Large Libration Amplitudes Research Articles

Modeling the vibrational dynamics of solid benzene: Hexafluorobenzene. The anatomy of a phase transition

We have studied the lowest temperature phase of the solid, C 6H 6:C 6F 6. The molecular dynamics of this phase (IV) are seen to consist of thermally activated six-fold rotational reorientations of the molecules about their hexad axis together with vibrations of the molecular chains which constitute the solid. In phase III we have observed, in addition to the solid state rotations, the onset of molecular diffusion. We suggest that the transition from phase IV to phase III occurs as a consequence of increasing amounts of disorder arising from these large amplitude librations or rotations. Relatively simple molecular and electrostatic models are employed to rationalize the different types of experimental data.

1H-NMR studies on thermochromism Ni(ii) complexes with N,N-diethylethylenediamine

The temperature dependence of the second moment (M2) of 1H NMR absorptions was measured in solid thermochromic bis(N,N-diethylethylenediamine)Ni(II) complexes. Perchlorate and tetrafluoroborate having a thermochromic phase transition at Ttr = 383 and 367 K, respectively, showed a discontinuous M2 change at Ttrr indicating that a marked change of the chelate-ring motions takes place at the transition. A small M2 value of ca. 8 G2 observed above the respective Ttr could be explained by the excitation of the chelate-ring puckering together with a large-amplitude librations of the whole complex ions. A gradual M2 decrease upon heating from 100 to 400 K was observed in bromide and iodide exhibiting continuous thermochromism. These M2 changes and the reported visible electron absorption maxima showed a quite analogous temperature dependence. This suggests that some kind of chelate-ring motion such as the puckering also takes place in the continuous thermochromism complexes.

Neutron diffraction study of the structure II clathrate hydrate: 3.5Xe.8CCl4.136D2O at 13 and 100 K

The crystal structure of the clathrate hydrate, 3.5Xe.8CCla.136D20, at 13 and 100K has been determined from single-crystal neutron diffraction data. The crystals are cubic, space group Fd3m, with ao = 17.192 (1)/~ at 13 K and 17.240 (2)/1 at 100 K. The structure was refined by least-squares methods with expansion coefficients of spherical harmonics as parameters describing rotational disorder of the CC14 molecules. The wR(F 2) indices are 0.040, 0.039 (13, 100 K) for 524, 522 reflections and 64, 61 parameters. The D20 molecules are disordered at 13 and 100 K in six hydrogen-bonded orientations of equal statistical weights, as in ice Ih. There are six nonequivalent hydrogen-bond interactions with O...D distances (at 13 K) between 1-738 (3) and 1-802 (1) ,~ and O...D--O angles between 174.8 (1) and 180 °. The covalent O---D lengths (uncorrected for thermal motion) are in the range 0-986 (1)-1.001 (2),~ and are decreased significantly from 13 to 100 K. The Xe atoms occupy statistically 22% of the dodecahedra and vibrate about the cage centers with r.m.s, displacements of 0.137 ,~ at 13 K and 0.179 ,~ at 100 K. The CC14 molecules exhibit large-amplitude libration motion about the C atom located at the center of the hexakaidecahedron. There are seven preferred molecular orientations with C--CI bonds directed toward the O vertices of the (D20)28 polyhedron. The C---C1 bond length from the radius parameter of the spherical distribution is 1.765 (2) ,/k at 13 K and 1-762 (3)/~ at 100 K, compared with the gas-phase value of 1.766 (3) ,~.

A Deuterium NMR Study of some Ammonium Tetraphenylborates

Abstract Deuterium nmr has been used to study the rotational dynamics of the ammonium ion in ammonium tetraphenylborate and of the cation in a series of methylammonium tetraphenylborates. The results of variable temperature 2H relaxation measurements (T1Z and T1Q) on the parent compound, ND4B(C6H5 )4 , lead to a low activation energy for reorientation of the ND4+ ion, 5.0 ± 0.5 kJ mol-1 , indicative of weak cation-anion interactions. Related studies of the tetramethyl-d12 ammonium salt indicate rapid jumps of the whole cation (τ ≪ 10-5S) over the complete temperature range investigated, 137 to 385 K, with an activation energy of 14.1 + 0.5 kJ mol-1 . Deuterium nmr lineshape studies of the methylammonium salt indicate rapid reorientation of the CD3 and ND3 groups about their C3 axes; however, the motion of the C - N axis is restricted to large amplitude librations. Similar studies of the dimethylammonium salt indicate methyl group jumps at 245 K; at temperatures above 320 K the cation also undergoes two-site jumps about the C2 axis. In the case of the trimethylammonium salt, the nmr lineshapes indicate methyl group jumps superimposed on C3 rotations of the complete cation about the N - H bond axis over the temperature interval 185-348 K. In all the tetraphenylborate salts studied, the 2H nmr lineshapes indicate substantial librational motion of the cation at room temperature.

