Various levels of approximation (Hartree-Fock, configuration interaction and double-configuration Hartree-Fock method) are compared for extensive and limited exponent optimization of the atomic orbitals of the wavefunctions. The potential energy curves for the lowest-lying 1Πu, 3Πu, 1Πg, 3Πg states of the hydrogen molecule are presented. The shapes of the curves on the highest level of approximation, i.e. with the optimal double-configuration wavefunction, are basically in agreement with previous, more sophisticated and time-consuming work. The influence of the various approximations is also studied for several one-electron properties: charge distribution of the wavefunction along and perpendicular to the molecular axis, quadrupole moment and core attraction energy distribution. Differences arise to the work of Zemke et al. , who used a limited exponent optimization with a larger basis set, in the Πg states where the π orbitals are very diffuse. The differences concern magnitude and location of minima and maxima of potential curves, as well as considerable changes in one-electron properties which depend strongly on the spatial distribution of the orbitals. © 1972 Springer-Verlag.