An earlier discussion of the use of statistical significance tests in the comparison of experimental and theoretical determinations of molecular structures is extended, and the application of multivariate tests is shown. The accuracy of atomic coordinates determined by Fourier or least-squares methods, irrespective of whether the peaks overlap or not, is discussed in detail. Formulae are given for the errors of molecular parameters in terms of the errors of the atomic parameters of the crystal structure. The methods are applied in a discussion of the latest results on naphthalene and anthracene, and it is shown that while it is hardly necessary to postulate any errors in the molecularorbital theory for anthracene, there are very significant discrepancies for naphthalene.
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Cruickshank et al. (1953) studied this question.