The limitations of generalization in sub-spectral analysis of N.M.R. spectra

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Abstract
The method of obtaining sub-spectral transformations for N.M.R. spectra is reformulated so that the conditions and limitations of transformability become obvious. Explicit formulae for abn and abc sub-spectral transformations are given. It is proved that sub-patterns of energy levels of type (1 : 2 : 1) and (1 : 3 : 3 : 1) can always be transformed into ab and abc sub-spectra, whereas the pattern (1 : 2 : 4 : 2 : 1) does not necessarily correspond to the symmetrical part of an aa′bb′ sub-spectrum. In spectra of the type AA′A′′A′′′XX′ the failure of the transformation method is shown to be due to the mixture of symmetry species products in the 4 × 4 matrix. The possibility of approximate sub-spectral transformations is discussed. An expansion of sub-spectral analysis to spectra of oriented molecules is indicated.