Table 3. Length (Lx) Dependence (in Å) of the Conductivity σx along the Length of the GNR in Units of (in Bold), and LUMO–HOMO Gaps in eV, for Various Constant Width (Ly) Armchair GNRs Consisting of n (n = 3, 4, 6, 8, 10, 13, 18, 20, 24)× Armchair Rings along the x-axis (Perpendicular to the Zigzag Edges) and m (m = 3, 4, 5) Rings along Their Width, with Widths about 9.2 Å (3 Rings, 3×), 11.7 Å (4 Rings, 4×), and 14.1 Å (5 Rings, 5×), Respectively.
3× | 4× | 6× | 8× | 10× | 13× | 18× | 20× | 24× | ||
---|---|---|---|---|---|---|---|---|---|---|
GNR width (Ly)/Å | properties | Lx/Å | Lx/Å | Lx/Å | Lx/Å | Lx/Å | Lx/Å | Lx/Å | Lx/Å | Lx/Å |
13.6 | 17.9 | 26.5 | 34.9 | 43.6 | 56.5 | 77.8 | 86.5 | 103.6 | ||
3× Ly = 9.2 | 0.03 | 0.08 | 0.37 | 1.04 | 2.31 | 5.88 | 18.53 | 26.66 | 53.20 | |
L–H(eV) | 1.239 | 0.729 | 0.263 | 0.144 | 0.102 | 0.074 | 0.051 | 0.046 | 2.68a 0.037 | |
4× Ly = 11.7 | 0.04 | 0.11 | 0.38 | 1.01 | 2.15 | 5.27 | 16.04 | 22.94 | 45.16 | |
L–H (eV) | 0.589 | 0.320 | 0.169 | 0.119 | 0.093 | 0.070 | 0.049 | 0.044 | 1.75a 0.037 | |
5× Ly = 14.1 | 0.04 | 0.11 | 0.39 | 1.11 | 2.19 | 5.28 | 16.62 | 24.54 | 48.93 | |
H–L (eV) | 0.386 | 0.254 | 0.156 | 0.114 | 0.090 | 0.068 | 0.049 | 0.044 | 0.45a 0.037 |
The underlined numbers in the last column correspond to the gap-defining (“effective”) LUMO–HOMO gaps (i.e., the gaps between HOMO–1 and LUMO+1 in the present case, see text).