Calculation of Absolute and Relative Acidities of Substituted Imidazoles in Aqueous Solvent I. A. Topol, G. J. Tawa,* and S. K. Burt Frederick Biomedical Supercomputing Center, SAIC Frederick, NCI Frederick Cancer Research and DeVelopment Center, P.O. Box B, Frederick, Maryland 21702-1201 A. A. Rashin BioChemComp, Inc., 543 Sagamore AVenue, Teaneck, New Jersey 07666 ReceiVed: July 16, 1997; In Final Form: October 10, 1997 X We calculate free energy changes of ionization reactions in aqueous solvent using a self-consistent reaction field method. In the calculations all species are treated as quantum mechanical solutes coupled to a solvent dielectric continuum. We show for a series of substituted imidazole compounds that both absolute and relative pK a values for the deprotonation of nitrogen on the imidazole ring can be obtained with an average absolute deviation of 0.8 units from experiment. This degree of accuracy is possible only if the solutes are treated at the correlated level using either G2 type or density functional theory. Inconsistencies in published experimental free energies of hydration that might undermine the reliability of the calculated absolute pK a values are discussed. 1. Introduction The ability to determine the pK a of the general ionization reaction AH f A - + H + in aqueous environments is important, especially for understanding the specific biological activity of molecules in the human body. 1 The theoretical and technical difficulties associated with accurate determination of absolute and relative pK a values in solvent have been well-documented. 2-11 A major difficulty in determining both absolute and relative pK a ’s is calculating the free energy change associated with deprotonation. The magnitude of this change (defines the pK a ) is very small compared to the absolute free energies of the reactants and products. Hence, precise calculations are neces- sary. Absolute pK a determination is further hindered by the fact that there is no known accurate determination, experimental or otherwise, for the solvation free energy of the proton. 12-14 Recently, however, the possibilities for accurate pK a calcula- tions have improved. One area of improvement which is relevant to small molecules is in the ab initio quantum chemical methods, e.g., density functional 15-20 and G2 21-23 type theories. These methods consistently yield proton affinities and proton- transfer enthalpies within 1-4 kcal/mol of experimental values. Another area of improvement has been in the development of self-consistent reaction field procedures that combine ab initio quantum mechanics with dielectric continuum solvation. 24-35 These procedures can give a remarkably accurate representation of the properties of molecules in aqueous environments. The goal in this current paper is to use these various recent developments in ab initio theory (G2 and DFT) and in solvation (dielectric continuum-SCRF) to create a methodology for calculating accurate absolute and relative pK a ’s for ionization reactions in aqueous solvent. We then revisit the substituted imidazole systems previously studied by one of us 6 to calculate both absolute and relative pK a values for the ionization of the ring nitrogens (See Figure 1). This is represented by where IMH + is an imidazole ring with both nitrogens protonated, IM is imidazole deprotonated at N 3 , and R ) H, NH 2 , CH 3 , or Cl on carbon C 2 of the imidazole ring. We find that both absolute and relative pK a values may be determined on average to within 0.8 pK a units. This type of accuracy is possible only if the solutes are treated at the correlated level using either G2 type or density functional theory. 2. Theory The calculation of pK a for the substituted imidazoles is based on the generalized thermodynamic cycle shown in Figure 2. Analysis of this cycle shows that the pK a for the reaction in aqueous solvent is given by 6 X Abstract published in AdVance ACS Abstracts, November 15, 1997. IMH + -R f IM-R + H + Figure 1. Removal of a proton from nitrogen N3 of a protonated imidazole system with an R group substituent bound to carbon C2 of the imidazole ring. R ) H, NH2, CH3, or Cl. Figure 2. The thermodynamic cycle used to describe the deprotonation process AH + f A + H + in solvent. AH + f A + H + (1) 10075 J. Phys. Chem. A 1997, 101, 10075-10081 S1089-5639(97)02316-5 CCC: $14.00 © 1997 American Chemical Society