Starting from scratch

If we are starting from scratch, we have to ``create'' a set of initial positions and velocities.

Positions are usually defined on a lattice, assuming a certain crystal structure. This structure is typically the most stable at T=0 with the given potential. Initial velocities may be taken to be zero, or from a Maxwellian distribution as described below.

Such initial state will not of course correspond to an equilibrium condition. However, once the run is started equilibrium is usually reached within a time of the order of 100 time steps.

Some randomization must be introduced in the starting sample. If we do not do so, then all atoms are symmetrically equivalent, and the equation of motions cannot do anything different that evolving them in exactly the same way. In the case of a perfect lattice, there would be no net force on the atoms for symmetry reasons, and therefore atoms would sit idle indefinitely.

Typical ways to introduce a random component are

1.

small random displacements are added to the lattice position. The amplitude of these displacements must not be too large, in order to avoid overlap of atomic cores. A few percent of the lattice spacing is usually more than adequate.

2.

the initial velocities are assigned taking them from a Maxwell distribution at a certain temperature T. When doing this, the system will have a small total linear momentum, corresponding to a translational motion of the whole system. Since this is somewhat inconvenient to have, it is common practice to subtract this component from the velocity of each particle in order to operate in a zero total momentum condition.

Initial randomization is usually the only place where chance enters a molecular dynamics simulation. The subsequent time evolution is completely deterministic.