Geometry analysis and systematic synthesis of highly. porous isoreticular frameworks with a unique topology

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1 Supplementary Information Geometry analysis and systematic synthesis of highly porous isoreticular frameworks with a unique topology Yue-Biao Zhang, Hao-Long Zhou, Rui-Biao Lin, Chi Zhang, Jian-Bin Lin, Jie-Peng Zhang* and Xiao-Ming Chen MOE Key Laboratory of Bioinorganic and Synthetic Chemistry, State Key Laboratory of Optoelectronic Materials and Technologies, School of Chemistry & Chemical Engineering, Sun Yat-Sen University, Guangzhou , P. R. China. * To whom correspondence should be addressed. Hzhangjp7@mail.sysu.edu.cn) S 1

$Moving the vertex (such as the green sphere Va) along the space diagonal of the cubic unit cell, means the fractional coordinates x =$

2 Supplementary Figure S1 Geometry details of the ncb net showing how ω, φ, and κ can be calculated from a single parameter x. Moving the vertex (such as the green sphere Va) along the space diagonal of the cubic unit cell, means the fractional coordinates x = y = z. S 2

3 (a) (b) φ / o 60 κ / o x x Supplementary Figure S2 Node geometry variation dependent on node position. S 3

4 Supplementary Figure S3 Perspective view of a distorted ncb net with unequal lengths of E 1 and E 2. Moving the green node (x, y, z) along the space diagonal (x = y = z) of the unit-cell also change the position of other symmetry-related nodes. Although the network connectivity and symmetry are retained, the node geometry and the edge lengths (also the length ratio d r between E 1 and E 2 ) are altered simultaneously. The figure shows that at d r = 3 = the triakis tetrahedron fuses as tetrahedron. 3 S 4

5 b c a N1 C1 C1 O2 C2 C4 C3 O2 C2 O2 O1 Ni1 C5 C7 C6 C7 C7 C7 C6 C5 N1 Supplementary Figure S4 Single-crystal structure of the trinuclear SBU in Ia. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). S 5

6 a b c C9 C11 C11 C10 C10 C11 C11 C9 O1 Ni1 O2 C8 O2 O2 C7 C7 C6 C6 C3 C3 C2 C4 C4 C2 C1 C5 C5 C1 N1 N1 N1 N1 Supplementary Figure S5 Single-crystal structure of the trinuclear SBU in IIa. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). Dashed bonds represent the disordering parts. S 6

7 b c a O5 C14 C13 N1 C1 C5 C3 C2 C4 C8 C7 O2 C6 O1 N1 Ni1 C9 O4 O5 C10 C12 C11 C12 C13 C11 C14 C10 C9 O4 O5 Supplementary Figure S6 Single-crystal structure of the trinuclear SBU in IIb. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). S 7

8 a b c Ni1 C13 C13 Ni1 O1 C12 C12 C11 C11 C13 C13 Ni1 O6 O5 C10 O6 O5 O5 O6 C6 C7 C8 C9 C5 C8 C4 C6 C9 C5 C2 C1 C2B C3 C1B C2A C1A C2 C1 N1 N1 Supplementary Figure S7 Single-crystal structure of the trinuclear SBU in IIIa. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). Dashed bonds represent the disordering parts. S 8

9 b c a C5A N1 C5 C4A C1 C1A C10 C11 C10A C4 C11A C6 C12 C8A C9 C3 C2A C7A C7 C8 C2 O1 O2 Ni1 O5 C18 C13 C14 O4 C15 O5 C17 C16 C16 C17 C18 C15 C14 O4 C13 O5 N1 Supplementary Figure S8 Single-crystal structure of the trinuclear SBU in IIIb. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). Dashed bonds represent the disordering parts. S 9

10 a b c C9 C10 C11 C11 C12 C11 C12 C13 C10 C13 C12 C12 C11 C9 O2 O1 C8 Ni1 O2 O2 N1 C6 C7 C6 C5 C5 C4 C3 C2 C2 C1 C1 N1 Supplementary Figure S9 Single-crystal structure of the trinuclear SBU in IIIc. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). S 10

11 a b c C11 C13 C12 C13 C13 C12 C13 O1 C11 C8 O2 C9 C10 O2 Ni1 C8 O2 C7 C7 C6 C5 C4 C2 C1 C2B C1B C1A C3 N1 C2A C2 C1 N1 Supplementary Figure S10 Single-crystal structure of the trinuclear SBU in IVa. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). Dashed bonds represent the disordering parts. S 11

12 N1 N1 c b a C5 C5 C4 C4 C1 C2 C1 C2 C3 C3 C6 C6 C7 C9 C8 C9 C10 C11 C10 O2B O2A C12 O2A O2B O2B O2A N1 C15 C16 C16 C15 O1 C18 C14 C18 C13 C14 C17 C17 C17 C17 C14 C18 C14 C18 Ni1 C15 C16 C16 C15 N1 C13 Supplementary Figure S11 Single-crystal structure of the trinuclear SBU in IVb. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). Dashed bonds represent the disordering parts. S 12

13 a b c C11 C12 C13 C13 C14 C15 C14 C14 C13 C11 C15 O1 C12 C14 C13 O2 C8 C10 Ni1 O2 C9 O2 C8 N1 C7 C6 C7 C5 C5 C4 C4 C3 C2 C2 C1 C1 N1 Supplementary Figure S12 Single-crystal structure of the trinuclear SBU in IVc. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). Dashed bonds represent the disordering parts. S 13

14 a b c C19 C17 C18 C19 C19 C19 C18 C17 C14 O2A C15 C12 O2B C16 O1 O2A C11 C14 C10 C10 O2B C13 Ni1 O2A C15 O2A C12 O2B C11 N1 C6 C5 C8 C9 C7 C4 C6 C5 C8 C9 C2 C1 C3 C2A C2B C1B C2 C1 C1A N1 Supplementary Figure S13 Single-crystal structure of the trinuclear SBU in Va. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). Dashed bonds represent the disordering parts. S 14

