TABLE III.

Tautomerization energies from ωB97X/6-31G* and model errors (kcal/mol) for the artificially expanded genetic information system (AEGIS) tautomer dataset.^a

		QM/Δ-MLP or MLP			DFTB			NDDO
	ωB97X	QDπ	AIQM1	ANI-2x	GFN2	DFTB3	ChIMES	ODM2	D3H4X	PM7
Tautomer pair	ΔE	Err	Err	Err	Err	Err	Err	Err	Err	Err
1b–1a	2.43	‒0.36	‒1.07	‒1.35	‒2.75*	‒6.25*	‒2.38	3.48	6.60	2.67
1c–1b	17.39	0.36	0.40	0.83	‒0.72	2.68	2.58	‒6.65	‒11.01	‒7.46
2b–2a	‒5.41	‒1.12	0.13	‒0.29	2.81	‒4.39	‒1.02	6.31*	12.62*	8.85*
2c–2b	4.95	1.22	‒0.74	2.30	‒2.61	4.74	1.54	‒7.50*	‒14.46*	‒10.85*
3b–3a	‒6.32	‒0.28	‒0.16	0.89	3.53	‒3.90	‒0.77	6.39*	12.95*	9.24*
3c–3b	4.05	‒0.15	‒0.15	3.05	‒2.48	4.44	1.02	‒7.07*	‒13.56*	‒9.97*
4b–4a	‒6.81	0.69	0.37	0.58	3.60	‒4.06	‒0.94	7.06*	13.49*	10.01*
4c–4b	2.76	0.06	‒0.82	1.14	‒1.90	5.47	1.98	‒6.48*	‒12.55*	‒8.93*
5b–5a	‒6.12	‒0.41	0.66	‒0.28	3.07	‒4.60	‒1.43	7.34*	13.36*	9.71*
5c–5b	3.23	‒0.57	‒0.57	0.49	‒1.92	5.97	2.56	‒6.59*	‒13.03*	‒9.41*
6b–6a	12.24	‒0.01	‒0.20	‒2.56	‒1.85	‒3.22	‒3.63	3.76	‒4.94	‒0.92
6c–6b	20.12	‒0.10	‒0.35	2.63	‒5.80	‒3.10	‒0.26	‒4.60	‒8.47	‒8.48
7b–7a	20.15	1.40	‒0.63	‒1.39	‒4.87	‒5.71	‒5.32	5.63	‒0.67	‒0.43
7c–7b	‒19.17	‒0.96	0.94	‒0.22	4.79	6.93	1.64	‒0.25	‒0.01	2.86
8b–8a	21.32	0.84	‒1.79	‒0.08	‒5.43	‒10.25	‒2.12	1.57	3.71	1.24
8c–8b	‒6.16	0.31	‒0.43	1.10	‒1.52	0.18	1.28	‒1.34	‒3.27	‒3.05
9b–9a	5.42	0.77	‒0.89	‒0.45	‒5.39	‒7.41*	‒4.94	4.64	‒3.31	‒3.53
9c–9b	‒10.02	‒0.74	0.40	0.29	3.20	6.10	1.29	‒0.76	‒1.38	1.91
10b–10a	7.95	2.11	‒0.57	‒2.50	‒1.83	0.77	‒3.26	3.28	‒3.84	‒1.36
10c–10b	22.20	‒2.92	‒2.92	‒5.08	‒6.40	‒15.21	0.78	‒9.14	‒11.36	‒9.26
10d–10c	4.01	0.04	1.54	2.86	‒1.71	5.13	‒3.27	9.90	12.36	7.71
11b–11a	‒0.86	‒0.63	‒0.19	‒0.36	‒0.47	‒4.04	‒0.58	3.42*	7.69*	4.68*
11c–11b	24.35	‒0.84	‒0.90	‒4.13	‒4.19	‒5.43	‒6.39	1.67	‒8.47	‒6.13
12b–12a	22.00	0.41	‒1.80	0.14	‒5.51	‒10.37	‒2.16	1.34	3.73	1.31
12c–12b	‒7.79	0.54	0.54	0.29	‒0.62	0.87	1.78	‒0.98	‒2.70	‒2.59
maE	…	0.71	0.77	1.41	3.16	5.25	2.20	4.69	7.98	5.70
rmsE	…	0.97	1.00	1.94	3.59	6.12	2.67	5.42	9.28	6.72

^a Models and datasets are described in Sec. II. Illustrations of each of the tautomerization reactions are provided in Fig. 7. Errors corresponding to wrong prediction of more stable tautomer are indicated by an asterisk (*).