  We introduce a rigorous, physically appealing, and practical way to measure
distances between exchange-only correlations of interacting many-electron
systems, which works regardless of their size and inhomogeneity. We show that
this distance captures fundamental physical features such as the periodicity of
atomic elements, and that it can be used to effectively and efficiently analyze
the performance of density functional approximations. We suggest that this
metric can find useful applications in high-throughput materials design.
