The electronegativity equalization method and the split charge equilibration applied to organic systems: Parametrization, validation, and comparison

An extensive benchmark of the electronegativity equalization method (EEM) and the split charge equilibration (SQE) model on a very diverse set of organic molecules is presented. These models efficiently compute atomic partial charges and are used in the development of polarizable force fields. The predicted partial charges that depend on empirical parameters are calibrated to reproduce results from quantum mechanical calculations. Recently, SQE is presented as an extension of the EEM to obtain the correct size dependence of the molecular polarizability. In this work, 12 parametrization protocols are applied to each model and the optimal parameters are benchmarked systematically. The training data for the empirical parameters comprise of MP2/Aug-CC-pVDZ calculations on 500 organic molecules containing the elements H, C, N, O, F, S, Cl, and Br. These molecules have been selected by an ingenious and autonomous protocol from an initial set of almost 500 000 small organic molecules. It is clear that the SQE model outperforms the EEM in all benchmark assessments. When using Hirshfeld-I charges for the calibration, the SQE model optimally reproduces the molecular electrostatic potential from the ab initio calculations. Applications on chain molecules, i.e., alkanes, alkenes, and alpha alanine helices, confirm that the EEM gives rise to a divergent behavior for the polarizability, while the SQE model shows the correct trends. We conclude that the SQE model is an essential component of a polarizable force field, showing several advantages over the original EEM.