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Dear Vasp users, I would like to have more details about the different crontributions to the total energy in the OUTCAR and espcially the "alpha Z" and "Ewald energy". Does any one knows exactly what they are ? Is the "Ewald energy" similar to a Madelung contribution ?
Regards
Florent

alpha Z and the Ewald energy define the electrostatic
interaction of the ions in a compensating electron gas.
The alpha Z component deals with the divergent parts (G=0).

The following parts are the Hartree and exchange correlation energy as
defined in the Kohn-Sham Hamiltonian. The entropy part stems from the
smearing (using the free energy as variational parameter, electronic entropy),
EBANDS from Kohn-Sham eigenvalues, and EATOM is the reference energy for the potential (which is defined in the POTCAR file).

Furthermore, you find a documentation of the respective terms of the Schroedinger
equation in the handouts of the VASP-workshop,
http://cms.mpi.univie.ac.at/vasp-workshop
especially in the session about dft (download especially
comput_mat.pdf, dft_introd.pdf, and accuracy.pdf (p.4 for EATOM))

Dear VASP Admin/Users,

1. I am wondering if the "PAW double counting" term in the OUTCAR has any physical meaning?

In PRB59, 1758 (1999), it is said that "in many band-structure codes, the total energy is evaluated as the sum of the Kohn-Sham eigenvalues minus double counting corrections". Is this the "PAW double counting" term that we see in the OUTCAR?

From the equation (48) in the above article, one can see that the "double counting" term has something to do with Hartree, exchange-correlation energies... Then,

2. How should we define the Madelung energy? i.e., what terms should we add up to get the Madelung energy?

I would be very glad if someone could tell me more about these matters.

Thanks!



<span class='smallblacktext'>[ Edited Wed Mar 22 2006, 11:50PM ]</span>

[quote author=0).

The following parts are the Hartree and exchange correlation energy as
defined in the Kohn-Sham Hamiltonian. The entropy part stems from the
smearing (using the free energy as variational parameter, electronic entropy),
EBANDS from Kohn-Sham eigenvalues, and EATOM is the reference energy for the potential (which is defined in the POTCAR file).

Furthermore, you find a documentation of the respective terms of the Schroedinger
equation in the handouts of the VASP-workshop,
http://cms.mpi.univie.ac.at/vasp-workshop
especially in the session about dft (download especially
comput_mat.pdf, dft_introd.pdf, and accuracy.pdf (p.4 for EATOM))

[/quote]

Hi,

[quote="admin"]alpha Z and the Ewald energy define the electrostatic
interaction of the ions in a compensating electron gas.
The alpha Z component deals with the divergent parts (G=0).

What means "The alpha Z component deals with the divergent parts (G=0)". Isn't the divergent term infinity?

The electron-ion, Hartree, and ion-ion interaction energies diverge individually. However, if you add the G=0 divergences up, it is a finite number. It can be shown that if the ionic potential is Coulomb, then the cancellation of the three G=0 terms is exact, i.e. the finite number is zero. Since VASP uses pseudopotentials, the summation of the three G=0 terms results in a non-zero finite number, which is called alpha.

[quote author=0).

[/quote]

Hi Admin,

Do you mean alpha Z and Ewald energy give the total electrostatic energy of the system? or I think of it in a wrong way? I want to know whether we can decompose the total energy from vasp into Kinetic, Coulomb, exchange and correlation energies, separately.

I was calculating adsorption of noble gas (Xe) on metal surface (111) at two different sites, of which the total energy is only slightly different:

The energies at site 1:

---------------------------------------------------
alpha Z PSCENC = 1057.06630392
Ewald energy TEWEN = 128376.65817811
-1/2 Hartree DENC = -145347.23431284
-exchange EXHF = 0.00000000
-V(xc)+E(xc) XCENC = 41.64037121
PAW double counting = 12658.25300008 -12074.80631272
entropy T*S EENTRO = -0.00031446
eigenvalues EBANDS = -575.59189787
atomic energy EATOM = 15740.57257888
---------------------------------------------------
free energy TOTEN = -123.44240568 eV


