<scp>X2</scp> ‐ <scp>PEC</scp> : A Neural Network Model Based on Atomic Pair Energy Corrections

With the development of artificial neural networks (ANNs), its applications in chemistry have become increasingly widespread, especially in the prediction of various molecular properties. This work introduces the X2-PEC method, that is, the second generalization of the X1 series of ANN methods developed in our group, utilizing pair energy correction (PEC). The essence of the X2 model lies in its feature vector construction, using overlap integrals and core Hamiltonian integrals to incorporate physical and chemical information into the feature vectors to describe atomic interactions. It aims to enhance the accuracy of low-rung density functional theory (DFT) calculations, such as those from the widely used BLYP/6-31G(d) or B3LYP/6-31G(2df,p) methods, to the level of top-rung DFT calculations, such as those from the highly accurate doubly hybrid XYGJ-OS/GTLarge method. Trained on the QM9 dataset, X2-PEC excels in predicting the atomization energies of isomers such as C₆H₈ and C₄H₄N₂O with varying bonding structures. The performance of the X2-PEC model on standard enthalpies of formation for datasets such as G2-HCNOF, PSH36, ALKANE28, BIGMOL20, and HEDM45, as well as a HCNOF subset of BH9 for reaction barriers, is equally commendable, demonstrating its good generalization ability and predictive accuracy, as well as its potential for further development to achieve greater accuracy. These outcomes highlight the practical significance of the X2-PEC model in elevating the results from lower-rung DFT calculations to the level of higher-rung DFT calculations through deep learning.