15 c b a N1 C5 C1 C4 C7' C8' C2 C6 C7 C8 C3 C10 C11 C9 C11' C10' C13 C14 C15 C12 C18 O2 C17 C16 Ni1 N1 O1 O5 C24 O5 C20 C19 O4 C21 C22 C22 C23 C23 C21 O4 C20 C19 C24 O5 Supplementary Figure S14 Single-crystal structure of the trinuclear SBU in Vb. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). Dashed bonds represent the disordering parts. S 15

16 a b c C15 C17 C16 C17 C17 C18 C18 C19 C16 C19 C18 C17 C18 O1 C15 Ni1 O2B C12 O2A C11 C14 C8 C6 C9 C10 C13 O2A O2B C7 O2A O2B C12 C11 C8 C6 C9 N1 C5 C2 C1 C4 C3 C1A C2A C1B C2B N1 C5 C2 C1 Supplementary Figure S15 Single-crystal structure of the trinuclear SBU in Vc. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). Dashed bonds represent the disordering parts. S 16

17 a b c C13 C14 C15 C15 C16 C17 C16 C15 C16 C13 C17 C18 C18 C14 C18 C18 C15 C16 O1 Ni1 O2 N1 O2 O2 C12 C10 C10 C11 C9 C9 C8 C7 C6 C6 C5 C4 C3 C2A C5 C2 C1 C1B C2B C1A N1 C2 C1 Supplementary Figure S16 Single-crystal structure of the trinuclear SBU in Vd. Atoms in an asymmetry unit are drawn with thermal ellipsoids of 50% probability (hydrogen atoms and some non-hydrogen atoms in the symmetry-related organic ligands are omitted for clarity). Dashed bonds represent the disordering parts. S 17

18 Intensity Ia a = (2) V = 10263(3) R wp = 3.18% Experimental Simulated Obsered Reflection R Difference p = 2.06% Background Theta / Deg. Supplementary Figure S17 Pawley refinement of the PXRD pattern for as-synthesized Ia. S 18

19 Intensity IIa a = (1) V = 14823(2) R wp = 3.83% Experimental Simulated Obsered Reflection R Difference p = 2.37% Background Theta / Deg. Supplementary Figure S18 Pawley refinement of the PXRD pattern for as-synthesized IIa. S 19

20 Intensity IIb a = (1) V = 16231(2) R wp = 3.26% Experimental Simulated Obsered Reflection R Difference p = 2.36% Background Theta / Deg. Supplementary Figure S19 Pawley refinement of the PXRD pattern for as-synthesized IIb. S 20

21 Intensity IIIa a = (2) V = 20636(5) R wp = 3.36% Experimental Simulated Obsered Reflection R Difference p = 2.02% Background Theta / Deg. Supplementary Figure S20 Pawley refinement of the PXRD pattern for as-synthesized IIIa. S 21

22 Intensity IIIb a = (2) V = 23843(5) R wp = 2.40% Experimental Simulated Obsered Reflection R Difference p = 1.52% Background Theta / Deg. Supplementary Figure S21 Pawley refinement of the PXRD pattern for as-synthesized IIIb. S 22

23 Intensity IIIc a = (1) V = 25659(3) R wp = 2.36% Experimental Simulated Obsered Reflection R Difference p = 1.58% Background Theta / Deg. Supplementary Figure S22 Pawley refinement of the PXRD pattern for as-synthesized IIIc. S 23

24 Intensity IVa a = (1) V = 27130(3) R wp = 2.25% Experimental Simulated Obsered Reflection R Difference p = 1.51% Background Theta / Deg. Supplementary Figure S23 Pawley refinement of the PXRD pattern for as-synthesized IVa. S 24

25 Intensity IVb a = (2) V = 32664(6) R wp = 2.48% Experimental Simulated Obsered Reflection R Difference p = 1.36% Background Theta / Deg. Supplementary Figure S24 Pawley refinement of the PXRD pattern for as-synthesized IVb. S 25

26 Intensity IVc a = (2) V = 34097(6) R wp = 3.47% Experimental Simulated Obsered Reflection R Difference p = 2.67% Background Theta / Deg. Supplementary Figure S25 Pawley refinement of the PXRD pattern for as-synthesized IVc. S 26

27 Intensity Va a = (3) V = 34649(9) R wp = 3.49% Experimental Simulated Obsered Reflection R Difference p = 2.76% Background Theta / Deg. Supplementary Figure S26 Pawley refinement of the PXRD pattern for as-synthesized Va. S 27

28 Intensity Vb a = (1) V = 39255(3) R wp = 3.35% Experimental Simulated Obsered Reflection R Difference p = 2.63% Background Theta / Deg. Supplementary Figure S27 Pawley refinement of the PXRD pattern for as-synthesized Vb. S 28

29 Intensity Vc a = (2) V = 44170(7) R wp = 3.49% Experimental Simulated Obsered Reflection R Difference p = 2.32% Background Theta / Deg. Supplementary Figure S28 Pawley refinement of the PXRD pattern for as-synthesized Vc. S 29

30 I + e Intensity I + d I + c I + b Theta /Deg. Supplementary Figure S29 Unidentified PXRD patterns of the crystalline products obtained in the unsuccessful synthetic experiments. S 30

31 H = 1000 Oe 80 χ M / cm 3 mol Fit from K C = 3.83 cm 3 K mol -1 θ = -6.3 K /χ m / mol cm T / K Supplementary Figure S30 Temperature dependence of χ M for guest-free IIIa in a 1000 Oe applied dc field, and fitting to the Curie-Weiss law in 150~300 K. S 31

