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

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