Isothermal-isobaric ensemble: Difference between revisions
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* V (Volume) | * V (Volume) | ||
The classical partition function, for a one-component atomic system in 3-dimensional space, is given by | The [[classical partition function]], for a one-component atomic system in 3-dimensional space, is given by | ||
<math> Q_{NpT} = \frac{\beta p}{\Lambda^3 N!} \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{\beta p}{\Lambda^3 N!} \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> | ||
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*<math> \beta = \frac{1}{k_B T} </math>; | *<math> \beta = \frac{1}{k_B T} </math>; | ||
*<math> \Lambda </math> is the | *<math> \Lambda </math> is the [[de Broglie wavelength]] | ||
*<math> \left( R^* \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math> | *<math> \left( R^* \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math> | ||
Revision as of 11:16, 26 February 2007
Variables:
- N (Number of particles)
- p (Pressure)
- T (Temperature)
- V (Volume)
The classical partition function, for a one-component atomic system in 3-dimensional space, is given by
![{\displaystyle Q_{NpT}={\frac {\beta p}{\Lambda ^{3}N!}}\int _{0}^{\infty }dVV^{N}\exp \left[-\beta pV\right]\int d(R^{*})^{3N}\exp \left[-\beta U\left(V,(R^{*})^{3N}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2b25a24f7c4f7a7cfa5de491a6d0593a5ed1364b)
where
- ;
- is the de Broglie wavelength
- represent the reduced position coordinates of the particles; i.e.
- is the potential energy, which is a function of the coordinates (or of the volume and the reduced coordinates)
References
- D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press