Polarizable Charge Equilibration Model for Transition-Metal Elements

The polarizable charge equilibration (PQEq) method was developed to provide a simple but accurate description of the electrostatic interactions and polarization effects in materials. Previously, we optimized four parameters per element for the main group elements. Here, we extend this optimization to the 24 d-block transition-metal (TM) elements, columns 4-11 of the periodic table including Ti-Cu, Zr-Ag, and Hf-Au. We validate the PQEq description for these elements by comparing to interaction energies computed by quantum mechanics (QM). Because many materials applications involving TM are for oxides and other compounds that formally oxidize the metal, we consider a variety of oxidation states in 24 different molecular clusters. In each case, we compare interaction energies and induced fields from QM and PQEq along various directions. We find that the original and J parameters (electronegativity and hardness) related to the ionization of the atom remain valid; however, we find that the atomic radius parameter needs to be close to the experimental ionic radii of the transition metals. This leads to a much higher spring constant to describe the atomic polarizability. We find that these optimized parameters for PQEq provide accurate interaction energies compared to QM with charge distributions that depend in a reasonable way on the coordination number and oxidation states of the transition metals. We expect that this description of the electrostatic interactions for TM will be useful in molecular dynamics simulations of inorganic and organometallic materials.