Constant-pressure Monte Carlo

In constant-pressure Monte Carlo a trial change in the volume becomes one of the Monte Carlo moves. The weighting function, w, is given by (Eq. 2 in )

$w\simeq c{\frac {V^{N}}{N!}}\exp \left\{-\beta [U(q^{N})+pV]\right\}$

for a change in volume, $\Delta V$, one has

$r={\frac {w_{\rm {new}}}{w_{\rm {old}}}}=\exp \left[-\beta \left(\Delta U+p\Delta V-Nk_{B}T\ln {\frac {V+\Delta V}{V}}\right)\right]$

If $r\geq 1$ then the move is accepted, and if $0<r<1$ then r is compared with a random number $0<x<1$. If $x\leq r$ then the move is accepted.

References

Related reading

• Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition (2002) § 5.4