CAN THE LINEAR COMBINATION OF ATOMIC ORBITAL COEFFICIENTS (THE WEIGHTFUNCTION) BE USED TO IMPROVE THE WAVE-FUNCTION

Numerical integration of the integral version of the Hartree-Fock equa tions recovers the usual Hartree-Fock-Root-haan equations. Comparing t he two methods, calculation of electronic properties using gaussian fu nctions shows that the linear combination of atomic orbital (LCAO) coe fficients of uncontracted basis sets are discretized weight functions. This correspondence emphasizes properties of the set of LCAO coeffici ents that can be used to evaluate deficiencies in the valence region o f atoms or molecules. Both geometric and conventional uncontracted bas is 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 functio ns must be added to some systems, particularly for anions. Weight func tions for neutral systems also show deficiencies in the valence region . The inclusion of only diffuse functions produces insignificant chang es in the total energies of neutral atoms and molecules. However, the observed tendency of the weight functions to zero in the valence regio n leads to three different procedures for improving the description of wavefunctions by conventional basis sets.