Prediction of 4f7-4f65d1 transition energy of Eu2+ in oxides based on first-principles calculations and machine learning

Abstract

In order to establish a method to predict the 4f⁷-4f⁶5d¹ transition energy of Eu²⁺ in oxides, linear regression models were created based on first-principles calculations and machine learning. The model clusters consisting of the central Eu²⁺ and O^2- ions closer than the nearest cation were constructed and the 4f⁷-4f⁶5d¹ absorption energy of Eu²⁺ in these clusters were calculated by first-principles many-electron calculation using the relativistic discrete variational multi-electron (DVME) method. However, the 4f⁷-4f⁶5d¹ absorption energies of Eu²⁺ in oxides calculated by relatively simple first-principles calculations tend to be overestimated by ca. 1.6 eV. In order to improve the accuracy of the prediction, we performed machine learning considering the calculated absorption energy as well as the other electronic and structural parameters as the attributes. As a result, the regression formula to predict the 4f⁷-4f⁶5d¹ absorption energy of Eu²⁺ in oxides has been created by machine learning. The 4f⁷-4f⁶5d¹ absorption energy predicted by this model are in good agreement with the experimental ones. Therefore, accuracy of the prediction was significantly improved compared to the simple first-principles calculations. In a similar way, a predictive model of the 4f⁶5d¹-4f⁷ emission energy of Eu²⁺ in oxides has been also created