VBSM: A Solvation Model Based on Valence Bond Theory † Peifeng Su, ‡ Wei Wu,* ,‡ Casey P. Kelly, § Christopher J. Cramer, § and Donald G. Truhlar* ,§ Department of Chemistry, State Key Laboratory of Physical Chemistry of Solid Surfaces, Centre for Theoretical Chemistry, Xiamen UniVersity, Xiamen 36105, P. R. China, and Department of Chemistry and Supercomputing Institute, UniVersity of Minnesota, 207 Pleasant Street S.E., Minneapolis, Minnesota 55455-0431 ReceiVed: December 11, 2007; ReVised Manuscript ReceiVed: February 18, 2008 A new solvation model, called VBSM, is presented. The model combines valence bond (VB) theory with parameters determined for the SM6 solvation model (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). VBSM, like SM6, is based on the generalized Born (GB) approximation for bulk electrostatics and atomic surface tensions to account for cavitation, dispersion, and solvent structure (CDS). The solvation free energy of VBSM includes (i) a self-consistent polarization term obtained by using VB atomic charges in a GB reaction field with a VB self-consistent field procedure that minimizes the total energy of the system with respect to the valence bond orbitals and (ii) a geometry-dependent CDS term to account for deviations from bulk-electrostatic solvation. Test calculations for a few systems show that the liquid-phase partial atomic charges obtained by VBSM are in good agreement with liquid-phase charges obtained by charge model CM4 (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). Free energies of solvation are calculated for two prototype test cases, namely, for the degenerate S N 2 reaction of Cl - with CH 3 Cl in water and for a Menshutkin reaction in water. These calculations show that the VBSM method provides a practical alternative to single-configuration self-consistent field theory for solvent effects in molecules and chemical reactions. 1. Introduction One of the major triumphs of modern physical chemistry has been elucidating the role of solvation effects in chemical structure and reactivity. 1–14 Reaction rate theory and dynamical simulations have elucidated such effects both with explicit 3,5–8,10,12 solvent and with implicit 4,9,11,14 solvent, often coupled to molecular orbital calculations. Valence bond (VB) theory, because it provides a natural way to describe chemical reactions, is very well suited to elucidating solvent effects on reactivity, and it has been employed by a number of workers for this purpose. 6,15–21 In the present article, we describe the incorpora- tion of an implicit universal solvation model, SM6, 22 in the Xiamen Valence Bond (XMVB) package. The XMVB package 23 is an ab initio nonorthogonal VB program. It employs both the spin-free approach 24 and the conventional Slater determinant approach 25 to VB theory and has a variety of capabilities, including VB self-consistent-field 26 (VBSCF), breathing orbitals VB 27,28 (BOVB), the bond-distorted- orbitals (BDO) method, 29 and VB configuration interaction 30 (VBCI). The orbitals used to construct VB configuration-state functions, which are called VB structures, may be localized to a single center or partially (or fully) delocalized. The present article illustrates the new solvation capability of XMVB by calculations that employ the VBSCF and BOVB methods with localized orbitals, which are also called hybrid atomic orbitals, and that employ BDO calculations with partially delocalized orbitals. SM6 treats the electrostatics due to bulk solvent by the generalized Born (GB) 31–37 approximation with self-consistent partial atomic charges. 37,38 The electrostatic free energy of solvation is augmented by terms proportional to the solvent- accessible surface areas 39 of the solute’s atoms times empirical geometry-dependent atomic surface tensions; these terms ac- count for cavitation, dispersion, and solvent-structure effects, where the solvent structure effects include short-range deviations of the electrostatics from the bulk electrostatic model. The empirical nature of the atomic surface tensions results in their also including all other effects not accounted for by the GB treatment of the bulk-solvent electrostatic free energy. The free- energy term associated with the sum of the negative electric polarization term (G P ) and the positive electronic energy term (ΔE E ) is called the bulk electrostatic free energy of solvation, ΔG EP , and the free-energy term associated with the atomic surface tensions is called G CDS (cavitation, dispersion, and solvent structure). We will consider two reactions as examples in this paper. First, we consider the Menshutkin reaction of ammonia with chloromethane in aqueous solution. Then, we consider the degenerate S N 2 reaction of chloride with chloromethane in aqueous solution. Section 2 presents the method, Section 3 presents the applications, and Section 4 presents the discussion. Concluding remarks are in Section 5. 2. Methods In the present paper, we make the assumption (which is usually quite reasonable) that the free energy of solvation may be calculated by using the gas-phase geometry in both the gas phase and solution. In the context of kinetics, this has been called the separable-equilibrium-solvation approximation. The standard- state solvation energy when the standard-state concentration is the same (e.g., 1 mol/L) in the gas phase and in the solution is then approximated as † Part of the “Sason S. Shaik Festschrift”. * Corresponding authors. E-mail: truhlar@umn.edu. ‡ Xiamen University. § University of Minnesota. J. Phys. Chem. A XXXX, xxx, 000 A 10.1021/jp711655k CCC: $40.75  XXXX American Chemical Society Published on Web 08/01/2008