Machine learning-based analysis of overall stability constants of metal-ligand complexes

Abstract

The stability constants of metal(M)-ligand(L) complexes are industrially important because they affect the quality of the plating film and the efficiency of metal separation. Thus, it is desirable to develop an effective screening method for promising ligands. Although there have been several machine-learning approaches for predicting stability constants, most of them focus only on the first overall stability constant of M-L complexes, and the variety of cations is also limited to less than 20. In this study, two Gaussian process regression models are developed to predict the first overall stability constant and the n-th (n > 1) overall stability constants. Furthermore, the feature relevance is quantitatively evaluated via sensitivity analysis. As a result, the electronegativities of both metal and ligand are found to be the most important factor for predicting the first overall stability constant. Interestingly, the predicted value of the first overall stability constant shows the highest correlation with the n-th overall stability constant of the corresponding M-L pair. Finally, the number of features is optimized using validation data where the ligands are not included in the training data, which indicates high generalizability. This study provides valuable insights and may help accelerate molecular screening and design for various applications.

Figure 1

(a) Total experimental results of each cation in the initial dataset, which is composed of 57 cations and 2706 ligands. (b) Distribution of each β_n in the initial dataset. The total amount of data, cations, and ligands are also displayed.

Figure 2

(a) The top 10 highest ranked features through sensitivity analysis using a Kullback–Leibler divergence as a measure for predicting β₁. (b) Predictive performance for the validation samples as a function of the number of features. Features are arranged in descending order of relevance. The black dashed line corresponds to the top 59 features. (c) Parity plot between true and predicted β₁ values of the validation data using the best GPR model. Error bars indicate 1σ uncertainty of the predicted value.

Figure 3

Relationships between experimental multi-order β_n and predicted β₁ of the corresponding M-L pair. The results of Pearson correlation coefficients (PCC) are also displayed.

Figure 4

(a) The top 10 highest ranked features through sensitivity analysis using a Kullback–Leibler divergence as a measure for predicting multi-order β_n. (b) Parity plot between true and predicted multi-order β_n values of the validation data using the best GPR model. Error bars indicate 1σ uncertainty of the predicted value.