Automatic structural elucidation of vacancies in materials by active learning

Maicon Pierre Lourenço; Lizandra Barrios Herrera; Jiří Hostaš; Patrizia Calaminici; Andreas M Köster; Alain Tchagang; Dennis R Salahub

doi:10.1039/d2cp02585j

Automatic structural elucidation of vacancies in materials by active learning

Phys Chem Chem Phys. 2022 Oct 27;24(41):25227-25239. doi: 10.1039/d2cp02585j.

Authors

Maicon Pierre Lourenço¹, Lizandra Barrios Herrera², Jiří Hostaš², Patrizia Calaminici³, Andreas M Köster³, Alain Tchagang⁴, Dennis R Salahub²

Affiliations

¹ Departamento de Química e Física - Centro de Ciências Exatas, Naturais e da Saúde - CCENS - Universidade Federal do Espírito Santo, 29500-000, Alegre, Espírito Santo, Brazil. maiconpl01@gmail.com.
² Department of Chemistry, Department of Physics and Astronomy, CMS Centre for Molecular Simulation, IQST Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada.
³ Departamento de Química, CINVESTAV, Av. Instituto Politécnico Nacional 2508, AP 14-740, México D.F. 07000, Mexico.
⁴ Digital Technologies Research Centre, National Research Council of Canada, 1200 Montréal Road, Ottawa, ON, K1A 0R6, Canada.

PMID: 36222106
DOI: 10.1039/d2cp02585j

Abstract

Finding the optimum structures of non-stoichiometric or berthollide materials, such as (1D, 2D, 3D) materials or nanoparticles (0D), is challenging due to the huge chemical/structural search space. Computational methods coupled with global optimization algorithms have been used successfully for this purpose. In this work, we have developed an artificial intelligence method based on active learning (AL) or Bayesian optimization for the automatic structural elucidation of vacancies in solids and nanoparticles. AL uses machine learning regression algorithms and their uncertainties to take decisions (from a policy) on the next unexplored structures to be computed, increasing the probability of finding the global minimum with few calculations. The methodology allows an accurate and automated structural elucidation for vacancies, which are common in non-stoichiometric (berthollide) materials, helping to understand chemical processes in catalysis and environmental sciences, for instance. The AL vacancies method was implemented in the quantum machine learning software/agent for material design and discovery (QMLMaterial). Also, two additional acquisition functions for decision making were implemented, besides the expected improvement (EI): the lower confidence bound (LCB) and the probability of improvement (PI). The new software was applied for the automatic structural search for graphite (C₃₆) with 3 (C_36-3) and 4 (C_36-4) carbon vacancies and C₆₀ (C_60-4) fullerene with 4 carbon vacancies. DFTB calculations were used to build the complex search surfaces with reasonably low computational cost. Furthermore, with the AL method for vacancies, it was possible to elucidate the optimum oxygen vacancy distribution in CaTiO₃ perovskite by DFT, where a semiconductor behavior results from oxygen vacancies. Throughout the work, a Gaussian process with its uncertainty was employed in the AL framework using different acquisition functions (EI, LCB and PI), and taking into account different descriptors: Ewald sum matrix and sine matrix. Finally, the performance of the proposed AL method was compared to random search and genetic algorithm.