The 1∑σ+ ground state of He 2 is investigated using the spin-optimized self-consistent-field (SOSCF) method. Molecular orbitals need not have g or u character. Over 40% of the correlation energy is included in the SOSCF function without giving up the concept of one orbital per electron, and a simple spin-coupling scheme, very close to maximal pairing, is obtained. Imposing symmetry restrictions on the orbitals leads to significantly higher energy and a more complicated coupling scheme. The dependence of orbitals on the internuclear distance is described.