Table 5.

Comparison of the three different approaches to obtain QM/MM hydration free energies with OM2 and the fixed charge force field.

Molecule	Expt. a	MM→QM b	MM→MM’→QM c	NBB d
water	$-6.31$	$-4.4\pm 0.2$	$-4.5\pm 0.2$	$-4.4\pm 0.2$
methanol	$-5.10$	$-2.7\pm 0.1$	$-2.9\pm 0.1$	$-2.8\pm 0.1$
ethanol	$-5.05$	$-3.0\pm 0.3$	$-3.1\pm 0.3$	$-3.1\pm 0.3$
methanethiol	$-1.24$	$-0.7\pm 0.1$	$-0.7\pm 0.1$	$-0.7\pm 0.1$
acetamide	$-9.68$	$-12.7\pm 0.4$	$-12.5\pm 0.4$	$-12.5\pm 0.4$
tetrahydrofuran	$-3.47$	$-3.9\pm 0.5$	$-4.1\pm 0.4$	$-4.2\pm 0.4$
benzene	$-0.86$	$-2.0\pm 0.2$	$-2.1\pm 0.2$	$-2.0\pm 0.2$
phenol	$-6.61$	$-5.0\pm 0.5$	$-5.2\pm 0.3$	$-5.2\pm 0.3$
aniline	$-5.49$	$-5.1\pm 0.5$	$-5.8\pm 0.2$	$-5.8\pm 0.2$
ethane	$1.83$	$1.8\pm 0.1$	$1.8\pm 0.1$	$1.8\pm 0.1$
hexane	$2.48$	$1.7\pm 0.3$	$1.6\pm 0.4$	$1.6\pm 0.4$
cyclohexane	$1.23$	$1.0\pm 0.2$	$0.9\pm 0.2$	$0.9\pm 0.2$
RMSD e		$1.5$	$1.5$	$1.5$
MSD f		$0.3$	$0.2$	$0.2$
$〈SD〉$ g		$0.3$	$0.2$	$0.2$

^a Experimental hydration free energies. ^b QM/MM hydration free energies obtained with the Zwanzig equation based on the CHARMM fixed charge force field. ^c QM/MM hydration free energies obtained with the Zwanzig equation based on a tailored force field that matches the gas phase bond lengths and angles, plus the correction for the free energy change between the original force field and the tailored force field. ^d QM/MM hydration free energies obtained with the NBB equation based on data from both the original force field and the tailored force field. ^e Root mean squared deviation from experimental data. ^f Mean signed deviation from experimental data. ^g Average standard deviation of simulations.