References for the total energy in VASP

[alpinnovianus]

Dear VASP experts,

I came across a few papers recently where supercells are made and their total energies are compared under different configurations.
For example,
Figure 2 of this paper: https://www.pnas.org/doi/full/10.1073/pnas.1910411116
or table 1 of this paper: https://www.nature.com/articles/s42005-021-00621-4

While it seems that the total energies computed via VASP or other DFT packages are commonly known quantities, I think it would be nice to be able to write explicitly the equations for the total energy that is computed with VASP and also including the reference energies for certain. I read in the wiki that the reference energies are based on the isolated atoms computed in the pseudopotential, but I want to confirm this aspect as a whole.

I believe there should already been a paper that states this total energy equation computed with VASP along with the reference energies explained since VASP has been around for many years.
Would you please guide me to such papers that I could quote and cite in my works?

Thank you very much for your guidance.

[martin.schlipf]

The best reference for the total energy in VASP with the PAW method that I'm aware of is Kresse and Joubert (1999). You can also consult the relevant wiki article, which contains some more references.

Regarding the reference energies, I am not completely sure what you want. If you want a table of reference energies for specific crystals or molecules, then this is an unusual request as these energies would not be transferable between codes. In contrast to the quantum chemistry community where almost everybody uses the same basis sets, in condensed matter physics, we have different basis sets and pseudopotentials. Therefore, we compare physical observables based on energy differences that should be transferable between codes. The most well-known work in this regard is the Δ test.

[alpinnovianus]

The best reference for the total energy in VASP with the PAW method that I'm aware of is Kresse and Joubert (1999). You can also consult the relevant wiki article, which contains some more references.

Regarding the reference energies, I am not completely sure what you want. If you want a table of reference energies for specific crystals or molecules, then this is an unusual request as these energies would not be transferable between codes. In contrast to the quantum chemistry community where almost everybody uses the same basis sets, in condensed matter physics, we have different basis sets and pseudopotentials. Therefore, we compare physical observables based on energy differences that should be transferable between codes. The most well-known work in this regard is the Δ test.

I'm sorry for being unclear. Let me try to rephrase my request as follows.

Suppose I want to present Table I of this paper: https://www.nature.com/articles/s42005-021-00621-4
https://www.nature.com/articles/s42005- ... 4/tables/1

In particular, I want to present the data listed in the 'energy' column in form of the above table, accompanied by an intuitive equation that explain this 'energy'.
For that, I believe I will need two ingredients:

• First, a list of the terms that form this total energy: (Hartree energy) + (exchange correlation energy) +.... ()

In fact, it is similar to what I can find in the OUTCAR, where the free energy is shown to be made up of several terms that are more explanatory:

Code: Select all

Free energy of the ion-electron system (eV)
  ---------------------------------------------------
  alpha Z        PSCENC =      5940.78324452
  Ewald energy   TEWEN  =    -76597.15246038
  -Hartree energ DENC   =    -25624.22804859
  -exchange      EXHF   =         0.00000000
  -V(xc)+E(xc)   XCENC  =      5331.25611792
  PAW double counting   =    130768.62475327  -135400.57600830
  entropy T*S    EENTRO =         0.00000000
  eigenvalues    EBANDS =     -5517.65706306
  atomic energy  EATOM  =     99205.15615738
  Solvation  Ediel_sol  =         0.00000000
  ---------------------------------------------------
  free energy    TOTEN  =     -1893.79330725 eV

  energy without entropy =    -1893.79330725  energy(sigma->0) =    -1893.79330725

I want to express each of these terms in their mathematical forms, and write a total energy equation as a simple sum of these terms that would be intuitive to the reader in recognizing what I mean by 'energy' in that Table I. (similar to how we decompose the Kohn-Sham energy to kinetic energy + E_H + E_xc + ..., and then followed by E_H = ....; E_xc = ...)

My focus is only to inform the reader what this total energy are made of.
For that purpose, I think I want separate the details of PAW formalism (i.e., how the density n is split into a few terms and how the projectors work) from the above total energy equation.
I believe I would not be the first person to have written the components of the total energy computed by VASP in his/her research paper, so I want to know if someone else has been able to succinctly write this equation in his/her publications.

• Second, what I mean by the 'reference energies' are the systems where we define 'zero' value. For example, in energy(sigma->0) = -1893.79330725 or in -Hartree energ DENC = -25624.22804859 above, what would these values be considered relative to? which system would correspond to the zero value?

The objective of this question is to know whether the total energy explaining the values in Table 1 is a relative value over, for example, the total energies of isolated atoms with zeros defined as corresponding to the coulomb energy of two electrons infinitely far apart: (or some other reference systems)

E = E(cell) - E(atoms), or something along this line of thought.

Hopefully the above exposition has clarified my request more clearly.
Thank you for your guidance.

[martin.schlipf]

The energies in the table you linked are a good example for the use of relative energies. The table caption states

Energies are given relative to the C-type antiferromagnetic phase.

so that you would always compute the energy difference of one magnetic configuration and the C-type AFM one. You would not report the contribution of e.g. the Hartree energy to this energy difference.

When you converge a VASP calculation, you typically want to make sure that the free energy and the two energies that include the entropy agree within your desired precision. Typically, you would then only use that value for all further calculations, like calculating the differences of various magnetic configurations. As I wrote in my previous reply, you can find the equations for the individual contributions to the total energy in the Kresse/Joubert paper but they are not of relevance to the reader and mostly used for debugging purposes. You can see in the individual contributions from the OUTCAR vary greatly in magnitude and sign. If you would slightly tweak the system e.g. by displacing one of the atoms, the contributions change by a very large amount. Only the resulting total energy would be almost the same, because the different contributions (almost) cancel.