Approximations to self-consistent field molecular wavefunctions.

Unparameterized and parameterized versions are outlined of a new method for approximating self-consistent field wavefunctions from first principles at the minimum basis set level for complex molecules containing hydrogen and first-row atoms. The Hartree-Fock self-consistent field equations for closed-shell molecules are solved, retaining all one-electron integrals, and approximating the two-electron Coulomb integrals, hybrid integrals, and exchange integrals of the form (i(A)j(A)[unk]i(A)j(A)) and (i(A)j(B)[unk]i(A)j(B)) for centers A and B. A symmetrically orthogonalized basis set is used and rotational invariance is achieved by transformation to local axes that are unique for atoms in anisotropic environments. Parameterization based upon first-principle self-consistent field wavefunctions for a large number of molecules yields F-matrix elements to 0.007 atomic units (au), density matrix elements to 0.007 electrons, orbital populations and atomic charges to 0.01-0.02 electrons, orbital energies to 0.01 au, and total energies to 0.02 au (all standard deviations), in computational times only a few times larger than those required for complete neglect of differential overlap calculations.