32 0.4 H = 1000 Oe 80 χ M / cm 3 mol Fit from K C = 3.99 cm 3 K mol -1 θ = K /χ m / mol cm T / K Supplementary Figure S31 Temperature dependence of χ M for guest-free IIIb in a 1000 Oe applied dc field, and fitting to the Curie-Weiss law in 150~300 K. S 32

33 0.4 H = 1000 Oe 80 χ M / cm 3 mol Fit from K C = 4.03 cm 3 K mol -1 θ = K /χ m / mol cm T / K Supplementary Figure S32 Temperature dependence of χ M for guest-free IIIc in a 1000 Oe applied dc field, and fitting to the Curie-Weiss law in 150~300 K. S 33

34 (a) (b) (c) Supplementary Figure S33 Cavities and apertures in Ia. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 34

35 (a) (b) (c) Supplementary Figure S34 Cavities and apertures in IIa. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 35

36 (a) (b) (c) Supplementary Figure S35 Cavities and apertures in IIb. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 36

37 (a) (b) (c) Supplementary Figure S36 Cavities and apertures in IIIa. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 37

38 (a) (b) (c) Supplementary Figure S37 Cavities and apertures in IIIb. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 38

39 (a) (b) (c) Supplementary Figure S38 Cavities and apertures in IIIc. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 39

40 (a) (b) (c) Supplementary Figure S39 Cavities and apertures in IVa. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 40

41 (a) (b) (c) Supplementary Figure S40 Cavities and apertures in IVb. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 41

42 (a) (b) (c) Supplementary Figure S41 Cavities and apertures in IVc. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 42

43 (a) (b) (c) Supplementary Figure S42 Cavities and apertures in Va. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 43

44 (a) (b) (c) Supplementary Figure S43 Cavities and apertures in Vb. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 44

45 (a) (b) (c) Supplementary Figure S44 Cavities and apertures in Vc. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 45

46 (a) (b) (c) Supplementary Figure S45 Cavities and apertures in Vd. (a) ca and aab, (b) cb and abc, (c) cc and acc. S 46

47 TG / % Ia IIa IIb 40.8 % 22.4 % 36.3 % TG / % IIIa IIIb IIIc 49.9 % 47.8 % 44.6 % T / o C T / o C TG / % IVa IVb IVc 57.5 % 55.4 % 52.0 % T / o C TG / % Va Vb Vc 63.7 % 50.5 % 58.1 % T / o C Supplementary Figure S46 TGA curves for as-synthesized isoreticular frameworks. S 47

48 320 o C 300 o C Intensity 280 o C *250 o C 200 o C 100 o C Theta / Deg. Supplementary Figure S47 Variable-temperature PXRD patterns for as-synthesized Ia showing T c 250 o C. S 48

49 260 o C Intensity *240 o C 220 o C 200 o C 160 o C 140 o C 120 o C 100 o C 25 o C Theta/Deg. Supplementary Figure S48 Variable-temperature PXRD patterns for as-synthesized IIa showing T c 240 o C. S 49

50 120 o C 110 o C Intensity *100 o C 25 o C Theta/Deg. Supplementary Figure S49 Variable-temperature PXRD patterns for as-synthesized IIb showing T c 100 o C. S 50

51 310 o C *300 o C 290 o C 280 o C Intensity 270 o C 260 o C 250 o C 200 o C 100 o C 25 o C Theta / Deg. Supplementary Figure S50 Variable-temperature PXRD patterns for as-synthesized IIIa showing T c 300 o C. S 51

52 250 o C *240 o C 230 o C Intensity 220 o C 210 o C 200 o C 100 o C 25 o C Theta / Deg. Supplementary Figure S51 Variable-temperature PXRD patterns for as-synthesized IIIb showing T c 240 o C. S 52

53 220 o C *210 o C 200 o C Intensity 180 o C 160 o C 140 o C 120 o C 100 o C 25 o C Theta / Deg. Supplementary Figure S52 Variable-temperature PXRD patterns for as-synthesized IIIc showing T c 210 o C. S 53

54 270 o C 260 o C Intensity *250 o C 240 o C 230 o C 220 o C 210 o C 200 o C 100 o C 25 o C Theta / Deg. Supplementary Figure S53 Variable-temperature PXRD patterns for as-synthesized IVa showing T c 250 o C. S 54

55 Intensity 240 o C 230 o C *220 o C 210 o C 200 o C 180 o C 160 o C 140 o C 120 o C 100 o C 25 o C Theta / Deg. Supplementary Figure S54 Variable-temperature PXRD patterns for as-synthesized IVb showing T c 220 o C. S 55

56 Intensity 240 o C 230 o C 220 o C *210 o C 200 o C 180 o C 160 o C 140 o C 120 o C 100 o C 25 o C Theta / Deg. Supplementary Figure S55 Variable-temperature PXRD patterns for as-synthesized IVc showing T c 210 o C. S 56

57 Intensity 220 o C 210 o C *200 o C 180 o C 160 o C 140 o C 120 o C 100 o C 25 o C Theta / Deg. Supplementary Figure S56 Variable-temperature PXRD patterns for as-synthesized Va showing T c 200 o C. S 57

58 200 o C 180 o C Intensity *160 o C 140 o C 120 o C 100 o C 25 o C Theta / Deg. Supplementary Figure S57 Variable-temperature PXRD patterns for as-synthesized Vb showing T c 160 o C. S 58

59 Intensity 210 o C 200 o C *180 o C 160 o C 140 o C 120 o C 100 o C 25 o C Theta / Deg. Supplementary Figure S58 Variable-temperature PXRD patterns for as-synthesized Vc showing T c 180 o C. S 59

