Formation energy and choice of reference states

[jared]

Hello,

I am trying to calculate the energy of formation for a set of perovskites. I have calculated the total energy for each compound, and I understand that I need to now calculate the energies of the constituents in their standard phases, following dH_formation = E_tot - SUM(x*E_tot,i), for each element i appearing x times in the composition.

These would typically be the chemical potentials of the elements in standard states, such as in the OQMD (or so I thought):

--> Elemental ground-state structures and chemical potentials predicted by DFT at 0 K
--> https://www.nature.com/articles/npjcompumats201510#t1

However the total energies output by ATK are very large (~20,000 eV for 20 atoms), and therefore do not give the correct results for dH. Following the tutorial on the subject (https://docs.quantumwise.com/tutorials/formation_energies/formation_energies.html), I see that for GaAs for example, one needs to calculate the bulk Ga and bulk As total energies. I therefore have 2 questions:

1. If the lowest energy phase should be chosen as the reference state, why can't the potentials in the above link be used? (i.e. why is the output so different than these values derived from VASP - I suspect this is about the PAW approach vs. GGA-PBE I am using).

2. How are the reference states to be chosen? I can download several different cif files of Ga and As phases from Crystallography Open DB. What reference states are actually used to get this number in the tutorial? (I have read the pointed to reference, and they also do not explicitly say how they calculate these numbers.)

It seems that the standard phases for all constituents must be calculated in the same ATK environment to keep the same DFT parameters (rather than compared with external values), and if this is true, I need to understand how to choose the correct phase. Thank you for the help!

[Ulrik G. Vej-Hansen]

1. Every DFT code has its own reference for zero energy, so it is in general impossible to compare total energies across codes. However, any differences should of course be comparable, if the same computational model has been used.

2. The choice of reference states is in general a scientific one, but for this purpose, the normal choice is to choose the most stable form of the constituent elements, calculated with the same method. In the tutorial you reference, the chemical potentials of the elements are calculated from the database bulk structures, relaxed with the same parameters, i.e. basis set, xc-functional, k-point density, etc. as the compound.

[jared]

Thank you for the quick reply! I am relatively new to DFT and therefore didn't know that the codes could be so different even with similar parameters.

To the point of question 2, I have only found cif files for example from the Crystallgraphic Open DB and other databases, no bulk configuration in a database in QW itself (leading to some ambiguity of which bulk structure to use). Otherwise, there is no bulk via File>Add>From Database... in the builder.

[Petr Khomyakov]

1. If the lowest energy phase should be chosen as the reference state, why can't the potentials in the above link be used? (i.e. why is the output so different than these values derived from VASP - I suspect this is about the PAW approach vs. GGA-PBE I am using).

PAW is the potential to describe core-electrons (somewhat similar to pseudopotential), whereas GGA-PBE is a particular type of the density functional in density functional theory. So, you cannot say "the PAW approach vs. GGA-PBE", as it is like comparing apples and oranges.  You can do PAW-potential+GGA-PBE calculation in VASP and some pseudopotential+GGA_PBE calculation in QuantumATK, and then compare the two calculations; that makes sense, but not PAW vs. GGA-PBE.

[jared]

Yes, thank you. I meant to say SG15 pseudo-potentials which are implemented in ATK. Thanks for the correction.

[Ulrik G. Vej-Hansen]

To the point of question 2, I have only found cif files for example from the Crystallgraphic Open DB and other databases, no bulk configuration in a database in QW itself (leading to some ambiguity of which bulk structure to use). Otherwise, there is no bulk via File>Add>From Database... in the builder.

You can certainly read in .cif files, and use those to generate the structure. See here, for more information: https://docs.quantumwise.com/tutorials/vnl_io_import/vnl_io_import.html

You can then optimize the geometry with ATK, as described here: https://docs.quantumwise.com/tutorials/geometry_optimization/geometry_optimization.html