Supporting Information for

Heterometallic MIILnIII (M = Co / Zn; Ln = Dy / Y) complexes with pentagonal bipyramidal 3d centres: syntheses, structures, and magnetic properties

Fu-Xing Shen,† Hong-Qing Li,† Hao Miao,† Dong Shao,† Xiao-Qin Wei,† Le Shi,†

Yi-Quan Zhang,*‡ Xin-Yi Wang*†.

†State Key Laboratory of Coordination Chemistry, Collaborative Innovation Center of Advanced Microstructures, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, 210023, China. E-mail: [email protected]

‡Jiangsu Key Laboratory for NSLSCS, School of Physical Science and Technology, Nanjing Normal University, Nanjing 210023, China. E-mail: [email protected]

1 Table of contents

Materials and Physical Measurements ...... 4

Figure S1. Experimental and simulated powder X-ray diffraction patterns for 1CoDy...... 5

Figure S2. Experimental and simulated powder X-ray diffraction patterns for 2ZnDy...... 5

Figure S3. Experimental and simulated powder X-ray diffraction patterns for 3CoY...... 5 -1 Figure S4. TG curve of compound 1CoDy at a rate of 10 Kmin under a N2 atmosphere...... 6 -1 Figure S5. TG curve of compound 2ZnDy at a rate of 10 Kmin under a N2 atmosphere...... 6 -1 Figure S6. TG curve of compound 3CoY at a rate of 10 Kmin under a N2 atmosphere...... 6

Figure S7. Crystal packing of complex 1 CoDy. Hydrogen atoms and the solvents are omitted for clarity...... 7

Figure S8. Crystal packing of complex 3 CoY. Hydrogen atoms and the solvents are omitted for clarity...... 7 Figure S9. Frequency dependence of in-phase () and out-of-phase () magnetic susceptibility of 1CoDy (1–1000 Hz) measured at 2.0 K at zero field...... 8

Figure S10. The magnetization curves for 1CoDy measured at 2, 3, and 5 K...... 9

Figure S11. The magnetization curves for 2ZnDy measured at 2, 3, and 5 K...... 9

Figure S12. The magnetization curves for 3CoY measured at 2, 3, and 5 K...... 9 Figure S13. Frequency dependence of the in-phase () and out-of-phase () magnetic susceptibilities of 2ZnDy measured at 2.0 K in various applied fields from 0 to 4500 Oe...... 10 Figure S14. Frequency dependence of the in-phase () and out-of-phase () magnetic susceptibilities of 3CoY measured at 2.0 K in various applied fields from 0 to 4500 Oe...... 10

Figure S15. Cole–Cole plots of ″ vs. ′ of 2 ZnDy at 2.0 K under various applied dc fields. The solid lines represent the best fit of the experimental results with the generalized Debye model. ...11

Figure S16. Cole–Cole plots of ″ vs. ′ of 3 CoY at 2.0 K under various applied dc fields. The solid lines represent the best fit of the experimental results with the generalized Debye model. ...11

Figure S17. Field dependence of the magnetic relaxation time at 2.0 K for 2ZnDy and its fitting by -1 4 2 τ = AH T +B1/(1 + B2H )...... 12

Figure S18. Field dependence of the magnetic relaxation time at 2.0 K for 3CoY and its fitting by -1 4 2 τ = AH T +B1/(1 + B2H )...... 12

Figure S19. Variable-temperature ac susceptibility data for 2 ZnDy collected under a 1000 Oe dc field over the frequency range of 1 to 999 Hz. The solid lines are simply guides for the eye...... 13

Figure S20. Variable-temperature ac susceptibility data for 3 CoY collected under a 1000 Oe dc field over the frequency range of 1 to 999 Hz. The solid lines are simply guides for the eye...... 13 Table S1. SHAPE analysis of the M(II) ion in complexes 1–3...... 14 Table S2. SHAPE analysis of the Ln(III) ion in complexes 1–3...... 14 Table S3. The select intramolecular distance and Angles for MII and LnIII in complexes 1–3...... 14 Table S4. Selected bond lengths (Å) and bond angles (°) for compound 1–3...... 15 Table S5. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of compounds 2ZnDy at 2 K under various dc fields according to the generalized Debye model...... 17 Table S6. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of compounds 3CoY at 2 K under various dc fields according to the generalized Debye model...... 17 Table S7. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of