60 (a) 100 (b) TG /% Solvent-exchanged Ia TG /% Solvent-exchanged IIIa T / o C T / o C (c) 100 (d) TG % Solvent-exchanged IIIb TG /% Solvent-exchanged IIIc T / o C T / o C Supplementary Figure S59 TGA curves of solvent-exchanged samples for Ia, IIIa, IIIb and IIIc. S 60

61 (a) Ia As-synthesized (b) IIIa As-synthesized Intensity Solvent-exchanged Guest-free Intensity Solvent-exchanged Guest-free Simulated Simulated Theta / Deg Theta / Deg. (c) IIIb As-synthesized (d) IIIc As-synthesized Intensity Solvent-exchanged Guest-free Intensity Solvent-exchanged Guest-free Simulated Simulated Theta / Deg Theta / Deg. Supplementary Figure S60 PXRD patterns of solvent-exchanged and guest-free samples for Ia, IIIa, IIIb and IIIc. S 61

62 H 2 Uptake / g/l Ia (absolute) IIIa (absolute) IIIb (absolute) IIIc (absolute) Ia (excess) IIIa(excess) IIIb(excess) IIIc(excess) P/ bar Supplementary Figure S61 Volumetric H 2 uptakes measured at 77 K up to 50 bar. S 62

63 ln(p/mmhg) (a) Ia 77 K 87 K Adj. R-Square Value Standard Error T a a a a a a a b b b T V a / mmol (b) ln(p/mmhg) IIIa 77 K 87 K Adj. R-Square Value Standard Error T a a a a a a b b T V a / mmol (c) ln(p/mmhg) IIIb 77 K 87 K Adj. R-Square Value Standard Error T a a a a b b T V a / mmol (d) ln(p/mmhg) IIIc 77 K 87 K Adj. R-Square Value Standard Error T a a a a b b T V a / mmol Supplementary Figure S62 Virial fitting statistics for H 2 adsorption enthalpies. S 63

64 V a / V sat Ia P / P IIIa V a / V sat IIIc IIIb P / P 0 Supplementary Figure S63 Detailed view of the normalized CO 2 isotherms measured at 195 K. The onset pressure of the second step is indicated by an arrow. S 64

65 1.0 M t / M e y = A*(1-exp(-k1*x))+(1-A)*(1-exp(-k2*x)) R 2 = A = ± k1 = ± 3E-4 k2 = ± 5E t / s Residuals t / s Supplementary Figure S64 A typical kinetic profile and double exponential fitting of the CO 2 adsorption for Ia. S 65

66 1.0 M t / M e y = A*(1-exp(-k 1 *x))+(1-a)*(1-exp(-k 2 *x)) R 2 = A = ± k 1 = ± k 2 =0.522 ± t / s Residuals t / s Supplementary Figure S65 A typical kinetic profile and double exponential fitting of the CO 2 adsorption for IIIa. S 66

67 1.0 M t / M e y = A*(1-exp(-k 1 *x))+(1-a)*(1-exp(-k 2 *x)) R 2 = A = ± k 1 = ± k 2 = ± Residuals t / s t / s Supplementary Figure S66 A typical kinetic profile and double exponential fitting of the CO 2 adsorption for IIIb. S 67

68 1.0 M t / M e y = A*(1-exp(-k 1 *x))+(1-a)*(1-exp(-k 2 *x)) R 2 = A = ± k 1 = ± k 2 = ± t / s Residuals t / s Supplementary Figure S67 A typical kinetic profile and double exponential fitting of the CO 2 adsorption for IIIc. S 68

69 0.06 IIIc k 1 / s IIIa IIIb Ia V a /V sat Supplementary Figure S68 Coverage dependent rate constant k 1 for the slow diffusing component. It can be seen that the k 1 values follow Ia < IIIa IIIb << IIIc, which could be explained by the size/shape difference of abc. The size/shape of abc in IIIa and IIIb are similar to that of CO 2, but that in Ia and IIIc is slightly smaller and much larger than that of CO 2, respectively. S 69

70 k 2 / s IIIc IIIa IIIb Ia 0.00 V a /V sat Supplementary Figure S69 Coverage dependent rate constant k 2 for the fast diffusing component. It can be seen that the k 2 values follow Ia << IIIa IIIb IIIc, which could be explained by the size/shape difference of acc. Because the sizes of acc in IIIa-IIIc are similar and much larger than that of CO 2, the k 2 values for IIIa-IIIc are similar and much larger than k 1. In contrast, the size of acc in Ia is much smaller than those in IIIa-IIIc. S 70

71 K IIIa IIIb 40 IIIc Ia V 0.3 a /V sat Supplementary Figure S70 Coverage dependent ratio of fast/slow rate constant K = k 2 /k 1. K values for IIIa and IIIb are similar because the size/shape of their abc apertures are similar to the those of CO 2, and sizes of their acc apertures are also similar. The K value for IIIc is obviously smaller than those of IIIa and IIIb because the size of its abc aperture is larger than those of IIIa, IIIb and CO 2, but size of its acc aperture is similar to those of IIIa and IIIb. Similarly, the K value for Ia is the smallest among the four structures because the size difference between its acc and abc is smallest. S 71

72 0.4 IIIc A IIIb IIIa Ia V a /V sat Supplementary Figure S71 Coverage dependent contribution A of the slow component described by k 1. Similar to the above discussion about the size/shape relations, the small abc apertures in IIIa and IIIb exhibits obvious restriction on the diffusion into the bcu cavities, which may be overwhelmed by increasing pressure. In other words, A values for IIIa and IIIb are smaller than that of IIIc, especially at the lowest coverage (corresponding to lowest adsorption pressures). In contrast, IIIc with obviously larger abc apertures has no such effect, and the main restriction likely arises from steric hindrance of the adsorbed CO 2. Therefore, at low coverage region, when coverage increases, the A values for IIIa and IIIb increase, but the A value for IIIc decreases. Compared with IIIa-IIIc, although the size of acc in Ia is very small, its A value is lower, which may be ascribed to its significantly smaller nbo channel (cc), which holds the CO 2 tightly (high adsorption affinity) and reduce the diffusion into the bcu cavity. Nevertheless, the changing trends of k 1, k 2, and the A values are also affected by many other factors such as change of adsorption stage from surface adsorption to capillary condensation. Accurate explanation of the kinetic data requires additional and more complicated measurements and theoretical calculations. S 72

