**Crystal Structure Prediction in Orthorhombic ABO _{3}
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 ABO_{3} 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 GdFeO_{3} 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 ABO_{3}
perovskites.

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