  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.
