Modeling Polarization through Induced Atomic Charges Gyo 1 rgy G. Ferenczy* ,² and Christopher A. Reynolds ‡ Department of Inorganic Chemistry and Department of Chemical Information Technology, Budapest UniVersity of Technology and Economics, Szent Gelle ´ rt te ´ r 4, H-1111 Budapest, Hungary, and Department of Biological Sciences, UniVersity of Essex, WiVenhoe Park, Colchester, Essex CO4 3SQ, United Kingdom ReceiVed: May 10, 2001; In Final Form: September 25, 2001 A distributed atomic charge model to account for intermolecular polarization is presented. The model is an approximation to the method of calculating induced dipoles from atomic polarizabilities. In this model, induced atomic dipoles are represented by charges on the atom itself plus neighboring atomic sites. The model therefore avoids the evaluation of charge-dipole and dipole-dipole interactions. Formulas for calculating the induced atomic charges are presented and the approximations involved are discussed. Numerical examples show that our model recovers a substantial part of the polarization energy while the gain in computational efficiency with respect to the induced dipole model is 2-4-fold, being in the upper range when gradients are also evaluated. The use of moments induced by permanent charges only, i.e., calculated without iteration, was found to give an effective approximation with a gain in computational efficiency of up to 7-fold. Analysis of the numerical discrepancies between the induced charge and the induced dipole model showed that the induced atomic charge model of polarization has a 10-40% error for close molecular interactions with the error at the lower end for water-water interactions at equilibrium geometries and it gives an improving approximation with increasing intermolecular separations. The ability of the induced charge model to improve the nonpolarizable TIP3P water model was investigated by comparing the properties of liquid water (e.g., density, diffusion coefficient, radial distribution function) predicted by molecular dynamics simulations. A noniterative polarization model combined with parameters consistent with experimental data (geometry, vacuum dipole moment, polarizability) and with adjusted Lennard-Jones parameters was shown to give properties in good agreement with experimental data. This result suggests that an effective polarizable force field can be built by combining the induced charge model with further energy components. It is argued that the induced charge model represents a significant step toward the best available distributed charge approximation to the induced dipole model and so conclusions drawn for the performance of the model bear significance to other distributed charge models. 1. Introduction Classical force fields used in Monte Carlo and molecular dynamics simulations typically employ effective pair potentials that include many-body effects in an average way. The increasing accuracy resulting from the development of current force fields raises the demand for the explicit inclusion of these many-body effects, particularly since the growth in computer power makes such approaches feasible. Here we present a simple model in which induced atomic dipoles are represented by charges on the atom itself plus neighboring atomic sites. Van Gunsteren and Berendsen 1 predicted that the inclusion of polarization in force fields would become possible by the end of the 1990s, and indeed, considerable advances in this field have been achieved. A rigorous theory for describing polariza- tion has been given by Stone, 2 whose method gives accurate induced moments for small clusters of molecules 3,4 but is currently impractical for large biomolecular systems. A simpler approach assigns solely isotropic dipole polarizabilities to atoms and calculates the energy of the system from permanent point charges and induced point dipoles. The classical contribution by Vesely 5 introduces the theory required to perform the molecular dynamics simulations on systems with polarizable point dipoles. Several related models, primarily for water, have since been reported. 6-14 Rick and Berne have developed a different scheme 15 that accounts for polarization by atomic charges whose values depend on the molecular conformation and Coulomb interactions with the environment. This fluctuating charge model avoids the use of higher rank multipole moments (e.g., dipoles), and the electronegativity equalization theorem- based evaluation of the charges renders the calculation very fast. An extension of the method 16 introduces fluctuating dipoles, thus making the method capable of describing out of plane polarization of planar molecules. In the related chemical potential equalization model 17-19 it is also possible to represent the charge distribution by point charges only. Drude oscillator models for polarization 20 also use atomic charges, and the effect of polarization is accounted for by changes in the position of the charges; 21 such approaches are widely used in solid-state simulations. In the present contribution, a novel method for describing polarization in classical force fields is described. This induced charge method invokes point charges only and is an approxima- tion to the polarization model based on induced point dipoles. The point charges depend on the environment and in this sense our induced charge method is related to the fluctuating charge * To whom correspondence should be addressed. ² Budapest University of Technology and Economics. Present address: Chinoin Rt., To ´ 1-5, H-1045 Budapest, Hungary. ‡ University of Essex. 11470 J. Phys. Chem. A 2001, 105, 11470-11479 10.1021/jp0117967 CCC: $20.00 © 2001 American Chemical Society Published on Web 11/28/2001