Compound characterization data — Bergin et al., 2026

Connor P. Bergin, Daniel J. C. Murchie, Stephen P. Argent, Jonathan McMaster, Soumalya Bhattacharyya, Ben S. Pilgrim. “A framework for accessing elusive intermediate-sized PdₙL₂ₙ (n = 8, 9) metal-organic cages.” ChemRxiv (2026). https://doi.org/10.26434/chemrxiv-2025-c7kv1/v3

1,1′-(perfluoronaphthalene-2,6-diyl)bis(1H-imidazole), L1
¹H NMR (400 MHz, DMSO-d₆)	δ 8.16 (s, 2H), 7.69 (s, 2H), 7.26 (s, 2H)
¹⁹F NMR (376 MHz, DMSO-d₆)	δ −131.58 (m, 2F), −145.62 (m, 2F), −148.88 (m, 2F)
¹H NMR (400 MHz, CD₃CN)	δ 7.89 (s, 2H), 7.44 (s, 2H), 7.25 (s, 2H)
¹⁹F NMR (376 MHz, CD₃CN)	δ −130.52 (m, 2F), −145.45 (m, 2F), −147.74 (m, 2F)
¹³C{¹H} NMR (125 MHz, DMSO-d₆)	δ 146.4 (d, J = 258.3 Hz), 142.4 (dd, J = 251.9, 14.3 Hz), 140.7 (dm, J = 253.5 Hz), 138.5, 129.5, 121.2, 116.5 (t, J = 14.9 Hz), 109.8 (m)
¹³C{¹⁹F} NMR (125 MHz, DMSO-d₆)	δ 146.4, 142.4, 140.7, 138.5 (ddd, J = 216.2, 10.7, 6.2 Hz), 129.5 (dt, J = 191.2, 10.9 Hz), 121.2 (ddd, J = 196.0, 17.2, 3.0 Hz), 116.5, 109.8
ESI-MS (MeOH)	m/z calculated for [M+H]⁺, [C₁₆H₆F₆N₄]⁺ 369.0569, found 369.0563
Single-crystal XRD	Chemical formula: C₁₆H₆F₆N₄; Mᵣ = 368.25; crystal system, space group: Monoclinic, P2₁/n; T = 120 K; a = 9.0753(2) Å, b = 7.8379(2) Å, c = 9.8556(2) Å; α = 90°, β = 106.111(2)°, γ = 90°; V = 673.51(3) Å³; Z = 2; radiation: Cu Kα; μ = 1.52 mm⁻¹; Rint = 0.025; R[F² > 2σ(F²)] = 0.030, wR(F²) = 0.086, S = 1.06; Δρmax = 0.25 e Å⁻³, Δρmin = −0.18 e Å⁻³; CCDC 2512720; structure image data were not transcribed
Additional NMR and ESI-MS spectra	Image data were not transcribed

2,6-di(1H-imidazol-1-yl)naphthalene, L2
¹H NMR (500 MHz, DMSO-d₆)	δ 8.43 (s, 2H), 8.29 (d, J = 2.3 Hz, 2H), 8.13 (d, J = 8.8 Hz, 2H), 7.96 (dd, J = 8.7, 2.3 Hz, 2H), 7.91 (s, 2H), 7.19 (s, 2H)
¹H NMR (500 MHz, CD₃CN)	δ 8.12 (s, 2H), 8.11–8.10 (m, 4H), 7.80 (dd, J = 8.8, 2.2 Hz, 2H), 7.63 (s, 2H), 7.20 (s, 2H)
¹³C NMR (125 MHz, DMSO-d₆)	δ 136.2, 135.0, 132.2, 130.6, 130.2, 121.3, 118.6, 117.8
HRMS (ESI, MeOH)	m/z calculated for [M+H]⁺, [C₁₆H₁₂N₄]⁺ 261.1096, found 261.1140
Single-crystal XRD	Chemical formula: C₁₆H₁₂N₄; Mᵣ = 260.30; crystal system, space group: Triclinic, P1; T = 120 K; a = 9.5138(5) Å, b = 10.9853(6) Å, c = 13.3209(7) Å; α = 74.016(5)°, β = 83.910(4)°, γ = 65.911(5)°; V = 1221.78(12) Å³; Z = 4; radiation: Cu Kα; μ = 0.70 mm⁻¹; Rint = 0.029; R[F² > 2σ(F²)] = 0.035, wR(F²) = 0.094, S = 1.03; Δρmax = 0.26 e Å⁻³, Δρmin = −0.21 e Å⁻³; CCDC 2512721; structure image data were not transcribed
Additional NMR and HRMS spectra	Image data were not transcribed

