We use the variance minimization method to determine accurate wave functions for first-row homonuclear diatomic molecules. The form of the wave function is a product of a sum of determinants and a generalized Jastrow factor. One of the important features of the calculation is that we are including low-lying determinants corresponding to single and double excitations from the Hartree-Fock configuration within the space of orbitals whose atomic principal quantum numbers do not exceed those occurring in the Hartree-Fock configuration. The idea is that near-degeneracy correlation is most effectively described by a linear combination of low-lying determinants whereas dynamic correlation is well described by the generalized Jastrow factor. All the parameters occurring in both the determinantal and the Jastrow parts of the wave function are optimized. The optimized wave functions recover 79%-94% of the correlation energy in variational Monte Carlo and 93%-99% of the correlation energy in diffusion Monte Carlo.