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A local mode model for tetrahedral molecules
Lauri Halonen,Mark S. Child +1 more
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In this article, a three parameter coupled Morse oscillator model fitted to the known stretching vibrational energy levels is used to predict the energies of all stretching overtone bands with total quantum number ν ⩽ 5> for the molecules CH4, SiH4, GeH4 and their deuterium and 13C isotopic substituents.Abstract:
A three parameter coupled Morse oscillator model fitted to the known stretching vibrational energy levels is used to predict the energies of all stretching overtone bands with total quantum number ν ⩽ 5> for the molecules CH4, SiH4, GeH4 and their deuterium and 13C isotopic substituents. Close local mode degeneracies, with splittings of 3 cm-1 or less, are predicted at the highest energies for all molecules except CD4. Such degeneracies prevail at all excitation levels for SiH4 and GeH4, but those for ν ⩽ 3> are removed by deuterium substitution. The overtone splitting patterns of different molecules and the effects of isotopic substitution are rationalized by means of a correlation diagram, in which the ratio of bond anharmonicity to interbond coupling strength is used to rank the molecules on a scale running from local mode to harmonic normal mode limits. The ranking by local mode character is GeH4 > SiH4 > GeD4 > CH4 > SiD4 > CD4. A model intensity calculation for CH4 confirms the local mode picture wi...read more
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Journal Article
Overtone frequencies and intensities in the local mode picture
M. S. Child,L. Halonen +1 more
TL;DR: In this article, the authors present du probleme et des methodes theoriques de calcul des intensites. Application aux systemes moleculaires XY 2 and XY 2.
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The variational method for the calculation of RO-vibrational energy levels
Stuart Carter,Nicholas C. Handy +1 more
TL;DR: In this article, the current status of the variational method for the determination of the rotational-vibrational energy levels of polyatomic systems is reviewed, and a description of the programs for this problem is given.
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A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrödinger equation in nine dimensions
Xiao-Gang Wang,Tucker Carrington +1 more
TL;DR: A contracted basis-iterative method for calculating numerically exact vibrational energy levels of methane (a 9D calculation) using products of eigenfunctions of bend and stretch Hamiltonians obtained by freezing coordinates at equilibrium.
Journal ArticleDOI
Stimulated emission spectroscopy: A complete set of vibrational constants for X̃ 1A1 formaldehyde
TL;DR: A complete set of 27 normal mode vibrational constants ω0 i and x i j as well as six harmonized vibrational frequencies ω i is obtained for the H2CO X1 A 1 state as mentioned in this paper.
References
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Handbook of Mathematical Functions
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Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels
TL;DR: In this paper, an exact solution for the Schroedinger equation representing the motions of the nuclei in a diatomic molecule, when the potential energy function is assumed to be of a form similar to those required by Heitler and London and others, was obtained.
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The anharmonic force field and equilibrium structure of methane
D.L. Gray,A.G. Robiette +1 more
TL;DR: In this article, the anharmonic force field of methane has been refined to fit spectroscopic data from the isotopic species 12CH4, 13 CH4, 12 CH4.
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The vibration-rotation energies of tetrahedral XY4 molecules : Part I. Theory of spherical top molecules
TL;DR: In this paper, the theory of vibration-rotational perturbations in tetrahedral XY 4 molecules has been reexamined in the light of the modern theory of angular momentum coupling, and it is shown that, even to third order of approximation, the splitting of a vibration rotation level into its tetralinear sublevels is governed only by perturbation terms of one basic symmetry in all states in which vibrational quanta of ν 1, ν 3, and ν 4 are excited and to a certain approximation in many of the infrared active states in
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