2ZnDy under 1.8 K-5.0 K according to the generalized Debye model...... 18

2 Table S8. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of 3CoY under 1.8 K-5.0 K according to the generalized Debye model...... 18 Table S9. Parameters fitted from the Arrhenius plots in Figure 5 considering multiple relaxation processes for 2ZnDy and 3CoY...... 19

Table S10. Wave functions with definite projection of the total moment | mJ > for the lowest two III Kramers doublets (KDs) of individual Dy fragments for complexes 1CoDy and 2ZnDy...... 19 −1 Table S11. Calculated energy levels (cm ), g (gx, gy, gz) tensors and mJ values of the lowest eight Kramers doublets (KDs) of individual DyIII fragment, and zero-field splitting parameters D (E) (cm−1), g tensors of the lowest spin-orbit state of individual CoII fragment of complexes 1−3 using CASSCF/RASSI with MOLCAS 8.2...... 20 −1 Table S12. Exchange energies (cm ) and main values of the g z for the lowest four exchange doublets of complex 1CoDy...... 21 Reference ...... 22

3 Materials and Physical Measurements

Infrared spectra (IR) data were measured on KBr pellets using a Nexus 870 FT-IR spectrometer in the 4000400 cm-1 range. Elemental analyses of C, H, and N were performed at an Elementar Vario MICRO analyzer. TG analyses were recorded on a

NETZSCH TG209F3 thermo analyzer under N2 atmosphere within the temperature range of 300−1000 K at a heating rate of 10 K min−1. Powder X-ray diffraction data (PXRD) were recorded at 298 K on a Bruker D8 Advance diffractometer with Mo-Kα X-ray source (λ = 0.71073 Å) operated at 40 kV and 40 mA. Magnetic susceptibility data were collected using Quantum Design SQUID VSM magnetometer on samples of crushed crystals. Direct current (dc) magnetic susceptibility measurements were performed in the temperature range of 2300 K under an applied field of 1000 Oe. Alternative current (ac) susceptibility measurements were performed with a 2 Oe ac oscillating field in an operating frequency range of 11000 Hz under a dc field of 0 or 1000 Oe. Magnetization data were collected in the 0 to 70 kOe field range at 2.0 K. Experimental susceptibilities were corrected for diamagnetism of the sample holders and that of the compounds according to Pascal’s constants.[S1]

X-ray Crystallography Single crystal x-ray crystallographic data were collected on a Bruker APEX II or APEX Duo diffractometer with a CCD area detector (Mo-Kα radiation, λ = 0.71073 Å). The APEXII program was used to determine the unit cell parameters and for data collection. The data were integrated and corrected for Lorentz and polarization effects using SAINT. Absorption corrections were applied with SADABS.[S2] The structures were solved by direct method and refined by full-matrix least-squares method on F 2 using the SHELXTL crystallographic software package.[S3] All the non-hydrogen atoms were refined anisotropic. Hydrogen atoms of the organic ligands were refined as riding on the corresponding non-hydrogen atoms. Additional details of the data collections and structural refinement parameters were provided in Table 1. Selected bond lengths and bond angles of 13 were listed in Table S1.

4 Figure S1. Experimental and simulated powder X-ray diffraction patterns for 1CoDy.

Figure S2. Experimental and simulated powder X-ray diffraction patterns for 2ZnDy.

5 Figure S3. Experimental and simulated powder X-ray diffraction patterns for 3CoY.

-1 Figure S4. TG curve of compound 1CoDy at a rate of 10 Kmin under a N2 atmosphere.

-1 Figure S5. TG curve of compound 2ZnDy at a rate of 10 Kmin under a N2 atmosphere.

6 -1 Figure S6. TG curve of compound 3CoY at a rate of 10 Kmin under a N2 atmosphere.

Figure S7. Crystal packing of complex 1CoDy. Hydrogen atoms and the solvents are omitted for clarity.

7 Figure S8. Crystal packing of complex 3CoY. Hydrogen atoms and the solvents are omitted for clarity.

8 Figure S9. Frequency dependence of in-phase () and out-of-phase () magnetic susceptibility of 1CoDy (1–1000 Hz) measured at 2.0 K at zero field.

9 Figure S10. The magnetization curves for 1CoDy measured at 2, 3, and 5 K.

Figure S11. The magnetization curves for 2ZnDy measured at 2, 3, and 5 K.

Figure S12. The magnetization curves for 3CoY measured at 2, 3, and 5 K.

10 Figure S13. Frequency dependence of the in-phase () and out-of-phase () magnetic susceptibilities of 2ZnDy measured at 2.0 K in various applied fields from 0 to 4500 Oe.