1,6-di(1H-imidazol-1-yl)pyrene, L3
¹H NMR (500 MHz, DMSO-d₆)	δ 8.52 (d, J = 8.2 Hz, 2H), 8.40 (d, J = 9.3 Hz, 2H), 8.21 (d, J = 8.0 Hz, 2H), 8.18 (s, 2H), 7.87 (d, J = 9.2 Hz, 2H), 7.76 (s, 2H), 7.31 (s, 2H)
¹³C NMR (125 MHz, DMSO-d₆)	δ 139.0, 131.9, 130.4, 129.3, 129.1, 126.0, 126.0, 125.2, 124.0, 122.6, 121.9
HRMS (ESI, MeOH)	m/z calculated for [M+H]⁺, [C₂₂H₁₄N₄]⁺ 335.1291, found 335.1324
Single-crystal XRD	Chemical formula: C₂₂H₁₄N₄; Mᵣ = 334.37; crystal system, space group: Monoclinic, P2₁/n; T = 120 K; a = 5.4538(1) Å, b = 11.1283(2) Å, c = 12.7719(3) Å; α = 90°, β = 95.672(2)°, γ = 90°; V = 771.35(3) Å³; Z = 2; radiation: Cu Kα; μ = 0.70 mm⁻¹; Rint = 0.021; R[F² > 2σ(F²)] = 0.036, wR(F²) = 0.098, S = 1.06; Δρmax = 0.24 e Å⁻³, Δρmin = −0.24 e Å⁻³; CCDC 2576008; structure image data were not transcribed
Additional NMR and HRMS spectra	Image data were not transcribed

2,7-di(1H-imidazol-1-yl)pyrene, L4
¹H NMR (400 MHz, DMSO-d₆)	δ 8.67 (s, 4H), 8.58 (s, 2H), 8.31 (s, 4H), 8.07 (s, 2H), 7.25 (s, 2H)
¹³C NMR (101 MHz, DMSO-d₆)	δ 136.2, 135.0, 131.5, 130.3, 128.3, 121.9, 118.6, 117.1
HRMS (ESI, MeOH)	m/z calculated for [M+H]⁺, [C₂₂H₁₄N₄]⁺ 335.1291, found 335.1285
Single-crystal XRD	Chemical formula: C₂₂H₁₄N₄·2.667(H₂O); Mᵣ = 383.44; crystal system, space group: Orthorhombic, Pbcn; T = 100 K; a = 23.0524(1) Å, b = 11.2435(1) Å, c = 7.11694(4) Å; α = 90°, β = 90°, γ = 90°; V = 1844.64(1) Å³; Z = 4; radiation: Synchrotron, 0.6889 Å; μ = 0.09 mm⁻¹; Rint = 0.034; R[F² > 2σ(F²)] = 0.049, wR(F²) = 0.152, S = 1.10; Δρmax = 0.47 e Å⁻³, Δρmin = −0.18 e Å⁻³; CCDC 2576009; structure image data were not transcribed
Additional NMR and HRMS spectra	Image data were not transcribed

Pd₈L₁₆ square antiprism 1 (L = 1,1′-(perfluoronaphthalene-2,6-diyl)bis(1H-imidazole))
¹H NMR (400 MHz, DMSO-d₆)	δ 9.13 (s, 16H, a), 8.90 (s, 16H, a′), 8.08 (s, 16H, b′), 7.96 (s, 16H, c′), 7.95 (s, 16H, b), 7.60 (s, 16H, c)
¹⁹F NMR (376 MHz, DMSO-d₆)	δ −129.96 to −130.48 (m, 32F), −144.87 to −145.67 (m, 32F), −148.26 to −149.12 (m, 32F)
ESI-MS (DMSO)	m/z [1(NO₃)₁₁]⁵⁺ calculated 1484.9811, found 1484.9844; [1(NO₃)₁₀]⁶⁺ calculated 1227.1530, found 1227.1576; [1(NO₃)₉]⁷⁺ calculated 1042.9900, found 1042.9929; [1(NO₃)₈]⁸⁺ calculated 904.8678, found 904.8710; [1(NO₃)₇]⁹⁺ calculated 797.4394, found 797.4420
NMR observations	Signals from other species were very minor both immediately after synthesis and after settling and were not quantified; ¹⁹F NMR spectroscopy did not reveal other species; VT NMR up to 373 K did not produce significant new signals
ESI-MS observation	Small amounts of Pd₉L₁₈ tricapped trigonal prism 1′ were detectable
Single-crystal XRD	Chemical formula: C₂₅₆H₉₆F₉₆N₆₄Pd₈·5(C₂H₆OS)·4(NO₃)·16[NO₃]·60[C₂H₆SO]·20[H₂O]; Mᵣ = 13421.98; crystal system, space group: Monoclinic, C2/m; T = 100 K; a = 36.9973(4) Å, b = 47.4613(4) Å, c = 32.3889(4) Å; α = 90°, β = 91.359(1)°, γ = 90°; V = 56857.0(10) Å³; Z = 4; radiation: Synchrotron, 0.6889 Å; μ = 0.56 mm⁻¹; Rint = 0.064; R[F² > 2σ(F²)] = 0.116, wR(F²) = 0.349, S = 1.26; Δρmax = 0.77 e Å⁻³, Δρmin = −0.56 e Å⁻³; CCDC 2512716; structure image data were not transcribed
Additional NMR and ESI-MS spectra	Image data were not transcribed

