Table 5. Active orbital occupation numbers (f
HOMO−5, …, f
HOMO−1, f
HOMO, f
LUMO, f
LUMO+1, …, and f
LUMO+5) for the lowest singlet states of zigzag-edged diamond-shaped graphene nanoflakes (
) as a function of the side length n, calculated using TAO-LDA.
| n | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| fHOMO−5 | 2.000 | 2.000 | 2.000 | 2.000 | 1.999 |
| fHOMO−4 | 2.000 | 2.000 | 2.000 | 2.000 | 1.997 |
| fHOMO−3 | 2.000 | 2.000 | 2.000 | 1.995 | 1.950 |
| fHOMO−2 | 2.000 | 2.000 | 1.990 | 1.905 | 1.672 |
| fHOMO−1 | 1.999 | 1.976 | 1.821 | 1.523 | 1.277 |
| fHOMO | 1.938 | 1.668 | 1.351 | 1.161 | 1.070 |
| fLUMO | 0.062 | 0.334 | 0.660 | 0.853 | 0.946 |
| fLUMO+1 | 0.000 | 0.021 | 0.170 | 0.479 | 0.745 |
| fLUMO+2 | 0.000 | 0.000 | 0.008 | 0.080 | 0.300 |
| fLUMO+3 | 0.000 | 0.000 | 0.000 | 0.004 | 0.040 |
| fLUMO+4 | 0.000 | 0.000 | 0.000 | 0.000 | 0.002 |
| fLUMO+5 | 0.000 | 0.000 | 0.000 | 0.000 | 0.001 |
| EST | 1.02 | 0.44 | 0.20 | 0.12 | 0.08 |
As the singlet-triplet energy gaps EST (in eV) of these alternant PAHs are positive, they all possess singlet ground states.