Figure S14. Frequency dependence of the in-phase () and out-of-phase () magnetic susceptibilities of 3CoY measured at 2.0 K in various applied fields from 0 to 4500 Oe.

11 Figure S15. Cole–Cole plots of ″ vs. ′ of 2 ZnDy at 2.0 K under various applied dc fields. The solid lines represent the best fit of the experimental results with the generalized Debye model.

Figure S16. Cole–Cole plots of ″ vs. ′ of 3 CoY at 2.0 K under various applied dc fields. The solid lines represent the best fit of the experimental results with the generalized Debye model.

12 Figure S17. Field dependence of the magnetic relaxation time at 2.0 K for 2ZnDy and its fitting by -1 4 2 τ = AH T +B1/(1 + B2H ).

Figure S18. Field dependence of the magnetic relaxation time at 2.0 K for 3CoY and its fitting by -1 4 2 τ = AH T +B1/(1 + B2H ).

13 Figure S19. Variable-temperature ac susceptibility data for 2 ZnDy collected under a 1000 Oe dc field over the frequency range of 1 to 999 Hz. The solid lines are simply guides for the eye.

Figure S20. Variable-temperature ac susceptibility data for 3 CoY collected under a 1000 Oe dc field over the frequency range of 1 to 999 Hz. The solid lines are simply guides for the eye.

14 Table S1. SHAPE analysis of the M(II) ion in complexes 1–3.

Label Shape Symmetry (1) Co1 (2) Zn1 (3) Co1 HP-7 Heptagon D7h 33.922 33.616 35.260 HPY-7 Hexagonal pyramid C6v 25.597 25.012 25.754 PBPY-7 Pentagonal bipyramid D5h 0.289 0.311 0.274 COC-7 Capped octahedron C3v 7.246 6.536 6.377 CTPR-7 Capped trigonal prism C2v 5.492 4.851 4.700 JPBPY-7 Johnson pentagonal bipyramid J13 D5h 4.262 4.073 4.271 JETPY-7 Johnson elongated triangular C3v 22.637 22.897 23.930 pyramid J7

Table S2. SHAPE analysis of the Ln(III) ion in complexes 1–3.

Label Shape Symmetry (1) Dy1 (2) Dy1 (3) Y1 DP-10 Decagon D10h 34.432 34.453 34.812 EPY-10 Enneagonal pyramid C9v 24.842 24.870 25.515 OBPY-10 Octagonal bipyramid D8h 16.180 16.154 16.761 PPR-10 Pentagonal prism D5h 11.689 11.876 11.785 PAPR-10 Pentagonal antiprism D5d 9.969 10.207 9.409 JBCCU-10 Bicapped cube J15 D4h 7.485 7.506 6.900 JBCSAPR-10 Bicapped square antiprism J17 D4d 3.417 3.243 3.451 JMBIC-10 Metabidiminished icosahedron J62 C2v 6.317 6.501 5.493 JATDI-10 Augmented tridiminished C3v 19.027 19.068 18.567 icosahedron J64 JSPC-10 Biaugmented trigonal prism C2v 3.930 3.867 4.263 SDD-10 Staggered Dodecahedron (2:6:2) D2 3.780 3.874 4.210 TD-10 Tetradecahedron (2:6:2) C2v 2.879 2.990 3.165 HD-10 Hexadecahedron (2:6:2) or (1:4:4:1) D4h 5.297 5.384 4.709

Table S3. The select intramolecular distance and Angles for MII and LnIII in complexes 1–3.

II III II III o Complex M Ln (Å) M –2-O–Ln ( ) 1 3.774(7) 112.460(1), 113.720(1) 2 3.756(12) 111.801(2), 112.835(2) 3 3.746(8) 112.906(8)

