Table 1.
Curve effect, in terms of θ (°), on the natural occupation numbers in ψA (HOMO) and ψB (LUMO), quinoidal contribution (q), Wiberg bond order (BO), C1–C2 distance (pm), and singlet-triplet energy gap (ΔEST, kcal mol–1) a.
| Entry | DR | Bent Angle θ (°) | Occupation Number | q | BO b | C1–C2 Singlet/Triplet | ΔEST
c ΔErel,S/ΔErel,T |
|
|---|---|---|---|---|---|---|---|---|
| ψA (HOMO) | ψB (LUMO) | |||||||
| 1 | DR1 | 0 (C1-C2-C6 = C10-C9-C5 = 180°) |
1.66 | 0.35 | 83.0 | 1.55 | 137.4/140.8 | 11.6 0.0/0.0 |
| 2 | 13 (160°) |
1.70 | 0.31 | 85.0 | 1.61 | 136.7/140.8 | 12.9 +4.4/+5.7 |
|
| 3 | 25 (140°) |
1.79 | 0.23 | 89.5 | 1.73 | 135.6/140.4 | 17.4 +17.0/+22.8 |
|
| 4 | 29 (135°) |
1.80 | 0.21 | 90.0 | 1.75 | 135.5/140.2 | 19.3 +21.0/+28.7 |
|
| 5 | DR2 | 0 (C1-C2-C6 = C8-C7-C12 = 180°) |
1.77 | 0.24 | 88.5 | 1.68 | 135.9/142.0 | 22.0 0.0/0.0 |
| 6 | 12 (160°) |
1.78 | 0.23 | 89.0 | 1.69 | 135.8/142.0 | 23.3 +4.0/+5.2 |
|
| 7 | 17 (140°) |
1.82 | 0.19 | 91.0 | 1.71 | 135.6/141.9 | 27.4 +15.4/+20.7 |
|
| 8 | 26 (120°) |
1.85 | 0.16 | 92.5 | 1.76 | 135.2/141.6 | 35.5 +32.4/+45.8 |
|
| 9 | DR3 | 0 (C1-C5-C6 = C10-C6-C5 = 180°) |
1.58 | 0.43 | 79.0 | 1.47 | 138.5/141.2 | 11.8 +0.0/+0.0 |
| 10 | 17 (160°) |
1.62 | 0.39 | 81.0 | 1.51 | 138.1/141.1 | 12.9 +5.9/+7.0 |
|
| 11 | 34 (140°) |
1.76 | 0.25 | 88.0 | 1.67 | 136.2/140.8 | 16.6 +23.1/+27.9 |
|
| 12 | 52 (120 °) |
1.87 | 0.14 | 93.5 | 1.75 | 135.6/140.2 | 26.7 +46.6/+61.4 |
|
| 13 | DR4 | 0 (C1-C5-C6 = C10-C13-C14 = 180°) |
1.65 | 0.36 | 82.5 | 1.54 | 137.5/140.6 | 15.2 +0.0/+0.0 |
| 14 | 12 (160°) |
1.68 | 0.33 | 84.0 | 1.57 | 137.2/140.5 | 16.0 +5.0/+5.8 |
|
| 15 | 24 (140°) |
1.76 | 0.25 | 88.0 | 1.68 | 136.0/140.3 | 18.3 +20.1/+23.2 |
|
| 16 | 35 (120°) |
1.82 | 0.19 | 91.0 | 1.73 | 135.6/140.0 | 24.0 +43.0/+51.7 |
|
a The structural optimization was performed in C2 (DR1, DR2 and DR4) and CS (DR3) symmetry at the (U)B3LYP/6-31G(d) level of theory. The occupation numbers in ψA and ψB were computed at the CASCF/cc-pVDZ level of theory, CASSCF(14,14) for DR1, CASSCF(12,12) for DR2, and CASSCF(16,16) for DR3 and DR4. The energies were obtained at the CASPT2/cc-pVDZ level of theory. b The Wiberg BO between C1 and C2 was determined by natural atomic orbital (NAO) and natural bond orbital (NBO) analyses at the B3LYP/6-31G(d) level of theory [60]. c The singlet-triplet energy gap, (ΔEST), was determined to be ES − ET. The energies, ΔErel,S/ΔErel,T, were relative to the absolute energy for θ = 0°.