Reorientational processes in solid (C 6H 6) 2Cr, (C 6H 6)Cr(CO) 3 and (C 6H 5Me)Cr(CO) 3

The reorientational motion of the benzene rings in solid (C 6H 6) 2Cr ( 1) and (C 6H 6)Cr(CO) 3 ( 2) and of the tricarbonyl group in solid (C 6H 5Me)Cr(CO) 3 ( 3), proposed on the basis of solid-state NMR experiments (wide-line 1H and 13C MAS) is studied by means of the pairwise potential energy method. Starting from the known crystal structures of the three species, relative potential energy barriers to motion and root mean square librational amplitudes at the bottom of the potential energy wells are evaluated and compared with the available anisotropic displacement parameters of the atoms involved in the process. The results show that the crystal packing in 2 and 3 forbids rotation of the Cr(CO) 3 group as a whole, while benzene reorientation encounters low potential energy barriers in both 1 and 2, in agreement with the spectroscopic information. An alternative interpretation of the dynamic behaviour shown by 3, based on large amplitude librations of both C 6H 5Me and Cr(CO) 3 groups, is put forward.

Molecular dynamics studies of the condensed phases of n-butane and their transitions

Molecular dynamics (MD) simulations of solid n-butane have been performed with the model described in paper I. All calculations were done on the massively parallel ICL DAP computer which made possible the large number of molecules (2048) and the long simulation runs. The structures of all three experimental phases as observed by neutron diffraction have been closely reproduced by the simulation. The plastic phase structure was not input into the simulation; instead the transition from the metastable phase II was simulated, yielding phase I after transition in very satisfactory agreement with experiment. The experimental phase III is metastable in our model since its energy is 1 per cent higher than the monoclinic structure of paper I. Analysis of the statics and dynamics of the plastic phase show that molecules are disordered about the long molecular axis, and re-orient about that axis between one major and three subsidiary sites. Large-amplitude libration means that the distribution about these sites is broad; the width of the major peak in the orientational distribution function is 40° in reasonable agreement with experiment. A rotational diffusion coefficient Dr =0·0716 rad2ps-1 and correlation time τ = 0·0363 ps were obtained.

Vibrational spectra, crystal dynamics and phase transitions of crystalline hexabromoethane and trichlorotribromoethane

The IR (20–1000cm −1) and Raman (5–1000cm −1) spectra of crystalline hexabromoethane (HBE) have been recorded. The internal modes are interpreted with the help of a normal coordinate analysis showing the importance of the flexibility of the CC bond. Eleven out of 21 expected lattice modes are observed and used to test known atom-atom potentials. None of these leads to very satisfactory agreement. Differential Scanning Calorimetry shows that trichlorotribromoethane (TCTB) has two phase transitions at 399 and 413 K. The comparison of both substances leads to a transition mechanism in two steps for TCTB and one step for HBE whereby large amplitude librations responsible for the transition could be identified from the spectroscopic study.

A b i n i t i o description of large amplitude motions in solid N2. III. Libron–phonon coupling

A new lattice dynamics scheme is proposed for handling librons, anharmonic translational vibrations, and translational-rotational coupling in molecular crystals. This scheme is an extension of earlier libron models which describe large amplitude librations or hindered rotations. The formalism is based on expanding the intermolecular potential in the molecular displacement coordinates, including cubic and quartic terms, while retaining the exact orientational dependence. Closed expressions are obtained via spherical tensor methods. After constructing separate mean field states for the molecular rotations and translations, using bases of tesseral harmonics and 3D harmonic oscillator functions, respectively, the intermolecular correlations are taken into account and simultaneously the translational-rotational coupling, by solving the equations of motion for the crystal according to the time-dependent Hartree or random-phase approximation. Application of the formalism to the ordered α and γ phases of solid nitrogen, using an ab initio potential, gave very satisfactory results.

Transient attitude dynamics of satellites with deploying flexible appendages

The paper presents a general formulation for librational dynamics of satellites with an arbitrary number, types, and orientation of deploying flexible appendages. The generalized force term is incorporated making the formulation applicable to a wide variety of situations where aerodynamic forces, solar radiation, earth's magnetic field, etc. become significant. In particular, the case of a beam-type flexible appendage deploying from a satellite in an arbitrary orbit is considered. The corresponding nonlinear, non-autonomous equations for in-plane and out-of-plane vibrations are derived, allowing for the variation of mass density and flexural rigidity along the length with time dependent deployment velocity and spin rate. Next, the attention is focused on the linearized analysis of the in-plane vibrational equation using the assumed-mode method and its substantiation through numerical integration. Finally, the paper presents results for both steady-state and transient attitude behaviour for a representative gravity gradient configuration for a range of initial conditions and system parameters. Results show the combined effect of flexibility and deployment on the dynamics of the system to be substantial. Disturbance of the appendage can excite large amplitude librations. On the other hand, the converse situation is not necessarily true. Furthermore, Coriolis loading, induced by the extending appendages, can become a limiting factor in arriving at a deployment strategy; an effect not pointed out in the literature.