Pd₈L₁₆ square antiprism 2 (L = 2,6-di(1H-imidazol-1-yl)naphthalene)
¹H NMR (500 MHz, DMSO-d₆)	δ 9.42 (s, 16H, a), 9.23 (s, 16H, a′), 8.43–7.95 (m, 96H, naphthalene), 8.24 (s, 16H, b′), 8.03 (s, 16H, b), 7.88 (s, 16H, c′), 7.50 (s, 16H, c)
ESI-MS (DMSO)	m/z [2(NO₃)₁₁]⁵⁺ calculated 1139.5620, found 1139.5657; [2(NO₃)₁₀]⁶⁺ calculated 939.3037, found 939.3047; [2(NO₃)₉]⁷⁺ calculated 796.2621, found 796.2655; [2(NO₃)₈]⁸⁺ calculated 688.9808, found 688.9928
Single-crystal XRD	Chemical formula: C₂₅₆H₁₉₂N₆₄Pd₈·4(NO₃)·12[NO₃]·50[C₂H₆SO]·30[H₂O]; Mᵣ = 10454.94; crystal system, space group: Triclinic, P1; T = 120 K; a = 28.3016(5) Å, b = 29.7763(5) Å, c = 37.7725(6) Å; α = 96.045(1)°, β = 107.518(2)°, γ = 109.872(2)°; V = 27772.1(9) Å³; Z = 2; radiation: Cu Kα; μ = 4.43 mm⁻¹; Rint = 0.070; R[F² > 2σ(F²)] = 0.125, wR(F²) = 0.385, S = 1.45; Δρmax = 1.46 e Å⁻³, Δρmin = −0.83 e Å⁻³; CCDC 2512717; structure image data were not transcribed

Pd₉L₁₈ tricapped trigonal prism 2′ (L = 2,6-di(1H-imidazol-1-yl)naphthalene)
¹H NMR (500 MHz, DMSO-d₆)	δ 9.42 (s, 12H, a), 9.25 (s, 12H, a′), 9.15 (s, 12H, a), 8.43–7.95 (m, 108H, naphthalene), 8.20 (s, 12H, b), 8.17 (s, 12H, b′), 8.15 (s, 12H, b), 7.87 (s, 12H, c*), 7.63 (s, 12H, c), 7.63 (s, 12H, c′)
ESI-MS (DMSO)	m/z [2′(NO₃)₁₃]⁵⁺ calculated 1289.7808, found 1289.7843; [2′(NO₃)₁₂]⁶⁺ calculated 1064.4860, found 1064.4902; [2′(NO₃)₁₁]⁷⁺ calculated 903.5612, found 903.5638; [2′(NO₃)₁₀]⁸⁺ calculated 782.8675, found 782.8697

Pd₈L₁₆ square antiprism 2 and Pd₉L₁₈ tricapped trigonal prism 2′ (L = 2,6-di(1H-imidazol-1-yl)naphthalene)
¹H NMR composition, immediately after synthesis	Approximately 49 % 2, 47 % 2′ and 4 % of a presumed Pd₆L₁₂ octahedron
¹H NMR composition (333 K)	45 % n = 8, 39 % n = 9 and 16 % n = 6
VT-NMR observation	The proportion of 2′ fell and the proportion of Pd₆L₁₂ octahedron grew as temperature increased
Additional NMR and ESI-MS spectra	Image data were not transcribed

