Machine-Learned Electronegativity Equalization Trained with Chemical Potential and Hardness of Atoms in Molecules

The electronegativity equalization method relates the energy of systems to two empirically determined parameters of each atom: the chemical potential and hardness. In its original form, these parameters are functions only of atomic number, and can be determined from ionization energies of free atoms or by empirical fitting to computed partial charges. More recently, machine learning has been used to model the dependence of these parameters on an atom's chemical environment. Although the machine learning method makes predictions of these parameters directly, it is trained using a loss function that depends only on the partial charges calculated from them. To our knowledge, accuracy of the predicted chemical potentials and hardness has not been measured directly, since these parameters are presumed unknown for an atom within a molecule.<br/><br/>We performed first-principles calculations of chemical potential and hardness of atoms within molecules using Bader analysis. A series of differently substituted molecules provided a finely sampled curve of energy as a function of charge for each atom, and the parameters were defined as its first and second derivatives. The theoretically calculated chemical potential and hardness serve as a basis for evaluating the performance of a graph neural network model for the dependence of these parameters on chemical environment. They can also be used for training the model, as an alternative to training with partial charges. Electronegativity equalization using these parameters can serve as the basis of a force field, which can be used for relaxing geometries of molecules bound to catalytic surfaces. In the future, similar methods may also be useful in machine-learned versions of semiempirical quantum methods such as Hückel theory, by enabling predictions of the machine learning model to be compared to theory on an atomic rather than molecular level.