  The classical treatment of plasmonics is insufficient at the nanometer-scale
due to quantum mechanical surface phenomena. Here, an extension to the
classical paradigm is reported which rigorously remedies this deficiency
through the incorporation of first-principles surface response functions - the
Feibelman d-parameters - in general geometries. Several analytical results for
the leading-order plasmonic quantum corrections are obtained in a
first-principles setting; particularly, a clear separation of the roles of
shape, scale, and material is established. The utility of the formalism is
illustrated by the derivation of a modified sum-rule for complementary
structures, a rigorous reformulation of Kreibig's phenomenological damping
prescription, and an account of the small-scale resonance-shifting of simple
and noble metal nanostructures. These insights open the technological design
space and deepen our fundamental understanding of nanoplasmonics beyond the
classical regime.
