P. Schiebel

Proton density and orientational potential in nickelhexammine salts: a thermodynamic analysis of rotation-translation coupling

The scattering densities of the orientationally disordered protons and deuterons in Ni(NX3)6Y2 (X=H or D; Y=Br, I, NO3 or PF6) are obtained from neutron single-crystal diffraction data at room temperature. While we observe a nearly circular density distribution for Y=PF6, a nuclear density distribution with four maxima on a square shows up for Y=Br, I and NO3. This is a pronounced deviation from the circular distribution that is expected from uniaxial rotational diffusion or reorientational jump models for the dynamics of the orientational disordered ammonia groups. All observed density distributions are consistently explained as the consequence of rotation-translation coupling in an anharmonic crystal potential. The calculated potential parameters, i.e. anharmonicity and strength of the coupling, depend on the type of anion present in the crystal frame. The weak anisotropy in the Y=NO3 and PF6 compounds is the consequence of a nearly eightfold non-crystallographic symmetry of the atoms establishing the hindrance potential.

The isotope effect and phase transitions in ammonium hexachloropalladate studied by neutron tunnelling spectroscopy

Above 30% deuteration, ammonium hexachloropalladate undergoes the phase transition Fm3m P21/n, with Tc increasing to 30.2 K for pure (ND4)2PdCl6. Rotational tunnelling of NH4 and NH3D was used to study this phase transition. The transition energies are related to the tunnelling matrix elements hi.NH3D can be described as a one-dimensional rotor, with the one-dimensional matrix elements being almost exactly the averages of the three-dimensional ones. In the high-temperature phase the intensities of the respective tunnelling transitions confirm a statistical occurrence probability of the isomers. In the low-temperature phase the strength of the rotational potential increases by about 30%. A broadening of the NH3D tunnelling line with decreasing temperature above the crystallographic phase transition is interpreted as an intermediate glass phase which evolves due to long-range dipolar coupling combined with positional disorder.

Neutron diffraction study of the orientational disorder in Ni(ND3)6Br2

The ND3 group is in the high temperature phase of the title compound dynamically disordered. Fourier maps derived from the analysis of neutron single crystal Bragg data with phases based on a split atom and a Frenkel model show uniquely that each D3 group has four density maxima occupying the corners of a square. Neither one nor three dimensional models of purely rotational disorder can describe the observations adequately.

Orientational disorder in Ni(ND3)6Br2: A two-dimensional thermodynamic rotation-translation model for the deuterium disorder

The ND3 group in Ni(ND3)6Br2 is orientationally disordered at room temperature: the D3 triangle gives rise to a density distribution with maxima on the corners of a square. We explain this observation as the consequence of a coupled rotational-translational motion of the molecule in a two-dimensional anharmonic single particle potential with tetragonal symmetry. Potential parameters are calculated from experimental data by a least squares procedure. From the total crystal potential of the D3 group we conclude that a combination of center of mass motion and rotation which is possible essentially without an energy barrier, is the basic process observed in quasielastic neutron scattering observations of the jump diffusion.

ND3-density distribution in orientationally disordered Ni(ND3)6Cl2 observed by means of neutron Laue diffraction

Neutron Laue diffraction combined with the maximum-entropy method yields a powerful tool for direct observation of the density distribution of dynamically disordered molecules. Laue diffraction investigation delivers a systematically incomplete data set in a very much shorter time than using a conventional four-circle diffractometer, and the maximum-entropy method is an easy tool to use to cope with the gaps in the data set. From the calculated proton-density distribution the molecular hindering potential was successfully derived in the case of Ni(ND3)6Cl2.

Coherent internal and centre of mass quantum rotation of methyl groups in the p-tert-butyl-calix[4]arene(2 :1)p-xylene supramolecular complex

The low-temperature inelastic neutron scattering spectrum measured for the p-tert-butylcalix[4]arene(2:1)p-xylene complex has been interpreted in the framework of a quantum dynamical model assuming a rotational motion of the p-xylene groups correlated to the translational motion of their centre of mass. By comparing the experimental data with calculated energies and intensities, the effective anharmonic and anisotropic molecular potential experienced by the methyl groups has been derived. The wavefunctions deduced from the spectroscopy results are used to calculate the proton density distribution in the plane of the motion.

Quantum mechanics of the rotation-translation coupling of NH3-groups in metal hexaammine salts

Abstract The family of metal hexaammine salts Me(NH3)6Y2 with MeNi, Co is characterized by a wealth of different distributions of the protons of the disordered NH3 group. We find a transition form nearly unhindered rotation with YPF6 to weak localization on the four corners of a square with YI. This is based on a gradually increasing rotation-translation coupling of the motion. Low-temperature measurements do not allow an interpretation of these phenomena in terms of Boltzmann densities. We have therefore calculated the proton density on the basis of a complete quantum mechanical Hamiltonian which takes into account the rotation-translation coupling caused by a fourth-order anharmonic crystal potential. The quantum mechanical model removes all the difficulties we encountered earlier with Boltzmann densities.

Partial conversion of neutron incoherent into coherent scattering by NH3 quantum rotators

Abstract Neutron diffraction experiments on powders are used to investigate the quantum mechanical behaviour of uniaxial rotators, i.e. NH3-molecules in Ni(NH3)6(PF6)2, Co(NH3)6(PF6)2 and Ni(NH3)6I2. A diffuse temperature dependent component of the total scattering, modulated ∼ sin QrH-H/QrH-H, is observed at a temperature of ≃ 20 K and below. This observation is due to the fact, that on cooling the sample to kT ∼ B (rotational constant) the rotational ground state is strongly populated. The ground state of a uniaxial free rotator, however, is completely polarized. As a consequence the scattering of those NH3 groups being in the ground state becomes coherent and is observable in diffraction experiments.

The crystal-field potential of solid at room temperature

Bragg intensities from neutron diffraction data for single crystals were used to determine the rotational potential at room temperature. The rotational potential is evaluated in terms of mixed rotator functions . The expansion coefficients , i.e. potential parameters, are obtained directly from experiment. The potential exhibits well developed minima, absolute ones at the Euler angle set and relative ones at . They correspond to the two orientations, i.e. pentagonal and hexagonal facing, of the molecules in their low-temperature arrangement. The overall potential barrier height of the absolute minimum is 400 K and the difference between the two types of minima is 270 K.

The Maximum Entropy Reconstruction of Patterson and Fourier Densities in Orientationally Disordered Molecular Crystals: A Systematic Test for Crystallographic Interpolation Models

Accurate density data are the primary information required for a thermodynamic model of molecular disorder. Neutron or X-ray Bragg scattering yields truncated and noisy data sets of unphased Fourier components. In the specific case of disordered molecular crystals, the phase problem can be bypassed by means of a density interpolation model using Frenkel atoms. The fitting to the data is usually quite good, and the validity of such a parametric model follows from the stability of the recovered phases with respect to the parameters. It is well established by now that MaxEnt is the best tool to retrieve 3-dim or projected 2-dim densities from phased data.