Effects of H/D substitution on thermal vibrations in piperazinium hexanoate-h11, d11

The crystal structures of piperazinium hexanoate-h11, 1/2C4H12N2(2+).C6H11O2-, and piperazinium hexanoate-d11, 1/2C4H12N2(2+).C6D11O2-, 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 (u(obs)2)-(u(ext)2) where (u(ext)2) 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/3-21G 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.