Invariant atomic orbitals by radial moment analysis of accurate molecular orbitals

Radial moment analysis of accurate molecular orbitals in extended Slater basis sets reveals approximately invariant atomic orbitals. These atomic orbitals are very similar to the solutions of the Hartree-Fock equations for the free atoms, but small, and possibly significant, regular differences are found. These atomic orbitals provide a suitable standard set of atomic orbitals for semiempirical molecular calculations, and provide theoretical support for the concept of atomic orbitals in molecules. Orbitals for first- and second-row elements and hydrogen are presented. Hydrogen is unique in showing an appreciable variation depending on the atom to which it is bonded.