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  • American Institute of Physics (AIP)  (5)
  • 2010-2014
  • 1985-1989  (5)
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  • 1
    Electronic Resource
    Electronic Resource
    Rotationally induced vibrational mixing in formaldehyde (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 2672-2683 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Almost-degenerate perturbation theory is used to derive an effective Hamiltonian describing the vibrational states of H2CO. Eigenvalues have been determined for energies up to 8600 cm−1 above the zero-point energy. Both curvilinear and rectilinear representations of the vibrational dynamics are presented and explored. Although differences are observed between the two effective Hamiltonian matrix elements, their eigenvalues generally agree to better than a wave number for the energies studied. Using the Watson Hamiltonian, the mechanism of rotationally induced vibrationally mixing is investigated as a function of K, the projection of the total angular momentum onto the body-fixed a axis. The combination of a-axis Coriolis coupling and Fermi couplings leads to extensive vibrational mixing between the rotational–vibrational states in this energy regime.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455965
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Rotation–vibration interactions between the two lowest frequency modes in formaldehyde (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 7201-7216 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Rotation–vibration interactions between the two lowest frequency normal modes of H2CO, the out-of-plane bend and the in-plane wag, are studied using classical trajectories. The dynamics is investigated for a range of rotational angular momenta, J, and energy values. Vibrational energy flow is elucidated by examining trajectories in several different canonical representations. The a-axis Coriolis term, which is quadratic in the normal coordinates, accounts for most of the coupling, as seen by comparing plots in the normal mode representation and one in which the Coriolis term has been subsumed into the zero-order Hamiltonian. In the former, the modes are more strongly coupled as the projection of J onto the body-fixed z axis increases; in contrast, the Coriolis adapted normal modes are more decoupled. Making use of the observed decoupling, the rovibrational Hamiltonian is reduced to an effective one degree-of-freedom rotational Hamiltonian whose dynamics depends on the vibrational excitation. Model spectra have been obtained using the semiclassical method of Gaussian wave packet propagation of Heller [J. Chem. Phys. 62, 1544 (1975)]. Semiclassical and full quantum results analogous to the observed classical dynamics are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455299
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  • 3
    Electronic Resource
    Electronic Resource
    Variable curvature coordinates for molecular vibrations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 350-363 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A class of curvilinear coordinates for describing molecular vibrations is presented. The coordinates are parametrized by their curvature. Eigenvalues and eigenfunctions for three model Hamiltonians have been calculated in these coordinates. We investigate how the separability of the eigenfunctions varies as the curvature of the coordinates is changed, and we introduce a quantitative measure of separability using natural modal expansions. For the C–H stretch–bend interaction in CHD3, improved separability is found when coordinates are used which have a greater curvature than bond-angle coordinates. We predict and explain the results of Sibert et al. [J. Phys. Chem. 87, 2032 (1983)], who found the Fermi coupling between the bend and symmetric stretch in CO2 to be the same in rectilinear and curvilinear coordinates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457467
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  • 4
    Electronic Resource
    Electronic Resource
    Theoretical studies of vibrationally excited polyatomic molecules using canonical Van Vleck perturbation theory (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 4378-4390 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The highly excited vibrational states of polyatomic molecules are investigated using canonical Van Vleck perturbation theory, implemented in a superoperator framework. This approach is used to transform a vibrational Hamiltonian to a new representation which has a form ideally suited to the study of the dynamics of interest. The key advantage is that the solution to the full problem is obtained in the new representation using significantly smaller basis sets than are needed to obtain the solutions in the original representation. The transformations are applied to the Hamiltonian operator itself, not the Hamiltonian matrix; this superoperator approach obviates the need for large basis sets. The tedious and complex algebra, that is required to perform these transformations, is readily implemented with FORTRAN codes. Combining these two features has enabled the investigations of vibrational dynamics in energy regimes and densities of states, unattainable by standard methods. These methods are applied to two model problems and to the study of the highly excited overtones of CHD3 with up to five quanta of excitation in the CH bond.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453797
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  • 5
    Electronic Resource
    Electronic Resource
    A three-dimensional semiclassical quantization of H2O (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 5092-5104 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The semiclassical mechanics of the vibrations of H2O is examined. The analysis makes use of the work of Sibert, Reinhardt, and Hynes [J. Chem. Phys. 77, 3595 (1982)] in which the two-dimensional stretching dynamics of "local mode'' molecules was examined. There an approximate but accurate Hamiltonian was derived via the techniques of nonlinear mechanics. Quantization of this Hamiltonian, which has the form of a hindered rotor, gives vibrational energies in excellent agreement with direct quantum calculations of the H2O model Hamiltonian. In the present treatment we significantly advance the techniques developed in the earlier work to incorporate the bending degree of freedom and to generalize the treatment to be able to examine more realistic potential energy surfaces. Our results, which extend to energies as high as 22 000 cm−1, are in good agreement with the corresponding quantum mechanical calculation of Child and Lawton [Chem. Phys. Lett. 87, 217 (1982)] and demonstrate that a twofold hindered rotor Hamiltonian provides a good description of the three-dimensional vibrational eigenvalues.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449723
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