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  • 1
    Electronic Resource
    Electronic Resource
    Statistical mechanics of rotationally inelastic molecule–surface scattering in the dynamical Lie algebraic method (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 4424-4432 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The dynamical Lie algebraic method is used for the description of statistical mechanics of rotationally inelastic molecule–surface scattering. A main advantage of this method is that it can not only give the expression for evolution operator in terms of the group parameters, but also provide the expression for the density operator for a given system. The group parameters may then be determined by solving a set of coupled nonlinear differential equations. Thus, the expressions of the statistical average values of the translational-to-rotational energy transfer, the interaction potential, and their dependence on the main dynamic variables for the system are derived in terms of the density operator formalism in statistical mechanics. The method is applied to the scattering of NO molecules from a static, flat Ag(111) surface to illustrate its general procedure. The results demonstrate that the dynamical Lie algebraic method can be useful for describing statistical dynamics of gas–surface scattering. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1285928
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  • 2
    Electronic Resource
    Electronic Resource
    Lie algebraic approach to potential energy surface for symmetric triatomic molecules (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 4466-4471 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Potential energy surfaces play an important role in studying theoretical chemistry. In this work, the expression of the potential energy surface containing information about the bending motion of triatomic molecules is derived by using the semiclassical limit of the algebraic Hamiltonian with the dynamical symmetry group U1(4)⊗U2(4). And, we also obtain the force constants. The method can be applied to a number of stable triatomic molecules, such as, H2O, H2S. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479210
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  • 3
    Electronic Resource
    Electronic Resource
    An application of the dynamical Lie algebraic method to energy transfer of the collinear scattering system AB+CD (1999)
    Springer
    Journal of mathematical chemistry 26 (1999), S. 221-232 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The dynamical Lie algebraic method has been applied to treat the V–V and T–V energy transfers in the collinear scattering system AB+CD. The expression for the vibrational transition probability, which contains the main dynamical parameters, is given analytically. By using this expression we probe into the V–V resonance and T–V resonance phenomena appearing in the process of energy transfer. We find that the transition probability of V–V resonance is in good agreement with that obtained using the resonant exchange hypothesis. Then the reliability of the resonant exchange hypothesis is confirmed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019146230655
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  • 4
    Electronic Resource
    Electronic Resource
    Application of dynamical Lie algebraic method to atom–diatomic molecule scattering (2000)
    Springer
    Journal of mathematical chemistry 28 (2000), S. 247-266 
    Details
    ISSN: 1572-8897
    Keywords: scattering ; anharmonic oscillator ; Lie algebra ; translational–vibrational energy transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The dynamical Lie algebraic approach developed by Alhassid and Levine combined with intermediate picture is applied to the study of translational–vibrational energy transfer in the collinear collision between an atom and an anharmonic oscillator. We find that the presence of the anharmonic terms indeed has an effect on the vibrational probabilities of the oscillator. The computed probabilities are in good agreement with those obtained using exact quantum method. It is shown that the approach of dynamical Lie algebra combining with intermediate picture is reasonable in the treating of atom–anharmonic oscillator scattering.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018878124232
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  • 5
    Electronic Resource
    Electronic Resource
    Potential energy surface for linear triatomic molecules: An algebraic method (2000)
    Springer
    Journal of mathematical chemistry 28 (2000), S. 193-200 
    Details
    ISSN: 1572-8897
    Keywords: potential energy surface ; bent triatomic molecules ; linear molecules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Recently, we proposed a new transformation between the angle of canonical coordinates and the bond angle to describe the bending motion in Potential Energy Surfaces (PES) of bent triatomic molecules. In this work we extend the transformation to include linear triatomic molecules. Results for the linear triatomic molecule N2O are reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018856713558
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  • 6
    Electronic Resource
    Electronic Resource
    Lie algebraic approach to the scattering system He + H2 (1989)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 36 (1989), S. 379-389 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this article, the Hamiltonian for the scattering of the He + H2 system is given by using the interaction potential V(X, Y, Θ) determined by experiments and the semiclassical method. From this Hamiltonian we find a dynamical algebra h6. The statistical expectation of the energy and the transition probability of H2, Pn→m, are derived; therefore, selection rules have been found easily.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560360320
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  • 7
    Electronic Resource
    Electronic Resource
    Semiclassical calculation of rotational excitation of atom-symmetric top scattering (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 65 (1997), S. 89-96 
    Details
    ISSN: 0020-7608
    Keywords: Semiclassical approach ; rotational excitation ; A-A variables ; Monte Carlo calculation ; total cross section ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A semiclassical approach is applied to calculating the state-to-state cross sections of rotational excitation of ammonia molecule scattering with the argon atom. Semiclassical theory is more useful in studying heavy molecular scattering. Ammonia molecule is regarded as a rigid symmetric top and argon as a structureless atom. The inversion motion of ammonia is not taken into account. We make use of classical action-angle variables to describe the degrees of freedom of the system. The ab initio potential is used, and at two different energies the computing of total cross sections are performed by using the Monte Carlo procedure. Good agreements with close-coupling calculations and crossed molecular beam experiment are obtained. The semiclassical approach thus appears to be valid for ammonia-argon scattering system.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 89-96, 1997
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 8
    Electronic Resource
    Electronic Resource
    Application of the Lie algebraic approach to diffractionally and rotationally inelastic molecule-surface scattering (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 981-989 
    Details
    ISSN: 0020-7608
    Keywords: Lie algebraic method ; diffractionally and rotationally scattering ; inelastic molecule-surface scattering ; transition probabilities ; scattering of H2 from LiF(001) surface ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Lie algebraic approach of Alhassid and Levine [Phys. Rev. A 18, 89 (1978)] is applied to the molecule-surface scattering. Specially, the diffractionally and rotationally inelastic scattering of a diatomic molecule from a solid surface is dealt with. Within the framework of the close-coupling method, we construct a Hamiltonian for the scattering system and use it to generate a dynamical algebra h6. By solving equations of motion for the group parameters, the scattering wave functions near the surface are obtained. Computed transition probabilities of diffractively and rotationally inelastic scattering of H2 from LiF(001) surface with the use of Lie algebraic method are seen to agree well with the coupled-channel calculations. The Lie algebraic method thus appears to have a wide range of validity for describing the dynamics of gas-surface scattering. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 981-989, 1997
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    Lie algebraic approach to the collinear collisions between two diatomic molecules (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 65 (1997), S. 159-165 
    Details
    ISSN: 0020-7608
    Keywords: Dynamic Lie algebraic method ; inelastic collision between two diatomic molecules ; vibrational transition probabilities ; vibrational energy transfer ; selection rules for the transitions ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We present the quantum mechanical studies on the vibrational energy transfer in the inelastic collinear collision between two diatomic molecules using a dynamic Lie algebraic method of Alhassid and Levine [Phys. Rev. A 18, 89 (1978)] within the semiclassical approximations. A dynamical algebra h15 is formed and used for calculating the transition probabilities and the expectation values of the interaction potential. Under the first-order approximation of the group parameters, the selection rules for the transitions among the vibrational levels have been obtained.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 159-165, 1997
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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