The determination of molecular structures by density functional theory. The evaluation of analytical energy gradients by numerical integration

An algorithm, based on numerical integration, has been proposed for the evaluation of analytical energy gradients within the Hartree–Fock–Slater (HFS) method. The utility of this algorithm in connection with molecular structure optimization is demonstrated by calculations on organics, main group molecules, and transition metal complexes. The structural parameters obtained from HFS calculations are in at least as good agreement with experiment as structures obtained from ab initio HF calculations. The time required to evaluate the energy gradient by numerical integration constitutes only a fraction (40%–25%) of the elapsed time in a full HFS-SCF calculation. The algorithm is also suitable for density functional methods with exchange-correlation potential different from that employed in the HFS method.