TABLE VII.

Hydration free energies (in kcal/mol) from F-MM-TIP3P (MM simulations with frozen-gas-phase-geometry small solute molecules and TIP3P water molecules) and MESS-E-QM/MM-NBB calculations using five density functionals and the 6–31G* basis set.

molecule	Expt	F-MM-TIP3P	MESS-E-QM/MM NBB
			BLYP	B3LYP	PBE0	M06-2X	ωB97X-D
water	−6.313	−6.19±0.09	−7.08±0.14	−7.72±0.15	−8.12±0.15	−8.37±0.15	−8.31±0.15
methanol	−5.102,31	−4.30±0.10	−3.81±0.06	−4.45±0.04	−4.75±0.04	−5.00±0.04	−5.03±0.04
ethanol	−5.0557	−4.01±0.10	−3.85±0.11	−4.50±0.12	−4.86±0.13	−5.10±0.14	−5.08±0.14
methanethiol	−1.242,31	−0.15±0.08	−3.09±0.33	−3.19±0.33	−3.45±0.38	−3.22±0.34	−3.40±0.36
acetamide	−9.681,56	−8.05±0.07	−11.19±0.21	−12.47±0.23	−13.04±0.25	−13.37±0.27	−13.52±0.26
tetrahydrofuran	−3.4731	−2.38±0.07	−3.29±0.08	−4.12±0.09	−4.39±0.09	−4.68±0.10	−4.75±0.10
benzene	−0.862,31	−0.38±0.12	−0.56±0.12	−0.90±0.12	−1.44±0.12	−1.35±0.12	−1.40±0.12
phenol	−6.612,31	−4.66±0.15	−5.92±0.14	−6.64±0.13	−7.43±0.13	−7.50±0.13	−7.55±0.13
aniline	−5.492,31	−5.58±0.18	−6.82±0.34	−7.43±0.33	−8.44±0.34	−8.26±0.32	−8.29±0.31
ethane	1.832,31	2.23±0.12	2.04±0.12	2.04±0.12	2.01±0.12	2.02±0.12	2.04±0.12
hexane	2.482,31	2.79±0.26	2.16±0.26	2.15±0.26	2.11±0.26	2.12±0.26	2.17±0.26
cyclohexane	1.232,31	1.60±0.11	1.03±0.10	1.02±0.10	0.98±0.10	1.00±0.10	1.02±0.10
MSE		0.77	−0.18	−0.67	−1.05	−1.12	−1.15
RMSE		0.97	1.00	1.25	1.59	1.64	1.69
R2		0.98	0.94	0.95	0.95	0.96	0.95