極化子缺陷在材料中普遍存在，在載流子遷移、電荷轉(zhuǎn)移和表面反應(yīng)等許多過(guò)程中發(fā)揮著重要作用。作為一類準(zhǔn)粒子，極化子一直是人們的研究熱點(diǎn)，同時(shí)也對(duì)物理、化學(xué)和材料等不同學(xué)科產(chǎn)生了深遠(yuǎn)的影響。其中，小極化子的波函數(shù)在空間上被限制在缺陷周圍的幾個(gè)埃尺寸內(nèi)，它可以在材料中遷移形成不同的空間分布，這對(duì)材料的性質(zhì)和功能將有很大影響。因此，預(yù)測(cè)極化子構(gòu)型是正確解釋實(shí)驗(yàn)和預(yù)測(cè)材料行為的關(guān)鍵。目前，針對(duì)極化子構(gòu)型的研究主要依賴于密度泛函理論（DFT）的第一性原理、分子動(dòng)力學(xué)模擬或者手動(dòng)選擇極化子構(gòu)型，但都存在自身缺陷。例如，第一性原理計(jì)算需要采用大型超晶胞來(lái)減弱極化子周期映像帶來(lái)的相互作用，使缺陷引起的極化子建模變得復(fù)雜，且對(duì)計(jì)算資源的要求非常高，從而阻礙了對(duì)巨大構(gòu)型空間的有效探索。

Fig. 1 Schematic representation of the ML model.

來(lái)自?shī)W地利維也納大學(xué)物理學(xué)院和計(jì)算材料科學(xué)中心的Cesare Franchini教授領(lǐng)導(dǎo)的團(tuán)隊(duì)提出了一種機(jī)器學(xué)習(xí)（ML）方法，來(lái)加速搜索和確定基態(tài)極化子的構(gòu)型。他們將ML模型在DFT生成的極化子構(gòu)型數(shù)據(jù)庫(kù)上進(jìn)行訓(xùn)練，通過(guò)設(shè)計(jì)描述符，對(duì)極化子和帶電點(diǎn)缺陷之間的相互作用進(jìn)行建模。作者將這種DFT+ML的研究策略應(yīng)用到了2個(gè)材料系統(tǒng)，即還原的金紅石TiO₂(110)和Nb摻雜的SrTiO₃(001)。結(jié)果表明，該策略可以正確識(shí)別任意載流子密度的基態(tài)極化子構(gòu)型，且該方法不僅能夠識(shí)別具有靜態(tài)摻雜/空位的極化子構(gòu)型，還可以進(jìn)一步擴(kuò)展到其他類型、其他材料的缺陷。該方法對(duì)于超胞具有任意可拓展性，能夠?qū)崿F(xiàn)大尺度模擬計(jì)算。相關(guān)論文近期發(fā)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 ? 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及其翻譯

Machine learning for exploring small polaron configurational space (用于探索小極化子構(gòu)型空間的機(jī)器學(xué)習(xí))

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.

摘要極化子缺陷在材料中普遍存在，并在載流子遷移、電荷轉(zhuǎn)移和表面反應(yīng)等許多過(guò)程中發(fā)揮著重要作用。確定小極化子的空間分布對(duì)于理解材料特性和功能至關(guān)重要。然而，當(dāng)使用第一性原理方法時(shí)，構(gòu)型空間的探索要求很大的計(jì)算資源。在本文中，我們提出了一種機(jī)器學(xué)習(xí)(ML)加速搜索來(lái)確定基態(tài)極化子構(gòu)型的方法。ML模型在密度泛函理論(DFT)生成的極化子構(gòu)型數(shù)據(jù)庫(kù)上進(jìn)行訓(xùn)練，DFT通過(guò)分子動(dòng)力學(xué)或隨機(jī)采樣實(shí)現(xiàn)。為了建立起構(gòu)型與穩(wěn)定性之間的映射，我們?cè)O(shè)計(jì)了描述符，用來(lái)對(duì)極化子和帶電點(diǎn)缺陷之間的相互作用進(jìn)行建模。我們使用DFT+ML的方法，探索了兩種表面系統(tǒng)的極化子構(gòu)型空間，即還原的金紅石TiO₂(110)和Nb摻雜的SrTiO₃(001)。ML輔助搜索提出了額外的極化子構(gòu)型，可用于確定任何電荷濃度下的最佳極化子分布。