Computational materials design often profits from the fact that some complicated contributions are not calculated for the real material, but replaced by results of models. We turn this approximation into a very general and in principle exact theory by introducing the concept of a connector, which is a prescription of how to use the results of a model system in order to simulate a real system. We set the conditions that must be fulfilled for the existence of an exact connector. We demonstrate that, and why, this approach is a very convenient starting point for approximations. We also show that the connector theory can be used to design new functionals, for example for density functional theory. We illustrate our purposes with simple but realistic examples.
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