Reconstructing Pristine Molecular Orbitals from Scanning Tunneling Microscopy Images via Artificial Intelligence Approaches

Abstract: Molecular orbital (MO) is one of the most fundamental concepts for molecules, relating to all branches of chemistry, while scanning tunneling microscopy (STM) has been widely recognized for its potential to measure the spatial distribution of MOs. However, the precise characterization of MO with high resolution in real space is a long-standing challenge owing to the inevitable interference of high-angular-momentum contributions from functionalized tips in STM. Here, leveraging advances in artificial intelligence for image recognition, we establish a physics-driven deep-learning network, named STM-Net, to reconstruct MOs from high-resolution STM images with a functionalized tip, taking advantage of the separable characteristics of different angular momentum contributions. We demonstrate that STM-Net can be directly applied to a variety of experimental observations, successfully reconstructing pristine MO features for molecules under diverse conditions. Moreover, STM-Net can adapt to various states of the functionalized tip and the substrate, illustrating the broad applicability of our physics-driven framework. These results pave the way for accurate characterization of MO with high resolution, potentially leading to new insights and applications for this fundamental concept in chemistry.