73 Supplementary Table S1 Predicted node geometries for 5 5 combinations of pyridylcarboxylates and dicarboxylates. Node Tricapped trigonal-prism E 2 /Å a b c d e SBU L 2 E 1 /Å 11.6 L P bdc 2 ndc 2 bpdc 2 edba 2 tpdc 2 d r I ina κ/ φ/ d r II pyac κ/ φ/ d r III pba κ/ φ/ d r IV pvba κ/ φ/ d r V pbpa κ/ φ/ S 73

74 Supplementary Table S2 Products (yield) obtained from the combinatorial syntheses. a. H 2 bdc b. H 2 ndc c. H 2 bpdc d. H 2 edba e. H 2 tpdc I. Ia (30%) C + A C + A C + A C + A Hina II. IIa (20%, PR) IIb (30%) A A A Hpyac III. IIIa (70%) IIIb (65%) IIIc (45%, PR) A A Hpba IV. IVa (40%) IVb (60%) IVc (10%) A A Hpvba V. Hpbpa Va (10%) Vb (15%) Vc (40%) Vd (<1%, PR) A # C and A stand for unidentified crystalline product and amorphous solid, respectively. PR stands for poor reproducibility. S 74

75 Supplementary Table S3 Crystallographic data for the isoreticular frameworks. Ia IIa IIb Formula C 30 H 18 N 3 Ni 3 O 13 C 36 H 24 N 3 Ni 3 O 13 C 42 H 27 N 3 Ni 3 O 13 Formula Weight Crystal System Cubic Cubic Cubic Space group I-43m I-43m P-43n α/å (3) (3) (6) V/Å (2) 14960(1) 17211(1) Z Radiation Mo K α Cu K α Mo K α T/K 103(2) 150(2) 103(2) D calc /g cm μ/mm Tot. /Uniq. Data 8627/ / /5660 R int Observed data [I > 2σ(I)] R 1 [I > 2σ(I)] a wr 2 (all data) b Goodness-of-fit on F Flack Parameter -0.03(3) 0.04(7) 0.03 (2) Largest diff. peak and hole/(e Å -3 ) a: R 1 = Σ{ F o - F c }Σ F o ; b: wr 2 = [Σw(F 2 o - F 2 c ) 2 /Σw(F 2 o ) 2 ] 1/2. S 75

76 Supplementary Table S3 Crystallographic data for the isoreticular frameworks (continued). IIIa IIIb IIIc Formula C 48 H 30 N 3 Ni 3 O 13 C 54 H 33 N 3 Ni 3 O 13 C 57 H 36 N 3 Ni 3 O 13 Formula Weight Crystal System Cubic Cubic Cubic Space group I-43m I23 I-43m α/å (1) (2) (2) V/Å (2) 23105(3) 25625(3) Z Radiation Mo K α Mo K α Mo K α T/K 103(2) 103(2) 103(2) D calc /g cm μ/mm Tot. /Uniq. Data 39468/ / /4588 R int Observed data [I > 2σ(I)] R 1 [I > 2σ(I)] a wr 2 (all data) b Goodness-of-fit on F Flack Parameter -0.01(2) 0.11(2) 0.02(1) Largest diff. peak and hole/(e Å -3 ) , a: R 1 = Σ{ F o - F c }/Σ F o ; b: wr 2 = [Σw(F o 2 - F c 2 ) 2 /Σw(F o 2 ) 2 ] 1/2. S 76

77 Supplementary Table S3 Crystallographic data for the isoreticular frameworks (continued). IVa IVb IVc Formula C 54 H 36 N 3 Ni 3 O 13 C 60 H 39 N 3 Ni 3 O 13 C 63 H 42 N 3 Ni 3 O 13. Formula Weight Crystal System Cubic Cubic Cubic Space group I-43m I-43m I-43m α/å (1) (1) (2) V/Å (1) 30691(1) 34480(3) Z Radiation Cu K α Cu K α Mo K α T/K 150(2) 150(2) 103(2) D calc /g cm μ/mm Tot. /Uniq. Data 13825/ / /6107 R int Observed data [I > 2σ(I)] R 1 [I > 2σ(I)] a wr 2 (all data) b Goodness-of-fit on F Flack Parameter 0.01(5) -0.02(3) 0.076(14) Largest diff. peak and hole/(e Å -3 ) a: R 1 = Σ{ F o - F c }/Σ F o ; b: wr 2 = [Σw(F o 2 - F c 2 ) 2 /Σw(F o 2 ) 2 ] 1/ S 77

78 Supplementary Table S3 Crystallographic data for the isoreticular frameworks (continued). Va Vb Vc Vd Formula C 66 H 42 N 3 Ni 3 O 13 C 72 H 45 N 3 Ni 3 O 13 C 75 H 48 N 3 Ni 3 O 13 C 78 H 51 N 3 Ni 3 O 13 Formula Weight Crystal System Cubic Cubic Cubic Cubic Space group I-43m I-43m I-43m I-43m α/å (1) (2) (1) (1) V/Å (1) 38884(4) 43629(1) 47803(2) Z Radiation Cu K α Mo K α Cu K α Cu K α T/K 150(2) 103(2) 150(2) 150(2) D calc /g cm μ/mm Tot. /Uniq. Data 17478/ / / /5433 R int Observed data [I > 2σ(I)] R 1 [I > 2σ(I)] a wr 2 (all data) b Goodness-of-fit on F Flack Parameter 0.1(2) -0.02(3) 0.02(2) 0.08(2) Largest diff. peak and hole/(e Å -3 ) a: R 1 = Σ{ F o - F c }/Σ F o ; b: wr 2 = [Σw(F 2 o - F 2 c ) 2 /Σw(F 2 o ) 2 ] 1/2. S 78

