Parametrized Models of Aqueous Free Energies of Solvation Based on Pairwise Descreening of Solute Atomic Charges from a Dielectric Medium Gregory D. Hawkins, Christopher J. Cramer,* and Donald G. Truhlar* Department of Chemistry and Supercomputer Institute, UniVersity of Minnesota, Minneapolis, Minnesota 55455-0431 ReceiVed: June 11, 1996; In Final Form: August 21, 1996 X The pairwise descreening approximation provides a rapid computational algorithm for the evaluation of solute shape effects on electrostatic contributions to solvation energies. In this article we show that solvation models based on this algorithm are useful for predicting free energies of solvation across a wide range of solute functionalities, and we present six new general parametrizations of aqueous free energies of solvation based on this approach. The first new model is based on SM2-type atomic surface tensions, the AM1 model for the solute, and Mulliken charges. The next two new models are based on SM5-type surface tensions, either the AM1 or the PM3 model for the solute, and Mulliken charges. The final three models are based on SM5-type atomic surface tensions and are parametrized using the AM1 or the PM3 model for the solute and CM1 charges. The parametrizations are based on experimental data for a set of 219 neutral solute molecules containing a wide range of organic functional groups and the atom types H, C, N, O, F, P, S, Cl, Br, and I and on data for 42 ions containing the same elements. The average errors relative to experiment are slightly better than previous methods, butsmore significantlysthe computational cost is reduced for large molecules, and the methods are well suited to using analytic derivatives. 1. Introduction In previous papers 1-10 we and our co-workers have introduced a new approach to solvation modeling based on the following elements. (1) Electrostatics are modeled by the generalized Born approximation 11-17 with atom-centered charges and dielectric descreening by other parts of the solute calculated from a conformationally sensitive solute-shape molecular model 1,18 based on overlapping atomic spheres. This electrostatic ap- proach is called density descreening (DD) because it is based on integrating an approximation to the free energy density 19 of the polarized dielectric medium over the region not occupied by the descreening solute. The original applications 1-4,18 of DD used a rectangular quadrature rule for the radial integrations about each atomic center. This approximation in calculating the volume integral over the dielectric free energy density caused a systematic error which was compensated by parametrization. 1-4 (As discussed extensively in previous papers, and as is always true in semiempirical work, the parametrization also makes up in part for any systematic physical deficiencies of the model, e.g., for the approximation of the dielectric field in the free energy density by the Coulomb field.) Later work carried out this radial quadrature by a converged trapezoidal rule. 5-10 (2) The atomic charges used in the electrostatic calculations are based on either class II 20 or class IV 21 charge models. (3) First solvation shell effects (i.e., short-range effects) attributable to deviations of the solvation free energies from the predictions of a purely homogeneous continuum model of the solvent are calculated from atomic solvent-accessible surface areas 22,23 with micro-interfacial atomic surface tensions depend- ing on the local nature of the solute. 24 The various functional forms of the surface tensions are denoted by SMx, in particular by the x in SMx, where x may be 1, 1,4 1a, 1,4 2, 2,4 3, 3,4 4, 6-9 or 5. 10 (The functional form of SM3 is the same as SM2.) (4) Solute electronic and geometric relaxation in the presence of the solvent are modeled by including the solute-solvent interactions and the solute-induced changes in the solvent- solvent interactions self-consistently in a solute Fock opera- tor, 1,12-16,25,26 and geometries are optimized in solution. Several general parametrizations of this kind of model have been proposed, 1-10 differing in the model used for the solute internal energy 27,28 and partial charges, 20,21 the quadrature method used for dielectric descreening calculations, 1,4,5,18 and the functional form used for the dependence of the surface tensions on the local nature of the solute. 1,2,6,10 Table 1 summarizes previous parametrizations. (The models for which the reference is “present” are new in this paper and are explained below.) In a recent letter, 29 we introduced a computationally appealing modification of our previous approach in which the three- dimensional quadratures 1,5,19 in the original dielectric descreen- ing calculations are replaced by a sum of pair terms involving scaled atoms, and we presented a preliminary set of parameters for solutes containing C, H, O, and N in aqueous solution. This electrostatic approach, which was inspired by the work of Schaefer and Froemmel, 30 is called pairwise descreening (PD). (The PD approach and the DD approach both utilize the approximation that the electric field is replaced by the Coulomb field in the free energy density.) The parameters required were the same as in the previous SM2 2 and SM2.1 5 models plus C, H, O, and N scale factors for the new step. This was called solvation model 2.2 because it closely resembles SM2 2 and SM2.1. 5 A major component of the widespread usefulness of modern electronic structure theory is associated with the availability of a variety of “levels” differing in cost and reliability. Thus, various combinations of computational choices may be more or less useful depending on the problem being studied. For example, one has various levels of one-electron basis sets and various degrees of the inclusion of electron correlation. The various methods of treating solvation in our own previous work, e.g., SM2 2 and SM4, 6 have not been developed in a level framework. Rather, they reflect different choices in the functional forms used for modeling first solvation shell effects and different algorithms for calculating electrostatic descreening X Abstract published in AdVance ACS Abstracts, November 15, 1996. 19824 J. Phys. Chem. 1996, 100, 19824-19839 S0022-3654(96)01710-8 CCC: $12.00 © 1996 American Chemical Society