Nuclear motion, thermal ellipsoids

Figure 1. Stereoscopic drawings of the molecular configuration of Mo2 r C H )2 CO)4t 2-H) g2-P CH )2) showing (a) thermal ellipsoids of nuclear motion for all atoms scaled to enclosed 50% probability (b) the atom labeling. The entire molecule possesses a pseudotwofold axis passing through the bridging hydrogen and phosphorus atoms.

Figure 8. The molecular structure of the [Cr2(CO)io(M2-tf)] anion for the bis(triphenylphosphine)-iminium salt showing (a) a view normal to the Cr-Cr axis (b) a view looking down the Cr-Cr axis. The Cr-Cr intemuclear separation is 3.349(13) A. The thermal ellipsoids of nuclear motion for all atoms are scaled to enclosed 50% probability.

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.

More complex mathematical treatment is necessary when the thermal motion is very large, as for hydrogen atoms in a room-temperature neutron structure analysis, or when it is curvilinear as in a hindered-rotor. The Uy second-rank tensor does not adequately describe the nuclear or electron-scattering density when the motion is far from harmonic or when it deviates from the familiar ellipsoidal probability form. Tb deal with such examples, more complex mathematic expressions using Gram Charlier or Edgeworth expansions are available [210]. 

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