Development of polarizable models for molecular mechanical calculations I: Parameterization of atomic polarizability

In this work, four types of polarizable models have been developed for calculating interactions between atomic charges and induced point dipoles. These include the Applequist, Thole linear, Thole exponential model, and the Thole Tinker-like. The polarizability models have been optimized to reproduce the experimental static molecular polarizabilities obtained from the molecular refraction measurements on a set of 420 molecules reported by Bosque and Sales. We grouped the models into five sets depending on the interaction types, that is, whether the interactions of two atoms that form the bond, bond angle, and dihedral angle are turned off or scaled down. When 1-2 (bonded) and 1-3 (separated by two bonds) interactions are turned off, 1-4 (separated by three bonds) interactions are scaled down, or both, all models including the Applequist model achieved similar performance: the average percentage error (APE) ranges from 1.15 to 1.23%, and the average unsigned error (AUE) ranges from 0.143 to 0.158 ų. When the short-range 1-2, 1-3, and full 1-4 terms are taken into account (set D models), the APE ranges from 1.30 to 1.58% for the three Thole models, whereas the Applequist model (DA) has a significantly larger APE (3.82%). The AUE ranges from 0.166 to 0.196 ų for the three Thole models, compared with 0.446 ų for the Applequist model. Further assessment using the 70-molecule van Duijnen and Swart data set clearly showed that the developed models are both accurate and highly transferable and are in fact have smaller errors than the models developed using this particular data set (set E models). The fact that A, B, and C model sets are notably more accurate than both D and E model sets strongly suggests that the inclusion of 1-2 and 1-3 interactions reduces the transferability and accuracy.