15 Table S4. Selected bond lengths (Å) and bond angles (°) for compound 1–3.

Complex 1 Complex 2 Complex 3 Dy(1)-O(2) 2.370(3) Dy(1)-O(2) 2.353(4) Y(1)-O(2) 2.367(2) Dy(1)-O(1) 2.381(3) Dy(1)-O(1) 2.375(4) Y(1)-O(2)#1 2.367(2) Dy(1)-O(3) 2.399(3) Dy(1)-O(3) 2.399(4) Y(1)-O(1)#1 2.417(3) Dy(1)-O(4) 2.423(4) Dy(1)-O(4) 2.425(4) Y(1)-O(1) 2.417(3) Dy(1)-O(8) 2.462(4) Dy(1)-O(8) 2.451(4) Y(1)-O(5) 2.451(3) Dy(1)-O(7) 2.470(4) Dy(1)-O(12) 2.462(4) Y(1)-O(5)#1 2.451(3) Dy(1)-O(12) 2.488(4) Dy(1)-O(7) 2.462(4) Y(1)-O(3)#1 2.467(3) Dy(1)-O(10) 2.532(4) Dy(1)-O(10) 2.516(4) Y(1)-O(3) 2.467(3) Dy(1)-N(3) 2.624(4) Dy(1)-N(3) 2.610(5) Y(1)-N(3) 2.618(3) Dy(1)-N(9) 2.649(4) Dy(1)-N(9) 2.654(5) Y(1)-N(3)#1 2.618(3) Co(1)-N(6) 2.116(4) Zn(1)-O(3) 2.136(4) Co(1)-O(2)#1 2.126(2) Co(1)-N(5) 2.126(4) Zn(1)-N(5) 2.140(5) Co(1)-O(2) 2.126(2) Co(1)-O(2) 2.133(3) Zn(1)-N(6) 2.142(5) Co(1)-N(6) 2.126(4) Co(1)-N(7) 2.133(4) Zn(1)-O(6) 2.150(5) Co(1)-N(5) 2.135(3) Co(1)-O(3) 2.137(3) Zn(1)-N(7) 2.152(5) Co(1)-N(5)#1 2.135(3) Co(1)-O(5) 2.172(5) Zn(1)-O(2) 2.155(4) Co(1)-O(6)#1 2.175(3) Co(1)-O(6) 2.181(5) Zn(1)-O(5) 2.175(5) Co(1)-O(6) 2.175(3) O(2)-Dy(1)-O(1) 120.41(11) O(2)-Dy(1)-O(1) 120.43(14) O(2)-Y(1)-O(2)#1 63.02(11) O(2)-Dy(1)-O(3) 62.70(10) O(2)-Dy(1)-O(3) 63.80(12) O(2)-Y(1)-O(1)#1 156.13(10) O(1)-Dy(1)-O(3) 152.97(14) O(1)-Dy(1)-O(3) 152.60(15) O(2)#1-Y(1)-O(1)#1 120.73(9) O(2)-Dy(1)-O(4) 158.49(13) O(2)-Dy(1)-O(4) 157.14(14) O(2)-Y(1)-O(1) 120.73(9) O(1)-Dy(1)-O(4) 68.11(13) O(1)-Dy(1)-O(4) 67.86(16) O(2)#1-Y(1)-O(1) 156.13(10) O(3)-Dy(1)-O(4) 119.88(11) O(3)-Dy(1)-O(4) 119.92(13) O(1)#1-Y(1)-O(1) 66.56(14) O(2)-Dy(1)-O(8) 86.36(12) O(2)-Dy(1)-O(8) 85.05(13) O(2)-Y(1)-O(5) 75.50(9) O(1)-Dy(1)-O(8) 82.39(13) O(1)-Dy(1)-O(8) 82.19(14) O(2)#1-Y(1)-O(5) 83.62(9) O(3)-Dy(1)-O(8) 124.17(12) O(3)-Dy(1)-O(8) 124.79(13) O(1)#1-Y(1)-O(5) 127.32(10) O(4)-Dy(1)-O(8) 74.89(13) O(4)-Dy(1)-O(8) 74.73(14) O(1)-Y(1)-O(5) 75.41(10) O(2)-Dy(1)-O(7) 80.65(12) O(2)-Dy(1)-O(12) 120.30(14) O(2)-Y(1)-O(5)#1 83.62(9) O(1)-Dy(1)-O(7) 129.48(13) O(1)-Dy(1)-O(12) 76.31(14) O(2)#1-Y(1)-O(5)#1 75.50(9) O(3)-Dy(1)-O(7) 77.05(12) O(3)-Dy(1)-O(12) 78.97(13) O(1)#1-Y(1)-O(5)#1 75.42(10) O(4)-Dy(1)-O(7) 79.45(13) O(4)-Dy(1)-O(12) 81.70(15) O(1)-Y(1)-O(5)#1 127.32(10) O(8)-Dy(1)-O(7) 51.54(12) O(8)-Dy(1)-O(12) 152.75(13) O(5)-Y(1)-O(5)#1 155.52(13) O(2)-Dy(1)-O(12) 118.72(12) O(2)-Dy(1)-O(7) 80.03(14) O(2)-Y(1)-O(3)#1 84.38(9) O(1)-Dy(1)-O(12) 76.70(13) O(1)-Dy(1)-O(7) 129.47(15) O(2)#1-Y(1)-O(3)#1 120.70(9) O(3)-Dy(1)-O(12) 79.07(12) O(3)-Dy(1)-O(7) 77.30(13) O(1)#1-Y(1)-O(3)#1 73.72(10) O(4)-Dy(1)-O(12) 81.77(13) O(4)-Dy(1)-O(7) 79.15(15) O(1)-Y(1)-O(3)#1 82.86(10) O(8)-Dy(1)-O(12) 153.17(13) O(8)-Dy(1)-O(7) 52.01(13) O(5)-Y(1)-O(3)#1 136.49(11) O(7)-Dy(1)-O(12) 136.50(12) O(12)-Dy(1)-O(7) 136.28(14) O(5)#1-Y(1)-O(3)#1 51.49(10) O(2)-Dy(1)-O(10) 73.86(12) O(2)-Dy(1)-O(10) 74.86(13) O(2)-Y(1)-O(3) 120.70(9) O(1)-Dy(1)-O(10) 79.35(13) O(1)-Dy(1)-O(10) 79.37(15) O(2)#1-Y(1)-O(3) 84.38(9) O(3)-Dy(1)-O(10) 76.08(12) O(3)-Dy(1)-O(10) 75.93(13) O(1)#1-Y(1)-O(3) 82.86(10) O(4)-Dy(1)-O(10) 127.55(13) O(4)-Dy(1)-O(10) 127.81(14) O(1)-Y(1)-O(3) 73.72(10)

