  Phase field crystals (PFC) are a tool for simulating materials at the atomic
level. They combine the small length-scale resolution of molecular dynamics
(MD) with the ability to simulate dynamics on mesoscopic time scales. We show
how PFC can be interpreted as the result of applying coarse-graining in time to
the microscopic density field of molecular dynamics simulations. We take the
form of the free energy for the phase field from the classical density
functional theory of inhomogeneous liquids and then choose coefficients to
match the structure factor of the time coarse-grained microscopic density
field. As an example, we show how to construct a PFC free energy for Weber and
Stillinger's two-dimensional square crystal potential which models a system of
proteins suspended in a membrane.
