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The relative orientation of the two magnetic orbitals, the CuII d orbital and the half-occupied π orbital of the tyrosyl radical, is the key to answering the question in the title. The arrangement shown (CuII-O-C bond angle of about 130° and a dihedral angle of about 90° between the x,y plane of the CuII polyhedron and the tyrosyl ring plane) leads to an overlap of the orbitals, which results in a singlet ground state.
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Müller et al. (1998) studied this question.