  We extend the phase field crystal model to accommodate exact atomic
configurations and vacancies by requiring the order parameter to be
non-negative. The resulting theory dictates the number of atoms and describes
the motion of each of them. By solving the dynamical equation of the model,
which is a partial differential equation, we are essentially performing
molecular dynamics simulations on diffusive time-scales. To illustrate this
approach, we calculate the two-point correlation function of a liquid.
