  We have reanalyzed the microscopic origin of the isotropic deviations that
are observed from the energy spacings predicted by the HDVV Hamiltonian.
Usually, a biquadratic spin operator is added to the HDVV Hamiltonian to
account for such deviations. It is shown here that this operator cannot
describe the effect of the excited atomic non-Hund states which brought the
most important contribution to the deviations. For systems containing more than
two magnetic centers, non-Hund states cause additional interactions that are of
the same order of magnitude as the biquadratic exchange and should have
significant effects on the macroscopic properties of extended systems.
