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1 Supporting Information Proton-Conducting Magnetic Coordination Polymers Soumava Biswas, Himanshu Sekhar Jena, Suresh Sanda, and Sanjit Konar* [a] chem_ _sm_miscellaneous_information.pdf

2 Figure S1. Asymmetric unit of 1 with atom labelling scheme (Color codes: Gd(cyano), O(red), C(gray), H(white)).

3 (a) (b) Figure S2. (a) Coordination environment around gadolinium ion found in 1 and (b) its polyhedral view. Figure S3. Illustration of two continuous cavities (A) and (B) found in 1 representing the orientation of coordinated water molecules inside the units.

4 Figure S4. Illustration of a discrete rectangular H-bonded unit R 2 2(8) constructed by the H-bonding interaction between metal-bound water and lattice water molecules. Figure S5. Illustration of 3D networks found in 1 through the H-bonded interactions between two adjacent 2D CPs through H-bonded interactions between lattice methanol and metal bound water and carboxylate groups found in 1.

5 Figure S6. Packing diagram of 1 showing the arrangements of lattice water molecules (in space filling diagram) (a) (b) (c) Figure S7. TG profile of 1 (a), 2 (b) and 3 (c) (assynthesized (black), activated (red) and activated sample exposed to 30% RH (red))

6 (a) (b) Figure S8. PXRD pattern of 1 (a), 2 (b) and 3(c) Figure S9. Illustration of binuclear gadolinium core found in 1 and the respective Gd-O-Gd bond angles and Gd-Gd distance.

7 Figure S10. Isothermal normalized magnetizations vs. field/temperature plot for complex 1 collected for temperatures ranging from 2 to 10 K. Figure S11. Isothermal magnetizations vs. field plot for complex 2 (left) and 3 (right) collected for temperatures ranging from 2 to 10 K.

8 Figure S12. Isothermal normalized magnetizations vs. field/temperature plot for complex 2 (left) and 3 (right) collected for temperatures ranging from 2 to 10 K. Figure S13. Temperature dependence of the in phase (χ ) ac susceptibility components for 3 at the indicated frequencies and in zero field

9 Figure S14. Temperature dependence of the in phase (χ ) and out of phase (χ ) ac susceptibility components for 2 at the indicated frequencies and in zero field Figure. S15. Plot of ln( χ''/χ ) vs. reciprocal temperature for 3, the red solid line represents the fitting in the range of 6.2 K 9 K.

10 (a) (b) (c) Figure S16. Temperature dependence of the in phase (χ ) (a) and out of phase (χ ) (b) ac susceptibility components for 3 at the indicated frequencies and in 1800 Oe DC field. Plot of ln( χ''/χ ) vs. reciprocal temperature (c) where red solid line represents the fitting in the range of 5.7 K 6.8 K.

11 (a) (b) (c) Figure S17. Nyquist plot at 298 K and 95% relative humidity for (a) 1, (b) 2 and (c) 3 Figure S18. Time dependent proton conductivity of the complexes. (a) (b) (c) Figure S19 Log σ (S cm -1 ) versus RH plots of the 1(a), 2(b) and 3(c).

12 Details of the simulation of the water vapor adsorption of 1 After removing the lattice solvent molecules a new cif. file was generated and the file was imported to Sorption module of the Material Studio 6.1 version. We run the program on the for water adsorption isotherm simulation in the fugacity range of 5.22 e-03 K Pa to K Pa using Monte Carlo method. The details of the generated results files as attached below for better understanding. (a) (b) Figure. S20.(a) Volumetric visualization of density distribution of water molecules in side framework of 1 (b) A clear representation of density distribution of water molecules in a 1D array inside the framework after hiding all atoms. Detail elemental analysis data of activated sample 1-3: The activated sample of each complex was prepared by grinding the crystalline materials to powder form and activate it by drying under 10-2 KPa continuous vacuum using BelPrepvacII at 80 C for 12 h. The obtained sample was measured for the elementary anaysis. The elementary analysis data for each complex are as follows: Activated complex 1 (C 18H 18Gd 2O 12): Elemental analysis (%): Calcd.(found) for C 18H 18Gd 2O 12 = [Gd 2(L) 3] n: C, (28.38), H, 2.45(2.14). Activated complex 2 (C 18H 18Tb 2O 12):Elemental analysis (%): Calcd.(found) for C 18H 18Tb 2O 12 = [Tb 2(L) 3] n: C, 29.05(28.83), H, 2.44(2.08). Activated complex 3 (C 18H 18Dy 2O 12):Elemental analysis (%): Calcd.(found) for C 18H 18Dy 2O 12= [Dy 2(L) 3] n: C, 28.78(28.22), H, 2.41(2.11).