16 O(8)-Dy(1)-O(10) 140.86(12) O(8)-Dy(1)-O(10) 140.41(14) O(5)-Y(1)-O(3) 51.49(10) O(7)-Dy(1)-O(10) 149.22(12) O(12)-Dy(1)-O(10) 50.91(14) O(5)#1-Y(1)-O(3) 136.49(11) O(12)-Dy(1)-O(10) 50.56(12) O(7)-Dy(1)-O(10) 149.30(14) O(3)#1-Y(1)-O(3) 151.99(13) O(2)-Dy(1)-N(3) 60.28(11) O(2)-Dy(1)-N(3) 60.09(14) O(2)-Y(1)-N(3) 60.14(8) O(1)-Dy(1)-N(3) 60.93(12) O(1)-Dy(1)-N(3) 60.91(15) O(2)#1-Y(1)-N(3) 120.56(8) O(3)-Dy(1)-N(3) 119.75(11) O(3)-Dy(1)-N(3) 120.01(14) O(1)#1-Y(1)-N(3) 118.16(9) O(4)-Dy(1)-N(3) 120.25(12) O(4)-Dy(1)-N(3) 119.98(15) O(1)-Y(1)-N(3) 61.16(9) O(8)-Dy(1)-N(3) 69.64(13) O(8)-Dy(1)-N(3) 69.56(15) O(5)-Y(1)-N(3) 67.12(10) O(7)-Dy(1)-N(3) 110.51(12) O(12)-Dy(1)-N(3) 112.55(14) O(5)#1-Y(1)-N(3) 113.04(10) O(12)-Dy(1)-N(3) 112.87(12) O(7)-Dy(1)-N(3) 111.08(14) O(3)#1-Y(1)-N(3) 69.39(11) O(10)-Dy(1)-N(3) 71.23(12) O(10)-Dy(1)-N(3) 70.85(14) O(3)-Y(1)-N(3) 110.43(10) O(2)-Dy(1)-N(9) 119.14(11) O(2)-Dy(1)-N(9) 119.59(13) O(2)-Y(1)-N(3)#1 120.56(8) O(1)-Dy(1)-N(9) 119.55(12) O(1)-Dy(1)-N(9) 119.39(14) O(2)#1-Y(1)-N(3)#1 60.14(8) O(3)-Dy(1)-N(9) 59.56(11) O(3)-Dy(1)-N(9) 59.64(13) O(1)#1-Y(1)-N(3)#1 61.16(9) O(4)-Dy(1)-N(9) 60.46(11) O(4)-Dy(1)-N(9) 60.37(14) O(1)-Y(1)-N(3)#1 118.16(9) O(8)-Dy(1)-N(9) 110.87(13) O(8)-Dy(1)-N(9) 110.60(14) O(5)-Y(1)-N(3)#1 113.04(10) O(7)-Dy(1)-N(9) 69.65(12) O(12)-Dy(1)-N(9) 67.46(14) O(5)#1-Y(1)-N(3)#1 67.12(10) O(12)-Dy(1)-N(9) 66.93(12) O(7)-Dy(1)-N(9) 68.89(13) O(3)#1-Y(1)-N(3)#1 110.43(10) O(10)-Dy(1)-N(9) 108.26(12) O(10)-Dy(1)-N(9) 108.98(13) O(3)-Y(1)-N(3)#1 69.39(11) N(3)-Dy(1)-N(9) 179.28(12) N(3)-Dy(1)-N(9) 179.65(14) N(3)-Y(1)-N(3)#1 179.28(12) N(6)-Co(1)-N(5) 