Table 2.

Free energy barriers (ΔG_av in kcal/mol) calculated for three competing reaction pathways of the cocaine hydrolysis.

Reaction pathway	ΔGav(aq) (SRS)a	ΔGav(aq) (pH 7.4)b	ΔΔGavc	ΔGav(antibody) (pH 7.4)d
cocaine + HO− → TS1ben-Re	16.9	25.9	−6.33 (−5.93)	19.6
cocaine + HO− → TS1ben-Si	19.6	28.6	−4.64	24.0
cocaine + HO− → TS1met	11.1	20.1	4.18	24.3

^aFree energy barriers determined by the first-principles electronic structure calculations (ref. ¹⁹) for the cocaine hydrolysis in water using the standard reference state (SRS), i.e. 1 M, for all molecular species, including [HO⁻] = 1 M, at T = 298.15 K.

^bFree energy barriers determined for the cocaine hydrolysis in water at the physiologic pH (7.4) at T = 298.15 K. The free energy barrier shift from the standard reference state of [HO⁻] = 1 M to pH 7.4 is 9.0 kcal/mol when T = 298.15 K.

^cThe free energy barrier shift from the cocaine hydrolysis in water to the antibody-catalyzed cocaine hydrolysis (determined by using the data in Table 1). The value −5.93 kcal/mol in parenthesis was the free energy barrier shift derived from the experimental rate acceleration (k_cat/k₀ = 23,000) using Eq.(11).

^dFree energy barriers calculated for the antibody-catalyzed cocaine hydrolysis at the physiologic pH (7.4) at T = 298.15 K.