Bonds Between Some Atoms are Missing

A rather frequent question we get is, why no bond is shown between certain atoms, and what influence this might have on the results. An example is shown below - as a result of stretching the structure (it’s from an example where we pull and pull on the two nanotubes until the system breaks), a lot of bonds are missing in the middle.


Actually, it is a common misconception that the bonds you (sometimes) see in the figures in papers or indeed in the 3D view in VNL actually mean anything. In fact, they don’t, at least not for DFT calculations, and typically also not for semi-empirical models like extended Hückel, DFTB, or even Slater-Koster orthogonal tight-binding (with some exceptions). The quantum-chemical models used in DFT etc do not contain a concept of bonds, only atomic positions.

So, you can even say that the bonds shown in the 3D view are just there to make the picture look nicer - to guide the eye regarding which atoms are close to each other, or to give an idea of the local coordination of a particular ion. The rule for when a bond is drawn between two atoms in VNL is very simple: if the atoms are closer than the sum of their covalent radii (+10%), a bond is shown, otherwise not. Now, if the structure is distorted a bit, the bonds may disappear because the atoms are just outside this radius, but there is no sudden change in how the interact, just a slightly smaller overlap of the radial basis functions because of the longer interatomic atom distance.

In the future we also plan to include models where the bonds do matter, like bonded force fields (classical potentials). It will also later be possible to control the rules for when bonds are drawn - and in that way you can achieve a picture like the one below. But, as mentioned, it really has no influence on the calculations.


Thus, in summary, the bonds in VNL are just for illustration, and not used in the calculations.