Advancing Scanning Probe Microscopy Simulations: A Decade of Development in Probe-Particle Models

The Probe-Particle Model combine theories designed for the simulation of scanning probe microscopy experiments, employing non-reactive, flexible tip apices to achieve sub-molecular resolution. In the article we present the latest version of the Probe-Particle Model implemented in the open-source ppafm package, highlighting substantial advancements in accuracy, computational performance, and user-friendliness. To demonstrate this we provide a comprehensive review of approaches for simulating non-contact Atomic Force Microscopy. They vary in complexity from simple Lennard-Jones potential to the latest full density-based model. We compared those approaches with ab initio calculated references, showcasing their respective merits. All parts of the ppafm package have undergone acceleration by 1-2 orders of magnitude using OpenMP and OpenCL technologies. The updated package includes an interactive graphical user interface and seamless integration into the Python ecosystem via pip, facilitating advanced scripting and interoperability with other software. This adaptability positions ppafm as an ideal tool for high-throughput applications, including the training of machine learning models for the automatic recovery of atomic structures from nc-AFM measurements. We envision significant potential for this application in future single-molecule analysis, synthesis, and advancements in surface science in general. Additionally, we discuss simulations of other sub-molecular scanning-probe imaging techniques, such as bond-resolved scanning tunneling microscopy and kelvin probe force microscopy, all built on the robust foundation of the Probe-Particle Model. Altogether this demonstrates the broad impact of the model across diverse domains of on-surface science and molecular chemistry.