In recent years, computer simulation methods have provided much insight
into several structural, dynamical and thermal properties of solids
and liquids. Computational methods are particularly well suited to the
study of low symmetry sys.terns (e.g., defects, surfaces, clusters), where
the complexity of analytical treatments may become overwhelming, and
of systems at finite temperature.
The key ingredients in computer simulations are interatomic forces.
The problem we wish to solve can be simply stated as follows: given
a set of N atoms having some positions r 1 •.. rN and linear momenta
p1 .•• PN, what forces will they experience ? Calculating these forces
ab initio is a very difficult task. Even if we are not interested in the
electronic· properties of the system, but only in ionic properties (e.g.,
vibrations, equilibrium structures, etc.), we must generally take into
full account the electronic aspect of the problem.
In the Born-Oppenheimer adiabatic approximation [1 J, the forces
can be obtained by considering the nuclei as fixed and searching for
the minimum energy state of the electronic system. This .may be done
using the Hartree-Fock approximation, or in a density functional theory
framework. The force acting on a nucleus is then determined as the
gradient of the total energy respect to a displacement of that nucleus.
After all nuclei have been moved accordingly to the forces computed in
_this way, the whole process may be iterated for the new configuration,
·thus performing a dynamical calculation. This approach, however, is
computationally extremely expensive, and not feasible when the number
of particles is of the order of ten or more....
