EFFECTS OF H D SUBSTITUTION ON THERMAL VIBRATIONS IN PIPERAZINIUM HEXANOATE-H(11),D(11)/

The crystal structures of piperazinium hexanoate-h(11), 1/2C(4)H(12)N( 2)(2+).C6H11O2-, and piperazinium hexanoated(11), d(11), 1/2C(2)N(2)(2 +).C6D11O2-, have been determined from neutron diffraction data collec ted at 15 K. Nuclear anisotropic displacement parameters have been ana lyzed to obtain the internal molecular displacements of the H and D nu clei, given by [u(obs)(2)] - [u(ext)(2)] where [u(ext)(2)] is the cont ribution assuming all H/D to be carried rigidly on the vibrating molec ular framework consisting of the heavier nuclei. In both crystal struc tures the cation ring is well fitted by the rigid-body model and the a nion chain by a model with two rigid segments. In the piperazinium cat ions the corresponding protons in the two structures have about the sa me 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 h(11) and d(11) anions have approximately the same vibrational directions. The interna l 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 usin g the force fields derived from ab initio quantum-mechanical calculati ons with HF/3-21G and HF/6-31G* basis sets. The values of the resulta nt H/D internal displacements for C-H(D) bond stretching and methylene out-of-plane vibrations are in good agreement with experiment. Howeve r, with either basis set, theory predicts methylene in-plane mean-squa re displacements significantly greater than the experimental values.