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

Abstract

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.

Simulating contrast inversion in atomic force microscopy imaging with real-space pseudopotentials

“…On the other hand, the FDE image with the chemically inert CO tip matches well with the full DFT case, with the noticeable difference of the copper sites being much brighter than in the full DFT case. Comparing the FDE forces with the full DFT forces shows reasonable agreement with a tip height offset of about 0.3Å, which is similar to that in a previous study 23 . These results suggest that the FDE method is better suited for simulating systems with chemically inert tips because the computational gains from the method can be obtained without loss of accuracy.…”

“…Modeling the underlying substrate in AFM simulations can be challenging because it can add lattice mismatch and greatly increase the size of the computational problem. In a previous study, we tested the effect of including a Cu substrate for pentacene and found no significant changes to the AFM image 23 . We omit it here for computational efficiency.…”

Elemental Identification by Combining Atomic Force Microscopy and Kelvin Probe Force Microscopy

“… 13 , 14 , 28 − 36 With these tips, it is possible to enter a regime where the tip–sample interaction is dominated by the Pauli repulsion between the last atom of the tip and the sample atom directly under it. 28 , 37 − 39 In addition to molecules, this technique has been used to measure atomic positions and surface corrugations of two-dimensional materials ( e . g ., graphene and hexagonal boron nitride).…”

Breaking a Dative Bond with Mechanical Forces

“…Here, we report the realization of a system containing an individual CO and FePc and subsequent AFM studies of the bond rupture process under vacuum conditions, so as to minimize the effects of environmental perturbations. Together with real-space pseudopotential density functional theory (DFT) calculations [22][23][24] modeling the events, this work advances our understanding of the origins of the measured forces in dative bond breaking.…”