# What's the reason for discrepancy between DFT calculated image and NC-AFM-acquired one in this article?

Looking at the images in this article, I've noticed that the molecule electron density images showed as calculated via DFT look very symmetric, while those obtained by NC-AFM appear somewhat distorted. Namely, the ring at the left (the one with $\ce{OH}$ group) looks elongated, while the one at right is, on the contrary, compressed in horizontal direction, and the $\ce{OH}$ group seems to be tilted to the $\ce N$ atom. Also, the calculated image seems much more smeared, while the measured one gives some highly localized density "rods" for the bonds.

I've made a gif-combination of these two images so that the difference was easier to see:

Here the B is DFT-calculated version, while F is one measured by NC-AFM.

I can suppose one or several of the following might be among the reasons for this:

1. The substrate of $\ce{Cu(111)}$ wasn't taken into account when calculating(?), while in the measurement it appears to distort the molecule

2. DFT, being an approximate method, gives too simplified results

3. Smear vs thin rods difference might because in the DFT case the picture is of electron density while in AFM case the image shows AFM frequency shifts, which is not necessarily the same.

4. The probe of the microscope distorts the molecule

What are the true reasons for the differences?

This is not really my field, but I've certainly followed it. I'd guess some combination of all of your reasons, plus one more.

• I think usually the substrate is considered, but imperfections and defects in the surface may not be properly considered.
• Perhaps, although I think this is probably less important than other causes.
• Exactly. DFT-computed electron density is not exactly what the AFM measures.
• The probe will certainly have different interactions with the molecule, and could be subtly asymmetric.

I'd guess the most likely culprit is different.

In AFM (and all scanned-probe methods) the substrate is rarely perpendicular to the probe. Some minor image correction is performed to "line-fit" the substrate.

Consider if you take a photo of a page on your desk. The page is probably slightly rotated in the plane of the desk, but the camera is almost never exactly parallel to the desk. This results in "keystoning".

The AFM software corrects for this effect, and users can fit a bit after data-collection, but it can cause subtle distortions.

1) Most definitely. Adsorbed molecules often are very distorted, up to chemical reaction with support, especially when reactive surface is used. Despite common misconception, even noble metal surfaces are quite reactive.

2) DFT, while being indeed inexact (as any calclation with limited size of basis set), catches major features of electronic density very well.

3) AFM stands for atomic force microscopy, which is not connected to electronic density directly. Now, naphthalene molecule features large $\pi$-system, which is very polarizable. Since nonvalent interatomic forces beyond electrostatic interactions usually increases with polarizability of interacting particles, I would expect $\pi$-systems to be highlighted on the NC-AFM images.

4) I'm not an expert on atomic-resolved microscopy, but I never read about this possibility in the articles I worked with, though the works I usually works with used STM. and SEM mostly.