Table 2 Bonding lengths, bonding angles and their standard deviations for the Cu2+ spins in the (111) Kagome lattice plane in triclinic Cu4(OH)6Cl2 at 100 K

From: Unique magnetic transition process demonstrating the effectiveness of bond percolation theory in a quantum magnet

Triangle of Cu3B-Cu3C-Cu4B

Cu3B-Cu3C = 3.402(3) Å

Cu3B-Cu4B = 3.416(2) Å

Cu3C-Cu4B = 3.440(3) Å

σ = 0.016 Å (0.46%)

∠Cu3B-Cu3C-Cu4B = 59.90(5)°

∠Cu3B-Cu4B-Cu3C = 59.50(5)°

∠Cu3C-Cu3B-Cu4B = 60.60(4)°

σ = 0.45° (0.76%)

∠Cu3B-O3B-Cu4B = 117.50(5)°

∠Cu3C-O1B-Cu4B = 118.650(18)°

∠Cu3B-O2C-Cu3C = 120.98(5)°

σ = 1.45° (1.22%)

Cu3A-Cu3B-Cu4A

Cu3A-Cu3B = 3.348(3)Å

Cu3A-Cu4A = 3.360(3)Å

Cu3B-Cu4A = 3.286(3)Å

σ = 0.032 Å (0.97%)

∠Cu3A-Cu3B-Cu4A = 60.84(3)°

∠Cu3B-Cu3A-Cu4A = 58.67(5)°

∠Cu3A-Cu4A-Cu3B = 60.48(5)°

σ = 0.945° (1.58%)

∠Cu3A-O2B-Cu3B = 116.61(5)°

∠Cu3A-O3A-Cu4A = 109.07(3)°

∠Cu4A-O1A-Cu3B = 121.48(5)°

σ = 5.11°(4.41%)

Cu4A-Cu4B-Cu4C

Cu4A-Cu4B = 3.440(3)Å

Cu4A-Cu4C = 3.514(3)Å

Cu4B-Cu4C = 3.485(3)Å

σ = 0.030 Å (0.87%)

∠Cu4A-Cu4B-Cu4C = 60.99(5)°

∠Cu4B-Cu4A-Cu4C = 60.14(5)°

∠Cu4A-Cu4C-Cu4B = 58.87(3)°

σ = 0.87° (1.45%)

∠Cu4A-O4B-Cu4B = 116.77(3)°

∠Cu4A-O4A-Cu4C = 128.57(5)°

∠Cu4B-O4C-Cu4C = 123.26(5)°

σ = 4.83° (3.93%)

Cu3A-Cu3C-Cu4C

Cu3A-Cu3C = 3.412(3)Å

Cu3C-Cu4C = 3.429(3)Å

Cu3A-Cu4C = 3.399(3)Å

σ = 0.012 Å (0.36%)

∠Cu3A-Cu4C-Cu3C = 59.95(4)°

∠Cu3C-Cu3A-Cu4C = 60.46(5)°

∠Cu3A-Cu3C-Cu4C = 59.59(5)°

σ = 0.36° (0.59%)

∠Cu3A-O1C-Cu4C = 116.25(5)°

∠Cu3A-O2A-Cu3C = 115.67(3)°

∠Cu3C-O3C-Cu4C = 113.57(5)°

σ = 1.15° (1.00%)

  1. For the labeling of Cu, refer to a visual view in Fig. 1a. All triangles of Cu are nearly regular with the Cu-Cu length σ less than 1°. The underlined Cu-O-Cu bonding has the smallest angle in each triangle, and is ferromagnetically coupled in the long-range ordered phase, while all other Cu ions are antiferromagnetically coupled.
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