Constant-pressure Monte Carlo

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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 (Ref 1 Eq. 2)

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

for a change in volume, $Δ V$ , one has

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

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.