THE APPLICATION OF AN OPTIMIZATION TECHNIQUE TO THE DEVELOPMENT OF UNIVERSAL BASIS-SETS

The Simplex method was used to define atomic and universal meshes using the integral discretization technique for the Griffin-Hill-Wheeler-Hartree-Fock equations. This technique represents a basis set as an exponential set of the form: alpha(i)(k) = exp[DELTA-OMEGA(o)(k) + (i - 1)DELTA-OMEGA(k)], i = 1, ..., N For atoms, the minimum total energy criterion was employed. For the universal basis, three different procedures were tested: (a) defining the universal basis using information on the isolated atoms, (b) determining the universal OMEGA-0(k) through atomic calculations and reoptimizing the DELTA-OMEGA(k) for different symmetries employing simultaneously a single atomic calculation as a reference point, and (c) optimizing the universal mesh using a statistical criterion such as the squares of the deviations of the total energy. The meshes obtained by the minimum total energy criterion or the squares of deviations of the total energy for the universal basis are accurate for the total energy but the weight functions are deficient in the valence region. Shifting the optimized OMEGA-0(k) to OMEGA-0'(k) - DELTA-OMEGA(k), fixing DELTA-0'(k), and reoptimizing DELTA-OMEGA(k) for each symmetry species produces a better description of weight functions at the expense of a less accurate total energy. In general, no significant statistical difference was observed for the various universal bases generated by procedures (a) and (b) or by (c) provided the shift correction was made to the latter. Application of these bases to diatomic molecules (N2, CO, P2, CS) showed that the universal bases are as accurate as those optimized for atomic systems. If the bases are transferred from atoms to molecules, the shift corrections to the weight functions of the atoms are not useful in molecular calculations. The almost equivalent molecular properties and the good total energies show that the best basis for molecular calculations is that optimized by procedure (c).