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| In molecular [[spectroscopy]], the '''Birge–Sponer method''' or '''Birge–Sponer plot''' is a way to calculate the [[dissociation energy]] of a molecule. By observing transitions between as many [[Molecular vibration|vibrational energy levels]] as possible, for example through electronic or [[infrared spectroscopy]], the difference between the energy levels, <math>\Delta G_{v+\frac{1}{2}}=G(v+1)-G(v)</math> can be calculated. This sum will have a [[maximum]] at <math>v_{max}</math>, representing the point of bond dissociation; summing over all the differences up to this point gives the total energy required to dissociate the molecule, i.e. to promote it from the [[ground state]] to an unbound state. This can be written:
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| <math>D_0=\sum_{v=0}^{v_{max}} \Delta G_{v+\frac{1}{2}}</math>
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| where <math>D_0</math> is the dissociation energy. If a [[Morse potential]] is assumed, plotting <math>\Delta G_{v+\frac{1}{2}}</math> against <math>v+1/2</math> should give a straight line, from which it is easy to extract <math>v_{max}</math> from the [[Zero of a function|intercept]] with the x-axis. In practice, such plots often give curves because of unaccounted anharmonicity in the potential; furthermore, the low population of the higher states (or the [[Franck-Condon principle]]) makes it difficult to experimentally obtain data at high values of <math>v</math>. Thus the [[extrapolation]] can be inaccurate and only an upper limit for the value of the dissociation energy can be obtained.
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| This method takes its name from [[Raymond Thayer Birge]] and [[Hertha Sponer]], the two physical chemists that developed it.
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| == References ==
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| *{{cite book |title= Basic Atomic and Molecular Spectroscopy|last= Hollas |first=Michael |year=2002 |publisher= [[Royal Society of Chemistry]]|isbn= 9780854046676|page= 81}}
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| *{{cite book|title=Vibrational Spectroscopy: Theory and Applications|last=Sathyanarayana|first=D.N.|year=2007|publisher=New Age International|isbn=9788122415179|page=18}}
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| {{DEFAULTSORT:Birge-Sponer method}}
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| [[Category:Spectroscopy]]
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Latest revision as of 00:50, 29 October 2014
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