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| [[File:Kasha-s-rule.png|thumb|300px|Scheme of Kasha's rule. A photon with energy <math>h\nu_1</math> excites an electron of fundamental level, of energy <math>E_0</math>, up to an excited energy level (e.g. <math>E_1</math> or <math>E_2</math>) or on one of the vibrational sub-levels. Vibrational relaxation then takes place between excited levels, which leads to dissipation of part of the energy (<math>\Delta E_d</math>), taking the form of a transition (internal conversion) towards the lowest excited level. Energy is then dissipated by emission of a photon of energy <math>h\nu_2</math>, which allows the system to go back to its fundamental state.]]
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| '''Kasha's rule''' is a principle in the [[photochemistry]] of [[Excited state|electronically excited]] molecules. The rule states that photon emission ([[fluorescence]] or [[phosphorescence]]) occurs in appreciable yield only from the lowest excited state of a given [[Multiplicity (chemistry)|multiplicity]]. It is named for American spectroscopist [[Michael Kasha]], who proposed it in 1950.<ref>[http://turmac13.chem.columbia.edu/PDF_db/History/characterization.PDF Characterization of Electronic Transitions in Complex Molecules]. Kasha, M. ''Discussions of the Faraday Society'', 1950, '''9''': p.14-19.</ref><ref>[[International Union of Pure and Applied Chemistry|IUPAC]]. [http://goldbook.iupac.org/K03370.html Kasha rule – Compendium of Chemical Terminology, 2nd ed. (the "Gold Book")]. Compiled by McNaught, A.D. and Wilkinson, A. Blackwell Scientific Publications, Oxford, 1997.</ref>
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| ==Description and explanation==
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| The rule is relevant in understanding the [[emission spectrum]] of an excited molecule. Upon absorbing a photon, a molecule in its electronic [[ground state]] (denoted ''S''<sub>0</sub>, assuming a [[singlet state]]) may – depending on the photon [[wavelength]] – be excited to any of a set of higher electronic states (denoted ''S''<sub>n</sub> where ''n''>0). However, according to Kasha's rule, [[Luminescence|photon emission]] (termed fluorescence in the case of an ''S'' state) is expected in appreciable yield only from the lowest excited state, ''S''<sub>1</sub>. Since only one state is expected to yield emission, an equivalent statement of the rule is that the emission wavelength is independent of the excitation wavelength.<ref>[http://forum.grenzwissen.de/postingimage/spiepaper709712.pdf "Unusual autofluorescence characteristic of cultured red-rain cells"]. Louis, J. and Kumar, A.S. Presented in [[SPIE]] Conference 7097, Aug 2008.</ref>
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| The rule can be explained by the [[Franck–Condon principle|Franck–Condon factor]]s for [[vibronic transition]]s. For a given pair of energy levels that differ in both vibrational and electronic [[quantum number]], the Franck–Condon factor expresses the degree of overlap between their vibrational [[wavefunction]]s. The greater the overlap, the quicker the molecule can undergo transition from the higher to the lower level. Overlap between pairs is greatest when the two vibrational levels are close in energy; this tends to be the case when the ''vibrationless'' levels of the electronic states coupled by the transition (where the vibrational quantum number ''v'' is zero) are close. In most molecules, the vibrationless levels of the excited states all lie close together, so molecules in upper states quickly reach the lowest excited state, ''S''<sub>1</sub>, before they have time to fluoresce. This process is known as [[Internal conversion (chemistry)|internal conversion]] (IC). However, the energy gap between ''S''<sub>1</sub> and ''S''<sub>0</sub> is greater, so here fluorescence occurs, since it is now kinetically competitive with IC.<ref name=klan>[http://books.google.co.uk/books?id=8IstqQf6ZckC&pg=PA40&lpg=PA40&dq=kasha%27s+rule&source=bl&ots=ArmEU3BEC7&sig=RV1DG7mCXuWRSFcXM1Q6YZ8UY3w&hl=en&ei=sjvkS8zINYmEmgPXj5CCBg&sa=X&oi=book_result&ct=result&resnum=9&ved=0CDoQ6AEwCDgK#v=onepage&q=kasha%27s%20rule&f=false ''Photochemistry of Organic Compounds: From Concepts to Practice'']. Klán, P. and Wirz, J. Wiley-Blackwell, 2009. p.40. ISBN 1-4051-6173-6.</ref><ref name=suppan>[http://books.google.com/books?id=Xq-vurqbVt4C&pg=PA56&dq=%22kasha%27s+rule%22&hl=en&ei=tL_TTPa5Lof1sgbMhfjtBA&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDcQ6AEwAw#v=onepage&q=%22kasha%27s%20rule%22&f=false ''Chemistry and Light'']. Suppan, P. Royal Society of Chemistry, 1994. p.56. ISBN 0-85186-814-2.</ref>
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| Exceptions to Kasha's rule arise when there are large energy gaps between excited states. An example is [[azulene]]: the classical explanation is that the ''S''<sub>1</sub> and ''S''<sub>2</sub> states lie sufficiently far apart that fluorescence is observed mostly from ''S''<sub>2</sub>.<ref name=klan /><ref name=suppan /> However, recent research has put forward that this may not be the case, and that fluorescence is seen from ''S''<sub>2</sub> because of crossing in the ''N''-dimensional potential surface allowing very fast internal conversion from ''S''<sub>1</sub> to ''S''<sub>0</sub>. {{Citation needed|date=April 2009}}
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| ==Kasha–Vavilov rule==
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| A corollary of Kasha's rule is the Kasha–[[Sergey Ivanovich Vavilov|Vavilov]] rule, which states that the [[quantum yield]] of luminescence is generally independent of the excitation wavelength.<ref name=klan /><ref>[[International Union of Pure and Applied Chemistry|IUPAC]]. [http://goldbook.iupac.org/K03371.html Kasha–Vavilov rule – Compendium of Chemical Terminology, 2nd ed. (the "Gold Book")]. Compiled by McNaught, A.D. and Wilkinson, A. Blackwell Scientific Publications, Oxford, 1997.</ref> This can be understood as a consequence of the tendency – implied by Kasha's rule – for molecules in upper states to relax to the lowest excited state non-radiatively. Again there are exceptions: for example [[benzene]] vapour.<ref name=klan />
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| ==See also==
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| *[[Stokes shift]], the difference between the absorption and emission frequencies, related to Kasha's rule.<ref>''[http://books.google.com/books?id=9d893122U6kC&q=stokes+shift#v=snippet&q=stokes%20shift&f=false Coordination Chemistry]'' Gispert, J.R. Wiley-VCH, 2008. p. 483. ISBN 3-527-31802-X.</ref>
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:Kasha's Rule}}
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| [[Category:Luminescence]]
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| [[Category:Quantum chemistry]]
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