13 Detail elemental analysis data of 30 % RH exposed sample 1-3: For such analysis, the activated sample of each complex were exposed to 30 % RH in a controlled humidity chamber for 12 h at room temperature The elementary analysis data for each complex are as follows: 30 % RH exposed sample of complex 1 (C 18H 26Gd 2O 16): Elemental analysis (%): Calcd.(found) for C 18H 26Gd 2O 16: C, 26.60(26.23), H, 3.22(3.11). 30 % RH exposed sample of complex 2 (C 18H 26Tb 2O 16):Elemental analysis (%): Calcd.(found) for C 18H 26Tb 2O 16: C, 26.49(26.03), H, 3.21(3.08). 30 % RH exposed sample of complex 3 (C 18H 26Dy 2O 16):Elemental analysis (%): Calcd.(found) for C 18H 26Dy 2O 16: C, 26.26(25.79), H, 3.18(2.91). Table S1. Relevant bond distances (Å) and bond angles ( ) around the Gd 3+ centers found in 1 Gd(1)- O(1) 2.377(2) Gd(2) O(1) 2.506(1) Gd(1) - O(6) 2.327(1) Gd(2) O(2) 2.467(1) Gd(1) - O(7) 2.459(1) Gd(2) O(3) 2.581(2) Gd(1) - O(8) 2.480(2) Gd(2) O(4) 2.352(1) Gd(1) - O(9) 2.490(2) Gd(2) O(5) 2.321(1) Gd(1) - O(10) 2.421(1) Gd(2) O(9) 2.469(1) Gd(1) - O(11) 2.497(2) Gd(2) O(10) 2.440(2) Gd(1) - O(12) 2.586(1) Gd(2) O(11) 2.394(2) Gd(1) - O(14) 2.452(2) Gd(2) O(13) 2.406(2) Gd(1) Gd(2) (3) Gd(2) Gd(1A) (3) Gd(1)-O1-Gd(2) (6) O(8)-Gd(1)-O(9) 52.33(5) Gd(1)-O9-Gd(2) (5) O(11)-Gd(1)-O(12) 50.84(5) Gd(1)-O10-Gd(2) (6) O(1)-Gd(2)-O(2) 52.34(5) Gd(1)-O11-Gd(2) (6) O(1)-Gd(2)-O(3) (5) O(1)-Gd(1)-O(6) 83.45(5) O(1)-Gd(2)-O(4) (5) O(1)-Gd(1)-O(7) 72.10(5) O(1)-Gd(2)-O(5) 78.72(5)

