A 1s, 2pσ valence bond wave function for the B1Σu+state of the hydrogen molecule is variationally optimized with respect to the two atomic orbital exponents for internuclear separations in the vicinity of the equilibrium value. The optimization is tested by use of the molecular virial theorem, and the resulting binding energy compares favourably with other calculations based on limited sets of atomic orbitals. The nature of the electron distribution in the state is analyzed by use of a particular kind of two electron correlation diagram. This analysis indicates that the actual electron distribution is largely ionic in the vicinity of the equilibrium separation in contrast to the formal covalency of the wave function. © 1969 Springer-Verlag.