A Relationship between the Sizes and Energies of Atomic Orbitals

Abstract

An approximate relationship of the form[Formula: see text]where [Formula: see text] is the mean potential acting upon and V the mean volume of an electron in a closed shell of an atom has previously been proposed. This concept of a simple relationship between the sizes and energies of atomic orbitals which is predicted by simple quantum mechanical arguments has been further examined in this present work. The potential energy for a series of two electron atoms and ions has been replaced by the total electronic energy as these two quantities are simply connected by the virial theorem. For polyelectronic atoms, a quantity per electron pair which sums to the total electronic energy has been used. The volume of the ith atomic orbital[Formula: see text]has been calculated from its size as previously defined in terms of the spherical quadratic operator evaluated at the orbital centroid of charge. A relationship of the above form between the sizes and energies of atomic orbitals holds well for core orbitals but gradually deteriorates on going from the innermost (core) to outermost (valence) shell.