CONNECTIONS BETWEEN THE RAYLEIGH-SCHRODINGER AND VAN VLECK PERTURBATION THEORIES AND THEIR APPLICATION TO RESONANCES IN MOLECULAR VIBRATIONS

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2010

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Ohio State University

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The similarities of Rayleigh-Schrodinger (RSPT) and Van Vleck (VVPT) perturbation theories are discussed. It is shown that a straightforward application of RSPT produces the VVPT Hamiltonian at the highest order of the contact transformations applied, which is always a diagonal matrix. VVPT Hamiltonians at an order higher than this are non-diagonal, but it is shown that a careful application of RSPT can produce the same matrices. The usefulness of these higher-order ``dressed" Hamiltonians in treating resonance is discussed, as well as specific discussions of first-order Fermi, second-order Darlington-Dennison, and higher-order resonances. Lastly, VVPT is discussed in a wavefunction-based context and RSPT in a Hamiltonian-based context, and the approaches are contrasted.

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Author Institution: Institute for Theoretical Chemistry, The University of Texas at Austin, Austin, Texas 78712

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http://hdl.handle.net/1811/46275

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Abstracts of OSU International Symposium on Molecular Spectroscopy 2010-2013