Atomic level anisotropy in the electrostatic modeling of lone pairs for a polarizable force field based on the classical Drude oscillator

Electron pairs in the valence shell of an atom that do not participate in the bonding of a molecule ("lone pairs") give rise to a concentrated electron density away from the atom center. To account for the asymmetry in the electron charge density that arises from lone pairs, an electrostatic model is developed that is parametrically anisotropic at the atomic level. The model uses virtual interaction sites with partial charges that are associated but not coincident with the nuclei. In addition, the model incorporates anisotropic atomic polarizabilities. The protocol previously outlined in Anisimov et al. [J. Chem. Theory Comput. 2005, 1, 153] for parametrizing the electrostatic potential energy of a polarizable force field using classical Drude oscillators is extended to incorporate additional lone pair parameters. To probe the electrostatic environment around the lone pairs, the static (molecule alone) and perturbed (molecule in the presence of a test charge) electrostatic potential (ESP) are evaluated and compared to high level quantum mechanical (QM) electronic structure calculations. The parametrization of the virtual sites relies on data from the QM static ESP. The contribution to the perturbed ESP from the electronic polarization of the molecule is used to resolve the components of the atomic polarizability tensor. The model is tested in the case of four molecules: methanol, acetone, methylamine, and pyridine. Interaction energies with water and sodium are used to assess the accuracy of the model. The results are compared with simpler models placing all the charge on the nuclei as well as using only isotropic atomic polarizabilities. Analysis shows that the addition of virtual sites reduces the average error relative to the QM calculations. In contrast to models with atom centered charges, the virtual site models correctly predict the minimum energy conformation for acetone and methanol, with water, to be closely coordinated with the lone pair direction. Furthermore, addition of anisotropic atomic polarizabilities to the virtual site model allows for precise fitting to the local perturbed QM ESP.