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  • 1
    Electronic Resource
    Electronic Resource
    Dynamical symmetry breaking and energy transfer pathways in local modes of benzene (1983)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 87 (1983), S. 2161-2167 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100235a024
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  • 2
    Electronic Resource
    Electronic Resource
    Approximate constants of motion for vibrational spectra of many-oscillator systems with multiple anharmonic resonances (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 6630-6635 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A theory of approximate dynamical constants of motion is presented for vibrational (and implicitly, rovibrational) spectra of polyatomics with multiple nonlinear resonances. The formalism is developed in terms of simple vector algebra. The theory is applied to Hamiltonians used in fits of experimental spectra of H2O, CHClF2, and acetylene, with attention to reduced dimension motion, assignability of spectra, and statistical analysis of chaotic spectra. The approximate constants may be of interest as bottlenecks to vibrational energy flow in polyatomics. They may also be useful in reducing the size of basis sets in quantum-mechanical calculations of rotation–vibration spectra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458930
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  • 3
    Electronic Resource
    Electronic Resource
    Localized chaos and partial assignability of dynamical constants of motion in the transition to molecular chaos (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 7196-7204 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The implications of approximate dynamical constants of motion for statistical analysis of highly excited vibrational spectra are investigated. The existence of approximate dynamical constants is related to localized chaos and partial assignability of a "chaotic spectrum.'' Approximate dynamical constants are discussed in a dynamical symmetry breaking formulation of the transition from periodic to quasiperiodic motion, and from quasiperiodic to chaotic motion. Level repulsion, leading to a Wigner distribution in the case of a strongly chaotic system, is shown to originate in dynamical symmetry breaking via the noncrossing rule that states of the same symmetry do not cross. It is argued that quantum numbers for dynamical constants must be correctly assigned to detect localized chaos in statistical spectroscopy. Two possible kinds of approximate constants, for a "total polyad number'' and a bend normal mode, are discussed in relation to two coupling schemes that could govern the transition to chaos in H2O.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458207
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  • 4
    Electronic Resource
    Electronic Resource
    Unified semiclassical dynamics for molecular resonance spectra (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 6086-6098 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A method is presented to depict the intramolecular dynamics of resonantly coupled vibrations, starting from the experimental overtone and combination spectrum. The nonlinear least-squares fit of the spectrum is used to obtain a semiclassical phase space Hamiltonian via the Heisenberg correspondence principle. This integrable Hamiltonian, corresponding to quasiperiodic motion, is used to generate a classical trajectory in phase space for each energy level in a resonance polyad. Polyad phase space profiles are shown to have complete mutual consistency starting from a fit in either the local or normal representation. It is argued that the best way to depict the phase space profile is on a spherical surface called the polyad phase sphere. Represented in this way, the local and normal mode phase spaces are seen to be a single entity, manifestly equivalent by a 90° rotation. The phase space trajectories can be converted into a coordinate space representation. This gives an easily visualized picture of the semiclassical intramolecular dynamics corresponding to each energy level. The polyad phase spheres from the fits of the experimental stretching spectra of H2O, O3 and SO2 are displayed. H2O and O3 are seen to be molecules with a local to normal modes transition, while SO2 is seen to be very near the pure normal modes limit. The experimentally determined phase space dynamics of H2O seen on the phase sphere are compared with the dynamics determined by Lawton and Child from trajectory calculations on the Sorbie–Murrell potential surface. The coordinate space trajectories corresponding to the phase spheres are compared with wave functions from the fit of the spectrum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456374
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  • 5
    Electronic Resource
    Electronic Resource
    Approximate constants of motion and energy transfer pathways in highly excited acetylene (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 8671-8672 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Approximate constants of motion of acetylene (C2H2), analyzed previously below 10 000 cm−1, are determined from analysis of a nonlinear least squares fit of the highly excited vibrational absorption spectrum. Although there are at least ten distinct Fermi resonance couplings in the measured spectrum up to 24 000 cm−1, there is one, and quite possibly two, good constants of motion. These constants are pointed out to be equivalent to a preferred energy transfer pathway discussed by Smith and Winn. It is suggested that these constants may also apply to "unassignable'' stimulated emission pumping spectra, which sample a different region of phase space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461251
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  • 6
    Electronic Resource
    Electronic Resource
    New assignment of Fermi resonance spectra (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 5821-5825 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new quantum number assignment is proposed for bend–stretch vibrational spectra with 2:1 Fermi resonance. Using a classification based on the catastrophe map and polyad phase spheres of the Fermi resonance fitting Hamiltonian, quantum numbers are assigned corresponding to the semiclassical dynamics of each energy level. The method is applied to assign experimental spectra of CH(CF3)3. The separability of the wave functions is discussed in terms of "nodal coordinates'' for which the new quantum numbers are constants of the motion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459577
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  • 7
    Electronic Resource
    Electronic Resource
