Bond-resolved STM with density-based methods

TL;DR

The paper advances bond-resolved STM modeling by merging an ab initio full-density framework (FDBM) with Chen's derivative rule to capture both s- and p-wave tunneling and CO-tip relaxation. By applying this to PTCDA/Ag(111) and TOAT/Cu(111), it demonstrates that substrate-induced electronic changes and CO deflection are critical for reproducing the intricate BRSTM contrasts and their evolution with tip height. The approach uses a single DFT calculation to generate all inputs for both HRAFM and BRSTM simulations, yielding quantitative agreement with experimental data across multiple systems and distances. This framework enhances BRSTM interpretation, supports future machine-learning-assisted structure discovery, and broadens the applicability of bond-resolved imaging to complex adsorbates and substrates.

Abstract

Bond-resolved STM (BRSTM) is a recent technique that combines the advantages of scanning tunneling microscopy (STM) with the outstanding intramolecular resolution provided by non-contact atomic force microscopy (ncAFM) using a CO-functionalized tips, offering unique insights into molecular interactions at surfaces. In this work, we present a novel and easily implementable approach for simulating BRSTM images, which we have applied to reproduce new experimental BRSTM data of Perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) on Ag(111), obtained with unprecedented control of tip-sample separation ($\sim$10~pm). Our method integrates the Full-Density-Based Model (FDBM) developed for High-Resolution Atomic Force Microscopy (HRAFM) with Chen's derivative approximation for tunneling channels, effectively capturing the contributions of both $σ$ and $π$ channels, while accounting for the CO-tip deflection induced by probe-sample interactions. This approach accurately reproduces the experimental results for both PTCDA/Ag(111) and 1,5,9-trioxo-13-azatriangulene (TOAT)/Cu(111) systems, including intricate tip-sample distance-dependent features. Furthermore, we also demonstrate the important role of substrate-induced effects, which can modify molecular orbital occupation and the relaxation of the CO probe, resulting in distinct BRSTM image characteristics.

Figures (9)

• Figure 1: Simulation framework to obtain BRSTM (red area) and HRAFM (green area) images from a single DFT calculation (blue area). The atomic positions, charge density, and electrostatic potential of the sample are fed into the vdW, SR, and ES calculations, respectively. For the last two, the tip's charge density is also included. The three calculated interactions are added together to obtain the static force. Then, the tip relaxation is performed following a tilting constraint, from which the CO deflection and the HRAFM signal (the force, as shown here, or, through a proper integration EVMAppSurfSci2023, the frequency shift) are obtained. For the tunneling part, the CO 5$\sigma$ orbital is approximated as an spherical s-like orbital and the 2$\pi^*$ as two p-like orbitals with its lobes pointing in the $x$ and $y$ cartesian axes in a plane parallel to the surface. Following Chen's approximation Chen1990Chen1998gross2011b, the squared modulus of the DFT wave function is used to obtain the $s$-tunneling component, and the square modulus of its lateral gradient is calculated to get the $p$ component. These two components are added and integrated over the applied bias to get the $s+p$ signal. Lastly, the probe position (the position of the O atom once the CO deflection has been determined from the HRAFM calculation) is used to obtain the approximate tunneling for each tip position, resulting in the BRSTM signal.
• Figure 2: Constant-height dI/dV images (3 nm$\times$3 nm) of PTCDA/Ag(111) measured with a CO-functionalized tip at a bias voltage of -200 mV. The closest tip-sample distance, 0 pm, corresponds to the tunneling set point of $I = 20$ nA and $V = -200$ mV at the center of a bright PTCDA molecule.
• Figure 3: Theoretical projected density of states of the PTCDA monolayer on Ag(111) (A molecule in blue and B in orange) with respect to the HOMO level ($E_{\mathrm{HOMO}}$), the Fermi level is represented by the vertical discontinuous lines. The top panel shows the pDOS for a DFT calculation using the experimental adsorption distance, the middle with the distance predicted using the DFT-D3 approximation for the vdW interaction, and the bottom one corresponds to the PTCDA monolayer in their relaxed adsorption configuration but without the metal substrate. Only the calculations at the experimental adsorption distance reproduce the position of the partially occupied LUMO found in the experiments.
• Figure 4: Individual force contributions (short-range Pauli repulsion, electrostatics and vdW --see Figure \ref{['fig:framework']}) and total sum (labelled Static) to the theoretical AFM image of FDBM at different tip-sample heights for PTCDA/Ag(111), taking as a reference the average position of the C atoms in the perylene core of both PTCDA molecules. The last column shows the total static image of the PTCDA monolayer without substrate. The gray scale is adjusted to the maximum and minimum value of each image, shown in the labels below each one (positive is repulsive and negative attractive).
• Figure 5: HRAFM images of PTCDA/Ag(111) with the static force map (left), the deflection of the CO on the tip on the static force map, shown as the shifts (2:3 scale) of the O atom projected onto the xy-plane (middle left), close-up of the area delimited by the orange rectangle (middle right), relaxed HRAFM images accounting for the CO deflections (right). The gray scale is adjusted to the maximum and minimum value of each image, shown in the labels below each one (positive corresponds to a repulsive force and negative to an attractive one).