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.

可极化电荷均衡（polarizable charge equilibration, PQEq）方法旨在为材料中的静电相互作用与极化效应提供简洁且精准的描述。此前，我们已针对主族元素完成了每个元素的四项参数优化。本研究将该参数优化流程拓展至元素周期表第4至11族的24种d区过渡金属（transition-metal, TM）元素，涵盖Ti至Cu、Zr至Ag以及Hf至Au的元素范围。我们通过将PQEq方法得到的相互作用能与量子力学（quantum mechanics, QM）计算结果进行对比，对上述过渡金属的PQEq描述效果开展验证。鉴于诸多涉及过渡金属的材料应用场景均为金属被正式氧化的氧化物及其他化合物，我们在24种不同的分子团簇中考虑了多种氧化态。针对每种情况，我们均对比了不同方向上QM与PQEq方法得到的相互作用能及感应电场。研究发现，与原子电离相关的原始χ和J参数（即电负性与硬度）依然有效；但我们发现原子半径参数需要与过渡金属的实验离子半径保持接近，这使得描述原子极化率的弹簧常数大幅升高。经上述优化后的PQEq参数所得到的相互作用能与QM结果吻合度较高，且电荷分布随过渡金属的配位数与氧化态呈现合理的变化规律。我们预期，这种针对过渡金属的静电相互作用描述方法，将在无机与有机金属材料的分子动力学模拟中具备应用价值。