Thermal Ellipsoid Analysis. Carroll K. Johnson and Michael N. Burnett, Chemical & Analytical Sciences Division, Oak Ridge National Lab., Oak Ridge, TN 37831,

Structure analysis characterizes the time and symmetry averaged chemical motif within the crystal's space group and unit cell. The six anisotropic displacement parameters (ADPs) for each atom of the motif define the displacement matrix for a 3D Gaussian probability density function (PDF) for that atom. Molecular thermal motion patterns are often interpreted visually through ORTEP drawings, which show thermal motion ellipsoids (TMEs) that contain a given fraction (e.g., 50%) of the PDF for each atom, ignoring the overlap of PDFs. ORTEP drawings also show chemical bonds which aid our visually intuitive interpretation of large amplitude displacement modes.

Analytic estimates of certain large amplitude vibration modes plus bond length and angle corrections are made through motion correlation models such as the Busing and Levy riding model, the Schomaker and Trueblood rigid-body model, and coupled rigid-body models that combine these two approaches. A new statistical motion-correlation model under development uses neighboring atom covariance blocks from the inverted least-squares structure refinement matrix rather than a mechanistic model. Higher order approximations past the TME model include the Gram Charlier statistical expansion and curvilinear motion mechanistic models.

For topological thermal-motion analysis, we sum over the PDFs to obtain a global density map and then find the zero-gradient peak, pass, pale, and pit critical points and their interconnecting separatrix paths to construct a critical net representation visualized through ORTEP. Topological characterization techniques are under developed as documented on the world wide web.

http://www.ornl.gov/ortep/topology.html

Research sponsored by the Laboratory Directed R&D Program of ORNL, managed by LMERC for the US DOE under Contract No. DE-AC05-96OR22464.