The Hartree-Fock-Heitler-London, HF-HL, method is a new ab initio approach which variationally combines the Hartree-Fock, HF, and the Heitler-London, HL, approximations, yielding correct dissociation products. Furthermore, the new method accounts for nondynamical correlation and explicitly considers avoided crossing. With the HF-HL model we compute the ground-state potential energy curves for H-2 [(1)Sigma(+)(g)], LiH [X (1)Sigma(+)], BeH [(2)Sigma(+)], BH [(1)Sigma(+)], CH [(2)Pi], NH [(3)Sigma(-)], OH [2 Pi], and FH [(1)Sigma(+)], obtaining in average 80% of the experimental binding energy with a correct representation of bond breaking. Inclusion of ionic configurations improves the computed binding energy. The computed dipole moment is in agreement with laboratory data. The dynamical and nondynamical correlation energies for atomic and molecular systems with 2-10 electrons are analyzed. For BeH the avoided crossing of the two lowest [(2)Sigma(+)] states is considered in detail. The HF-HL function is proposed as the zero-order reference wave function for molecular systems. To account for the dynamical correlation energy a post-HF-HL technique based on multiconfiguration expansions is presented. We have computed the potential energy curves for H-2 [(1)Sigma(+)(g)] HeH [(2)Sigma(+)], LiH [X-1 Sigma(+)], LiH [A(1)Sigma(+)], and BeH [(2)Sigma(+)]. The corresponding computed binding energies are 109.26 (109.48), 0.01 (0.01), 57.68 (58.00), 24.19 (24.82), and 49.61 (49.83) kcal/mol, with the experimental values given in parentheses. The corresponding total energies are -1.1741, -3.4035, -8.0695, -7.9446, and -15.2452 hartrees, respectively, the best ab initio variational published calculations, H-2 excluded.