Table 1.
Representative aluminum models
| Ring | Edge type | Ext rot (E) | Int rot (I) | Dist of E (α) | DAD (D) | Twist (T) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 611 | ||||||||||||||||
| Pent | Sym | 0.00 | 0.00 | −31.51 | 0.00 | 0.00 | 0.00 | 31.51 | 15.76 | −15.76 | ||||||
| Hex | Green | −16.34 | 12.03 | 52% | 28.37 | −2.16 | ||||||||||
| Hex | Twist | −15.17 | −12.03 | 48% | 3.14 | −13.60 | ||||||||||
| Hex | Sym | 0.00 | 0.00 | 31.51 | 0.00 | 0.00 | 0.00 | −31.51 | −15.76 | 15.76 | ||||||
| Hex | Twist | 15.17 | 12.03 | −3.14 | 13.60 | |||||||||||
| Hex | Green | 16.34 | −12.03 | −28.37 | 2.16 | |||||||||||
| Sum | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |||||||||
| 621 | ||||||||||||||||
| Pent | Red | −8.65 | 8.37 | −48.45 | −3.78 | 18% | 17.02 | −0.14 | 44.67 | 22.34 | −26.12 | |||||
| Hex | Green | −21.98 | 3.76 | 45% | 25.74 | −9.11 | ||||||||||
| Hex | Twist | −17.82 | −15.91 | 37% | 1.91 | −16.87 | ||||||||||
| Hex | Twist | 17.82 | 15.91 | 48.45 | 3.78 | −1.91 | 16.87 | −44.67 | −22.34 | 26.12 | ||||||
| Hex | Green | 21.98 | −3.76 | −25.74 | 9.11 | |||||||||||
| Pent | Red | 8.65 | −8.37 | −17.02 | 0.14 | |||||||||||
| Sum | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |||||||||
| 623 | ||||||||||||||||
| Pent | Sym | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||||||
| Hex | Green | −12.90 | 14.55 | 27.45 | 0.83 | |||||||||||
| Hex | Green | 12.90 | −14.55 | −27.45 | −0.83 | |||||||||||
| Pent | Sym | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ||||||
| Hex | Green | −12.90 | 14.55 | 27.45 | 0.83 | |||||||||||
| Hex | Green | 12.90 | −14.55 | −27.45 | −0.83 | |||||||||||
| Sum | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |||||||||
| 631 | ||||||||||||||||
| Pent | Sym | 0.00 | 0.00 | −42.82 | 0.00 | 0.00 | 0.00 | 42.82 | 21.41 | −21.41 | ||||||
| Pent | Red | −16.65 | 0.03 | 39% | 16.68 | −8.31 | ||||||||||
| Hex | Green | −26.17 | −0.03 | 61% | 26.14 | −13.10 | ||||||||||
| Hex | Sym | 0.00 | 0.00 | 42.82 | 0.00 | 0.00 | 0.00 | −42.82 | −21.41 | 21.41 | ||||||
| Hex | Green | 26.17 | 0.03 | −26.14 | 13.10 | |||||||||||
| Pent | Red | 16.65 | −0.03 | −16.68 | 8.31 | |||||||||||
| Sum | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |||||||||
| 632 | ||||||||||||||||
| Pent | Red | −14.94 | 3.57 | −18.91 | −0.11 | 18.51 | −5.69 | 18.80 | 9.40 | −9.51 | ||||||
| Hex | Green | −29.50 | 2.13 | 31.63 | −13.69 | |||||||||||
| Hex | Green | 25.53 | −5.81 | −31.34 | 9.86 | |||||||||||
| Pent | Twist | 3.89 | 3.85 | 19.00 | 0.16 | −0.04 | 3.87 | −18.84 | −9.42 | 0.07 | ||||||
| Hex | Twist | 2.81 | 1.84 | −0.97 | 2.33 | |||||||||||
| Pent | Red | 12.30 | −5.53 | −17.83 | 3.39 | |||||||||||
| Sum | 0.09 | 0.05 | −0.04 | 0.07 | −0.04 | −0.02 | −9.44 | |||||||||
| 531 | ||||||||||||||||
| Pent | Sym | 0.00 | 0.00 | |||||||||||||
| Pent | Blue | −15.05 | −1.24 | −31.01 | 0.76 | 49% | 13.81 | −8.15 | 31.77 | 15.89 | −15.13 | |||||
| Hex | Red | −15.96 | 2.00 | 51% | 17.96 | −6.98 | ||||||||||
| Hex | Red | 15.96 | −2.00 | 31.01 | −0.76 | −17.96 | 6.98 | −31.77 | −15.89 | 15.13 | ||||||
| Pent | Blue | 15.05 | 1.24 | −13.81 | 8.15 | |||||||||||
| Sum | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |||||||||
| 532 | ||||||||||||||||
| Hex | Twist | −5.99 | −5.70 | −11.20 | 3.52 | 53% | 0.29 | −5.85 | 14.72 | 7.36 | −3.84 | |||||
| Pent | Blue | −5.21 | 9.22 | 47% | 14.43 | 2.01 | ||||||||||
| Pent | Blue | 5.21 | −9.22 | 11.20 | −3.52 | −14.43 | −2.01 | −14.72 | −7.36 | 3.84 | ||||||
| Hex | Twist | 5.99 | 5.70 | −0.29 | 5.85 | |||||||||||
| Pent | Sym | 0.00 | 0.00 | 0.00 | 0.00 | |||||||||||
| Sum | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |||||||||
Angles of interest (in degrees) associated with all of the edges of representative hex-Rings and pent-Rings composed of aluminum atoms. Edge lengths were constrained to 2.5 Å, and internal angles were constrained to 108° in pentagonal faces and 120° in hexagonal faces. Electrostatic interactions were turned off. The equilibrium geometry of each Ring structure was determined by molecular mechanics calculations (MMFF94) (20–24) in Spartan ‘04. External rotation (E) and internal rotation (I) were measured. DAD (D) and twist (T) were calculated from E and I according to Eqs. 1 and 2.