14 O(1)-Gd(1)-O(8) (5) O(1)-Gd(2)-O(9) (5) O(1)-Gd(1)-O(9) (5) O(1)-Gd(2)-O(10) (5) O(1)-Gd(1)-O(10) 70.80(5) O(1)-Gd(2)-O(11) 65.72(5) O(1)-Gd(1)-O(11) 66.11(5) O(1)-Gd(2)-O(13) 79.38(5) O(1)-Gd(1)-O(12) (5) O(1)-Gd(2)-O(13) 79.38(5) O(1)-Gd(1)-O(14) 98.65(5) O(2)-Gd(2)-O(3) 71.50(5) O(7)-Gd(1)-O(6) 72.12(5) O(2)-Gd(2)-O(4) 77.17(5) O(7)-Gd(1)-O(8) 81.22(5) O(2)-Gd(2)-O(5) (5) O(7)-Gd(1)-O(9) 86.62(5) O(2)-Gd(2)-O(10) (5) O(7)-Gd(1)-O(10) 75.32(5) O(2)-Gd(2)-O(10) (5) O(7)-Gd(1)-O(11) (5) O(2)-Gd(2)-O(11) 93.79(5) O(7)-Gd(1)-O(12) (5) O(2)-Gd(2)-O(13) 82.32(6) O(7)-Gd(1)-O(6) (5) O(13)-Gd(2)-O(3) 67.98(5) O(8)-Gd(1)-O(6) 77.20(5) O(13)-Gd(2)-O(4) (6) O(8)-Gd(1)-O(9) 52.33(5) O(13)-Gd(2)-O(5) 71.10(5) O(8)-Gd(1)-O(10) (5) O(13)-Gd(2)-O(9) (5) O(8)-Gd(1)-O(11) (5) O(13)-Gd(2)-O(10) 78.03(5) O(8)-Gd(1)-O(12) 78.73(5) O(13)-Gd(2)-O(11) (5) O(8)-Gd(1)-O(14) (5) O(3)-Gd(2)-O(10) 52.01(5) O(9)-Gd(1)-O(6) (5) O(3)-Gd(2)-O(4) 77.48(5) O(9)-Gd(1)-O(10) 65.34(5) O(3)-Gd(2)-O(5) (5) O(9)-Gd(1)-O(11) (5) O(3)-Gd(2)-O(9) (5) O(9)-Gd(1)-O(12) (5) O(3)-Gd(2)-O(10) 52.01(5) O(9)-Gd(1)-O(14) 77.04(5) O(3)-Gd(2)-O(11) (5) O(10)-Gd(1)-O(6) (5) O(4)-Gd(2)-O(5) (5) O(10)-Gd(1)-O(11) (5) O(4)-Gd(2)-O(6) 74.77(5) O(10)-Gd(1)-O(12) (5) O(4)-Gd(2)-O(10) 89.00(5) O(10)-Gd(1)-O(14) 70.67(5) O(4)-Gd(2)-O(11) 73.58(5) O(14)-Gd(1)-O(6) (5) O(5)-Gd(2)-O(9) 74.20(5)

15 O(14)-Gd(1)-O(11) 69.97(5) O(5)-Gd(2)-O(10) 94.16(5) O(14)-Gd(1)-O(12) 71.62(5) O(5)-Gd(2)-O(11) 78.94(5) O(6)-Gd(1)-O(11) 75.52(5) O(9)-Gd(2)-O(10) 65.37(5) O(6)-Gd(1)-O(12) 72.45(5) O(9)-Gd(2)-O(12) 69.45(5) O(11)-Gd(1)-O(12) 50.84(5) O(10)-Gd(2)-O(11) (5) Table S2. Relevant bond distances (Å) and bond angles ( ) around the Tb 3+ centers found in 2 Tb1 - O (2) O13-Tb1-O (6) Tb1 - O (2) O9-Tb1-O (6) Tb1 - O (2) O9-Tb1-O (6) Tb1 - O (1) O9-Tb1-O (6) Tb1 - O (2) O2-Tb1-O (6) Tb1 O (2)) O2-Tb1-O (6) Tb2 O (2) O8-Tb2-O (6) Tb2 - O (2) O8- Tb2-O (6) Tb2 O (2) O8- Tb2-O (6) Tb2 O (1) O8- Tb2-O (6) Tb2 O (2) O8- Tb2-O (6) Tb2 O (2) O8- Tb2-O (6) O8-Tb1- O (5) O8- Tb2-O (6) O8-Tb1- O (6) O8- Tb2-O (6) O8-Tb1-O (6) O3-Tb2-O (6) O8-Tb1-O (6) O3-Tb2-O (6) O8-Tb1- O (6) O3-Tb2-O (6) O8-Tb1- O (6) O3-Tb2-O (6) O8-Tb1 O (6) O3-Tb2- O (5) O8-Tb1-O (6) O3-Tb2-O (5) O3-Tb1-O (6) O3-Tb2-O (6) O3-Tb1-O (6) O4-Tb2- O (6) O3-Tb1-O (6) O4-Tb2-O (6) O3-Tb1-O (6) O4-Tb2-O (6) O3-Tb1 O (6) O4-Tb2-O (6) O3-Tb1-O (6) O4-Tb2- O (6) O3-Tb1-O (6) O4-Tb2-O (6)

