Crystal Structure Prediction in Orthorhombic ABO₃ Perovskites by Multiple Linear Regression and Artificial Neural Networks

Slobotka Aleksovska*, Sandra Dimitrovska and Igor Kuzmanovski
Institute of Chemistry, Faculty of Natural Sciences and Mathematics,
University “Sts. Cyril and Methodius” Skopje, Republic of Macedonia
E-mail: bote@iunona.pmf.ukim.edu.mk; tel: ++389 02 3117055 ext. 910; fax: ++389 02 3226865

Abstract
The unit cell parameters and the fractional atomic coordinates of the orthorhombic perovskites of ABO₃ type are expressed as a function of the effective ionic radii of the constituents using two approaches: multiple linear regression and artificial neural networks. For this purpose, 46 orthorhombic perovskites of GdFeO₃ type (spa ce group Pnma) with accurately refined structures are included in the analysis: 41 in calibration set, and 5 in test set. The predictive strength of the proposed model is very high. This is shown by the values of the coefficients of correlation (R_adj)² which are higher than 0.9 for all dependent variables and by the agreement between the actual and predicted values for the dependent variables, obtained by both methods. This simple mathematical model can be used: to predict the crystal structure of members in this series; as starting model for crystal structure refinement; to test the actual crystallographic data of ABO₃ perovskites.

Keywords: Perovskites, crystal structures, artificial neural networks, multiple linear regression.