A set of single-configuration self-consistent field molecular orbital wavefunctions for the 1Σ ground state of BeO is presented. A potential curve which is approximately 0.3 eV above the Hartree—Fock potential curve for the molecule is presented, together with the results of a spectroscopic analysis on it. A further calculation at a nuclear separation corresponding to the minimum in the computed potential curve, which gives a total molecular energy of —89.44787 a.u., is presented. This is probably less than 0.1 eV above the Hartree—Fock limit. The mean value of the dipole moment of the molecule computed with this wavefunction is 7.29 D. A comprehensive selection of other mean values computed at points along the potential curve, and for the more accurate calculation at the minimum in the curve, is given.