scf total energy when U+V are non-zero is different between QE and QE+SIRIUS

[gsavva]

The total energies calculated using QE and QE-SIRIUS when the Hubbard U & V values are non-zero are different:

QE        !    total energy              =    -373.24928416 Ry
QE-SIRIUS !    total energy              =    -370.86624286 Ry

I'm using the input file of example10 (LiCoO2, non-magnetic insulator) as found in q-e/HP/examples https://gitlab.com/QEF/q-e/-/tree/develop/HP/examples.

The Hubbard U & V parameters are both changed from 0.0001 to 3.0

HUBBARD {ortho-atomic}
U Co-3d 3.0
V Co-3d O-2p 1 2 3.0

The input file, pseudopotentials, execution script and output files are available here: non_zero_U_V.zip

The version of QE used is 7.1
QE-SIRIUS was installed via spack so the branch used is q-e-sirius@develop-ristretto and sirius@develop.
The output files contain the exact commit hashes of the executables used.

For comparison, if the U & V values are not changed and thus example10 runs as provided (U, V = 0.0001), then QE and QE-SIRIUS calculate total energies as below:

QE        !    total energy              =    -373.36904960 Ry
QE-SIRIUS !    total energy              =    -373.36894085 Ry

[toxa81]

This small difference is ok. The GGA XC implementation is slighlty different between QE and LibXC. Whas is important is that forces and stress are similar.

[gsavva]

I initially started this comparison testing of forces & stresses (QE vs QE_SIRIUS) using a non-zero Hubbard U for the Hubbard atoms to evaluate (a) the total forces and (b) the Hubbard contribution to forces.
However, for some systems I had convergence issues (already communicated to @simonpintarelli ) and the total energies were different (as in the example reported above).
I'm now working on forces & stresses comparison without changing the U value (set to 0.0001 in the examples)

[gsavva]

Updating the issue with more results for different values of Hubbard U and V.
Using example10 as above, found in q-e/HP/examples.

U = 1e-4
V = 1e-4
QE     !    total energy              =    -373.36904960 Ry
SIRIUS !    total energy              =    -373.36894085 Ry

U = 3.0
V = 3.0
QE     !    total energy              =    -373.24928416 Ry
SIRIUS !    total energy              =    -370.86624283 Ry

U = 6.0
V = 0.0001
QE     !    total energy              =    -373.13921250 Ry
SIRIUS !    total energy              =    -368.92175896 Ry

U = 6.5
V = 0.0001
QE     !    total energy              =    -373.12143594 Ry
SIRIUS !    total energy              =    -368.61994388 Ry

U = 6.5
V = 0.7
QE     !    total energy              =    -373.12144331 Ry
SIRIUS !    total energy              =    -368.61994274 Ry
 

[mtaillefumier]

A factor 2 was missing in the calculation of the kinetic energy (the one-electron contribution). q-e-sirius now works fine for U \neq 0 V = 0.
U+V is still giving a different total energy though.

[mtaillefumier]

Should be fixed by PR #788. The mistake was a factor 2.0 during the calculation of the hubbard U contribution to the hubbard potential. The generalized version of Hubbard (reduce to dudarev version) is on by default.

[gsavva]

Testing results (@mtaillefumier):

HP/examples/example10 (LiCoO2, non-magnetic insulator): OK

U = 6.5
V = 0.7
QE     !    total energy              =    -373.12144331 Ry
SIRIUS !    total energy              =    -373.12142824 Ry

HP/examples/example01 (same as example10, without V): OK

U = 7.8
QE     !    total energy              =    -373.07581518 Ry
SIRIUS !    total energy              =    -373.07580009 Ry

HP/examples/example06 (Ni2MnGa, ferromagnetic metal): OK

U Mn-3d 5.0
U Ni-3d 8.3
QE     !    total energy              =    -585.95912167 Ry
SIRIUS !    total energy              =    -585.95908712 Ry
QE          total magnetization       =     5.18 Bohr mag/cell
SIRIUS      total magnetization       =    17.50 Bohr mag/cell

**Note that the energies were correct even before the fix (#788). The difference in magnetization is discussed in #786
HP/examples/example08 (NiO2, 2D system, nonmagnetic insulator): OK

U Ni-3d 8.65
QE     !    total energy              =    -167.47501933 Ry
SIRIUS !    total energy              =    -167.47572923 Ry

[toxa81]

New round of tests should be done with electronic-structure/q-e-sirius#60

[gsavva]

@toxa81 I'm checking this...