72.73(16) O(3)-Zn(1)-N(5) 142.05(16) O(2)#1-Co(1)-O(2) 71.17(12) N(6)-Co(1)-O(2) 144.16(15) O(3)-Zn(1)-N(6) 144.72(17) O(2)#1-Co(1)-N(6) 144.41(6) N(5)-Co(1)-O(2) 72.13(14) N(5)-Zn(1)-N(6) 72.90(19) O(2)-Co(1)-N(6) 144.41(6) N(6)-Co(1)-N(7) 72.66(16) O(3)-Zn(1)-O(6) 89.4(2) O(2)#1-Co(1)-N(5) 141.99(10) N(5)-Co(1)-N(7) 145.39(16) N(5)-Zn(1)-O(6) 85.7(2) O(2)-Co(1)-N(5) 72.39(9) O(2)-Co(1)-N(7) 142.05(14) N(6)-Zn(1)-O(6) 89.2(2) N(6)-Co(1)-N(5) 72.64(7) N(6)-Co(1)-O(3) 144.74(14) O(3)-Zn(1)-N(7) 72.13(16) O(2)#1-Co(1)-N(5)#1 72.39(9) N(5)-Co(1)-O(3) 142.08(14) N(5)-Zn(1)-N(7) 145.72(19) O(2)-Co(1)-N(5)#1 141.99(10) O(2)-Co(1)-O(3) 71.05(12) N(6)-Zn(1)-N(7) 72.82(19) N(6)-Co(1)-N(5)#1 72.64(7) N(7)-Co(1)-O(3) 72.38(13) O(6)-Zn(1)-N(7) 94.1(2) N(5)-Co(1)-N(5)#1 145.28(15) N(6)-Co(1)-O(5) 93.30(17) O(3)-Zn(1)-O(2) 71.66(14) O(2)#1-Co(1)-O(6)#1 94.99(10) N(5)-Co(1)-O(5) 94.5(2) N(5)-Zn(1)-O(2) 71.57(16) O(2)-Co(1)-O(6)#1 85.66(10) O(2)-Co(1)-O(5) 82.65(16) N(6)-Zn(1)-O(2) 143.44(17) N(6)-Co(1)-O(6)#1 89.60(8) N(7)-Co(1)-O(5) 87.3(2) O(6)-Zn(1)-O(2) 96.5(2) N(5)-Co(1)-O(6)#1 92.71(11) O(3)-Co(1)-O(5) 89.55(19) N(7)-Zn(1)-O(2) 142.06(17) N(5)#1-Co(1)-O(6)#1 87.05(11) N(6)-Co(1)-O(6) 92.5(2) O(3)-Zn(1)-O(5) 89.35(18) O(2)#1-Co(1)-O(6) 85.66(10) N(5)-Co(1)-O(6) 85.85(17) N(5)-Zn(1)-O(5) 94.8(2) O(2)-Co(1)-O(6) 94.99(10) O(2)-Co(1)-O(6) 91.76(19) N(6)-Zn(1)-O(5) 92.40(18) N(6)-Co(1)-O(6) 89.60(8) N(7)-Co(1)-O(6) 95.87(18) O(6)-Zn(1)-O(5) 178.4(2) N(5)-Co(1)-O(6) 87.05(11) O(3)-Co(1)-O(6) 86.52(19) N(7)-Zn(1)-O(5) 86.42(19) N(5)#1-Co(1)-O(6) 92.71(11) O(5)-Co(1)-O(6) 174.0(2) O(2)-Zn(1)-O(5) 82.23(16) O(6)#1-Co(1)-O(6) 179.21(15)

