. 2018 Oct 19;23(10):2695. doi: 10.3390/molecules23102695

Table 3.

Hydration free energies of QM/MM with different QM methods based on trajectories of the CHARMM Drude force field.

Molecule	Expt. ^a	OM2	HF	MP2	M06-2X	B3LYP	BLYP	AM1
water	$- 6.31$	$- 2.8 \pm 0.2$	$- 6.3 \pm 0.2$	$- 4.4 \pm 0.2$	$- 5.4 \pm 0.2$	$- 4.6 \pm 0.2$	$- 3.2 \pm 0.2$	$- 1.8 \pm 0.2$
methanol	$- 5.10$	$- 3.2 \pm 0.2$	$- 4.7 \pm 0.3$	$- 4.6 \pm 0.4$	$- 4.3 \pm 0.2$	$- 3.7 \pm 0.2$	$- 3.3 \pm 0.3$	$- 1.7 \pm 0.2$
ethanol	$- 5.05$	$- 2.9 \pm 0.4$	$- 3.5 \pm 0.4$	$- 3.6 \pm 0.2$	$- 3.2 \pm 0.3$	$- 2.7 \pm 0.2$	$- 2.3 \pm 0.4$	$- 0.7 \pm 0.5$
methanethiol	$- 1.24$	$- 1.0 \pm 0.2$	$- 2.8 \pm 0.4$	$- 1.8 \pm 0.2$	$- 2.0 \pm 0.3$	$- 1.4 \pm 0.3$	$- 0.1 \pm 0.4$	$- 2.0 \pm 0.2$
acetamide	$- 9.68$	$- 7.5 \pm 2.7$	$- 2.6 \pm 2.2$	$- 2.8 \pm 1.3$	$- 1.9 \pm 1.6$	$- 1.5 \pm 1.6$	$- 0.6 \pm 1.7$	$- 3.0 \pm 2.9$
tetrahydrofuran	$- 3.47$	$- 3.8 \pm 0.5$	$- 2.6 \pm 0.3$	$- 2.3 \pm 0.2$	$- 1.6 \pm 0.2$	$- 1.2 \pm 0.2$	$- 0.5 \pm 0.3$	$- 1.6 \pm 0.5$
benzene	$- 0.86$	$- 2.3 \pm 0.3$	$- 1.1 \pm 0.4$	$- 0.9 \pm 0.2$	$- 0.7 \pm 0.3$	$- 0.4 \pm 0.2$	$0.0 \pm 0.2$	$- 0.3 \pm 0.3$
phenol	$- 6.61$	$- 8.1 \pm 0.8$	$- 9.9 \pm 1.2$	$- 10.4 \pm 0.4$	$- 9.5 \pm 0.9$	$- 8.8 \pm 0.7$	$- 8.4 \pm 0.4$	$- 3.8 \pm 0.4$
aniline	$- 5.49$	$- 5.8 \pm 0.6$	$- 7.4 \pm 1.1$	$- 7.1 \pm 0.4$	$- 7.1 \pm 0.7$	$- 6.1 \pm 0.5$	$- 5.5 \pm 0.5$	$- 3.2 \pm 0.5$
ethane	$1.83$	$1.9 \pm 0.1$	$2.2 \pm 0.2$	$2.4 \pm 0.2$	$2.3 \pm 0.2$	$2.4 \pm 0.2$	$2.9 \pm 0.2$	$2.5 \pm 0.2$
hexane	$2.48$	$2.4 \pm 0.3$	$2.5 \pm 0.6$	$2.7 \pm 0.3$	$2.9 \pm 0.3$	$2.9 \pm 0.3$	$3.3 \pm 0.3$	$2.7 \pm 0.3$
cyclohexane	$1.23$	$1.8 \pm 0.3$	$1.9 \pm 0.3$	$2.0 \pm 0.2$	$2.1 \pm 0.2$	$2.2 \pm 0.2$	$2.5 \pm 0.2$	$1.9 \pm 0.3$
RMSD ^b		$1.6$	$2.4$	$2.5$	$2.6$	$2.7$	$3.2$	$3.2$
MSD ^c		$0.6$	$0.3$	$0.6$	$0.8$	$1.3$	$1.9$	$2.3$
R $^{2}$ ^d		$0.85$	$0.63$	$0.64$	$0.61$	$0.61$	$0.57$	$0.78$
RMSD *		$1.4$	$1.4$	$1.5$	$1.3$	$1.3$	$1.7$	$2.2$
MSD *		$0.3$	$- 0.5$	$- 0.1$	$0.0$	$0.5$	$1.1$	$1.6$
R $^{2}$ *		$0.82$	$0.92$	$0.88$	$0.90$	$0.90$	$0.87$	$0.84$

^a Experimental hydration free energies. ^b Root mean squared deviation from experimental data. ^c Mean signed deviation from experimental data. ^d Square of the Pearson correlation coefficient between calculated and experimental hydration free energies. * marks results that exclude ethanol and acetamide due to the associated high uncertainties.