Isothermal-isobaric ensemble

From SklogWiki

Ensemble variables:

N is the number of particles
p is the pressure
T is the temperature

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

$Q_{NpT} = \frac{\beta p}{\Lambda^3 N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^*)^{3N} \exp \left[ - \beta U \left(V,(R^*)^{3N} \right) \right]$

where

$\left. V \right.$ is the Volume:

$\beta := \frac{1}{k_B T}$ , where $k B$ is the Boltzmann constant

$\left. \Lambda \right.$ is the de Broglie thermal wavelength

$\left( R^* \right)^{3N}$ represent the reduced position coordinates of the particles; i.e. $\int d ( R^*)^{3N} = 1$

$\left. U \right.$ is the potential energy, which is a function of the coordinates (or of the volume and the reduced coordinates)

[edit] References

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

Isothermal-isobaric ensemble

From SklogWiki

[edit] References

Views

Personal tools

Navigation

Help

Search

Toolbox