79 Supplementary Table S4 Selected bond lengths and angles, and the atom position of the centered oxygen atom. O1 Ni1-O1 Ni1-O1-Ni1 Ni1-O2 Ni1- Ni1-N1 O1-Ni-N1 x /Å / /Å /Å /Å / Ia (2) 2.004(4) 119.6(2) 2.059(3) 2.039(3) 2.108(4) 178.5(2) IIa (2) 1.998(2) 120.0(2) 2.049(2) 2.058(3) 2.076(4) 171.3(2) IIb (1) 1.999(4) 119.3(1) 2.074(2) 2.068(2) 2.048(4) 2.049(2) 2.097(2) 177.2(1) IIIa (1) 2.001(2) 118.7(2) 2.015(4) 2.087(3) 2.071(2) 2.089(3) 175.0(2) IIIb (1) 1.982(2) 120.0(2) 2.063(2) 2.038(2) 2.064(2) 2.067(2) 2.078(2) 178.1(1) IIIc (1) 1.985(2) 119.4(1) 2.054(3) 2.041(1) 2.081(2) 175.8(1) IVa (1) 1.985(2) 117.5(3) 2.052(2) 2.067(2) 2.091(3) 173.5(8) IVb (2) 1.973(2) 119.7(1) 2.036(2) 2.23(2) 2.041(2) 2.053(4) 172.6(1) IVc (1) 1.980(2) 119.9(2) 2.047(2) 2.044(2) 2.050(2) 179.9(8) Va (3) 1.97(1) 116.8(5) 1.96(4) 2.15(4) 2.05(1) 2.03(1) 173.9(4) Vb (1) 1.989(2) 119.0(1) 2.022(2) 2.076(2) 2.070(2) 2.058(2) 2.089(2) 178.1(2) Vc (1) 1.977(2) 119.8(2) 2.102(2) 2.036(2) 2.081(7) 2.050(1) 2.075(1) 178.9(1) Vd (1) (2) 119.9(4) 2.065(2) 2.059(2) 2.043(3) 179.1(1) NOTE: O1, hydroxy, positions have been uniformed as x = y = z and 0 < x < 1 for comparison; O2, oxygen atom of pyridylcarboxylates;, oxygen atom of dicarboxylates; N1, nitrogen atom of pyridylcarboxylates. S 79

80 Supplementary Table S5 Pore metrics calculated from the crystal structures. Void /% D calc. /g cm -3 V p /cm 3 g -1 A acce ca cb cc /m 2 g -1 Dia. aab Void Size/Å abc Void Dia. acc Void Å Å % W. H. Å 2 % Å Å % Ia IIa IIb IIIa IIIb IIIc IVa IVb IVc Va Vb Vc Vd NOTE: D calc, V p, A conn and A acce, are calculated framework density, pore volume, and accessible surface area. S 80

81 Supplementary Methods Geometry Analysis: Mathematical relation between node position and relative edge length. The ideal ncb net is embedded in the cubic crystal system, space group I-43m and can be also be described in lower-symmetry space groups such as I23 (subgroup of I-43m) or P-43n 55 without changing the connectivity, length, or geometry. As shown in Supplementary Fig. S1, the relative edge lengths of E 1 /E 2 could be deduced from three nodes V A, V B and V C. Their coordinates are V A (x, y, z), V B (-y+0.5, x+0.5, -z+0.5) and V C (y+0.5,-x+0.5,-z+0.5). The nodes locates at the special positions of 3m symmetry (space diagonal of the cubic cell), where x = y = z, and 0 < x < 0.5 for symmetry equivalent to the case of 0.5 < x < 1. Distance E AB between the two coordinates is: EAB = [ x ( x + 0.5)] + [ x ( x + 0.5)] + [ x ( x + 0.5)] = 32x 16x + 3 ; 2 and distance E BC is: EBC = [( x + 0.5) ( x + 0.5)] + [( x + 0.5) ( x + 0.5)] + [( x + 0.5) ( x + 0.5)] = 2 2x So that the relative edge length can be defined by E 1 over E 2, being expressed as 2 64x 32x d r = E1 / E2 = = 6( ) + (1) 8x 8x 3 3 Equation 1 shows a minimum d r = 3 3 when x =, which stands for the case that the 3 8 capped trigonal-pyramid become a plane with the apex falls in the plane of the base to fuse the triakis tetrahedron into a tetrahedron (Supplementary Fig. S2). Mathematical relation of relative edges length v.s. node geometric parameters. S 81

82 As shown in Supplementary Fig. S1, the node geometry depends on the node position, or x. The three parameters ω, φ, and κ can be calculated as follows: As ω is a face angle of regular tetrahedron, it is a constant of 60, in despite of the changing of node position. So that ω = 60 (2) φ EBC 1 The φ angle is related to the ratio of edge lengths, which is sin = =, so 2 2EAB 2d r 1 2arcsin( ) 2d r that ϕ = 180 (3) π Combining the equation 1, the x dependence and the d r dependence of φ angle can also be plotted in Supplementary Fig. S3a. The κ angle is related to the angle of AOD as shown in Supplementary Fig. S1b, wherein there are o OAD + κ = 90 and the position of V D (y-0.5, -x+0.5, -z+0.5). The L AO, L DO and E AD distance can be calculated as L = A O 3x, L D O = 3 ( 0.5 x ), E = 8x 2 4x AD , respectively. Considering the law of cosines in triangular, there is a relation of 2 2 o AO + EAD LAO EAD cos(90 κ ) L 2 = L 2 OD, so that cos(90 o 3x κ ) = 2 + (8x 2 2 3x 4x ) 3(0.5 x) 8x 2 4x = 96x 8x x x 1 π arccos x 48x + 9 κ = 180 (4) π The x dependence and d r dependence of κ angle can be plotted in Supplementary Fig. S3b. S 82

