Atomic fragment approximation from a tensor network

We propose atomic-fragment approximation (AFA), which uses the tensor network (TN) as a platform to estimate the molecular properties through “adding up” fragment properties. The AFA framework employs graph neural networks to predict the matrix product states (MPSs) for atoms and matrix product operators (MPOs) for bonds, which are then contracted to obtain the full TN for the full molecule. Subsequent neural network layers then predict molecular properties based on the TN contraction outcome. AFA addresses the limitation of density functional approximation (DFA) by reusing previously calculated results and maintaining constant complexity in fragment contraction regardless of the fragment size. We further show that AFA can overcome error accumulation by optimizing the intermediate fragments. AFA demonstrates the ability to predict the reaction intermediates by calculating and comparing the bond-breaking energies. The experiment also showcases excellent accuracy in reaction intermediate prediction and reaction energy prediction.