Pd₉L₁₈ tricapped trigonal prism 3 (L = 2,6-di(1H-imidazol-1-yl)naphthalene)
¹H NMR (500 MHz, DMSO-d₆)	δ 9.31 (s, 12H, a), 9.11 (s, 12H, a′), 9.02 (s, 12H, a), 8.36–7.93 (m, 108H, naphthalene), 8.20 (s, 12H, b), 8.16 (s, 12H, b′), 8.06 (s, 12H, b), 7.82 (s, 12H, c*), 7.55 (s, 12H, c′), 7.47 (s, 12H, c)
ESI-MS (DMSO)	m/z [3(BF₄)₁₃]⁵⁺ calculated 1354.2294, found 1354.2266; [3(BF₄)₁₂]⁶⁺ calculated 1114.0234, found 1114.0201; [3(BF₄)₁₁]⁷⁺ calculated 942.4477, found 942.4440; [3(BF₄)₁₀]⁸⁺ calculated 813.8909, found 813.8894
¹H NMR composition, immediately after synthesis	Approximately 71 % 3, 23 % Pd₈L₁₆ square antiprism 3′ and 6 % of a presumed Pd₆L₁₂ octahedron
¹H NMR composition, after settling	Approximately 71 % n = 9, 23 % n = 8 and 5 % n = 6
¹H NMR composition (333 K)	65 % n = 9, 27 % n = 8 and 8 % n = 6
Single-crystal XRD	Chemical formula: C₂₈₈H₂₁₆N₇₂Pd₉·6(BF₄)·12[BF₄]·50[C₂H₆SO]·50[C₂H₃N]·30[H₂O]; Mᵣ = 13705.04; crystal system, space group: Monoclinic, C2/c; T = 100 K; a = 45.8439(6) Å, b = 46.5554(7) Å, c = 30.9406(4) Å; α = 90°, β = 90.243(1)°, γ = 90°; V = 66035.3(16) Å³; Z = 4; radiation: Synchrotron, 0.6889 Å; μ = 0.45 mm⁻¹; Rint = 0.045; R[F² > 2σ(F²)] = 0.131, wR(F²) = 0.386, S = 1.62; Δρmax = 1.33 e Å⁻³, Δρmin = −0.65 e Å⁻³; CCDC 2512719; structure image data were not transcribed
Additional NMR and ESI-MS spectra	Image data were not transcribed

Pd₆L₁₂ octahedron 4 (L = 2,6-di(1H-imidazol-1-yl)naphthalene)
¹H NMR (500 MHz, CD₃CN)	δ 8.99 (s, 24H, a), 8.20–8.11 (m, 48H, naphthalene), 7.83–7.78 (m, 24H, naphthalene), 7.72 (s, 24H, b), 7.57 (s, 24H, c)
ESI-MS (CH₃CN)	m/z [4(BF₄)₉]³⁺ calculated 1514.2556, found 1514.2497; [4(BF₄)₈]⁴⁺ calculated 1113.9401, found 1113.9392; [4(BF₄)₇]⁵⁺ calculated 873.9507, found 873.9485; [4(BF₄)₆]⁶⁺ calculated 713.7912, found 713.7893; [4(BF₄)₅]⁷⁺ calculated 599.3915, found 599.3905
Single-crystal XRD	Chemical formula: C₁₉₂H₁₄₄N₄₈Pd₆·12.016(BF₄)·7.5(C₂H₃N)·4(C₂N)·30[C₂H₃N]; Mᵣ = 6496.73; crystal system, space group: Monoclinic, P2₁/c; T = 100 K; a = 19.8168(2) Å, b = 24.7689(3) Å, c = 32.4170(4) Å; α = 90°, β = 95.1105(11)°, γ = 90°; V = 15848.3(2) Å³; Z = 2; radiation: Synchrotron, 0.6889 Å; μ = 0.40 mm⁻¹; Rint = 0.044; R[F² > 2σ(F²)] = 0.077, wR(F²) = 0.235, S = 0.96; Δρmax = 2.42 e Å⁻³, Δρmin = −0.94 e Å⁻³; CCDC 2512718; structure image data were not transcribed

Pd₈L₁₆ square antiprism 4′ (L = 2,6-di(1H-imidazol-1-yl)naphthalene)
¹H NMR (500 MHz, CD₃CN)	δ 8.92 (s, 16H, a), 8.71 (s, 16H, a′), 8.20–8.11 (m, 64H, naphthalene), 7.83–7.78 (m, 32H, naphthalene), 7.79 (s, 16H, b′), 7.65 (s, 16H, b), 7.64 (s, 16H, c′), 7.41 (s, 16H, c)
ESI-MS (CH₃CN)	m/z [4′(BF₄)₁₁]⁵⁺ calculated 1194.2032, found 1194.1953; [4′(BF₄)₁₀]⁶⁺ calculated 980.6682, found 980.6631; [4′(BF₄)₉]⁷⁺ calculated 828.1433, found 828.1411; [4′(BF₄)₈]⁸⁺ calculated 713.7495, found 713.7477; [4′(BF₄)₇]⁹⁺ calculated 624.7766, found 624.7754

