# How would one find a material's equilibrium structure at any specific temperature?

Let's take an example of a simple FCC material, a binary alloy. Above absolute zero K, the alloy will start to disorder and become an FCC solid solution. The alloy would develop defects as it disorders. What would the best strategy (workflow) to find this alloy's equilibrium structure at $$x$$ K be?

One workflow that I can think of:

1. Geometry optimization at $$0$$ K using DFT.
2. Lattice dynamics study of the alloy to get its volume (V) vs temperature (T) data, i.e. V = f(T).
3. Find V at $$x$$ K, $$V_x$$.
4. Create a DFT supercell of the alloy with $$V_x$$. Use this cell to find formation energies (thermal stability) and phonon bandstructures (dynamic stability) of various possible disordered structures.

When I think of MD calculations, I think of the time evolution of the system. What, then, does it mean to simulate temperature-based evolution of the system in MD or ab initio MD?

• +1. I suppose molecule dynamics could also be used to approximate the equilibrium structure at an arbitrary temperature. Commented Sep 25, 2021 at 22:50
• You can use Molecular Dynamics (MD) to determine the equilibrium structure of the material at a given temperature. However, the difference between inter-atomic potentials used in MD and DFT could mean that you would either have to evaluate all required properties using MD or obtain the supercell from MD and proceed with the 4th step that you have mentioned (which probably might cause errors due to the difference in inter-atomic interactions). Use [icme.hpc.msstate.edu/mediawiki/index.php/… as an example.
– PBH
Commented Sep 26, 2021 at 15:40
• @PBH, this makes me think of what really is the difference between DFT and MD when it comes to such calculations. Is it that DFT potentials are parameter-free, hence more universal? Also, the link in your comment doesn't open. Commented Sep 27, 2021 at 6:13
• @HitanshuSachania, the above link is correct but I have mistakenly typed a "]" at the end of the link. I think that this post on Quora does a sufficient job in answering your question regarding the difference between DFT and MD.
– PBH
Commented Sep 27, 2021 at 7:06
• This repeats some of the Quora link from @PBH, but just to clarify on DFT vs MD: DFT is a way to calculate energies/forces. MD is a way to use energies/forces. MD frequently uses molecular mechanics (MM), which is a different way to calculate energies/forces (much faster than DFT, but much more approximate and makes a lot of assumptions that DFT does not). People frequently incorrectly say "MD" (or "classical MD") when they mean MM. They also incorrectly refer to DFT+MD as "quantum dynamics," which is another thing entirely. (Two pet peeves!) Commented Sep 27, 2021 at 14:20

This can be made more accurate by not just choosing some predetermined forcefield, but by actually using an electronic structure method (like DFT) to calculate the forces between your atoms for their respective geometry at each step of the MD simulation. This is called or ab initio MD, and it can be very slow, so you may want to use CPMD as described in the answers by myself and Tyberius here: What are the types of ab initio Molecular Dynamics?. To explain dwhswenson's comment, I'll say that you can even take this further and do full quantum dynamics if you want even more accuracy, meaning that instead of using Newton's classical equation F = ma, you could literally solve the time-dependent Schroedinger equation $$\frac{d|\psi(t)\rangle}{dt} = -\frac{i }{\hbar}\hat{H}(t) |\psi(t)\rangle$$, but as I very recently explained in my answer to this: Deviation caused by using DFT in Non-Adiabatic Molecular Dynamics, that you would be limited to a very small system and considering that your "force" calculations from DFT (or even coupled-cluster or more more sophisticated methods) will be limited in accuracy for the types of problems for which this calculation would even be relevant.