Distributed basis sets of s-type Gaussian functions are determined by invoking the variation principle for the Hartree-Fock ground states of the H 2 , LiH, and BH molecules at their respective experimental equilibrium geometries. The calculated energy expectation values supported by these finite basis sets are compared with finite difference Hartree-Fock energies reported by Kobus et al. A distributed basis set of 54 s-type Gaussian functions distributed along the internuclear axis is shown to support an accuracy of 0.05 Hartree for the Hartree-Fock ground-state energy of the H 2 molecule while a similar set containing 50 functions leads to an accuracy of 0.8 Hartree for the ground-state energy of the LiH molecule. For the BH ground state, a Hartree-Fock energy in error by 1.7 Hartree is supported by a variationally optimized distributed basis set of 65 s-type Gaussian functions distributed along the internuclear axis. The parameters, that is, the exponents and positions, defining the variationally optimized distributed basis sets are presented and discussed.