Pd₆L₁₂ octahedron 4 and Pd₈L₁₆ square antiprism 4′ (L = 2,6-di(1H-imidazol-1-yl)naphthalene)
¹H NMR composition, immediately after synthesis	Approximately 45 % 4, 42 % 4′ and 14 % Pd₉L₁₈ tricapped trigonal prism
¹H NMR composition, after settling	52 % n = 8, 27 % n = 6 and 21 % n = 9
¹H NMR composition (333 K)	50 % n = 8, 31 % n = 6 and 19 % n = 9
Additional NMR and ESI-MS spectra	Image data were not transcribed

Pd₈L₁₆ square antiprism 5 (L = 1,1′-(perfluoronaphthalene-2,6-diyl)bis(1H-imidazole))
¹H NMR (500 MHz, DMSO-d₆)	δ 9.01 (s, 16H), 8.75 (s, 16H), 8.07 (s, 16H), 7.95 (s, 16H), 7.93 (s, 16H), 7.60 (s, 16H)
¹⁹F NMR (376 MHz, DMSO-d₆)	δ −130.06 to −130.38 (m, 32F), −144.85 to −145.21 (m, 32F), −148.35 to −148.80 (m, 32F), −150.80 (br, 13F, 10BF₄), −150.86 (br, 51F, 11BF₄)
ESI-MS (DMSO)	m/z [5(BF₄)₁₁]⁵⁺ calculated 1539.6223, found 1539.6210; [5(BF₄)₁₀]⁶⁺ calculated 1268.5175, found 1268.5146; [5(BF₄)₉]⁷⁺ calculated 1074.8712, found 1074.8716; [5(BF₄)₈]⁸⁺ calculated 929.6365, found 929.6347; [5(BF₄)₇]⁹⁺ calculated 816.6761, found 816.6785
NMR observations	Signals from other species were very minor both immediately after synthesis and after settling and were not quantified; ¹⁹F NMR spectroscopy did not reveal other species; low-intensity unassigned signals appeared above 333 K in the VT-NMR experiment
ESI-MS observation	Small amounts of Pd₉L₁₈ tricapped trigonal prism 5′ were detectable
Additional NMR and ESI-MS spectra	Image data were not transcribed

Pd₈L₁₆ square antiprism 6 (L = 1,1′-(perfluoronaphthalene-2,6-diyl)bis(1H-imidazole))
¹H NMR (500 MHz, CD₃CN)	δ 8.60 (s, 16H), 8.40 (s, 16H), 7.74 (s, 16H), 7.65 (s, 16H), 7.57 (s, 16H), 7.51 (s, 16H)
¹⁹F NMR (376 MHz, CD₃CN)	δ −128.45 to −128.75 (m, 32F), −144.64 to −144.98 (m, 32F), −146.41 to −146.96 (m, 32F), −151.71 (br, 13F, 10BF₄), −151.76 (br, 51F, 11BF₄)
ESI-MS (CH₃CN)	m/z [6(BF₄)₁₁]⁵⁺ calculated 1539.6223, found 1539.6214; [6(BF₄)₁₀]⁶⁺ calculated 1268.5175, found 1268.5175; [6(BF₄)₉]⁷⁺ calculated 1074.8712, found 1074.8717; [6(BF₄)₈]⁸⁺ calculated 929.6365, found 929.6373; [6(BF₄)₇]⁹⁺ calculated 816.6761, found 816.6739
NMR observations	Signals from other species were very minor both immediately after synthesis and after settling and were not quantified; ¹⁹F NMR spectroscopy did not reveal other species; the square antiprism remained the major species up to 343 K, with no new signals
ESI-MS observation	Small amounts of Pd₉L₁₈ tricapped trigonal prism 6′ were detectable
Additional NMR and ESI-MS spectra	Image data were not transcribed

Pd₉L₁₈ tricapped trigonal prism 7 (L = 1,6-di(1H-imidazol-1-yl)pyrene)
¹H NMR (500 MHz, DMSO-d₆)	δ 9.10 (s, 12H, a), 8.95 (s, 12H, a′), 8.94 (s, 12H, a), 8.59–7.60 (m, 144H, pyrene), 8.25 (s, 12H, b′), 8.25 (s, 12H, b), 8.20 (s, 12H, b), 8.19 (s, 12H, c*), 7.93 (s, 12H, c), 7.74 (s, 12H, c′)
ESI-MS (DMSO)	m/z [7(NO₃)₁₂]⁶⁺ calculated 1286.6996, found 1286.7297; [7(NO₃)₁₁]⁷⁺ calculated 1094.0300, found 1094.0574; [7(NO₃)₁₀]⁸⁺ calculated 949.5278, found 949.5503; [7(NO₃)₉]⁹⁺ calculated 837.1371, found 837.1559; [7(NO₃)₈]¹⁰⁺ calculated 747.2246, found 747.2434

