Journal ArticleDOI
Diagnostic least squares
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TLDR
In this paper, a method for finding physically reasonable parameters and confidence limits for parameters is described based on parameter scaling and diagonalization of the matrix of the normal equations, which is based on the assumption that the relationships provided by the observations are not really linearly independent when the random errors in the observations were considered.About:
This article is published in Journal of Computational Physics.The article was published on 1970-12-01. It has received 87 citations till now. The article focuses on the topics: Non-linear least squares & Least squares.read more
Citations
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An effective Hamiltonian for diatomic molecules . Ab initio calculations of parameters of HCl
TL;DR: In this paper, the form of the effective Hamiltonian for a diatomic molecule in an electronic state intermediate between Hund's cases is reexamined, and the formulas for the parameters assist in the comparison with ab initio calculations.
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On the calculation and interpretation of centrifugal distortion constants: A statistical basis for model testing: The calculation of the force field
TL;DR: In this article, the relationship between the distortion parameters and the force field for XYZ-type molecules is reviewed in order to remove ambiguities and inconsistencies presently found in the literature, and procedures for exploiting the statistics associated with a least square analysis of the data are presented as a guide for model testing and for detecting misassignments and mismeasurements.
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Spectra and structure of organophosphorus compounds. XXIII. Microwave spectra, electric dipole moment, and molecular structure of two conformers of ethyldifluorophosphine
TL;DR: In this article, the microwave spectrum of CH3CH2PF2 has been investigated in the region from 18.0 to 39.5 GHz, and the ground state and seven vibrationally excited states have been assigned for the more stable gauche conformer (phosphorus lone pair with respect to CH3 group).
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Lowest-Lying Conformers of Alanine: Pushing Theory to Ascertain Precise Energetics and Semiexperimental Re Structures.
TL;DR: It is shown that Ala possesses no symmetry, has several large-amplitude nuclear motions, and exhibits conformers with different hydrogen bonding patterns, it is one of the most difficult cases where reliable equilibrium structures have now been determined.
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Global analysis of the NaNe excimer band systems: A molecule between Hund’s cases
TL;DR: In this paper, least squares fit 244 transitions in the mutually perturbing NaNe A 2 Π-X 2 Δ−X 2 Σ+ and B 2 Δ −X 2 D−B 2 Δ+ excimer band systems using a Hund's case "c" basis.
References
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Journal ArticleDOI
A least‐squares analysis of the diffuse X‐ray scattering from carbons
TL;DR: In this paper, a matrix method is described whereby a linear combination of such theoretical curves may be fitted to the observed intensities with minimum total square errors the coefficiente in the combination so found at once provide an estimate of the distribution of molecular sizes within the material.
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Microwave Spectrum of Acryloyl Fluoride
J. J. Keirns,Robert F. Curl +1 more
TL;DR: In this article, the microwave spectrum of HF||H2C=C-C=O has been studied in the region 8-26 GHz and two planar rotational isomers have been assigned.
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Linear dependence in least squares analysis, with an application to internal rotation
TL;DR: In this article, the authors reviewed the technique of fitting experimental results to many-parameter formulas by least squares, with reference to the occurrence of linear dependences in the normal equations.
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Microwave Spectrum of 14N16O17O
TL;DR: In this paper, the oddelectron expectation values on oxygen have been determined for 150 hyperfine transitions belonging to the 808→717 and 919→100,10 rotational transitions of 14N16O17O in the microwave region.
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Machine computation of force constants—I. Problems of convergence and degree of indeterminacy of computed best-fit values
M.J. Bruton,L.A. Woodward +1 more
TL;DR: In this paper, the latent roots and latent vectors of the normal matrix involved in a quadratic field were used to force a convergence in cases where the usual technique fails and explore the extent to which the resulting force-constant values are determined by the experimental data used.