Symmetry transformations used to generate equivalent atoms for 3CoY, #1: -X, Y, 0.5-Z.

17 Table S5. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of compounds 2ZnDy at 2 K under various dc fields according to the generalized Debye model.

3 -1 3 -1 H / kOe S / cm mol K T / cm mol K  / s  s 0.2 3.56 4.81101 0.00120 0.10715 2.15E-5 0.4 1.81635 4.73773 0.00182 0.18822 6.53E-5 0.6 1.09113 4.68185 0.00255 0.18479 2.05E-4 0.8 0.5701 4.56227 0.00293 0.21998 3.74E-4 1.0 0.40331 4.52044 0.00332 0.22995 6.51E-4 1.5 0.19952 3.60212 0.00300 0.20928 1.06E-3 2.0 0.17458 3.26806 0.00246 0.17144 3.30E-4 2.5 0.01868 2.79137 0.00184 0.27027 4.44E-4 3.0 0.05818 2.26425 0.00130 0.24823 8.75E-5 3.5 0.04766 2.02591 9.300E-4 0.29997 5.45E-4 4.0 0.09667 1.79372 7.210E-4 0.28007 1.29E-3 4.5 0.08468 1.38781 5.770E-4 0.29974 4.78E-4

Table S6. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of compounds 3CoY at 2 K under various dc fields according to the generalized Debye model.

3 -1 3 -1 H / kOe S / cm mol K T / cm mol K  / s  s 0.2 0.53791 0.75326 2.3E-4 0.20531 3.14E-5 0.4 0.31145 0.76106 2.9E-4 0.18244 1.47E-4 0.6 0.20245 0.75217 3.3E-4 0.14082 9.94E-5 0.8 0.13784 0.76248 3.8E-4 0.15790 1.90E-4 1.0 0.11480 0.75299 3.9E-4 0.12400 1.26E-4 1.5 0.07787 0.72881 3.7E-4 0.10416 9.09E-5 2.0 0.03191 0.69904 3.1E-4 0.11170 1.28E-4 2.5 0.01631 0.69568 2.7E-4 0.16502 2.60E-4 3.0 0.00769 0.68030 2.5E-4 0.22064 9.07E-4 3.5 0.05808 0.61065 2.3E-4 0.15178 9.93E-4 4.0 0.01766 0.58199 1.7E-4 0.20686 2.05E-4 4.5 0.00466 0.56005 1.6E-4 0.28092 8.81E-4

18 Table S7. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of

2ZnDy under 1.8 K-5.0 K according to the generalized Debye model.

3 -1 3 -1 T / K S / cm mol K T / cm mol K  / s  s 1.8 0.27180 6.07507 0.06517 0.25944 7.49E-4 2.0 0.22784 5.20592 0.04452 0.27640 9.14E-4 2.2 0.22174 4.71029 0.03554 0.26727 8.78E-4 2.4 0.20375 4.41414 0.02890 0.26676 5.83E-4 2.6 0.19138 4.10504 0.02236 0.24797 3.21E-4 2.8 0.14734 3.92100 0.01742 0.27029 4.77E-4 3.0 0.12905 3.70782 0.01355 0.28785 4.47E-4 3.2 0.10208 3.51832 0.00939 0.29409 8.94E-4 3.4 0.10126 3.33525 0.00636 0.27723 1.82E-3 3.6 0.10000 3.20125 0.00446 0.28458 1.81E-3 3.8 0.05029 3.04004 0.00284 0.27950 1.05E-3 4.0 0.02820 2.89738 0.00191 0.28860 1.50E-3 4.2 0.02270 2.77082 0.00126 0.27681 1.59E-3 4.4 0.01259 2.66711 8.800E-4 0.27213 1.26E-3 4.6 1.50E-4 2.60000 6.600E-4 0.29967 1.39E-3 4.8 0.01150 2.50000 5.000E-4 0.30000 1.52E-3 5.0 0.10001 2.30000 4.000E-4 0.26902 3.08E-3

Table S8. Relaxation fitting parameters from the least-square fitting of the Cole-Cole plots of 3CoY under 1.8 K-5.0 K according to the generalized Debye model.

