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:


The substrate of $\ce{Cu(111)}$ wasn't taken into account when calculating(?), while in the measurement it appears to distort the molecule
DFT, being an approximate method, gives too simplified results
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.
The probe of the microscope distorts the molecule


What are the true reasons for the differences?
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.