. 2016 Jul 26;6:30562. doi: 10.1038/srep30562

Table 2. Active orbital occupation numbers ( f _HOMO and f _LUMO) for the lowest singlet states of n-PP, n-acene, and n-phenacene (n = 3–20), calculated using TAO-LDA.

n	n-PP			n-acene			n-phenacene
n	f_HOMO	f_LUMO	E_ST	f_HOMO	f_LUMO	E_ST	f_HOMO	f_LUMO	E_ST
3	1.999	0.001	2.51	1.996	0.004	1.87	2.000	0.002	2.74
4	1.998	0.002	2.24	1.972	0.028	1.26	1.999	0.001	2.45
5	1.997	0.003	2.06	1.900	0.100	0.85	1.999	0.001	2.35
6	1.996	0.004	1.93	1.759	0.242	0.59	1.999	0.001	2.25
7	1.995	0.006	1.83	1.561	0.441	0.43	1.998	0.001	2.17
8	1.994	0.007	1.74	1.353	0.653	0.34	1.998	0.001	2.11
9	1.993	0.008	1.67	1.168	0.844	0.29	1.998	0.001	2.05
10	1.992	0.008	1.62	1.020	1.000	0.26	1.998	0.002	2.00
11	1.992	0.009	1.57	1.123	0.904	0.23	1.998	0.002	1.96
12	1.991	0.010	1.52	1.218	0.816	0.21	1.998	0.002	1.92
13	1.991	0.010	1.48	1.293	0.746	0.19	1.998	0.002	1.89
14	1.990	0.010	1.45	1.351	0.690	0.17	1.997	0.002	1.85
15	1.990	0.011	1.42	1.397	0.645	0.16	1.997	0.002	1.83
16	1.990	0.011	1.39	1.435	0.608	0.15	1.997	0.002	1.80
17	1.989	0.011	1.36	1.351	0.638	0.14	1.997	0.002	1.77
18	1.989	0.012	1.33	1.259	0.737	0.13	1.997	0.002	1.75
19	1.989	0.012	1.31	1.176	0.827	0.12	1.997	0.002	1.73
20	1.989	0.012	1.29	1.099	0.910	0.11	1.997	0.002	1.71

As the singlet-triplet energy gaps E_ST (in eV) of these alternant PAHs are positive, they all possess singlet ground states.

Table 2. Active orbital occupation numbers ( f HOMO and f LUMO) for the lowest singlet states of n-PP, n-acene, and n-phenacene (n = 3–20), calculated using TAO-LDA.