Table 3.

PDLD/S-LRA energies^a

System	$\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathit{sol}}^{w\to p}(\text{I})$b	pKa(SBH+) b	$\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathit{sol}}^{w\to p}(\text{II})$c	Δ GPTd
water	–	7.0	–	6.5
bR	+2.6	8.9	0.4	6.7
K	+0.3	7.2	− 1.0	5.7
L	+3.8	9.8	0.5	6.2
M1	+4.0	9.9	1.2	7.1
M2	+2.6	8.9	− 3.0	1.3
M2′	+3.7	9.7	− 3.5	1.4
M22	+3.0	9.2	− 4.0	0.5

^aEnergies in kcal/mol, where R82 and D212 are ionized; Asp85 is designated by A in the equations below.

^b $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathit{sol}}^{w\to p}(\text{I})=\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathit{sol}}^{w\to p}({\text{SBH}}^{+},{\text{A}}^{-}\to {\text{SBH}}_{\text{np}},{\text{A}}^{-})$ is the change in the solvation of the Schiff base upon transfer from water to the protein site, calculated when D85 is negatively charged and where the ‘solvation’ energy in the protein includes the interaction with D85. Here ‘np’ and ‘po’ designate nonpolar and polar, respectively. The corresponding pK_a of the Schiff base (when D85 is ionized) is given in pK_a units (pK_a = 7.0+ ΔΔG_sol/1.38).

^c $\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathit{sol}}^{w\to p}(\text{II})=\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathit{sol}}^{w\to p}({\text{SBH}}^{+},{\text{A}}^{-}\to {\text{SBH}}_{\text{np}},{\text{A}}_{\text{np}})$

^dΔG_PT is evaluated as $\mathrm{\Delta }{G}_{PT}^p=\mathrm{\Delta }{G}_{PT}^w(\infty )+\mathrm{\Delta }\mathrm{\Delta }{G}_{\mathit{sol}}^{w\to p}(\text{II})+\mathrm{\Delta }\mathrm{\Delta }{\text{G}}_{\text{sol}}^{\text{w}\to \text{p}}({\text{SB}}_{\text{np}},{\text{AH}}_{\text{np}}\to {\text{SB}}_{\text{po}},{\text{AH}}_{\text{po}})-\mathrm{\Delta }{V}_{QQ}^{w\to p}/20+\mathrm{\Delta }{V}_{QQ}^{\mathit{polar}}/4$. Here, $\mathrm{\Delta }{V}_{QQ}^{ip}$ is the gas-phase charge-charge interaction between SB⁺ and A⁻, and the factor 20 represents the estimate of the dielectric effect for the charge-charge interaction in short distances in water (see related cycle in [111]). $\mathrm{\Delta }{V}_{QQ}^{\mathit{polar}}$ is the gas-phase interaction between the polar pair.