Velocities may be initialized by implementing Maxwell-Boltzmann statistics, by randomization of velocities, or by zeroing velocities.
When the Maxwell-Boltzmann method is selected, the algorithm assigns velocities
according to Maxwell-Boltzmann statistics at a specified temperature. The
algorithm capitalizes on the fact that the Maxwell-Boltzmann speed
distribution
is simply the composition of three identical
Gaussians, each of which represents the velocity distribution of a given Cartesian axis. The standard deviation of the aforementioned
Gaussian is equal to
and the Gaussian is normalized with a height
of 
. The Box-Muller algorithm described in
Sec. 
is used in generating the normal (Gaussian)
velocity distribution in each coordinate.
When the ``random'' velocity initialization method is selected, each ion is assigned a random velocity in the x-, y-, and z- directions. Then the velocities of all ions are scaled such that their kinetic energy corresponds to the desired temperature.
The final velocity-initialization method--- zero velocities---
simply removes all kinetic energy from the system.