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The Laporte rule is a rule that explains the intensities of absorption spectra for chemical species. It is a selection rule that rigorously applies to atoms, and to molecules that are centrosymmetric, i.e. with an inversion centre. It states that electronic transitions that conserve parity are forbidden. Thus transitions between two states that are each symmetric with respect to an inversion centre will not be observed. Transitions between states that are antisymmetric with respect to inversion are forbidden as well. In the language of symmetry, g (gerade = even (German)) → g and u (ungerade = odd) → u transitions are forbidden. Allowed transitions must involve a change in parity, either g → u or u → g.

For atoms s and d orbitals are gerade, and p and f orbitals are ungerade. The Laporte rule implies that s to s, p to p, d to d, etc. transitions should not be observed in atoms or centrosymmetric molecules. Practically speaking, only d-d transitions occur in the visible region of the spectrum. The Laporte rule is most commonly discussed in the context of the electronic spectroscopy of transition metal complexes. However, low-intensity f-f transitions in the actinide elements can be observed in the near-infrared region.^[1]^[2]

Optical properties of transition metal complexes

Octahedral complexes have a center of symmetry and thus should show no d-d bands. In fact, such bands are observed, but are weak, having intensities orders of magnitude weaker than "allowed" bands. The extinction coefficients for d-d bands are in the range 5–200.^[3]

The allowedness of d-d bands arises because the centre of symmetry for these chromophores is disrupted for various reasons. The Jahn–Teller effect is one such cause. 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 are weakly allowed.^[4]

The Laporte rule is powerful because it applies to complexes that deviate from idealized O_h symmetry. For example, the d-d transitions for [Cr(NH₃)₅Cl]²⁺ are weak (ε < 100) even though the complex is only of C_4v symmetry.^[5]

The Laporte rule helps explain the intense colors often observed for the tetrahedral complexes. The tetrahedral point group lacks the inversion operation, so the Laporte rule does not apply.^[6] Illustrative of this effect are the disparate extinction coefficients for octahedral vs tetrahedral complexes of Co(II). For [Co(H₂O)₆]²⁺, which is pink, ε ≈ 10. For [CoCl₄]^2-, which is deep blue, ε ≈ 600.^[5]

Note on spin-selection rule

Complementing the Laporte rule, is the spin-selection rule, which forbids transitions that involve changes in spin state. Violations of both the Laporte and spin-selection rules results in particularly low extinction coefficients. Illustrative of this combined effect is the faintness of even concentrated solutions of octahedral Mn(II) and Fe(III) complexes.

History

The rule is named after Otto Laporte who published it in 1925 with William Frederick Meggers.^[7]

References

^ Cary, Samantha K.; Vasiliu, Monica; Baumbach, Ryan E.; Stritzinger, Jared T.; Green, Thomas D.; Diefenbach, Kariem; Cross, Justin N.; Knappenberger, Kenneth L.; Liu, Guokui; Silver, Mark A.; DePrince, A. Eugene; Polinski, Matthew J.; Van Cleve, Shelley M.; House, Jane H.; Kikugawa, Naoki (2015-04-16). "Emergence of californium as the second transitional element in the actinide series". Nature Communications. 6 (1): 6827. doi:10.1038/ncomms7827. ISSN 2041-1723. PMC 4410632. PMID 25880116.
^ Wolford, Nikki J.; Yu, Xiaojuan; Bart, Suzanne C.; Autschbach, Jochen; Neidig, Michael L. (2020-10-27). "Ligand effects on electronic structure and bonding in U(III) coordination complexes: a combined MCD, EPR and computational study". Dalton Transactions. 49 (41): 14401–14410. doi:10.1039/D0DT02929G. ISSN 1477-9234. OSTI 1850721. PMID 33001085. S2CID 222172077.
^ Robert J. Lancashire (13 September 2006). "Selection Rules for Electronic Spectra of Transition Metal Complexes". University of the West Indies, Mona.
^ Atkins, Peter; Paula, Julio de (2010) [1st. Pub. 1978]. "Chapter 13". Physical Chemistry. Oxford University Press. p. 494.
^ ^a ^b Hans Ludwig Schläfer and Günter Gliemann (1969). Basic Principles of Ligand Field Theory. London: Wiley-Interscience. ISBN 0471761001.
^ Miessler, Gary L.; Tarr, Donald A. (1999). Inorganic Chemistry (2 ed.). Prentice-Hall. pp. 377–8.
^ 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.