Bugfix: fixes the offdiagonal terms of some quantities

Description

Bugfix: fixes the off-diagonal terms of some noncollinear quantities

• The off-diagonal paramagnetic current was missing 1/2i prefactor
• The paramagnetic current and KED off diagonal terms were inverted (down-up instead of up-down)

News snippet

Bugfix: fixes the off-diagonal terms of some noncollinear quantities

Checklist

• I have checked that my code follows the Octopus coding standards
• I have added tests for all the new features added in this request.

changed milestone to %10.0

added Bug label

Codecov Report

Merging #954 into release-10.0 will increase coverage by 1.85%. The diff coverage is 0.00%.

@@               Coverage Diff                @@
##           release-10.0     #954      +/-   ##
================================================
+ Coverage         69.20%   71.06%   +1.85%     
================================================
  Files               506      506              
  Lines             98380    98783     +403     
================================================
+ Hits              68088    70204    +2116     
+ Misses            30292    28579    -1713     

Impacted Files	Coverage Δ
src/states/states_elec.F90	84.27% <0.00%> (+0.59%)
src/math/cufft.cc	7.14% <0.00%> (-2.86%)
src/math/fft_inc.F90	65.34% <0.00%> (-2.70%)
src/math/fft.F90	70.81% <0.00%> (-1.19%)
src/hamiltonian/functionals.F90	80.27% <0.00%> (-0.62%)
src/main/main.F90	92.15% <0.00%> (-0.58%)
src/system/linear_solver_inc.F90	63.67% <0.00%> (-0.07%)
src/hamiltonian/vxc_inc.F90	67.85% <0.00%> (+<0.01%)
src/basic/utils.F90	95.97% <0.00%> (+0.02%)
src/td/td_write.F90	58.39% <0.00%> (+0.03%)
... and 43 more

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assigned to @micael.oliveira

@nicolastd Just to be sure, the convention we are using is this one,

$\rho^{\alpha\beta} = \sum_i \psi_i^{\beta^\dagger} \psi_i^\alpha$

right? (at least that's the one I used whenever I implemented some non-collinear spin stuff in Octopus)

Yes, this is what we are using. I checked that this is what we do for the density. As you can see, gradient and Laplacian of the density had the same definition, but not the paramagnetic current and tau.

Great, I just wanted to make sure we were being consistent.

approved this merge request

mentioned in commit 12e43f56

merged

added Bugfix in Changelog labels