Pd₈L₁₆ square antiprism 7′ (L = 1,6-di(1H-imidazol-1-yl)pyrene)
¹H NMR (500 MHz, DMSO-d₆)	δ 9.03 (s, 16H, a), 8.88 (s, 16H, a′), 8.59–7.60 (m, 128H, pyrene), 8.25 (s, 16H, b′), 8.25 (s, 16H, b), 8.07 (s, 16H, c′), 7.84 (s, 16H, c)
ESI-MS (DMSO)	m/z [7′(NO₃)₁₁]⁵⁺ calculated 1376.6121, found 1376.6449; [7′(NO₃)₁₀]⁶⁺ calculated 1136.8455, found 1136.8740; [7′(NO₃)₉]⁷⁺ calculated 965.5836, found 965.6021; [7′(NO₃)₈]⁸⁺ calculated 837.1371, found 837.1559; [7′(NO₃)₇]⁹⁺ calculated 737.2344, found 737.2481

Pd₉L₁₈ tricapped trigonal prism 7 and Pd₈L₁₆ square antiprism 7′ (L = 1,6-di(1H-imidazol-1-yl)pyrene)
¹H NMR composition, immediately after synthesis	Approximately 49 % 7, 45 % 7′ and 6 % Pd₆L₁₂ octahedron
¹H NMR composition, after settling	Estimated ratio of about 7:3 n = 9 to n = 8; accurate compositions could not be determined because the spectra became broader
¹H NMR composition (333 K)	42 % n = 9, 45 % n = 8 and 13 % n = 6
VT-NMR observation	The amount of n = 9 fell as temperature increased, and Pd₆L₁₂ octahedron became visible above 333 K
Additional NMR and ESI-MS spectra	Image data were not transcribed

Pd₉L₁₈ tricapped trigonal prism 8 (L = 1,6-di(1H-imidazol-1-yl)pyrene)
¹H NMR (500 MHz, DMSO-d₆)	δ 9.00 (s, 12H, a), 8.87 (s, 12H, a′), 8.78 (s, 12H, a), 8.59–7.60 (m, 144H, pyrene), 8.26 (s, 12H, b), 8.24 (s, 12H, b′), 8.22 (s, 12H, b), 8.07 (s, 12H, c*), 7.94 (s, 12H, c), 7.79 (s, 12H, c′)
ESI-MS (DMSO)	m/z [8(BF₄)₁₂]⁶⁺ calculated 1336.2370, found 1336.2363; [8(BF₄)₁₁]⁷⁺ calculated 1133.0594, found 1133.0575; [8(BF₄)₁₀]⁸⁺ calculated 980.5511, found 980.5514; [8(BF₄)₉]⁹⁺ calculated 861.9336, found 861.9301; [8(BF₄)₈]¹⁰⁺ calculated 767.0396, found 767.0410; [8(BF₄)₇]¹¹⁺ calculated 689.3990, found 689.4004; [8(BF₄)₆]¹²⁺ calculated 624.7819, found 624.7414

Pd₈L₁₆ square antiprism 8′ (L = 1,6-di(1H-imidazol-1-yl)pyrene)
¹H NMR (500 MHz, DMSO-d₆)	δ 8.93 (s, 16H, a), 8.82 (s, 16H, a′), 8.59–7.60 (m, 128H, pyrene), 8.26 (s, 16H, b′), 8.24 (s, 16H, b), 8.15 (s, 16H, c′), 7.87 (s, 16H, c)
ESI-MS (DMSO)	m/z [8′(BF₄)₁₁]⁵⁺ calculated 1431.2532, found 1431.2512; [8′(BF₄)₁₀]⁶⁺ calculated 1178.2300, found 1178.2060; [8′(BF₄)₉]⁷⁺ calculated 997.4647, found 997.4645; [8′(BF₄)₈]⁸⁺ calculated 861.9058, found 861.9072; [8′(BF₄)₇]⁹⁺ calculated 756.4711, found 756.4717; [8′(BF₄)₆]¹⁰⁺ calculated 672.2234, found 672.2223

