Evaluation of libration amplitudes from NMR second moments: Application to three [N(CH₃)₄]⁺ halides

We investigate the possibility that moderate discrepancies between observed and calculated NMR second moments reported in the literature may be due to lattice vibration effects. Simplified versions of a previously derived general formula for the libration-affected intramolecular contributions to the second moment are introduced and used for the evaluation of average amplitudes of libration of the tetramethylammonium cation in three of its halide salts. Two possible types of motions are examined: isotropic libration of the cation as a whole and anisotropic librations of the methyl groups around their triad axes. Our comparison of librational amplitudes determined from second moments with those calculated using ir experimental frequencies indicates that the methyls' librations are the principal source for the reported second moment discrepancies.