16 O18-Tb1-O (6) O10-Tb2- O (6) O18-Tb1-O (6) O10-Tb2-O (6) O18-Tb1-O (6) O10-Tb2-O (6) O18-Tb2-O (6) O10-Tb2-O (6) O18-Tb2-O (6) O10-Tb2-O (6) O18-Tb2-O (6) O7-Tb2-O (6) O5-Tb1-O (6) O7-Tb2-O (6) O5-Tb1-O (6) O7-Tb2-O (6) O5-Tb1-O (6) O7-Tb2-O (6) O5-Tb1-O (6) O12-Tb2-O (6) O5-Tb1-O (6) O12-Tb2-O (6) O13-Tb1-O (6) O12-Tb2-O (6) O13-Tb1-O (6) O5-Tb2-O (5) O13-Tb1-O (6) O5- Tb2-O (6) O1- Tb2-O (6) Table S3. Relevant bond distances (Å) and bond angles ( ) around the Dy 3+ centers found in 3. Dy1-O (1) Dy2-O (2) Dy1-O (1) Dy2-O (1) Dy1-O (1) Dy2-O (1) Dy1-O (2) Dy2-O (1) Dy1-O (1) Dy2-O (1) Dy1-O (2) Dy2-O (2) Dy1-O (2) Dy2-O (1) Dy1-O (1) Dy2-O (2) Dy1-O (1) Dy2-O (1) O1- Dy1- O (4) O2-Dy2-O (5) O1-Dy1- O (4) O2-Dy2-O (5) O1-Dy1- O (5) O2-Dy2-O (5) O1-Dy1-O (5) O2-Dy2-O (5) O1-Dy1-O (4) O2-Dy2-O (5)

17 O1-Dy1-O (5) O2-Dy2-O (5) O1-Dy1-O (5) O2-Dy2-O (5) O1-Dy1-O (5) O2-Dy2-O (5) O2-Dy1-O (5) O3-Dy2-O (5) O2 Dy1--O (5) O3-Dy2-O (5) O2-Dy- O (5) O3-Dy2-O (5) O2-Dy1- O (5) O3-Dy2-O (5) O2-Dy1- O (5) O3-Dy2-O (4) O2-Dy1-O (5) O3-Dy2-O (5) O2-Dy1- O (5) O3-Dy2-O (5) O6-Dy1-O (5) O5-Dy2-O (5) O6-Dy1-O (5) O5-Dy2-O (5) O6-Dy1-O (5) O5-Dy2-O (5) O6-Dy1-O (5) O5-Dy2-O (5) O6-Dy1-O (5) O5-Dy2-O (5) O6-Dy1-O (5) O5-Dy2-O (5) O9-Dy1-O (5) O8-Dy2-O (5) O9 Dy1 O (5) O8-Dy2-O (5) O9 Dy1 O (5) O8-Dy2-O (5) O9- Dy1O (5) O8-Dy2-O (5) O9 Dy1 O (5) O8-Dy2-O (5) O12 Dy1-O (5) O9-Dy2-O (5) O12 Dy1-O (5) O9-Dy2-O (4) O12 Dy1-O (5) O9-Dy2-O (5) O12 Dy1-O (5) O9-Dy2-O (5) O3 Dy1 -O (5) O14-Dy2-O (5) O3-Dy1-O (5) O14-Dy2-O (5) O3 -Dy1-O (5) O14-Dy2-O (5) O4- Dy1-O (5) O6-Dy2-O (5)

