Optimization of numerical orbitals in molecular MO-LCAO calculations

The problem of the numerical determination of the atomic orbitals used in the construction of molecular orbitals in MO-LCAO calculations is studied. This gives rise to a two-fold optimization problem; the Roothaan-Hall Hartree-Fock problem of minimizing the energy with respect to the molecular orbital expansion coefficients and the variational problem of optimizing the atomic orbitals. The variational equations for the atomic orbitals are derived and the methods of solution described. The methods of computing the required multicenter integrals for numerical orbitals using Fourier transform methods are also reviewed. The calculation of energy gradients within this framework is discussed. Results are presented for a number of small molecules. Possible advantages of this approach are smaller basis sets are required and the wave functions at the nuclei can be much better approximated than with Gaussian-type orbitals. As well, the fact that orbitals are better approximated implies that basis set superposition errors for dissociation energies calculated in the Hartree-Fock approximation will be reduced. (C) 2003 Wiley Periodicals, Inc.