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

Phase Field Crystals as a Coarse-Graining in Time of Molecular Dynamics