18 O4-Dy1-O (5) O6-Dy2-O (5) O11-Dy1-O (5) O7-Dy2-O (5) Dy1-O2-Dy (5) Dy2-O3-Dy (5) Dy1-O6-Dy (5) Dy1-O9-Dy (5) Dy1-O3-Dy (5) Dy2-O6-Dy (5) Table S4. Relevant H-bond parameters found in 1. Donor-H Acceptor D - H H A D A D - H A Symmetry O(13) -H(13C) O(16) 0.83(4) 1.92(4) 2.747(3) 176(3) 1-x,-1/2+y,1/2-z O(13) -H(13D) O(18) 0.85(4) 1.78(4) 2.633(3) 175(4) 1-x,-1/2+y,1/2-z O(14) - H(14C) O(15) 0.85(4) 2.02(4) 2.848(2) 163(4) x,1/2-y,-1/2+z O(14) - H(14D) O(15) 0.79(4) 2.06(4) 2.843(2) 171(3) 1-x,1/2+y,1/2-z O(15) - H(15C) O(4) 0.90(4) 1.98(3) 2.866(2) 170(3) x, y, z O(15) - H(15D) O(10) 0.74(3) 2.70(4) 3.201(2) 122(3) -x+1,-y,-z+1 O(16) - H(16) O(17) 0.84(2) 2.02(3) 2.802(3) 154(2) -x,1-y,1-z O(17) - H(17) O(12) 0.84(2) 1.99(3) 2.793(3) 159(2) x,1/2-y,1/2+z O(18) - H(18C) O(7) 0.87(4) 2.18(4) 3.042(3) 171(4) 1-x,1/2+y,1/2-z O(18) - H(18D) O(6) 0.74(5) 2.54(4) 3.048(2) 128(4) x,1/2-y,1/2+z O(18) -H(18D) O(8) 0.74(5) 2.29(5) 2.978(2) 155(4) x,1/2-y,1/2+z C(16) -H(16) O(16) 0.99(2) 2.90(1) 3.726(3) 140(2) x, y, z C(10) -H(10) O(3) 0.99(2) 2.79(1) 3.403(3) 120(2) x,-y+1/2,z+1/2 C(11) -H(11) O(2) 0.99(2) 2.76(2) 3.451(3) 125(2) x,-y+1/2,z+1/2 C(17) -H(17) O(15) 0.99(3) 2.82(2) 3.467(4) 124(2) x,-y+1/2,z+1/2 C(11) -H(11) O(3) 0.99(2) 2.78(1) 3.448(3) 125(1) x,-y+1/2,z+1/2 C(12) -H(12) O(2) 0.99(2) 2.63(2) 3.378(3) 132(1) x,-y+1/2,z+1/2 C(17) -H(17B) O(13) 0.99(2) 2.91(2) 3.594(3) 127(1) -x+1,-y+1,-z+1

19 Table S5. Relevant H-bond parameters found in 2. Donor-H Acceptor D - H H A D A D - H A Symmetry O13--H1D--O x,y,z O12--H5A--O x,1/2-y,1/2+z O12--H6A--O x,1/2+y,1/2-z O13--H13--O x,1-y,1-z C4--H00B--O x,1/2-y,1/2+z C12--H00H--O x,1/2-y,1/2+z C15--H00O--O x,1/2-y,1/2+z Table S6. Relevant H-bond parameters found in 3. Donor-H Acceptor D - H H A D A D - H A Symmetry O(15) --H(15)..O(1) (3) 158 -x,1-y,1-z O(18) --H(18)..O(15) (3) 153 -x,1-y,1-z C(8) --H(8B)..O(11) (3) x,1/2+y,1/2-z C(14) --H(14B)..O(14) (3) x,1/2+y,1/2-z Table S7. Comparison of Proton Conductivity of some magnetic MOFs or coordination polymers at specified condition. Complex Proton Conductivity [S cm -1 ] Temperature [K] Humidity [RH%] Ref. in main text Co[Cr(CN) 6] 2/3 zh 2O 1.7x V[Cr(CN) 6] 2/3 zh2o 2.6x (NH 4) 4[MnCr 2(ox) 6] 3 4H 2O 1.7x (a) {NEt 3(CH 2COOH)}[MnCr (ox) 3] 1x (c) {NH(prol) 3}[MCr(ox) 3] 1x (a) [H 3O] 2[Mn 7(μ 3-H) 4(C 14H 8O 6S) 6(H 2O) 4] (H 2O) 2(DMF) x (b) {[Dy 2(L) 3(H 2O) 2] n 2n(CH 3OH) 2n(H 2O) 1.1x This work

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