Predicting chemical hardness: A study using machine learning and artificial neural networks

While the computational cost to explore chemical compound space guided by quantum-chemical properties is ever increasing, the search for more alternatives becomes more active by the day. In this work, we focus on the chemical hardness using the PBE/cc-pVDZ level of theory. First, the chemical hardness was computed for 5000 molecules based on a definition by Tozer and De Proft (Journal of Physical Chemistry A 2005, 109 (39), 8923–8929). A detailed assessment of the structural characteristics of soft and hard molecules as well as a similarity search for different ranges of the chemical hardness were carried out. Next, a kernel ridge regression (KRR) model and neural network (NN) were trained on this data set using 3 different features sets. These feature sets consisted of a selective molecular quantum number (MQN) set, the complete MQN vectors and Coulomb matrices. The best performing models, KRR and NN using the MQN vectors as input, obtain similar metrics: [MAE:0.27eV; RMSE:0.37eV; R2:-0.024; Accuracy:91.8%] for the kernel ridge regression model and [MAE:0.28eV; RMSE: 0.37eV; R2:0.581; Accuracy:91.8%] for the neural network. Based on the R2, the neural network was selected as superior model. This model was capable of making predictions with 0.3 eV error, while only taking a few milliseconds to compute. The side note must be made that these models have the best performance within the 3 to 6 eV range.