83 Syntheses: Materials: The ligands H 2 tpdc, Hpba and Hpvba were synthesized according to literature Hpbpa was synthesized through two steps of Suzuki-Miyaura coupling reactions. The 4-(4-bromophenyl)pyridine was obtained following a literature procedure 59. The mixture of 4-(4-bromophenyl)pyridine (2.30 g, 10 mmol), 4-boronobenzoic acid (1.70 g, 10 mmol) and Na 2 CO 3 (3.20 g, 30 mmol) dissolved in the mixed solvent of DMF (50 ml) and water (10 ml) was degassed and protected under argon. After the addition of Pd(PPh 3 ) 4 (0.5g, 0.5 mmol), the mixture was heated and refluxed at 110 C for 24h. After cooling down, gray precipitation was filtered, and recrystallized with pyridine after acidification (yield 85%). M.P. > 300 o C. 1 H NMR (300Hz, DMSO-d 6 ): δ 8.64 (d, J = 6.0 Hz, 2H), 8.03 (d, J = 8.1 Hz, 2H), (m, 6H), 7.77 (d, J = 6.0 Hz, 2H). FT-IR(KBr pellet, cm -1 ): (w), (w), (w), (m), (s), (w), (w), (w), (m), (m), (s), (m), (m), (m), (m), (w), (m), (w), (w), (s), (s), (), (w), (m), (w), (m), (w), (w), (w). Characterization of isoreticular frameworks: FT-IR spectra were recorded using Bruker EQUINOX 55 FT-IR Spectrometer (KBr, cm -1 ): Ia: 3431(m), 2934(w), 1648(s), 1553(m), 1492(m), 1387(s), 1265(w), 1233(w), 1185(w), 1060(w), 1018(m), 951(w), 870(w), 820(m), 779(w), 751(m), 695(m), 588(w), 539(w), 447(w). IIa: 3789(w), 3484(s), 2928(m), 1657(s), 1610(s), 1500(m), 1384(s), 1255(w), 1098(m), 1018(w), 985(w), 868(w), 826(m), 752(m), 661(w), 602(w), 558(w), 514(w). IIb: 3407(m), 2937(w), 1631(s), 1628(s), 1499(m), 1397(s), 1263(m), 1188(m), 1097(vw), 1017(w), 985(m), 925(vw), 863(vw), 828(m), 788(m), 732(vw), 601(m), 518(w), 477(m). IIIa: 3423(m), 2935(w), 1638(s), 1564(w), 1520(w), 1397(s), 1264(w) 1222(w), 1187(w), 1035(w), 1014(m), 871(w), 833(w), 814(m), 783(m), 749(w), 591(w), 479(w). IIIb: 3423(m), 2934(m), 1643(s), 1565(w), 1492(m), 1397(s), 1357(w), 1264(m), 1223(w), 1187(m), 1096(w), 1059(w), 1035(m), 1013(m), 925(w), 873(w), S 83

84 784(m), 756(m), 706(w), 591(w), 560(w), 474(m). IIIc: 3423(m), 2934(m), 1638(s), 1560(m), 1397(s), 1264(w), 1187(w), 1013(m), 834(w), 783(w), 757(w), 704(w), 679(w), 591(w), 476(w). IVa: 3421(m), 2929(m), 1664(s), 1607(vs), 1498(s), 1387(s), 1255(w), 1180(w), 1098(w), 1016(w), 960(w), 849(w), 812(w), 778(w), 751(w), 700(w), 676(w), 590(w), 542(w), 442(w). IVb: 3423(m), 2934(m), 1631(s), 1496(m), 1398(s), 1264(w), 1187(w), 1016(m), 850(w), 778(w), 700(w), 677(w), 592(w), 544(w), 475(w). IVc: 3424(m), 2935(m), 1633(s), 1543(m), 1397(s), 1265(w), 1187(w), 1016(m). 850(w), 817(w), 775(m), 701(w), 678(w), 592(w), 544(w), 475(w), 433(w). Va: 3420(m), 2900(w), 1660(s), 1500(m), 1380(s), 1250(w), 1200(m), 1000(w), 820(m), 790(m), 750(w), 650(w), 800(m), 480(w). Vb: 3442(m), 2937(w), 1632(s), 1506(m), 1400(s), 1358(w), 1264(m), 1223(w), 1189(m), 1060(w), 1016(m), 962(vw), 924(vw), 824(m), 785(m), 744(w), 705 (vw), 646(w), 593(m), 535(vw), 477(w). Vc: 3425(m), 2935(w), 1630(s), 1508(m), 1399(s), 1222(vw), 118(m), 1014(vw), 1060(m), 962(vw), 823(m), 784(m), 743(w), 704 (w), 679 (vw), 646(w), 593(m), 536(vw), 476(w). Magnetic properties were measured with guest-free samples contained in gelatin capsules, which were mounted in straws to provide an invariant diamagnetic background that did not influence the SQUID detection coils. DC susceptibility measurements were carried out in applied field of 1000 Oe after cooling the sample in zero applied field. The data were corrected for the diamagnetism, and then fitted to the Curie-Weiss law in the temperature range 150 K < T < 300 K. The magnetic susceptibility values (χ M ) of the samples were monotonously increasing as the temperature decreased from 300 K, and reached their maximum respectively at 5.0, 4.5 and 4.5 K, below which the values decreased again. Fitting the data between 150 and 300 K to the Curie-Weiss equation gave C = 3.83 cm 3 K mol -1, θ = 6.3 K for IIIa, C = 3.99 cm 3 K mol -1, θ = 12.6 K for IIIb, C = 4.03 cm 3 K mol -1, θ = 15.7 K for IIIc, respectively. The C values are consistent with the value (3.88 cm 3 K mol -1 ) of two non-interacting high spin Ni II ions and an isolated high spin Ni III ion, given g = 2.0. A similar compound [Ni II 2Ni III (μ 3 -OH)(L) 3 ] [L = pyridine-3,5-bis(phenyl-4- carboxylate)] was reported by M. Schröder et al 63. For comparison, for 2Ni 2+ (H.S.) + 1Ni 3+ (L.S.) C = cm 3 K mol -1, for 3Ni 2+ (H.S.) C = 3.0 cm 3 K mol -1, and for S 84

