Exact electrostatic theory of Fermi-energy response at metallic interfaces

The response of the Fermi energy to external perturbations governs key physical observables at metallic interfaces. Although this response admits a local formulation in terms of the Fukui function, its evaluation has traditionally been limited by inherent approximations, fundamentally rooted in the difficulty of adding a finite charge in a periodic system. We present an exact resolution to this problem that, within an electronic-structure framework capturing metallic behavior, exploits the screening properties of electronic conductors to compute Fukui functions via a finite electric field. The resulting linear-response theory yields strictly quadratic error scaling of Fermi-level shifts across representative platinum surfaces, achieving sub-meV accuracy up to fields of 0.1 V/Å. The approach is further validated by reproducing work-function changes under molecular perturbations, and by providing mean-field estimates of electrode potentials that yield capacitance--voltage curves consistent with experiment. Our findings establish a rigorous foundation for a local theory relating electrostatic screening and Fermi-energy variations at metallic interfaces.