Anharmonic contributions to dynamic electron densities caused by large librations of molecules

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The effect of large librations of molecules on electron density distributions is investigated with the already published structures of β-NaN3, p-nitropyridine N-oxide and anthracene, and with some model calculations for C, N, O atoms. For this purpose, the temperature factor of the atom concerned is expanded with cumulants, and the smearing function of the nuclear positions and the dynamic electron density is calculated by an Edgeworth series. The results are represented as difference densities p(anharmonic) - p(harmonic) ≡ p(A - H) maps. For the end N atom in β-NaN3 at 295 K and for the C(7) atom in p-nitropyridine N-oxide at 30 K, these maps contain minima of 0.53 e Å-3 (N) and 0.22 e Å-3 [C(7)] in front of the nuclei, and maxima of 0.44 e Å-3 (N) and 0.21 e Å-3 [C(7)] behind the nuclei. Thus, due to large librations, the density is shifted from in front of the nuclei towards the back of the nuclei, as viewed from the centre of libration. The magnitude of the region of non-vanishing p(A - H) density largely depends on the magnitude of the atomic motions (temperature). With the end N (295 K) mentioned above the radius of this region around the nucleus is about 0.5 Å, and with C (7) about 0.2 Å. Apart from the temperature, the p(A - H) densities are essentially determined by the distance of the atom from the centre of libration, and by the ratio of the librational/translational contributions to the atomic motions. A procedure is described to estimate the extrema in the p(A - H) densities in an actual structure.