[QE-users] users Digest, Vol 140, Issue 8

[Mw. Dr. K. Doblhoff-Dier (k.doblhoff-dier)]

Dear Wai-Ga David Ho,

Without having looked into the code, from what I recall:

ad 1 and 2: I would be careful in calling the explicitly treated electrons
"valence states", but yes, the energies should refer to the energies resulting
from the explicitly treated electrons and the pseudo-cores in your system.

ad 3.: Modern pseudo-potentials are non-local in nature. In a single determinant
picture, this means that a different potentials applies for electrons having
different l,m-quantum numbers (semi-local form) or different n-l-m orbitals
(separable or fully non-local form). Usually, part of the potential, containing
the long range part, (or the total potential of one of the channels) is defined
as "local" and applies to all l,m-quantum numbers/orbitals. A "correction" is
then still needed for the other channels, this is the "non-local" part of the
interaction energy. There are lots of good introductions around, but for a quick
view of the equations, you could, for example, have a look at the PhD thesis of
Peter David Haynes: https://www.tcm.phy.cam.ac.uk/~pdh1001/thesis/node19.html
<https://www.tcm.phy.cam.ac.uk/~pdh1001/thesis/node19.html> (see eqns. 3.75 an
3.76).

Hope that helps,

Best regards,

Katharina Doblhoff-Dier, Leiden University


> 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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