Add total energy module

[RandomDefaultUser]

In GitLab by @RandomDefaultUser on Jan 18, 2021, 10:00

Now that we have examples from Sandia, we need to add this asap.

[RandomDefaultUser]

In GitLab by @RandomDefaultUser on Jan 19, 2021, 21:40

Total energy works (as tested on QE DOS and densities). The only thing missing is a test using the LDOS, for which I am currently lacking either a small example to be run locally or the installation of the updated total_energy module on hemera.

By Fiedler, Lenz (FWU) - 146409 on 2021-01-19T21:40:44 (imported from GitLab)

[RandomDefaultUser]

In GitLab by @RandomDefaultUser on Jan 21, 2021, 13:20

@schmer52: The error of 0.2 Ry above is the total error, meaning that this results in a deviation of about 10 meV/atom in the 256 Al cell.

By Cangi, Dr. Attila (FWU) - 139621 on 2021-01-21T13:20:54 (imported from GitLab)

[RandomDefaultUser]

In GitLab by @RandomDefaultUser on Jan 21, 2021, 13:21

But I agree, our numbers look good.

By Cangi, Dr. Attila (FWU) - 139621 on 2021-01-21T13:21:27 (imported from GitLab)

[RandomDefaultUser]

In GitLab by @RandomDefaultUser on Jan 20, 2021, 13:45

Update: Using the LDOS (which seems to be better than the DOS for this example, I don't understand why) I get -180.61445255890345 Ry, which is even better.

By Fiedler, Lenz (FWU) - 146409 on 2021-01-20T13:45:39 (imported from GitLab)

[RandomDefaultUser]

In GitLab by @RandomDefaultUser on Jan 20, 2021, 12:57

The total energy module works and Mani is installing it on hemera.
I tested the module using the 36 Atom Al supercell also mentioned in #28 . The QE calculation of this supercell gives

     estimated scf accuracy    <          1.7E-09 Ry
     smearing contrib. (-TS)   =      -0.00243886 Ry
     internal energy E=F+TS    =    -179.00615680 Ry

     The total energy is F=E-TS. E is the sum of the following terms:
     one-electron contribution =      83.67164706 Ry
     hartree contribution      =      10.80127314 Ry
     xc contribution           =     -95.48558928 Ry
     ewald contribution        =    -177.99348773 Ry

Using QE, I extracted the density and DOS from this calculation (I skipped the LDOS for this test, to avoid any potential errors.)
Drawing on the DOS I get

    smearing contribution (FESL) = -0.002340884052959653
    band energy (FESL) = 22.582953317130595

and drawing on the density I get

    Rho* V_hxc (FESL) = 59.95625424
    hartree contribution (FESL) = 10.8012743
    xc contribution (FESL) = -95.72383858
    ewald contribution (FESL) = -179.35386304

This yields a total energy of -181.7395606503153 Ry compared to QE -179.00615680 Ry. Given the limited scope of the calculation I feel this is a reasonably
good agreement. Do you agree @cangi21 @schmer52 or should I investigate this matter further? I will definitely verify the results once I can use the module in hemera.
The restriction to 36 is mainly because my local machine cannot handle 256 atoms.
In any case I will merge the branch for now.

By Fiedler, Lenz (FWU) - 146409 on 2021-01-20T12:57:58 (imported from GitLab)

[RandomDefaultUser]

In GitLab by @RandomDefaultUser on Jan 20, 2021, 16:10

Great progress! The deviation between the QE total energy and the LDOS total energy looks right.
I looked at the numbers of the comparison between these two energies with the Sandia code. There the deviation was about 0.2 Ry. That example was a supercell with 256 atoms and a cartesian mesh with 8 million points. Quantities that have an influence on the accuracy are the DFT parameters (k points) but also the cartesian mesh plays a significant role.
Overall, I would say everything looks good here.
Once everything is set up on hemera, we can assess the Sandia results.

By Cangi, Dr. Attila (FWU) - 139621 on 2021-01-20T16:10:20 (imported from GitLab)

[RandomDefaultUser]

In GitLab by @RandomDefaultUser on Jan 20, 2021, 22:49

Sorry for being late on this one.

The numbers look good! @cangi21 was that 0.2 Ry or Ry/atom? I can only think in meV/atom :) The numbers above would result in a difference of 1033 meV/atom, which is not huge but still sizable. I have not yet an intuition for the errors that one would expect.

Regarding the tested system: When calculating with the same cutoff, k-grid spacing (in 1/Ang) and same FESL SNAP grid spacing (or well grid density...), then the difference measured in energy/atom must be independent of the system size, so you could do local tests with primitive cells, if I'm not mistaken.

By Schmerler, Dr. Steve (FWCC) - 131252 on 2021-01-20T22:49:07 (imported from GitLab)

[RandomDefaultUser]

In GitLab by @RandomDefaultUser on Jan 21, 2021, 09:47

@cangi21 : Not only is the mesh different, the k-grid is also only 6x6x6 in this example compared to the 8x8x8 in the paper. We'll see how it performs with the Sandia data but I am optimistic as well.

@schmer52 : That makes sense, I could rerun the QE calculations with a bigger k-grid, but considering that Mani said he would have the new module up on hemera tomorrow I think I will wait for that and then just test on the LDOS data there.

By Fiedler, Lenz (FWU) - 146409 on 2021-01-21T09:47:24 (imported from GitLab)

[RandomDefaultUser]

In GitLab by @DanielKotik on Mar 23, 2021, 18:00

mentioned in commit 66f9eb8