Open AccessThe comparison of theoretical and experimental determinations of molecular structures, with applications to naphthalene and anthracene
Author(s) -
Cruickshank D. W. J.,
Robertson A. P.
Publication year - 1953
Publication title -
acta crystallographica
Language(s) - English
Resource type - Journals
ISSN - 0365-110X
DOI - 10.1107/s0365110x53001976
Subject(s) - anthracene , naphthalene , computational chemistry , chemistry , multivariate statistics , fourier transform , mathematics , statistics , organic chemistry , mathematical analysis
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 multi- variate 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 anthra- cene, and it is shown that while it is hardly necessary to postulate any errors in the molecular- orbital theory for anthracene, there are very significant discrepancies for naphthalene.