    Catastrophe map classification of the generalized normal–local transition in Fermi resonance spectra (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 5805-5820 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Catastrophe theory is used to classify the dynamics of spectra of resonantly coupled vibrations, based on earlier work on the bifurcation structure of the Darling–Dennison and 2:1 Fermi resonance fitting Hamiltonians. The goal is a generalization of the language of the "normal–local transition'' to analyze experimental spectra of general resonant systems. The set of all fixed points of the Hamiltonian on the polyad phase sphere for all possible molecular parameters constitutes the catastrophe manifold. The projection of this manifold onto the subspace of molecular parameters is the catastrophe map. The map is divided into zones; each zone has its own characteristic phase sphere structure. The taxonomy of global phase sphere structures within all zones gives the classification of the semiclassical dynamics. The 1:1 system, with normal–local transition, is characterized by cusp catastrophes, with elementary pitchfork bifurcations. In contrast, the 2:1 system is characterized by fold catastrophes, with elementary transcritical bifurcations. The catastrophe map can be used in a new method to classify experimental spectra on the basis of the system's underlying semiclassical dynamics. The catastrophe map classification appears to persist for nonintegrable, chaotic Hamiltonians, indicating the utility of catastrophe theory for understanding the morphology of chaotic systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459576
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  • 8
    Electronic Resource
    Electronic Resource
    Phase space bifurcation structure and the generalized local-to-normal transition in resonantly coupled vibrations (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 2251-2268 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The generalization of the local-to-normal transition seen in symmetric triatomics is considered for nonsymmetric molecules and 2:1 Fermi resonance systems. A straightforward generalization based on a division of phase space into local and normal regions is not possible. Instead, classification of the phase space bifurcation structure is presented as the complete generalization of the local–normal concept for all spectroscopically relevant systems of two vibrations interacting via a single nonlinear resonance. The polyad phase sphere (PPS) is shown to be the natural arena to analyze the bifurcation structure for resonances of arbitrary order. For 1:1 and 2:1 resonances, the bifurcation problem is reduced to one or two great circles on the phase sphere. All bifurcations are shown to be examples of elementary bifurcations of vector fields in one dimension. The classification of the bifurcation structure is therefore governed and greatly simplified by the theory of the universal unfolding and codimension of elementary bifurcations. The implications for large-scale bifurcation structure and transport in molecules with chaotic motion are briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458018
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  • 9
    Electronic Resource
    Electronic Resource
    Potential energy surfaces from highly excited spectra using the bootstrap fitting method: Two-dimensional surfaces for water and ozone (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 4714-4725 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The bootstrap fitting procedure is implemented to obtain molecular potential energy surfaces for the stretching degrees of freedom of ozone using experimental spectra of highly excited vibrational states probed in recent experiments. The method has three key features: first, the use of a flexible anharmonic potential with parameters optimized in a nonlinear least-squares fit; second, the implementation of the bootstrap algorithm for fitting vibrational levels even in regions where the classical dynamics are globally chaotic; and third, the employment of a basis-set reduction technique called algebraic resonance quantization for the computation of eigenvalues of the potential. The approach was tested by using the stretching eigenvalues from a realistic empirical potential for water as input. Excellent agreement between the bootstrap potential and the empirical surface was found using levels up to 25 000 cm−1 with as few as 4 parameters. The method was then applied to experimental stretching levels of ozone. The potential energy surface obtained by our technique for the stretching modes of ozone is believed to be the best surface currently available up to 6500 cm−1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460583
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  • 10
    Electronic Resource
    Electronic Resource
    Bootstrap approach to fitting spectra of molecules with classically chaotic dynamics (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 159-175 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The detailed level-by-level fitting of spectra of systems with strongly chaotic classical dynamics is investigated. Fitting of these "unassignable chaotic spectra'' is advocated as a desirable counterpart to statistical analysis, giving a detailed probe of molecular potential surfaces and intramolecular dynamics, including phase-space "bottlenecks.'' The role of "assigning'' levels in a spectral fit is discussed. It is concluded that what is really necessary for fitting is to "label'' the spectrum, in a sense made precise. There is no barrier, in principle, to fitting chaotic spectra that may be unassignable in terms of the usual zero-order quantum numbers such as normal modes. The difficulties introduced into the labeling process by experimental factors of spectral resolution and sensitivity are considered. The occurrence of missing levels or features is identified as the key labeling problem. A "bootstrap'' method is introduced to label and fit a spectrum with missing levels. The "bootstrap'' method works by using the knowledge obtained at each energy range of the fit to successively label and fit higher energies. The bootstrap method is tested on simulated experimental spectra. A program called fitter uses the bootstrap procedure successfully to identify missing levels, label and fit the spectrum, [AV:and reproduce the molecular potential. The occurrence of doublets in highly excited spectra is noted as possible spectral evidence of a bottleneck giving rise to chaotic local modes. Fitting of large-scale "clump'' features is discussed as a means to probe energy flow dynamics and potentials of "doorway'' modes of molecules. Fitting of features or individual levels on successively finer energy scales is discussed as a probe of subsequent energy flow dynamics through "interior'' modes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459588
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