Table 1.

Oxidation free energies of metal complexes calculated with direct QM∕MM MD and QM∕MM-MFEP methods. Units are in eV.

		ΔG	ΔGvib	ΔG+ΔGvib	ΔGZPE	ΔGabs	$\Delta G_{\mathrm{abs}}^{\mathrm{expt}}$
$\mathrm{Fe}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6^{2∕3+}$	Direct	⋯	⋯	5.82a	⋯	⋯	5.0∕5.6d
	MFEP	5.70	0.04	5.74b	0.10	5.84c
$\mathrm{Ru}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6^{2∕3+}$	Direct	⋯	⋯	5.14a	⋯	⋯	4.4∕5.1d
	MFEP	5.01	0.03	5.04b	0.06	5.10c

^aValues reported in Ref. 33, which already included the free energy contributions from vibrational dynamics.

^bIn order to compare with the results using the direct QM∕MM MD method, the vibrational contributions ΔG_vib are estimated and added to the results for QM∕MM-MFEP method.

^cΔG_abs are the absolute redox free energies, included the corrections from both vibrational dynamics ΔG_vib and zero-point energies ΔG_ZPE. The results using direct QM∕MM MD method did not include ΔG_ZPE.

^dThe experimental absolute free energies are obtained by taking absolute oxidation free energy for SHE to be from 4.2 to 4.84 eV (Refs. ⁷³, ⁷⁴, ⁷⁵, ⁷⁶, ⁷⁷).