In this work, we investigate the application of coarse-graining (CG) methods to molecular dynamics (MD) simulations. These methods provide access to length and time scales previously inaccessible to traditional materials simulation techniques. However, care must be taken when applying any coarse-graining strategy to ensure that we preserve the material properties of the system we are interested in.
We discuss common CG strategies, including their strengths, weaknesses and ease of application. The theory of coarse-graining is discussed within the framework of statistical mechanics, together with an analytic derivation of the CG partition function for a harmonic potential. We then apply this theory to a simple system of two interacting dimers, obtaining expressions for the CG free and internal energy. This example serves as a motivation for how to coarse-grain more realistic systems numerically. We introduce five different approaches to generating a CG potential, which we have termed the rigid and relaxed approximation, the constrained pair approach, the unconstrained box approach and the entropic approach. We apply each of these techniques to a
system of C60 molecules, comparing our results against reference fully atomistic MD simulations of the same system. We find that the constrained pair approach provides an optimal balance between ease of generation and accuracy when compared to the reference model.