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| {{Unreferenced|auto=yes|date=December 2009}}
| | The author is known as Wilber Pegues. Ohio is where his home is and his family members enjoys it. Invoicing is my occupation. The favorite pastime for him and his kids is to play lacross and he would by no means give it up.<br><br>Also visit my site; telephone psychic ([http://www.onbizin.co.kr/xe/?document_srl=320614 www.onbizin.co.kr]) |
| The '''vibrational partition function''' traditionally refers to the component of the [[canonical partition function]] resulting from the vibrational degrees of freedom of a system. The vibrational partition function is only well-defined in model systems where the vibrational motion is relatively uncoupled with the system's other degrees of freedom. | |
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| ==Approximations==
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| ===Quantum Harmonic Oscillator===
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| The most common approximation to the vibrational partition function uses a model in which the [[vibrational eigenmodes]] or [[normal mode|vibrational normal modes]] of the system are considered to be a set of uncoupled quantum harmonic oscillators. It is a first order approximation to the partition function which allows one to calculate the contribution of the vibrational degree of freedom of molecules towards thermodynamic variables. A quantum harmonic oscillator has an energy spectrum characterized by: | |
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| <math>E_{j,i}=\hbar\omega_j(i+\frac{1}{2})</math>
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| where j is an index representing the vibrational mode, and i is the quantum number for each energy level of the jth vibrational mode. The vibrational partition function is then calculated as:
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| <math>Q_{vib}=\prod_j{\sum_i{e^{-\frac{E_{j,i}}{kT}}}}</math> | |
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| ==See also==
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| * [[Partition function (mathematics)]]
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| {{Statistical mechanics topics}}
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| {{DEFAULTSORT:Vibrational Partition Function}}
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| {{Physics-stub}}
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| [[Category:Partition functions]] | |
Latest revision as of 15:52, 14 December 2014
The author is known as Wilber Pegues. Ohio is where his home is and his family members enjoys it. Invoicing is my occupation. The favorite pastime for him and his kids is to play lacross and he would by no means give it up.
Also visit my site; telephone psychic (www.onbizin.co.kr)