Thermal ellipsoids, isotropic

Figure 7. The two analogous Ni H fragments (a and b) in [P/i4P]2+-[Ni 2(CO)2 H2]2 (3), and the Ni H fragment (c) in [Ph4As]3+-[Nii2(CO)2itf]3-.Me2CO (4), showing hydrogen atoms in the octahedral interstices. The mean Ni-H distances and 20% isotropic thermal ellipsoids of nuclear motion were obtained from the neutron diffraction experiments.

The isotropic thermal ellipsoid at Na was very large, indicating the presence of 2 or more nonequivalent Na+ ions at this position. Attempts to separate it into 2 nonequivalent Na+ ion positions failed. The final model (see Table lie) is the result of anisotropic refinement of all positions, except Na which was refined isotropically, with occupancies fixed. The final difference Fourier function, whose estimated standard deviation is 0.06 eA-, was featureless. See Tables lie and III, and Figure 2, for additional information. 

Fig. 1. The structure of l,6-diaininohexanecadinium(II) tetracyanonickel-ate(II)- -toluidine (1/1). Hydrogen atoms are omitted thermal ellipsoid with 30% probability isotropic spheres of 4.0 for the atoms of guest molecule. (i) A perspective view of the unit cell, (ii) A perspective view along a-axis. (iii) A perspective view along b-axis.

A general synthesis of pincer N-heterocyclic carbenes with pyridines as the bridging unit is presented below. The combination of 2 with 2-iodoethanol or 3-bromopropanol gave 10a and 10b, respectively (10). The combination of the halide salt of 10a or 10b with an equimolar amount of AgaO gives the silver biscarbene polymers 11a and 11b, respectively. Conq)ound 11a has been crystallographically characterized The hydroxide salts 11a and lib are very soluble and slowly decompose in water. The deconq)osition leads to a slow release of silver atoms. The thermal ellipsoid plot (atoms shown isotropically) of 11a is shown in Figure 4. 

One of the primary features of the Gay-Berne potential is the presence of anisotropic attractive forces which should allow the observation of thermally driven phase transitions and this has proved to be the case. Thus using the parametrisation proposed by Gay and Berne, Adams et al. [9] showed that GB(3.0, 5.0, 2, 1) exhibits both nematic and isotropic phases on varying the temperature at constant density. This was chosen to be close to the transitional density for hard ellipsoids with the same ellipticity indeed it is generally the case that to observe a nematic-isotropic transition for Gay-Berne mesogens the density should be set in this way. The long range orientational order of the phase was established from the non-zero values of the orientational correlation coefficient, G2(r), at large separations and the translational disorder was apparent from the radial distribution function. 

The atomic environment within the crystal is usually far from isotropic, and the next simplest model of atomic motion (after the isotropic model just described) is one in which the atomic motion is represented by the axes of an ellipsoid this means that the displacements have to be described by six parameters (three to define the lengths of three mutually perpendicular axes describing the displacements in these directions, and three to define the orientation of these ellipsoidal axes relative to the crystal axes), rather than just one parameter, as in the isotropic case. Atomic displacement parameters, and their relationship to thermal vibrations and spatial disorder in crystals are covered in more detail in Chapter 13. 

In a crystal, displacements of atomic nuclei from equilibrium occur under the joint influence of the intramolecular and intermolecular force fields. X-ray structure analysis encodes this thermal motion information in the so-called anisotropic atomic displacement parameters (ADPs), a refinement of the simple isotropic Debye-Waller treatment (equation 5.33), whereby the isotropic parameter B is substituted by six parameters that describe a libration ellipsoid for each atom. When these ellipsoids are plotted [5], a nice representation of atomic and molecular motion is obtained at a glance (Fig. 11.3), and a collective examination sometimes suggests the characteristics of rigid-body molecular motion in the crystal, like rotation in the molecular plane for flat molecules. Lattice vibrations can be simulated by the static simulation methods of harmonic lattice dynamics described in Section 6.3, and, from them, ADPs can also be estimated [6]. 

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