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Least-Squares Mass-Dependence Molecular Structures

Authors
Publisher
Elsevier Inc.
Publication Date
Volume
196
Issue
1
Identifiers
DOI: 10.1006/jmsp.1999.7843
Keywords
  • Structure Determination
  • Isotope Effects
  • Vibration–Rotation Interactions
Disciplines
  • Mathematics

Abstract

Abstract The major part of the difference between the zero-point and equilibrium moment of inertia of a molecule is a homogeneous function of degree 1 2 in the atomic masses. The use of explicit mathematical models of is studied here as a means of determining near-equilibrium molecular structures from the zero-point moments of inertia of a range of isotopomers. It is found that models with more than two parameters per axis generally give strongly correlated fits for the number of isotopomers typically available. The two-parameter model , where N is the number of atoms, m i are the atomic masses, and M is the molecular mass, usually gives well-conditioned fits with standard deviations in the parts-per-million range, and structures called that are often close to equilibrium structures. Laurie-type corrections for hydrogen atoms and parameters to describe isotopic rotations of the ϵ tensor can also be included.

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