Numerical integration of the integral version of the Hartree-Fock equations recovers the usual Hartree-Fock-Root-haan equations. Comparing the two methods, calculation of electronic properties using gaussian functions shows that the linear combination of atomic orbital (LCAO) coefficients of uncontracted basis sets are discretized weight functions. This correspondence emphasizes properties of the set of LCAO coefficients that can be used to evaluate deficiencies in the valence region of atoms or molecules. Both geometric and conventional uncontracted basis sets were employed in the calculation of weight functions for atoms and diatomic molecules. To observe the same qualitative behaviour as for geometric bases in the weight functions for the conventional basis sets when uncontracted, the latter were preprocessed to avoid linear dependence. Analysis of the weight functions shows why diffuse functions must be added to some systems, particularly for anions. Weight functions for neutral systems also show deficiencies in the valence region. The inclusion of only diffuse functions produces insignificant changes in the total energies of neutral atoms and molecules. However, the observed tendency of the weight functions to zero in the valence region leads to three different procedures for improving the description of wavefunctions by conventional basis sets.10017587