[QE-users] General questions on pw.x's SCF output using pw2casino flag

[Wai-Ga Ho]

Hello QE community,


Some time ago, I was attempting to use the -pw2casino flag to deconstruct the total energy in terms of its physical contributions, such as its kinetic energy term, etc (see https://www.mail-archive.com/users@lists.quantum-espresso.org/msg35391.html for my previous post).


I've succeeded when using ultrasoft pseudopotentials, but I now have some further questions related to the output from the -pw2casino SCF option. I attempted to find some answers online, but was unable to find documentation or forum discussions, and I was also unable to figure out what was being implemented in the pw2casino.f90 and pw2casino_write.f90 codes I found on github...


Anyways, my questions mainly have to deal with the physical interpretations of the deconstructed energy values.


When using the pw2casino flag, the contributions given to us are:

 - Kinetic energy
 - Local energy
 - Non-Local energy
 - Ewald energy
 - xc contribution
 - hartree energy


Now from my understanding of KS density functional theory, the total energy is comprised of the following:

-Kinetic energy (itinerancy of electrons in their KS orbitals)

-Hartree energy (the classical Coulomb interaction between electrons)

-Ewald energy (the classical Coulomb interaction between nuclei)

-External energy (the classical Coulomb interaction between the electron density and the nuclei)

-XC energy (everything else i.e. exchange, correlation, and a bit of kinetic energy error from taking the KS ansatz)


Furthermore, from a DFT approach that uses PAW pseudopotentials, I know that we have to map between all-electron and pseudo expectation values, so that we make a distinction between pseudoenergies and the more physical all-electron energies (see here for more information https://journals.aps.org/prb/abstract/10.1103/PhysRevB.50.17953). Now the PAW formalisms and approach are generalizable to other pseudopotential methods, so I assume that we deal with the same kind of all-electron vs pseudo distinction when using ultrasoft pseudopotentials.



Now that I've laid out the basic prerequisite knowledge I currently have, my questions about the pw2casino energy deconstruction are as follows:

1) The output of the total energy is understood to be the pseudoenergy (i.e. the energy of the system in the pseudospace of ultrasoft potentials where the hard nuclear potentials are being weakened by the core electrons). Am I correct in assuming the deconstructed contributions are pseudoenergies well? Because they sum up to the total pseudoenergy that is output.
2) As a continuation off of 1), does this mean that the Kinetic Energy produced using the pw2casino flag only sums over the valence states  (since our core electrons are approximately frozen out in this pseudopotential approach)?
3) What are the physical meanings behind the "Local energy" and "Non-local energy" values that are being output by pw2casino? If we compare my list of contributions to the list produced by pw2casino, it seems as if these two energy contributions are connected to the External energy i.e. the energy between electron and nuclei. If this is correct, and in light of our pseudopotential approach, does this mean that the "Local energy" corresponds to that of the core electrons while the "Non-local" energy are for the valence electrons?
4) Question 3) was asked assuming that the output from pw2casino for the kinetic, ewald, XC, and hartree contributions are in line with my understanding of the energy contributions. Am I missing anything in this respect, or do they all match up?

If anyone can answer any of my questions or offer any further insight into the physical meaning behind these energy values or how they are calculated, it would be very much appreciated.

And if this is helpful for anyone, I am using PWSCF v.5.0.2 and the following pseudopotentials for MgO:
- Mg.pbe-spnl-rrkjus_psl.1.0.0.UPF
- O.pbe-nl-rrkjus_psl.1.0.0.UPF

Thank you,
Wai-Ga David Ho, Dept of Physics at Florida State University and NHMFL

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