Samples the phase space of a constant-P, constant-T ensemble with the
appropriate phase space probability. In addition to the particle
moves performed at constant , changes of the volume are
attempted and accepted/rejected according to an evaluation of the
enthalpy change. A simple LJ simulation of the NPT type is sketched here:
For given and , let the instantaneous volume be
and the particle positions , .
Choose a particle and perform a trial move
in the usual manner.
Compute the energy difference between the trial configuration and
the given one:
, where
etc.
Accept or reject the trial configuration with probability
(6.1)
Repeat this basic MC step for a number of particles; usually all
particles are treated in sequence.
Now perform a trial volume change
;
all particle coordinates are (implicitely) scaled by
,
which entails a change in energy of .
Compute the enthalpy change
(6.2)
and accept/reject the new volume according to
(6.3)
This ends the MC cycle.
As usual, the maximum particle step and the maximum volume change are
adjusted to achieve an acceptance ratio near .
Note 1: If you are lucky, the model pair potential may be written in the
scalable form
where is a scaled distance, and
is the scaling factor. In such cases the total potential energy after
a volume change need not be recalculated from scratch; rather, we have
. As an example, take the
term in the Lennard-Jones potential. When scaling all distances
from to , where
, we have
Note 3: A JAVA applet for NPT MC (and for many other simulation
techniques), may be found on the web page of David Kofke, U of Buffalo,
www.cheme.buffalo.edu/courses/ce530/Applets/applets.html
F. J. Vesely / University of Vienna