Table 5.

Computed First and Second Deprotonation Energies (kcal/mol) Using HF/6–311+G(d,p) and Signed Errors from the PHO-QM/MM Calculation on Dicarboxylic Acids in the All-Trans Conformation^a

HO2CCH2CB1[H2(CH2)nH2]CB2CH2CO2H	ΔE1		ΔE2
	HF	PHO	HF	PHO
n = 1	−364.7	−5.6	−402.7	− 1.5
n = 2	−357.1	−5.2	−395.3	0.7
n = 3	−356.5	−5.0	−392.5	−0.3
n = 4	−357.8	−5.0	−388.0	−0.9

^aHydrogen atoms and methylene groups in square parentheses are modeled by the CHARMM force field. Deprotonation energies are defined as follows, where R indicates different lengths of methylene groups. $\begin{array}{l}\mathrm{\Delta }{E}_1=E\left({\mathrm{H}\mathrm{O}}_2\mathrm{C}\left[R\right]{\mathrm{C}\mathrm{O}}_2^{-}\right)-E\left({\mathrm{H}\mathrm{O}}_2\mathrm{C}\left[R\right]{\mathrm{C}\mathrm{O}}_2\mathrm{H}\right)\\ \mathrm{\Delta }{E}_2=E{(}^{-}{\mathrm{O}}_2\mathrm{C}\left[R\right]{\mathrm{C}\mathrm{O}}_2^{-})-E\left({\mathrm{H}\mathrm{O}}_2\mathrm{C}\left[R\right]{\mathrm{C}\mathrm{O}}_2^{-}\right)\end{array}$