Isothermal-isobaric ensemble

The isothermal-isobaric ensemble has the following 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

$Q_{NpT}=\frac{\beta p}{{\mathrm{\Lambda }}^{3N}N!}\underset{0}{\overset{\mathrm{\infty }}{\int }}dV{V}^N\exp [-\beta pV]\int d(R^{*}{)}^{3N}\exp [-\beta U(V,(R^{*}{)}^{3N})]$

where

• $V$ is the Volume:

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

• $\mathrm{\Lambda }$ is the de Broglie thermal wavelength

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

• $U$ is the potential energy, which is a function of the coordinates (or of the volume and the reduced coordinates)

Related reading

• Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition (2002) ISBN 0-12-267351-4