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 χ 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.