# How can I justify that in DFT entalphy is Gibbs free energy?

I am working in my final undergraduate Project about predicting belite (Ca2Si04) polymorphs using DFT calculations and I need to justify why my SIESTA run is looking for minimum enthalpy and not free energy. I have a vague idea that is because DFT is perfomed using T=0K but I cannot find any article that supports it. I need to use references, so please if you could provide it I'd grateful.

Thanks!

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Jan 12 at 9:48
• $G = H - TS$. What happens when $T=0$? Jan 12 at 22:19
• Do you actually aim at predicting polymorphs at zero temperature? If yes, then Hayden's answer (H - 0 * S = H) works perfectly well. If no, then the answer will involve other factors like, e.g. it is much more difficult to minimize the free energy than minimize the (zero-temperature) enthalpy. Jan 13 at 12:54
• I found another similar question here : mattermodeling.stackexchange.com/questions/1228/… My calculation is not done at zero temperature (at least I haven't specified it) but I think that DFT itself does it because the Born-Oppenheimer approximation makes the nucleus static so temperature makes no sense... Well, that is what I think, and if that is true I need references Jan 13 at 14:34
• Here is a widely cited go-to reference that works 0K and >0K calculations and phase diagrams: journals.aps.org/prb/abstract/10.1103/PhysRevB.65.035406 There are many more similar ones by Reuter around the same time (2001-2003 or so). And a book chapter: link.springer.com/chapter/10.1007/978-1-4020-3286-8_10 They focus on surfaces, but the same workflow applies to polymorphs and everything else. Jan 16 at 20:55

DFT is most commonly used to calculate minimized energy structures. This is likely what your project is on, unless you're doing ab initio molecular dynamics, or excited state DFT (e.g. time-dependent DFT) calculation. In this case, your calculations are equivalent to finding the lowest enthalpy ground state minus the vibrational zero point energy. Enthalpy $$H$$ will be equal to the total energy $$E$$ unless you're also applying some external stress (i.e. pressure), which would correct the enthalpy by a $$PV$$ term.
Since your calculations are at $$T =0$$ (equations of motion are not even employed), the energy (or enthalpy) minimization is also equal to the Gibbs free energy $$G$$.
If you want to determine which polymorph is most stable at finite temperature and pressure (lowest $$G$$), you need a more sophisticated calculation than straightforward DFT structure minimization. A common method is to correct the minimized energy for vibrational energy based on a harmonic or quasiharmonic vibrational calculation.