Isothermal-isobaric ensemble: Difference between revisions

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Isothermal-Isobaric ensemble:
Variables:
Variables:


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* T (Temperature)
* T (Temperature)


Classical Partition Function (Atomic system, one-component, 3-dimensional space):
The classical partition function, for a one-component atomic system in 3-dimensional space, is given by


<math> Q_{NpT} = \frac{1}{\Lambda^3} \int_{0}^{\infty} d V  V^{N} \exp \left[ - \beta p V \right] \int d ( R^{3N} ) \exp \left[ - \beta U \left(V,(R)^{3N} \right) \right]
<math> Q_{NpT} = \frac{1}{\Lambda^3} \int_{0}^{\infty} d V  V^{N} \exp \left[ - \beta p V \right] \int d ( R^{3N} ) \exp \left[ - \beta U \left(V,(R)^{3N} \right) \right]
</math>
</math>


where
:<math> \beta = \frac{1}{k_B T} </math>


* <math> \beta = \frac{1}{k_B T} </math>


* to be continued ...


== References ==
== References ==


# D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press
# D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press

Revision as of 11:44, 21 February 2007

Variables:

  • N (Number of particles)
  • p (Pressure)
  • T (Temperature)

The classical partition function, for a one-component atomic system in 3-dimensional space, is given by

where


References

  1. D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press