The electronic structure and equilibrium geometry of La_2/3Sr_1/3MnO₃ are studied theoretically by means of density functional calculations. The doping is treated by introducing holes and a compensating jellium background. The results for the local density approximation (LDA) agree with previous LDA calculations, with an equilibrium volume 5.3% too small and with both majority and minority spin states present at the Fermi level for the relaxed system. The generalised gradient approximation (GGA) offers a qualitatively improved description of the system, with a more realistic volume, and a half-metallic behaviour for the relaxed structure, which enables studies needing theoretical relaxation. The ideal MnO₂-terminated (001) surface is then described with explicit doping.