The aim here is to calculate equilibrium properties of a material, given only
the intermolecular potential. (e.g. for an atomic system the Lennard-Jones
6-12 potential could be used).
From statistical mechanics it can be shown that many properties of a material
can be calculated from:
which is the ensemble average value of the property X. -this
is a weighted average (using exp(-U/kT)) over all possible
configurations. U is the configurational energy of the system.
kT is the Boltzmann constant times the temperature and the integral is
over all possible coordinates of the Lennard-Jones particles (there are
3N coordinates for N particles in three dimensions).
We could calculate <X> by choosing random configurations and then weight weigth them with
exp(-U/kT) but this is extremely inefficient. An alternate method is to choose
the configurations with weight exp(-U/kT) and then weight them evenly, i.e.:
j is chosen with weight exp(-U(j)/kT), where U(j) is the
configurational energy of configuration j.
On the next page we will discuss how this can be done efficiently.
© Peter H.
Nelson 1995-1997. All rights reserved.
Last updated December 10, 1997