Pd₉L₁₈ tricapped trigonal prism 8 and Pd₈L₁₆ square antiprism 8′ (L = 1,6-di(1H-imidazol-1-yl)pyrene)
¹H NMR composition (333 K)	Approximately 57 % 8 and 44 % 8′, with no Pd₆L₁₂ octahedron
VT-NMR observation	The amount of n = 9 fell as temperature increased, and Pd₆L₁₂ octahedron became visible above 353 K
ESI-MS observation	Signals from Pd₁₀L₂₀, Pd₁₁L₂₂ and Pd₁₂L₂₄ species were observed in addition to 8 and 8′
Additional NMR and ESI-MS spectra	Image data were not transcribed

Pd₉L₁₈ tricapped trigonal prism 9 (L = 2,7-di(1H-imidazol-1-yl)pyrene)
¹H NMR (500 MHz, DMSO-d₆)	δ 9.59 (s, 12H, a), 9.44 (s, 12H, a′), 9.39 (s, 12H, a), 8.84 (s, 24H, e′), 8.79 (s, 24H, e), 8.75 (s, 24H, e), 8.45 (s, 12H, b), 8.38 (s, 24H, d), 8.38 (s, 24H, d′), 8.35 (s, 12H, b′), 8.27 (s, 24H, d), 8.20 (s, 12H, b), 8.07 (s, 12H, c*), 7.63 (s, 12H, c′), 7.56 (s, 12H, c)
ESI-MS (DMSO)	m/z [9(NO₃)₁₄]⁴⁺ calculated 1961.0433, found 1961.0438; [9(NO₃)₁₃]⁵⁺ calculated 1556.4371, found 1556.4404; [9(NO₃)₁₂]⁶⁺ calculated 1286.6996, found 1286.7022; [9(NO₃)₁₁]⁷⁺ calculated 1094.0300, found 1094.0327; [9(NO₃)₁₀]⁸⁺ calculated 949.5278, found 949.5303; [9(NO₃)₉]⁹⁺ calculated 837.1371, found 837.1397

Pd₈L₁₆ square antiprism 9′ (L = 2,7-di(1H-imidazol-1-yl)pyrene)
¹H NMR (500 MHz, DMSO-d₆)	δ 9.59 (s, 16H, a), 9.39 (s, 16H, a′), 8.82 (s, 32H, e), 8.75 (s, 32H, e′), 8.45 (s, 16H, b′), 8.41 (s, 32H, d), 8.28 (s, 32H, d′), 8.22 (s, 16H, b), 8.02 (s, 16H, c′), 7.58 (s, 16H, c)
ESI-MS (DMSO)	m/z [9′(NO₃)₁₂]⁴⁺ calculated 1736.2621, found 1736.2643; [9′(NO₃)₁₁]⁵⁺ calculated 1376.6121, found 1376.6146; [9′(NO₃)₁₀]⁶⁺ calculated 1136.8455, found 1136.8482; [9′(NO₃)₉]⁷⁺ calculated 965.5836, found 965.5874; [9′(NO₃)₈]⁸⁺ calculated 837.1371, found 837.1379

Pd₉L₁₈ tricapped trigonal prism 9 and Pd₈L₁₆ square antiprism 9′ (L = 2,7-di(1H-imidazol-1-yl)pyrene)
¹H NMR composition, immediately after synthesis	Approximately 53 % 9, 45 % 9′ and 3 % Pd₆L₁₂ octahedron
¹H NMR composition, after settling	62 % 9, 36 % 9′ and 3 % Pd₆L₁₂ octahedron
¹H NMR composition (333 K)	61 % n = 9, 36 % n = 8 and 3 % n = 6
VT-NMR observation	The amount of n = 9 fell as temperature increased, and Pd₆L₁₂ octahedron became visible above 333 K
Additional NMR and ESI-MS spectra	Image data were not transcribed

Pd₉L₁₈ tricapped trigonal prism 10 (L = 2,7-di(1H-imidazol-1-yl)pyrene)
¹H NMR (500 MHz, DMSO-d₆)	δ 9.48 (s, 12H, a), 9.27 (s, 12H, a′), 9.15 (s, 12H, a), 8.74 (s, 24H, e′), 8.69 (s, 24H, e), 8.66 (s, 24H, e), 8.42 (s, 12H, b), 8.37 (s, 24H, d), 8.37 (s, 24H, d′), 8.34 (s, 12H, b′), 8.26 (s, 24H, d), 8.22 (s, 12H, b), 8.00 (s, 12H, c*), 7.56 (s, 12H, c′), 7.53 (s, 12H, c)
ESI-MS (DMSO)	m/z [10(BF₄)₁₂]⁶⁺ calculated 1336.2370, found 1336.2764; [10(BF₄)₁₁]⁷⁺ calculated 1133.0594, found 1133.0909; [10(BF₄)₁₀]⁸⁺ calculated 980.5511, found 980.5779; [10(BF₄)₉]⁹⁺ calculated 861.9336, found 861.9546; [10(BF₄)₈]¹⁰⁺ calculated 767.0396, found 767.0646; [10(BF₄)₇]¹¹⁺ calculated 689.3990, found 689.4203; [10(BF₄)₆]¹²⁺ calculated 624.7819, found 624.8013

