小极化子构型空间：DFT+机器学习

极化子缺陷在材料中普遍存在，在载流子迁移、电荷转移和表面反应等许多过程中发挥着重要作用。作为一类准粒子，极化子一直是人们的研究热点，同时也对物理、化学和材料等不同学科产生了深远的影响。其中，小极化子的波函数在空间上被限制在缺陷周围的几个埃尺寸内，它可以在材料中迁移形成不同的空间分布，这对材料的性质和功能将有很大影响。因此，预测极化子构型是正确解释实验和预测材料行为的关键。目前，针对极化子构型的研究主要依赖于密度泛函理论（DFT）的第一性原理、分子动力学模拟或者手动选择极化子构型，但都存在自身缺陷。例如，第一性原理计算需要采用大型超晶胞来减弱极化子周期映像带来的相互作用，使缺陷引起的极化子建模变得复杂，且对计算资源的要求非常高，从而阻碍了对巨大构型空间的有效探索。

Fig. 1 Schematic representation of the ML model.

来自奥地利维也纳大学物理学院和计算材料科学中心的Cesare Franchini教授领导的团队提出了一种机器学习（ML）方法，来加速搜索和确定基态极化子的构型。他们将ML模型在DFT生成的极化子构型数据库上进行训练，通过设计描述符，对极化子和带电点缺陷之间的相互作用进行建模。作者将这种DFT+ML的研究策略应用到了2个材料系统，即还原的金红石TiO₂(110)和Nb掺杂的SrTiO₃(001)。结果表明，该策略可以正确识别任意载流子密度的基态极化子构型，且该方法不仅能够识别具有静态掺杂/空位的极化子构型，还可以进一步扩展到其他类型、其他材料的缺陷。该方法对于超胞具有任意可拓展性，能够实现大尺度模拟计算。相关论文近期发布于npj Computational Materials 8: 125 (2022)。

Fig. 2 Results of methodology when applied to TiO2(110).

Editorial Summary

Small polaron configurational space: DFT+ Machine learning

Polaron defects are ubiquitous in materials and play an important role in many processes involving carrier mobility, charge transfer and surface reactivity. As a type of quasiparticle, polarons represent an exciting field of research with profound impact in different disciplines ranging from physics to chemistry and material science. Specifically, small polarons, whose wave function is spatially confined within a few Å around their trapping site, can travel through the material forming different spatial distributions (polaron configurations) that have a strong impact on the properties and functionality of the material. Predicting favorable polaron configurations is key to correctly interpret experimental measurements and predict the behaviors of materials. Current research on polaron configurations mainly rely on density function theory (DFT) based first-principles calculations, molecular dynamics (MD) and manual selection, but they all have the intrinsic drawbacks. For instance, the DFT modelling of defects-induced polarons is complicated by the need to adopt large supercells in order to attenuate artificial interactions between periodic images of the polaron, which hampers an efficient exploration of the huge configurational space and makes the calculations computationally very demanding. 

Fig. 3 Collection of results when applying the methodology to SrTiO3(001).

A team led by Prof. Cesare Franchini from the Faculty of Physics and Center for Computational Materials Science, University of Vienna, Austria, proposed a machine-learning (ML) accelerated search that determines the ground state polaronic configuration. They trained the ML model on databases of polaron configurations generated by DFT, and designed descriptors modelling the interactions among polarons and charged point defects. The proposed DFT+ML strategy was applied to two prototypical polaronic materials considering different types of doping: the oxygen-defective rutile TiO₂(110) surface and the Nb-doped perovskite SrTiO₃(001) surface. Results showed that the ML-aided strategy correctly identifies the ground-state polaron configuration for arbitrary carrier density, and the model can be applied to the identification of polaron configurations with static dopant/vacancy patterns, which can be further extended to consider optimized configurations with mobile point defects considering other type of defects and other materials. This approach has the arbitrary scalability with respect to the supercell size, enabling access to large scale simulations.This article was recently published in npj Computational Materials 8,: 125 (2022).

原文Abstract及其翻译

Machine learning for exploring small polaron configurational space (用于探索小极化子构型空间的机器学习)

Viktor C. Birschitzky, Florian Ellinger, Ulrike Diebold, Michele Reticcioli & Cesare Franchini 

Abstract Polaron defects are ubiquitous in materials and play an important role in many processes involving carrier mobility, charge transfer and surface reactivity. Determining small polarons’ spatial distributions is essential to understand materials properties and functionalities. However, the required exploration of the configurational space is computationally demanding when using first principles methods. Here, we propose a machine-learning (ML) accelerated search that determines the ground state polaronic configuration. The ML model is trained on databases of polaron configurations generated by density functional theory (DFT) via molecular dynamics or random sampling. To establish a mapping between configurations and their stability, we designed descriptors modelling the interactions among polarons and charged point defects. We used the DFT+ML protocol to explore the polaron configurational space for two surface-systems, reduced rutile TiO₂(110) and Nb-doped SrTiO₃(001). The ML-aided search proposes additional polaronic configurations and can be utilized to determine optimal polaron distributions at any charge concentration.

摘要极化子缺陷在材料中普遍存在，并在载流子迁移、电荷转移和表面反应等许多过程中发挥着重要作用。确定小极化子的空间分布对于理解材料特性和功能至关重要。然而，当使用第一性原理方法时，构型空间的探索要求很大的计算资源。在本文中，我们提出了一种机器学习(ML)加速搜索来确定基态极化子构型的方法。ML模型在密度泛函理论(DFT)生成的极化子构型数据库上进行训练，DFT通过分子动力学或随机采样实现。为了建立起构型与稳定性之间的映射，我们设计了描述符，用来对极化子和带电点缺陷之间的相互作用进行建模。我们使用DFT+ML的方法，探索了两种表面系统的极化子构型空间，即还原的金红石TiO₂(110)和Nb掺杂的SrTiO₃(001)。ML辅助搜索提出了额外的极化子构型，可用于确定任何电荷浓度下的最佳极化子分布。