paper we extend the physical and mathematical properties of RIS and develop the corresponding kinetic theory. RIS theory is applied to a model of a hindered rotor and 3-phospholene. It is shown that the RIS kinetic model accurately predicts trajectory simulations of conformer population decay. Comparisons with standard RRKM theory are included. A discussion on the extension of RIS theory to quantum reactive dynamics and its relevance to laboratory experiments is also included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456915
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  • 2
    Electronic Resource
    Electronic Resource
    Reactive islands as essential mediators of unimolecular conformational isomerization: A dynamical study of 3-phospholene (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 3392-3404 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper we focus on the detailed nonlinear classical dynamics of conformational isomerization. In particular we concentrate on systems which admit phase space structures we call "reactive islands.'' Our calculations are on a two degree of freedom model of the molecule 3-phospholene with an experimentally fit potential energy surface by Harthcock and Laane. The reactive islands (RIS) are embedded within and are part of chaotic regions of phase space. We find that the RIS are constructed from a linear stability analysis of the period 1 orbit at the transition state or approximated by a similar analysis on reactive periodic orbits. The two approaches converge as the order of the reactive periodic orbit increases. It is found that the fully constructed RIS have well defined regions of reactivity and thus mediate the process of conformational isomerization.The overlap areas of the RIS give important kinetic information such as probabilities for trapped to reactive motion, reactive to trapped motion, and primary back reaction. The implications of this work lie in precisely identifying the microscopic dynamical pathway for isomerization. The results of this work and its relation to the related work of Gray and Rice as well as its relation to contemporary work in modern dynamics is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456914
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  • 3
    Electronic Resource
    Electronic Resource
    Projection operator formalism for the characterization of molecular eigenstates: Application to a 3:4 resonant system (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 7772-7779 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A projection operator formalism is used to quantify the normal/resonant character of eigenstates of a vibrational Hamiltonian with two degrees of freedom. We show how the application of the formalism quantifies the resonant character of these eigenstates, in the form of a probability, and how this probability is related to the width of the resonance in classical phase space. Normal and resonant quantum numbers shared by a given eigenstate are found to be canonically related.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457244
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  • 4
    Electronic Resource
    Electronic Resource
    Classical resonances, Fermi resonances, and canonical transformations for three nonlinearly coupled oscillators (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 86 (1987), S. 6295-6308 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Classical resonances arising from the interaction of three nonlinearly coupled oscillators are studied from both a theoretical and numerical perspective. In particular, our study focuses on ternary classical resonances defined by n1ω1 +n2ω2 −n3ω3 =0. We discuss some of the experimental and quantum mechanical consequences of binary and ternary classical resonances (e.g., Fermi resonances and vibration–rotation coupling). Numerically we show that it is possible to construct a three-dimensional map such that ternary classical resonances can be systematically found. Theoretically, we show that canonical transformations exist between resonant and nonresonant motion. These transformations predict various structural features of the three-dimensional numerical maps which are subsequently observed in a model numerical calculation. Finally we argue that the methods and ideas presented in this paper are generic and can be used for more general systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452466
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  • 5
    Electronic Resource
    Electronic Resource
    Semiclassical quantization by circuit counting: Application to SO2 (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 882-888 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper a semiclassical quantization method is developed whose formulation and application is simple, general and accurate. We call this method semiclassical quantization by circuit counting (SQCC). SQCC is based upon evaluating the action integral along a trajectory until it undergoes a near recurrence. Several near recurrences are used to obtain a set of independent equations which can then be inverted to yield the actions for the trajectory. Once the actions are obtained a linear extrapolation is used to calculate semiclassical energies. We apply the method to two model systems: (1) three uncoupled Morse oscillators and (2) a realistic three degree of freedom model of SO2. SQCC is found to work very well for these systems. We discuss some of the advantages and disadvantages of SQCC and its application to systems with more than three coupled molecular degrees of freedom.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455211
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  • 6
    Electronic Resource
    Electronic Resource
    Cylindrical manifolds in phase space as mediators of chemical reaction dynamics and kinetics. I. Theory (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 8310-8328 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A microcanonical kinetic theory of reactions based upon the structure within phase space is developed. It is shown that the dynamics of reaction across an energetic barrier is mediated by invariant manifolds embedded in phase space that have the geometry of simple cylinders. The ideas are developed by considering molecular systems modeled by two vibrational degrees of freedom, a reaction coordinate and a "bath'' coordinate. The kinetic theory is constructed by focusing on the dynamics between n mapping planes ("n-map'') and the "reactive island'' (RI) structure within them. We discuss how the structure of the conformer population decay in isomerization reactions can be obtained from the RI kinetic model. Formal solutions of the kinetic equations are discussed with specific attention given towards the calculation of the isomerization reaction rate. The formal theory is developed in Paper I of this series. Numerical considerations and applications to the reaction dynamics of model molecular systems with two degrees of freedom will be given in Paper II and extension of the theory and applications to multidimensional systems will be given in Paper III.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460116
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  • 7
    Electronic Resource
    Electronic Resource
    Cylindrical manifolds in phase space as mediators of chemical reaction dynamics and kinetics. II. Numerical considerations and applications to models with two degrees of freedom (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 8329-8341 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In Paper I we discussed the existence of cylindrical manifolds embedded in phase space which mediate the dynamics of chemical reactions. A kinetic theory of population decays and decay rate constants was developed which we called "reactive island'' (RI) theory. In this paper we discuss the details of the numerical implementation of the theory and then apply it to several molecular models (with two coupled degrees of freedom) representing isomerization between two and three states. Numerical simulations of population decays and asymptotic decay rate constants are compared to the RI theoretical predictions as well as the predictions from the Purely Random Theory (PRT) and Transition State Theory (TST) of reactions. Of the ten systems studied we find that RI theory is generally in good to excellent agreement with the numerical simulations. Only one system exhibits significant deviation between the RI and numerical results. This deviation is seen to be a result of a strong intraconformer dynamical bottleneck. Finally, we compare the theoretical prediction and the numerical simulation for the average n-map mapping time Trxn and find that the agreement, within numerical error, is exact irrespective of the character of the dynamics (i.e., chaotic or regular).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460065
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  • 8
    Electronic Resource
    Electronic Resource
    Second-order correction to the arbitrary trajectory method of semiclassical quantization (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 4722-4726 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper we extend the arbitrary trajectory approach to semiclassical quantization developed in an earlier paper. A numerical method is developed and tested that uses a second-order correction to extrapolate several energy eigenvalues from a single trajectory. The method is based upon finding the second-order action derivatives of the Hamiltonian. We test the scheme on a Hamiltonian previously analyzed by Swimm and Delos. We find that about 100 energy eigenvalues can be fairly accurately obtained with three reference trajectories (24 total trajectories). Strengths, weaknesses, and future applications of the method are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452836
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  • 9
    Electronic Resource
    Electronic Resource
    LUCY: A FORTRAN implementation of semiclassical spectral quantization
    Amsterdam : Elsevier
    Computer Physics Communications 51 (1988), S. 115-134 
    Details
    ISSN: 0010-4655
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0010-4655(88)90066-5
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  • 10
    Electronic Resource
    Electronic Resource
    Total projection probabilities on non-orthogonal states: Calculation of electronic populations in molecules
    Amsterdam : Elsevier
    Chemical Physics Letters 151 (1988), S. 296-300 
    Details
    ISSN: 0009-2614
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0009-2614(88)85291-6
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