Reducing degrees of freedom in many particle systems

Particle based simulations are a powerful tool to understand molecular mechanisms and interactions in many fields of science. Strictly speaking, one should solve the Schrödinger equation, but that is not possible for nearly all systems or interest. In practice one often wants a representation of atoms as point particles or even coarser representations. The question is then how to best model the interactions between these coarse-grained particles. A systematic approach is desirable to go from e.g. a description of electrons and nuclei to atoms or from atoms to a “chemical moiety” model. I will discuss the formal, but intractable, solution to this problem as well as more or less systematic approaches for obtaining an (free-)energy expression for the reduced system. I will show some example systems to illustrate the artifacts of different approaches.