Both top-down and bottom-up localization schemes are proposed for constructing localized molecular orbitals (LMOs) of open-shell systems, via least change from fragments to molecule. The success of both schemes stems from (1) the primitive fragment LMOs that are local not only in space but also in energy and (2) the "conquer step" that allows arbitrary assignment of the unpaired electrons to fragments. Moreover, integral occupations are retained, so as to facilitate subsequent treatment of electron correlation and excitation.
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