Stability Analysis of Substituted Cobaltocenium [Bis(cyclopentadienyl)cobalt(III)] Employing Chemistry-Informed Neural Networks

Cationic cobaltocenium derivatives are promising components of the anion exchange membranes because of their excellent thermal and alkaline stability under the operating conditions of a fuel cell. Here, we present an efficient modeling approach to assessing the chemical stability of substituted cobaltocenium CoCp2+, based on the computed electronic structure enhanced by machine learning techniques. Within the aqueous environment, the positive charge of the metal cation is balanced by the hydroxide anion through formation of the CoCp2+OH- complexes, whose dissociation is studied within the implicit solvent employing the density functional theory. The data set of about 118 the CoCp2+OH- complexes based on 42 substituent groups characterized by a range of electron-donating (ED) and electron-withdrawing (EW) properties is constructed and analyzed. Given 12 carefully chosen chemistry-informed descriptors of the complexes and relevant fragments, the stability of the complexes is found to strongly correlate with the energies of the highest occupied and lowest unoccupied molecular orbitals, modulated by a switching function of the Hirshfeld charge. The latter is used as a measure of the electron-withdrawing-donating character of the substituents. On the basis of this observation from the conventional regression analysis, two fully connected, feed-forward neural network (FNN) models with different unit structures, called the chemistry-informed (CINN) and the quadratic (QNN) neural networks, together with a support vector regression (SVR) model are developed. Both deep neural network models predict the bond dissociation energies of the cobaltocenium complexes with mean relative errors less than 10.56% and average absolute errors less than 1.63 kcal/mol, superior to the conventional regression and the SVR model prediction. The results show the potential of QNN to efficiently capture more complex relationships. The concept of incorporating the domain (chemical) knowledge/insight into the neural network structure paves the way to applications of machine learning techniques with small data sets, ultimately leading to better predictive models compared to the classical machine learning method SVR and conventional regression analysis.