Universal scaling relations for free and bonded atoms

摘要

Scaling relations, relating the energy and expectation value ofrminus;1in free and bonded atoms, are studied. In the limit of a large number of electrons these relations are functions of the ratioq=N/Z, whereNis the number of electrons andZis the nuclear charge. It is shown that theqdependence of such relations may be rather accurately predicted from the Thomasndash;Fermi and local density functional theories even for small values ofN. The validity of the theoretical prediction is demonstrated by a comparison between the theoretical and the calculated Hartreendash;Fock values for a large number of atoms and ions. The same comparison is made for bonded atoms as defined by the theory of quantum topology. It is found that both free and bonded atoms obey the proposed relations to a similar degree of accuracy.