The atomic-cell-orbital version of multiple-scattering theory for energy-band calculations is derived by matching surface integrals on the honeycomb lattice of atomic-cell interfaces. This contrasts with conventional derivations of full-potential multiple-scattering theory, based on integral equations in a Green-function formalism. These theories are shown to be equivalent when the conventional derivation of Williams and Morgan is reformulated in terms of surface integrals. The present derivation shows that energy-independent structure constants can be used, that the effects of geometrical structure and physical potential can be strictly separated, and that there are no near-field corrections. © 1990 The American Physical Society.