Method for Slater-Type Density Fitting for Intermolecular Electrostatic Interactions with Charge Overlap. I. the Model

The effects of charge overlap, or charge penetration, are neglected in most force fields and interaction terms in QM/MM methods. The effects are however significant at intermolecular distances near the van der Waals minimum. In the present study, we propose a method to evaluate the intermolecular Coloumb interaction using Slater-type functions, thus explicitly modeling the charge overlap. The computational cost of the method is low, which allows it to be used in large systems with most force fields as well as in QM/MM schemes. The charge distribution is modeled as a distributed multipole expansion up to quadrupole and Slater-type functions of angular momentum up to L = 1. The exponents of the Slater-type functions are obtained using a divide-and-conquer method to avoid the curse of dimensionality that otherwise is present for large nonlinear optimizations. A Levenberg-Marquardt algorithm is applied in the fitting process. A set of parameters is obtained for each molecule, and the process is fully automated. Calculations have been performed in the carbon monoxide and the water dimers to illustrate the model. Results show a very good accuracy of the model with relative errors in the electrostatic potential lower than 3% over all reasonable separations. At very short distances where the charge overlaps is the most significant, errors are lower than 8% and lower than 3.5% at distances near the van der Waals minimum.