Density-Based Simulation of Constant-Current Atomic Force Microscopy Enables Quantitative Non-Planar Molecular Imaging

Abstract High-resolution atomic force microscopy (AFM) with functionalized tips has enabled bond-resolved imaging of molecular structures on surfaces. However, conventional constant-height operation limits the quantitative characterization of nonplanar, bulky, or strongly corrugated adsorbates. Here, we introduce a density-based simulation framework for constant-current AFM (cc-AFM) that unifies tunneling feedback and probe-particle force modeling within a consistent first-principles approach. The method employs the electronic density obtained from density functional theory to generate STM height profiles, which are coupled to probe-particle simulations while considering tip deflection, oscillation averaging, and probe–tip tunneling. We benchmark the approach by using cc-AFM measurements of Hexafluoropentacene on Cu(111) and 2-iodotriphenylene on Ag(111), two systems exhibiting pronounced molecular corrugation and electronic asymmetry. The simulations reproduce the experimentally observed full-molecule contrast, current-dependent image evolution, and subtle bond-level features. By establishing a unified density-driven framework for constant-current AFM, this work enables quantitative three-dimensional structural imaging of complex adsorbates and provides a transferable methodology for interpreting coupled STM/AFM experiments across a wide range of nanoscale systems.