3 -1 3 -1 T / K S / cm mol K T / cm mol K  / s  s 1.8 0.09343 0.83166 4.7E-4 0.15382 4.73E-5 2.1 0.06636 0.73965 3.4E-4 0.18600 1.75E-4 2.4 0.06751 0.63522 2.4E-4 0.16285 9.50E-5 2.7 0.01247 0.57245 1.6E-4 0.20937 2.48E-4 3.0 0.01676 0.51295 1.3E-4 0.18153 2.09E-4 3.3 0.08563 0.50820 1.0E-4 0.11988 1.95E-4 3.6 0.08173 0.42822 8.0E-5 0.11066 5.35E-5 4.0 0.03329 0.39051 6.0E-5 0.15314 8.98E-5 4.5 0.07966 0.35284 5.2E-5 0.14492 1.11E-5 5.0 0.08343 0.31789 5.0E-5 0.10947 5.81E-5

19 Table S9. Parameters fitted from the Arrhenius plots in Figure 5 considering multiple relaxation processes for 2ZnDy and 3CoY.

Complex 2 Value Standard error R2 A 0.0352 0.0021

B1 0.8604 0.0845 0.99

B2 6.0532 0.0213 C 0.0032 0.0032 n 2.63 0.6245 0.98 -7 -7 0 4.71 × 10 s 2.78 × 10

Ueff 32.9 K 5.57 Complex 3 Value Standard error R2 A 0.1077 0.0044

B1 2.9688 0.2434 0.99

B2 7.6276 1.6147 C 5.6605 6.0440 n 4.9752 0.6252 0.98 -5 -5 0 5.79 × 10 s 1.43 × 10

Ueff 7.5 K 0.59

Table S10. Wave functions with definite projection of the total moment | mJ > for the lowest two III Kramers doublets (KDs) of individual Dy fragments for complexes 1CoDy and 2ZnDy.

E/cm−1 Wave functions 0.0 16%|±15/2>+36%|±13/2>+6%|±11/2>+21%|±9/2>+13%|±5/2> Complex 1 14.9 8%|±15/2>+14%|±11/2>+34%|±9/2>+14%|±5/2>+16%|±3/2>+11%|±1/2> 0.0 46%|±15/2>+33%|±13/2>+6%|±11/2>+9%|±9/2>+4%|±7/2> Complex 2 33.6 8%|±11/2>+33%|±7/2>+23%|±5/2>+20%|±3/2>+12%|±1/2>

20 −1 Table S11. Calculated energy levels (cm ), g (gx, gy, gz) tensors and mJ values of the lowest eight Kramers doublets (KDs) of individual DyIII fragment, and zero-field splitting parameters D (E) (cm−1), g tensors of the lowest spin-orbit state of individual CoII fragment of complexes 1−3 using CASSCF/RASSI with MOLCAS 8.2.

Complex 1 Dy Co KDs –1 E/cm g mJ D (E) g 0.334 2.337 1 0.0 3.988 ±13/2 36.8 (−0.9) 2.320 13.947 2.003 0.706 2 14.9 2.899 ±9/2 13.613 0.380 3 52.4 0.693 ±11/2 13.638 0.072 4 74.3 1.278 ±3/2 15.737 3.401 5 150.4 5.027 ±7/2  11.413 7.606 6 191.4 6.811 ±5/2 2.931 2.705 7 218.2 5.476 ±1/2 9.905 1.092 8 263.0 1.774 ±15/2 15.660 Complex 3 Co D (E) g  2.391 40.8 (−1.0) 2.375 2.008 Complex 2 Dy KDs –1 E/cm g mJ 0.270  1 0.0 0.940 ±15/2 16.640

21 0.380 2 33.6 1.637 ±7/2 16.625 0.282 3 58.7 1.056 ±13/2 13.526 0.431 4 83.7 1.283 ±1/2 14.822 3.202 5 160.8 4.882 ±9/2 10.673 7.827 6 196.2 5.824 ±3/2 3.127 1.590 7 233.3 3.880 ±5/2 7.999 1.284 8 275.0 4.137 ±11/2 14.615

−1 Table S12. Exchange energies (cm ) and main values of the g z for the lowest four exchange doublets of complex 1CoDy.

–1 E/cm gz

0.0 18.837 1 0.7 18.837

2.4 9.157 2 3.4 9.157

14.9 17.487 3 15.5 17.487

18.0 9.833 4 18.5 9.833

22 Reference

(S1) O. Kahn, Molecular Magnetism, VCH, Weinheim, Germany, 1993.

(S2) (a) SAINT Software Users Guide, Version 7.0, Bruker Analytical X-Ray Systems, Madison, WI, 1999. (b) Sheldrick, G. M. SADABS, Version 2.03, Bruker Analytical X-Ray Systems, Madison, WI, 2000. (S3) Sheldrick, G. M.; SHELXTL, Version 6.14, Structure Determination Software Suite, Bruker AXS, Inc., Madison, WI, 2000–2003.

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