From Orbital Models to Accurate Predictions

As shovm in Fig. 5 the overlap form factor / ( <) is zero at <=0 and passes through a maximum as n increases. The simple molecular orbital model thus predicts a form factor for an antiferromagnet reduced from the free ion value, but somewhat expanded in shape because of the overlap moment. Although many other factors such as the introduction of orbital effects via spin orbit coupling, the polarization of filled inner shells, the polarization of partially occupied outer orbitals, and variations in the 3d radial functions need to be considered before a detailed form factor analysis can be attempted in any particular situation, it was satisfying that the first accurately determined ionic form factor, for Ni2+ in NiO (27), behaved qualitatively in this manner. Unfortunately few other form factors have been accurately determined since then, but the behavior is not always so apparently straightforward. 

The general statement that the energy required to remove an electron from an atom or a molecule, is equal to minus the orbital energy of the electron that is removed, is known as Koopman s theorem. The general theorem can be proven if we use an atomic or molecular orbital model and assume that ionization is not followed by relaxation. Comparison with experiments shows that predictions based on Koopman s theorem usually are accurate to about 10%. The accuracy would be even poorer if there was not a fortunate cancellation of errors ... 

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