Extending Shannon's ionic radii database using machine learning

In computational material design, ionic radius is one of the most important physical parameters used to predict material properties. Motivated by the progress in computational materials science and material informatics, we extend the renowned Shannon's table from 475 ions to 987 ions. Accordingly, a rigorous machine learning (ML) approach is employed to extend the ionic radii table using all possible combinations of oxidation states (OS) and coordination numbers (CN) available in crystallographic repositories. An ionic-radius regression model for Shannon's database is developed as a function of the period number, the valence orbital configuration, OS, CN, and ionization potential. In the Gaussian process regression (GPR) model, the reached $R^2$ accuracy is 99% while the root mean square error of radii is 0.0332 Å. The optimized GPR model is then employed for predicting a new set of ionic radii for uncommon combinations of OS and CN extracted by harnessing crystal structures from materials project databases. The generated data are consolidated with the reputable Shannon's data and are made available online in a database repository.

Figure 1

Workflow for extending the Shannon's ionic radii database using machine learning and data harvesting. (a) Ionic radii machine learning model for the existing Shannon's database using physically guided features. (b) Collection of missing ions data from material repositories and its comparison with Shannon's database in terms of CN: 1–14. (c) Consolidation of both Shannon table and missing species' ionic radii databases from predicted values using missing ions' data and regression model.

Figure 2

Data comparison for the chemical environment in terms of oxidation state (OS) and coordination number (CN) from Shannon and the present ML work. (a) Regions for features OS and CN covered by Shannon and ML work. (b) CN: 1–14 present in both the databases considered. (c) CN present in each OS analyzed with an inset showing total Shannon and ML work data. In all these graphs, ML work consists of 512 unique ionic information harvested.

Figure 3

Results from regression analysis for Shannon's data (testing set) using a feature vector containing period number, CN, OS, outer shell valence electrons in orbitals $s, p, d, f$, and $exp(-E_{\text{IP}})$ for ionic radius prediction. (a) Best performing Gaussian process regression (GPR) model for predicting $R_i$ with an inset showing absolute deviation error (true $R_i$ predicted $R_i$), (b) rank correlation coefficient for $R_i$ with the feature vector, and (c) distribution for absolute deviation and corresponding standard deviation ($\sigma$) of 0.0398 Å.

Figure 4

Extension to new ions with results from the prediction and consolidated database. (a) Ionic radii predicted from ML work (GPR model) merged with Shannon's database as a function of atomic number. (b) General behavior of ionic radius as a function of coordination number and oxidation state for $N=987$ consolidated species. (c) Histogram of Shannon's empirical database and current ML work showing the similarity of the ionic radii distribution.