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 )

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

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

$r=\frac{w_{\mathrm{n}\mathrm{e}\mathrm{w}}}{w_{\mathrm{o}\mathrm{l}\mathrm{d}}}=\exp [-\beta (\mathrm{\Delta }U+p\mathrm{\Delta }V-N{k}_{B}T\ln \frac{V+\mathrm{\Delta }V}{V})]$

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