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Fig. 3. The energy splitting of the ground 5I8 multiplet of HoIII in 1 (a), 2 (b), and 3 (c) obtained from the ab initio calculations. Only the lowest energy part was presented. The resulting energy barriers of the Orbach relaxation were shown in green colour. The numbers above each arrow represent the corresponding matrix element of the transversal magnetic moment while the Δtun shows the tunnelling gap of the indicated doublets. Red arrows indicate the less possible whereas blue arrows show the most probable relaxation pathway. The scheme is obtained for the L–W models (Table S8†).