Abstract
Scaling relations, relating the energy and expectation value of r−1 in free and bonded atoms, are studied. In the limit of a large number of electrons these relations are functions of the ratio q = N/Z, where N is the number of electrons and Z is the nuclear charge. It is shown that the q dependence of such relations may be rather accurately predicted from the Thomas–Fermi and local density functional theories even for small values of N. The validity of the theoretical prediction is demonstrated by a comparison between the theoretical and the calculated Hartree–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.
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