TABLE I.

Singlet and triplet energetics of representative aromatic hydrocarbons calculated with GW-BSE@BHLYP with the full-BSE (denoted simply BSE above) and the TDA. We consider benzene (Benz), naphthalene (Naph.), anthracene (Anth.), tetracene (Tetra.), pentacene (Penta.), hexacene (Hexa.), azulene (Azu.), benzo[e]pyrene (BP), and dibenzo[a, c]anthracene (DBAn). MSD and MAD with respect to CCSD(T) are also shown (see text). All energies are in units of eV.

${\text{𝑳}}_{\text{𝒂}}\text{𝐬𝐭𝐚𝐭𝐞𝐬}$
	Singlets			Triplets
	BSE	TDA	CCSD(T)a	BSE	TDA	CCSD(T)a
Benz.	5.89	6.13	6.5437	3.60	3.94	$4.26\pm 0.11$ 37,61
Naph.	4.34	4.59	$4.81\pm 0.02$ 8,37	2.65	2.93	$3.20\pm 0.11$ 37,61
Anth.	3.38	3.63	$3.68\pm 0.02$ 8,62	2.01	2.29	$2.41\pm 0.07$ 61,62
Tetra.	2.42	2.72	2.948	1.08	1.36	1.7661
Penta.	1.88	2.21	2.428	0.57	0.91	1.3761
Hexa.	1.48	1.84	2.058	<0b	0.58	1.0061
Azu.	2.00	2.12	1.9462	1.35	1.42	2.1862
BP	3.65	3.82	4.0962	1.95	2.41	2.8262
DBAn	3.48	3.69	3.9162	1.90	2.30	2.7362
MSD	−0.43	−0.18		−0.74	−0.39
MAD	0.44	0.22		0.74	0.39

${\text{𝑳}}_{\text{𝒃}}\text{𝐬𝐭𝐚𝐭𝐞𝐬}$
	Singlets			Triplets
	BSE	TDA	CCSD(T)a	BSE	TDA	CCSD(T)a
Benz.	5.10	5.15	5.0837	4.39	4.42	4.8637
Naph.	4.30	4.32	$4.19\pm 0.06$ 8,37	3.76	3.79	4.0937
Anth.	3.82	3.79	$3.58\pm 0.01$ 8,62	3.42	3.43	3.5262
Tetra.	3.33	3.37	3.258	3.11	3.18
Penta.	3.10	3.13	3.028	2.79	2.83
Hexa.	2.91	2.98	2.868	b	2.66
Azu.	3.34	3.49	3.6462	2.09	2.19	2.2062
BP	3.57	3.60	3.5062	2.96	3.11	3.3462
DBAn	3.58	3.61	3.5762	3.34	3.43	3.3562
MSD	0.04	0.08		−0.23	−0.17
MAD	0.11	0.12		0.23	0.20

^aCCSD(T) data from the literature.

^bThe BSE Hamiltonian contains negative eigenvalues (read text).