By Magdolna Hargittai, Istvan Hargittai
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Additional resources for Advances in Molecular Structure Research, Volume 3, First Edition (Advances in Molecular Structure Research)
P) from n experimental data Yi (i = 1 . . . n), the starting equations of the linear least-squares method are, after the model equations have been linearized in the neighborhood of the expected solution, y=XI3+~ (27) where X is the Jacobian matrix and e the vector of residuals (which should not be confused with the vibrati6nal correction eg used elsewhere in this paper). In the following we shall assume that the errors are independent and that the experimental data are of equal precision (uncorrelated, unity-weighted case).
So, a small eigenvalue is an indication of collinearity. Watson et al.  advocates the use of the diagonal elements of the inverse of the correlation matrix. This notion has later been generalized by Femenias  and then by Grabow et al. . ' To palliate the weaknesses of the existing diagnostics, he has introduced the condition indexes and has shown that they can be easily used to determine the strength and number of near-dependencies. First the columns of the Jacobian matrix X are scaled to have 25 Determination of Reliable Structures from Rotational Constants unit length (each term of the vector column Xi is divided by the norm IIXill).
119]. But some experimental data were rather inaccurate; for instance the axial rotational constants of CH335C1 and CH337C1 are too different to be reliable. 0854 A, seems to be too large to be compatible with the isolated stretching frequency of the C - H bond as well as with the results of high level ab initio calculations . Since that time, a 37 Determination of Reliable Structures from Rotational Constants Table 19. Data Used for the Least-Squares Determination of the re Structure of CH3Cl [ 178] Data a Exp.
Advances in Molecular Structure Research, Volume 3, First Edition (Advances in Molecular Structure Research) by Magdolna Hargittai, Istvan Hargittai