The energy at site 2:
---------------------------------------------------
alpha Z PSCENC = 1056.91493097
Ewald energy TEWEN = 128376.45871064
-1/2 Hartree DENC = -145344.66902862
-exchange EXHF = 0.00000000
-V(xc)+E(xc) XCENC = 41.63693035
PAW double counting = 12658.30538857 -12074.85364512
entropy T*S EENTRO = -0.00032545
eigenvalues EBANDS = -577.80127102
atomic energy EATOM = 15740.57257888
---------------------------------------------------
free energy TOTEN = -123.43573079 eV


The difference of the total energies at two different sites is only 0.0067 eV, which is reasonable. However, the difference of the (alpha Z+Ewald energy) is about 0.35 eV, which does not make sense to me. Since it is a weakly bound system, I expect the difference of the electrostatic energies at these two different sites to be very small, several meV or less. Therefore, I do not understand the (alpha Z+Ewald energy) energy shown above.

Any comments will be appreciated!


Chen

The electrostatic energy of a system should include the electrostatic interaction between ion-ion (Ewald), electron-electron (Hartree), and ion-electron. The information about ion-electron electrostatic interaction is embedded inside the eigenvalues.

Note that the individual number for the Ewald energy, and Hartree energy by themselves is not really meaningful. Only the total electrostatic energy of the system is a meaningful number. This is because in a plane wave code, the reference zero of the electrostatic potential is defined to be the average electrostatic potential of the unit cell, rather than defining the zero to be the "vacuum."

This is really helpful, thanks very much!

Dear all,

i am in principal trying to do the same as ffdeli, so i want to compare kinetic energy, electrostatic energy and exchange-correlation energy. however i am still not exactly sure, how to do this, and what each contribution to the free energy mean.

alphaZ + Ewald: electrostatic energy of ion-ion interaction
-1/2 Hartree: one part of the first double counting corrections, i assume to get E_H, one takes this value times (-1/2) ?
-exchange: I can't find out what this is about. Is it E_XC (according to the admin's statement)? then why is it included here? it should be part of the eigenvalues and there is no double counting correction for this contribution.
-V(xc)+E(xc): rest of the first double counting corrections
PAW double counting: double counting corrections 2&3
entropy T*S: is clear
eigenvalues: the one electron energies; here E_kin, E_electrostatic (electron electron and electron core) and E_XC are embedded
atomic energy: in principal E_kin of the cores

my questions now are:

1) is my understanding of the different contributions right?

2) if i am right so far, i would like to know where this (in my opinion additional) "-exchange" is coming from and why it is included into the calculation of the free energy.

3) is there any possibility to separate now the energy into E_kin, E_electrostatic and E_XC? Or am i right, that E_kin as well as the ion-electron electrostatic energy is embedded into the eigenvalues and one just can't do this separation into this three energy contributions?







<span class='smallblacktext'>[ Edited Mon May 30 2011, 09:22PM ]</span>

[quote="juhL"]
atomic energy: in principal E_kin of the cores
[/quote]
3) is there any possibility to separate now the energy into E_kin, E_electrostatic and E_XC? Or am i right, that E_kin as well as the ion-electron electrostatic energy is embedded into the eigenvalues and one just can't do this separation into this three energy contributions?
[/quote]
I think VASP already calculated E_XC. You can modify the source code slightly to print it out.

The electrostatic energy is the sum of ion-electron electrostatic interaction, the Hartree energy, the Ewald ion-ion, and the alpha term. As already noted by you, the terms are printed out already, except the ion-electron term. The ion-electron term is the expectation value of the pseudopotential. I don't know if VASP calculated it somewhere. If it doesn't, you've to do some coding to obtain the value.

For the kinetic energy, it is the expectation value of the Laplacian operator. I believe VASP should have calculated it somehow. You've to look at the source code to find out. Note the this kinetic energy is the single-particle kinetic energy. The many-particle contribution of the kinetic energy is within the correlation energy.

hi,

okay, i was kind of hoping to get around of getting into the source code, but thanks a lot, that helps!