Symmetrization of the occupation matrices

Description

Symmetrization of the occupation matrices for DFT+U with k-point symmetries.

In order to get good results for DFT+U calculations with k-point symmetries, it is important to symmetrize the density matrix. For spherical harmonics, this is easily done as a rotated spherical harmonics is a linear combination of the spherical harmonics.

The code ow automatically symmetrizes the occupation matrices if k-point symmetries or density symmetrization are activated.

News snippet

Symmetrization of the occupation matrices for DFT+U with k-point symmetries.

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.

src/hamiltonian/lda_u.F90

@@ -1148,7 +1148,7 @@ contains
     type(grid_t),         intent(in)    :: gr
     type(states_elec_t),  intent(in)    :: st
 
-    integer :: nsym, iop, ios, iatom, iatom_sym, im, ios_sym
+    integer :: nsym, iop, ios, iatom, iatom_sym, ios_sym
 
     PUSH_SUB(build_symmetrization_map)
 
@@ -1203,7 +1203,7 @@ contains
     type(symmetries_t),   intent(in)    :: symm
     real(real64),         intent(inout) :: weight(:,:,:)
 
-    integer :: im, imp, iop, ll, mm
+    integer :: im, imp, iop, mm
     real(real64), allocatable :: orb(:,:), orb_sym(:), ylm(:)
     type(submesh_t) :: sphere
     real(real64) :: rc, norm, origin(space%dim)