Laporte rule

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The Laporte rule is a spectroscopic selection rule that only applies to centrosymmetric molecules (those with an inversion centre) and atoms. It states that electronic transitions that conserve parity, either symmetry or antisymmetry with respect to an inversion centre — i.e., g (gerade = even (German)) → g, or u (ungerade = odd) → u respectively—are forbidden. Allowed transitions in such molecules must involve a change in parity, either gu or ug. As a consequence, if a molecule is centrosymmetric, transitions within a given set of p or d orbitals (i.e., those that only involve a redistribution of electrons within a given subshell) are forbidden.[1]

A designation of g for an orbital means there is symmetry with respect to an inversion center. That is, if all the atoms are inverted across the inversion center, the resulting orbital would look exactly the way it did before having inversion applied to it. (This includes same orientation in space). A designation of u means the orbital is antisymmetric with respect to the inversion center, and changes sign everywhere upon inversion. The rule originates from a quantum mechanical selection rule that, during an electron transition, parity should be inverted.

However, forbidden transitions are allowed if the centre of symmetry is disrupted, and indeed, such apparently forbidden transitions are then observed in experiments. Disruption of the centre of symmetry occurs for various reasons, such as the Jahn-Teller effect and asymmetric vibrations. Complexes are not perfectly symmetric all the time. Transitions that occur as a result of an asymmetrical vibration of a molecule are called vibronic transitions, such as those caused by vibronic coupling. Through such asymmetric vibrations, transitions that would theoretically be forbidden, such as a d → d transition, are weakly allowed.[2]

The rule is named after Otto Laporte.[3] It is relevant, in particular, to the electronic spectroscopy of transition metals. Octahedral complexes have a center of symmetry (exact or approximate) so that d → d transitions are forbidden by the Laporte rule and are observed to be quite weak. However tetrahedral complexes have no center of symmetry so that the Laporte rule does not apply, and have more intense spectra.[4]

See also[edit]

References[edit]

  1. ^ Robert J. Lancashire (13 September 2006). "Selection Rules for Electronic Spectra of Transition Metal Complexes". University of the West Indies, Mona. 
  2. ^ Atkins, Peter; Paula, Julio de (2010) [1st. Pub. 1978]. "Chapter 13". Physical Chemistry. Oxford University Press. p. 494. 
  3. ^ Laporte, O.; Meggers, W.F. (1925). "Some rules of spectral structure" (abstract). Journal of the Optical Society of America 11 (5): 459. doi:10.1364/JOSA.11.000459. 
  4. ^ Miessler, Gary L.; Tarr, Donald A. (1999). Inorganic Chemistry. Prentice-Hall (2nd ed.). pp. 377–8.