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Subsections
The constant volume ensemble is not very convenient for the study of
phase transitions. Some experimental values, like the excess
properties, are measured at constant pressure, not at constant volume,
therefore it would be nice to have a method to simulate the isobaric
conditions also. The average of the value
in
the NPT ensemble is given as:

here we again made the transformation to the ``primed'' coordinates,
rescaling them by the box dimensions. Now we have to develop a Markov
chain that samples the phase space with the probability distribution
proportional to
.Metropolis algorithm is implemented in the same way as for NVT
ensemble, but now we also allow the volume to change. We have two
kinds of the Monte Carlo moves: particles displacement, performed the
same way as in the NVT simulations, and Volume change. The
acceptance criterium is, of course, modified now, as instead of the
energy difference between the old and new states, it is based on the
difference of enthalpies:
|  |
(7) |
- 1.
- Prepare the initial configuration of the system with the desired
density (box size and number of particles). Usually just a simple
cubic lattice works.
- 2.
- Loop through the particles:
- Pick up a particle and decide its new position by choosing
the displacement components at random
(
is a random number from 0 to
1,
is the maximum allowed displacement).
- Calculate the energy change, induced by the displacement
and decide, whether accept it or not,
according to the Metropolis criterium.
- If the new configuration is accepted, update position,
energy, etc.
- Pick the next particle, etc.
- 3.
- Make a volume change as
. Calculate new energy of
the system. and
from equation (7), and decide,
whether to accept it or not, based on the Metropolis criterium.
- 4.
- Calculate necessary averages, print out the results, etc. Go
back to step 2.
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Up: Calculation of Thermodynamic Properties.
Previous: Thermodynamic Properties in NVT
© 1997
Boris Veytsman
and Michael Kotelyanskii
Thu Nov 13 19:07:05 EST 1997