. Author manuscript; available in PMC: 2014 Oct 24.

Published in final edited form as: J Phys Chem B. 2013 May 30;117(42):10.1021/jp4020146. doi: 10.1021/jp4020146

Table 3.

Summary of the results obtained with our different studies^a

System	model	path	Δg_PT^‡ + Δg_REF + ΔΔ g_NQM^b	Δg^‡	Δg_1W^‡ − Δg_2W^‡
PO₃⁽⁻⁾ with 1 QM H₂O	PM3/MM	1W PT	19.4+15.5−3.6	31.3	3.3
PO₃⁽⁻⁾ with 2 QM H₂O	PM3/MM	2W PT	15.3+15.5−2.8	28.0
PO₃⁽⁻⁾ with 1 QM H₂O	BLYP//6-31G*/MM	1W PT	6.5+21.0−1.0	26.5	4.1
PO₃⁽⁻⁾ with 2 QM H₂O	BLYP//6-31G*/MM	2W PT	1.4+21.0+0.0	22.4
PO₃⁽⁻⁾ with 1 QM H₂O	B3LYP//6-31G*/MM	1W PT	14+21−2.5	32.5	10.1
PO₃⁽⁻⁾ with 2 QM H₂O	B3LYP//6-31G*/MM	2W PT	1.4+21+0.0	22.4
MHDP with 2 QM H₂O	PM3/MM	2W PT	16.2+15.5−2.9	28.8	0.2
MHDP with 2 QM H₂O	PM3/MM	1W PT	15.9+15.5−2.9	28.5
MHDP with 2 QM H₂O	B3LYP//6-31G*/COSMO	1W PT	15+21−2.7	33.3	9.6
	B3LYP//6-31G*/COSMO	2W PT	3+21−0.3	23.7
	B3LYP//6-31G*/MM	1W PT	12.3+21−2.2	31.1	8.7
	B3LYP//6-31G*/MM	2W PT	1.4+21+0.0	22.4
MDP interpolated^c	B3LYP//6-31G*/MM	2W PT→1W PT			~ 8.0
MDP with Mg²⁺ and 6 QM H₂O	B3LYP//6-31G*/MM	1W PT	18+22.5−3.3	37.2

Energies in kcal/mol.

The NQM corrections were estimated using the EVB approximation of the B3LYP/MM surface of MHDP and the QCP approach (see the main text). We obtained −2.7 kcal/mol for the 1W PT and −0.3 kcal/mol for the 2W PT. The EVB barriers were 15 and 3 for 1W and 2W respectively (better agreement with the BLYP results could be easily obtained but were not needed in view of the interpolation used here). For the other systems we estimated the corrections by interpolating the calculated NQM by the relative height of the classical barrier. That is, we used $Δ Δ g_{NQM} = - 2.7 - (Δ g^{\neq} - 15) (\frac{2.7 - 0.3}{15 - 3})$ , using the results of MHDP as the basis for the linear interpolation.

Here the 2 kcal/mol corrections reflect the estimate the effect of moving from MHDP to MDP since in this case the negative charge of the leaving group increases the pKa of the protonated form of the oxygen that accepts the proton.