Thermal ellipsoid

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conformation of the organic molecule, diphenyl ether, formulae C12H10O or (C6H5)2O, abbreviated Ph2O. Carbons (C ) are shown in black, hydrogens (H) in grey-white, and the oxygen (O) in red. The thermal ellipsoids are set at a 50% probability level, and the positions of atoms and the anisotropies of position reflected in the ellipsoids derive from a crystal structure of the molecule.[1]
Lewis acid, SbF5.[3]

Thermal ellipsoids, more formally termed atomic displacement parameters or anisotropic displacement parameters, are

anisotropic (different magnitudes in different directions in space), an ellipsoid is a convenient way of visualising the vibration and therefore the symmetry and time averaged position of an atom in a crystal. Their theoretical framework was introduced by D. W. J. Cruickshank in 1956 and the concept was popularized through the program ORTEP (Oak Ridge Thermal-Ellipsoid Plot Program), first released in 1965.[4]

Thermal ellipsoids can be defined by a tensor, a mathematical object which allows the definition of magnitude and orientation of vibration with respect to three mutually perpendicular axes. The three principal axes of the thermal vibration of an atom are denoted , , and , and the corresponding thermal ellipsoid is based on these axes. The size of the ellipsoid is scaled so that it occupies the space in which there is a particular probability of finding the electron density of the atom. The particular probability is usually 50%.[5]

See also

References

  1. ^ Angshuman R. Choudhury, Kabirul Islam, Michael T. Kirchner, Goverdhan Mehta & Tayur N. Guru Row, 2004, "In situ cryocrystallization of diphenyl ether:  C−H···π mediated polymorphic forms," J. Am. Chem. Soc., 126(39), pp 12274–12275, DOI: 10.1021/ja046134k, see [1] accessed 23 June 2105.
  2. PMID 18700751
    .
  3. ISBN 978-0-12-023618-3
    . Retrieved 23 June 2015.
  4. ^ "ORTEP". www.umass.edu. Retrieved 2022-04-21.
  5. ISBN 978-3540206446
    .
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