Pd₈L₁₆ square antiprism 10′ (L = 2,7-di(1H-imidazol-1-yl)pyrene)
¹H NMR (500 MHz, DMSO-d₆)	δ 9.48 (s, 16H, a), 9.21 (s, 16H, a′), 8.75 (s, 32H, e), 8.67 (s, 32H, e′), 8.44 (s, 16H, b′), 8.42 (s, 32H, d), 8.26 (s, 32H, d′), 8.22 (s, 16H, b), 7.98 (s, 16H, c′), 7.55 (s, 16H, c)
ESI-MS (DMSO)	m/z [10′(BF₄)₁₁]⁵⁺ calculated 1431.2532, found 1431.2982; [10′(BF₄)₁₀]⁶⁺ calculated 1178.2099, found 1178.2485; [10′(BF₄)₉]⁷⁺ calculated 997.4647, found 997.4917; [10′(BF₄)₈]⁸⁺ calculated 861.9058, found 861.9546; [10′(BF₄)₇]⁹⁺ calculated 756.4711, found 756.4931; [10′(BF₄)₆]¹⁰⁺ calculated 672.2234, found 672.2439; [10′(BF₄)₅]¹¹⁺ calculated 603.2025, found 603.2180

Pd₉L₁₈ tricapped trigonal prism 10 and Pd₈L₁₆ square antiprism 10′ (L = 2,7-di(1H-imidazol-1-yl)pyrene)
¹H NMR composition, immediately after synthesis	Approximately 50 % 10, 46 % 10′ and 4 % Pd₆L₁₂ octahedron
¹H NMR composition, after settling	53 % 10, 42 % 10′ and 5 % Pd₆L₁₂ octahedron
¹H NMR composition (333 K)	48 % n = 9, 43 % n = 8 and 8 % n = 6
VT-NMR observation	The amount of n = 9 fell as temperature increased, and Pd₆L₁₂ octahedron became visible above 353 K
Additional NMR and ESI-MS spectra	Image data were not transcribed

Pd₉L₁₈ tricapped trigonal prism 3 (L = 2,6-di(1H-imidazol-1-yl)naphthalene)
¹H NMR solvent-effect spectra (400 MHz, 298 K, DMSO-d₆ and CD₃CN)	Image data were not transcribed

Pd₈L₁₆ square antiprism 2 and Pd₉L₁₈ tricapped trigonal prism 2′ (L = 2,6-di(1H-imidazol-1-yl)naphthalene)
¹H NMR after NMe₄BF₄ addition (400 MHz, 298 K, DMSO-d₆)	Minimal effect on the equilibrium of the system; no change was observed after 7 days at 22 °C; image data were not transcribed

Pd₉L₁₈ tricapped trigonal prism 3 (L = 2,6-di(1H-imidazol-1-yl)naphthalene)
¹H NMR after NMe₄NO₃ addition (400 MHz, 298 K, DMSO-d₆)	A visible effect on the composition of the mixture and an apparent slight increase in the proportion of Pd₈L₁₆ were observed; image data were not transcribed

Cage systems 1–6
¹H NMR after self-assembly for 1 h at 298 K and annealing for 1 h at 333 K	For cages 1, 5 and 6, there was little difference between the spectra before and after annealing; for cage 6, self-assembly at 298 K produced an identifiable amount of n = 9 that was retained upon heating; for cage systems 2/2′, 3/3′ and 4, annealing produced slight increases in n = 6 and n = 8 and slight decreases in n = 9; image data were not transcribed

Cage systems 1, 2/2′, 3/3′ and 5
¹H NMR self-assembly monitoring (500 MHz, 298 K, DMSO-d₆)	For cages 1 and 5, additional peaks observed at shorter timescales were reduced after 1 h and self-assembly appeared largely complete; for cages 2/2′, small peaks likely attributable to n = 6 were observable up to 1 h, after which the peaks were predominantly from n = 8 and n = 9, with the relative amount of n = 9 continuing to grow up to one week before decreasing upon annealing at 333 K in favor of some n = 6 and n = 8; for cages 3/3′, peaks attributable to n = 6 remained observable up to one week but decreased over time, and annealing at 333 K produced a small increase in n = 8 and decrease in n = 9; heating generally sharpened the NMR spectra; image data were not transcribed