First-Principles Atomic Force Microscopy Image Simulations with Density Embedding Theory

We present an efficient first-principles method for simulating noncontact atomic force microscopy (nc-AFM) images using a "frozen density" embedding theory. Frozen density embedding theory enables one to efficiently compute the tip-sample interaction by considering a sample as a frozen external field. This method reduces the extensive computational load of first-principles AFM simulations by avoiding consideration of the entire tip-sample system and focusing on the tip alone. We demonstrate that our simulation with frozen density embedding theory accurately reproduces full density functional theory simulations of freestanding hydrocarbon molecules while the computational time is significantly reduced. Our method also captures the electronic effect of a Cu(111) substrate on the AFM image of pentacene and reproduces the experimental AFM image of Cu2N on a Cu(100) surface. This approach is applicable for theoretical imaging applications on large molecules, two-dimensional materials, and materials surfaces.