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:
Accept or reject the trial configuration with probability
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
and accept/reject the new volume according to
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
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