We present an ab initio based method which gives clear insight into the int
erplay between the band-f hybridization, the band-f coulomb exchange, and t
he crystal-field interactions, as the degree of 4f localization is varied a
cross a series of strongly correlated cerium systems. The predictions for t
he ordered magnetic: moments, magnetic structure, and ordering temperatures
are in excellent agreement with experiment, including the occurence of a m
oment collapse of non-Kondo origin. In contrast. spin and orbitally polariz
ed ah initio density functional calculations and LDA + U calculations fail
to predict, even qualitatively, the trend of the unusual magnetic propertie
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