Quantum-Accurate Modeling of Ferroelectric Phase Transition in Perovskites from Message-Passing Neural Networks

Abstract

Graph-based message-passing neural networks (MPNNs) have been proposed to facilitate computational research on materials at the atomic scale, which represent the chemical structure as an indirect graph and incorporate the message-passing scheme to learn the interaction between atoms. Here, we employ the MPNN framework to investigate the temperature-dependent structural phase transitions of perovskites. We take two prototypical ferroelectric perovskites, BaTiO3 and PbTiO3, as examples to demonstrate the application of this approach. Our results show that well-trained MPNN models achieve a similar level of accuracy as density functional theory (DFT) calculations in terms of both energy and force, with an accuracy of a few meV per atom. This level of accuracy fulfills the requirement for investigating structural changes. By integrating MPNN models as calculators in molecular dynamics simulations, we investigated the structural phase transitions of the two compounds and reproduced their phase transition sequences. The simulated phase transition temperatures and lattice parameters are comparable to the experimental or DFT results. Moreover, we examined the influence of exchange–correlation functionals on the trained MPNN models. This study demonstrates that MPNN, which can serve as a universal energy model, presents an appealing approach to treating the structural properties of perovskites.

Modeling ferroelectric phase transitions with graph convolutional neural networks

“…神经网络 [16][17][18][19][20] 具有显著的特点, 能够很好地用于 对材料的势能面和力场进行建模. 图卷积神经网络 将原子间的几何关系映射成一张无向图, 图里的结 点表示原子, 边表示具有相互作用的原子对, 同时 对结点和边赋予相应的特征.…”

“…这些因 素使得卤族钙钛矿的理论建模更加复杂. 在以往的 工作中, Chen等 [73] 利用有效哈密顿量法对CsPbI 3 的相变和碘八面体转动进行模拟, Jinnouchi等 [74] 利用高斯核回归 [75] 方法对有机卤族钙钛矿Methy- 序-无序性和离子迁移等, 正如我们之前的工作 [18] 所展示的.…”

“…对于铁电材料建模的一类常用方法是有效哈 密顿量方法, 自有效哈密顿量提出的近三十年来, 已成功应用于许多钙钛矿铁电材料的静态和动态 性质的研究中 [76,77] 的物理概念提取铁电体势能面的关键特征, 然而, 由于单硫族化合物独特的电子特性, 存在介于共价 键和离子键(或金属键)之间的metavalent键 [18,78] ,…”

“…其次, 对于卤族钙钛矿而言, 八面体的转动会 导致细微的能量变化, 其势函数更加复杂, 难以通 过传统的方法进行精确建模 [18,78] . 本文通过和结构有关的序参量来表征体系的 结构变化, 进而确定体系的相变温度.…”

“…因此, 对于基于图 卷积神经网络的分子动力学模拟来说, 直接通过分 析体系结构的变化(如晶格常数、原子位移)来判 断相变更为方便. 以往的工作 [18,19] 表明, 通过分析 体系结构的变化来判断相变是可靠的.…”