Abstract
<jats:p>Density Functional Approximations (DFAs) predict global thermodynamic properties with great success, but energetic precision can be driven by error cancellations that purely energetic scrutiny cannot resolve, which calls for complementary spatial observables. Constructing one is not straightforward: recovering the exact exchange–correlation potential from a correlated density is an ill-posed inverse problem, and we show that the magnitude of any error metric defined directly on the potential is governed by the regularization of that inversion rather than by the physics—varying by more than an order of magnitude at essentially fixed densityalthough the position of the maximum error remains robust. This work introduces MAPA (Metric for Assessing Potential Accuracy) and establishes its mathematical and numerical properties. MAPA pairs two complementary, non-overlapping measurements: the position of the potential-error maximum, robust even where its magnitude is not, and a magnitude obtained by projecting that error through the static Kohn–Sham linear response function. The functional error in the potential is projected through the static Kohn–Sham linear response function, so that what is measured is the electron density the error would displace: a physically interpretable quantity rather than a construction on a gauge-dependent potential. The projection is analytically gauge invariant, annihilates the null-space component that regularization introduces, and is numerically invariant to the regularization parameter, with no hidden free parameters. The response function is generalized to fractional occupations and retains occupied–occupied transitions, which become indispensable once the reference is multireference and the Kohn–Sham occupations are non-integer.</jats:p>