# Consideration of static atomic displacements in electronic structure calculations

I am hoping to discuss some details of electronic structure calculations. I am not an expert on this topic, so please forgive any abuse of terminology. It is my understanding that first principles electronic structure calculations are based on perfect translational symmetry of a crystalline lattice. Further, that the first round of calculations traditionally treat the atomic nuclei as fixed points due to the large disparity in nuclei and electron velocities, and after the initial electronic structure is solved, one can then turn on the nuclear motions and understand the interaction between the nuclear and electronic motions. The heart of my question is: is it possible to investigate local distortions of structures using existing techniques? By a local distortion, I mean a distortion which does not disrupt the long range crystalline periodicity, but results in a very different local atomic environment?

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Since I was looking at this I took the opportunity to put some tags on it, but feel free to fix the tags if there are better choices. – David Zaslavsky♦ May 16 '12 at 18:19

## 1 Answer

A technique is to perform a supercell calculation where in the calculation is performed over several cells instead of a single unit cell. The desired change is made to a single cell within this larger structure. This does make your change periodic, but if the supercell is large enough, then the change can be made essentially local. This method has been used to generate electronic structures for substitutional series like FeSi$_{(1-x)}$Ge$_x$ and $\text{X}_x\text{W}_{(1-x)}\text{O}_3$ (X=Nb,V,Re) (link). So, a small structural change is not out of the question. I know wien2k and quantum espresso have a scripts for generating supercell, but I don't know what other major packages do. VASP does not seem to.

As to how big a supercell to make, I don't know. I have not actively looked for one, but I have not found a resource giving such guidance. I'd suggest starting as small as possible, possibly $2\times2\times1$ or $2\times2\times2$, and increasing the size until the effect seems localized to the interior of the supercell. Obviously, this will put a strain on your computing power, so the smaller the better.

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the preview of the second formula looks correct, but the "published" version does not. Hmmm. – rcollyer Dec 24 '11 at 12:16
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