85 1Ni 2+ (H.S.) + 2Ni 3+ (H.S.) C = 4.75 cm 3 K mol -1. S 85

86 H 2 Adsorption enthalpies calculation: Virial fitting: A virial-type expression was used (eq 1), which is composed of parameters a i and b i, which are independent of temperature. In eq. 1, P is the pressure in atm, N is the adsorbed amount in mmolg -1, T is the temperature in Kelvin, a i and b i are the virial coefficients, and m and n represent the numbers of coefficients required to adequately describe the isotherms. The values of the virial coefficients a 0 through a m were then used to calculate the isosteric heat of adsorption (eq 2). In eq. 2, Q st is the coverage-dependent isosteric heat of adsorption and R is the universal gas constant. Clausius-Claperyron Equation: m n 1 i i ln P = ln N + ain + bi N (1) T Q st i= 0 = R m i= 0 a N ( ln P) Qst = ( 1 T ) R The Clausius-Claperyron equation is a standard method for calculation of coverage-dependent Q st using measured temperature-pressure-coverage isotherm data points. Hence, it can not give Q st at zero coverage, and the Q st at very low surface coverage has a quite large error because the adsorption apparatus cannot work well at very low pressure (e.g. low accuracy of the pressure gauges, leaking, etc.). The virial fitting method can effectively predict low coverage and zero coverage Q st by fitting the high surface coverage data points, but it is not suitable for isotherms with complicate shapes. i i i= 0 (2) (3) S 86

87 CO 2 Adsorption Kinetics The double exponential (DE) model is described by the following equation: M M t e k1t k2t = A( 1 e ) + (1 A)(1 e ) where M t is the uptake at time t, M e is the equilibrium uptake, k 1 and k 2 are the rate constants, and A and (1 - A) are the fractional contributions for process mechanisms corresponding to adsorption rate constants k 1 and k 2, respectively. This model describes two kinetic processes each with different relaxation times. Here, k 1 was assigned to the rate constants of the diffusion from the nbo channel into the bcu cavities through the isosceles triangular aperture abc defined by one dicarboxylate and two pyridylcarboxylate, while k 2 was assigned to the rate constants of the diffusion inside the nbo channel. S 87

88 Supplementary References: 55 Beitone, L. et al. Order disorder in the super-sodalite Zn 3 Al 6 (PO 4 ) 12, 4tren, 17H 2 O (MIL-74): a combined XRD NMR assessment. J. Am. Chem. Soc. 125, , (2003). 56 Campbell, T. W. Dicarboxylation of terphenyl. J. Am. Chem. Soc. 82, , (1960). 57 Gong, Y. & Pauls, H. W. A convenient synthesis of heteroaryl benzoic acids via Suzuki reaction. Synlett, , (2000). 58 Kashida, H., Ito, H., Fujii, T., Hayashi, T. & Asanuma, H. Positively charged base surrogate for highly stable base pairing through electrostatic and stacking interactions. J. Am. Chem. Soc. 131, , (2009). 59 Wang, Y. et al. Twisted π-electron system electrooptic chromophores. structural and electronic consequences of relaxing twist-inducing nonbonded repulsions. J. Phys. Chem. C 112, , (2008). 60 Sheldrick, G. M. A short history of SHELX. Acta Crystallogr. A 64, , (2008). 61 Dolomanov, O. V., Bourhis, L. J., Gildea, R. J., Howard, J. A. K. & Puschmann, H. OLEX2: A complete structure solution, refinement and analysis program. J. Appl. Crystallogr. 42, , (2009). 62 Spek, A. L. PLATON/SQUEEZE: An effective cure for the disordered solvent syndrome in crystal structure refinement (Utrecht University, The Netherlands). 63 Jia, J. et al. Twelve-connected porous metal-organic frameworks with high H 2 adsorption. Chem. Comm., , (2007). S 88

Supporting Information. Ze-Min Zhang, Lu-Yi Pan, Wei-Quan Lin, Ji-Dong Leng, Fu-Sheng Guo, Yan-Cong Chen, Jun-Liang Liu, and Ming-Liang Tong*

Supporting Information. Ze-Min Zhang, Lu-Yi Pan, Wei-Quan Lin, Ji-Dong Leng, Fu-Sheng Guo, Yan-Cong Chen, Jun-Liang Liu, and Ming-Liang Tong* Supporting Information Wheel-shaped nanoscale 3d-4f {Co II 16Ln III 24} clusters (Ln = Dy and Gd) Ze-Min Zhang, Lu-Yi Pan, Wei-Quan Lin, Ji-Dong Leng, Fu-Sheng Guo, Yan-Cong Chen, Jun-Liang Liu, and Ming-Liang