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As already pointed out in [1 — 3], when studying the vibrations of non-rigid l,4-di-X-butyne-2 molecules (X = F, CI) belonging to the symmetry group G4 [1], we were unable to find a set of symmetry coordinates which factorizes the kinetic energy matrix G [4]. I t has been moreover found [2] that the representation of the symmetry group G4+ in terms of the internal coordinates R defined in agreement with [4], is different from the representation ZPx of the same group given in terms of the cartesian coordinates X. A third still different representation of G4+ has been obtained for the same molecule [5] by using a method proposed by Gussoni and Zerbi [6], This method, which allows the calculation of internal symmetry coordinates, consists in the diagonalization of the G matrix according to

On the Unique Determination of the Completely Reduced Representation of the Symmetry Group for Non-Rigid Molecules