How much energy difference could be used to distinguish optimized results from different initial geometries for the same structure?

Is there a threshold? Could I say that my final geometries are the same with 'energy difference = 0.05 meV/atom' ?

• @robert If it is a gas-phase molecule can you describe what exactly what you are trying to do?
– mykd
Aug 5 '20 at 15:12
• To check if your structure is optimized, you need to look at the forces on the atoms. If you set out to relax the cell and the atoms themselves, a good threshold is 0.0001 eV/Angstrom (This is the default value on Quantum ESPRESSO). Aug 5 '20 at 17:09
• +1. But there might be two energy-equivalent minima in the energy landscape, so the energy at one optimized geometry will be the same as the energy at a different geometry. In this case the energy difference between the two geometries will be 0.000... eV and 0.000... eV/atom. Am I understanding the question wrong? Aug 5 '20 at 23:24
• @NikeDattani I agree: for a floppy molecule it's easy to have several geometries whose energy agrees to, say, 0.05 meV per atom, but the geometries are still quite different and lead to different properties. Dividing by the number of atoms makes no sense unless you're dealing with simple crystals. Aug 6 '20 at 8:51
• In my view this is an ill-posed question - going by the strict definition, different final geometries are obviously not the same, and the question does not provide enough context to understand what @Alfred considers "the same". Unless more context can be provided, I vote to close this question. Aug 14 '20 at 11:44

The best way to distinguish whether you have indeed converged to the same structure also requires checking the minimal geometry itself, by both visual and computational means. You might establish the similarity of the structure by fingerprints, for example; e.g. show that $$R = \sum_{i}^{N_{\rm atoms}} ({\bf x}_i - {\bf x}_i')^2$$, where $${\bf x}$$ and $${\bf x}'$$ are your two structures, is small. (Note that permutations of the nuclei is allowed so you should minimize $$R$$ with respect to swaps of identical atoms.)