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 )

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle w \simeq c \frac{V^N}{N!} \exp \left\{ -\beta [ U(q^N) +pV ] \right\} }

for a change in volume, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r \ge 1} then the move is accepted, and if Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 < r < 1} then r is compared with a random number Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 < x < 1} . If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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