Accurate Calculation of Interatomic Forces with Neural\nNetworks Based on a Generative Transformer Architecture

Using\nneural networks to express electronic wave functions represents\na new paradigm for solving the Schrödinger equation in quantum\nchemistry. For practical quantum chemistry simulations, one needs\nto know not only energies of molecules, but also accurate forces acting\non constituent atoms. In this work, we achieve the accurate calculation\nof interatomic forces on QiankunNet, a platform that combines transformer-based\ndeep neural networks with efficient batched autoregressive sampling.\nOur approach permits the application of the Hellmann–Feynman\ntheorem to force calculations without introducing corrective Pulay\nterms. The results show that the calculated interatomic forces are\nin close agreement with those derived from the full configuration\ninteraction method, irrespective of whether the system is a simple\nmolecule or a strongly correlated electron system like a linear hydrogen\nchain. Furthermore, the calculated interatomic forces are employed\nfor atomic relaxation in the torsional rotation process of ethylene,\nand the energy barrier obtained from the scanned potential energy\nsurface is in excellent agreement with the experiment. Our work contributes\nto the application of artificial intelligence to broader quantum chemistry\nsimulations, such as modeling challenging chemical transformations\nwhere electron correlations are difficult to describe.