Density Functional Theory relies on universal functionals characteristic of a given system. Those functionals in general are different for the electron gas and for jellium (electron gas with uniform background). However, jellium is frequently used to construct approximate functionals for the electron gas (e.g., local density approximation, gradient expansions). The precise relationship of the exact functionals for the two systems is addressed here. In particular, it is shown that the exchange - correlation functionals for the inhomogeneous electron gas and inhomogeneous jellium are the same. This justifies theoretical and quantum Monte Carlo simulation studies of jellium to guide the construction of functionals for the electron gas. Related issues of the thermodynamic limit are noted as well.
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