Acta Cryst. (1996). B52, 357-368 [ doi:10.1107/S0108768195011025 ]
Abstract: The crystal structures of piperazinium hexanoate-h11, 
C4H12N2+2.C6H11O-2, and piperazinium hexanoate-d11, C4H12N2+2.C6D11O-2, have been determined from neutron diffraction data collected at 15 K. Nuclear anisotropic displacement parameters have been analyzed to obtain the internal molecular displacements of the H and D nuclei, given by <u2obs> - <u2ext> where <u2ext> is the contribution assuming all H/D to be carried rigidly on the vibrating molecular framework consisting of the heavier nuclei. In both crystal structures the cation ring is well fitted by the rigid-body model and the anion chain by a model with two rigid segments. In the piperazinium cations the corresponding protons in the two structures have about the same internal vibrational directions and magnitudes except for the two N-H protons, perhaps owing to differences in N-H
O hydrogen bonding. The internal vibrations of corresponding H/D in the h11 and d11 anions have approximately the same vibrational directions. The internal mean-square displacements of the H nuclei are systematically greater than the values of the corresponding D nuclei by an average factor 1.7 (3). For both anions, normal-mode analyses have been carried out using the force fields derived from ab initio quantum-mechanical calculations with HF/3-21 G and HF/6-31G** basis sets. The values of the resultant H/D internal displacements for C-H(D) bond stretching and methylene out-of-plane vibrations are in good agreement with experiment. However, with either basis set, theory predicts methylene in-plane mean-square displacements significantly greater than the experimental values.
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