[Pw_forum] Comparing LDA+U simulations

[Pietro Bonfa']

Dear You,

I'm working with LDA+U on a magnetic system with hexagonal symmetry.

Up until now I have been using the atomic orbitals projection scheme and
I get occupation values like:

Last iteration:
atom    9   Tr[ns(na)] (up, down, total) =   4.40532  0.48496  4.89028
   spin  1
    eigenvalues:
  0.837  0.837  0.903  0.914  0.914
    eigenvectors:
  0.000  0.000  1.000  0.000  0.000
  0.222  0.121  0.000  0.656  0.001
  0.121  0.222  0.000  0.001  0.656
  0.233  0.424  0.000  0.000  0.343
  0.424  0.233  0.000  0.343  0.000
    occupations:
  0.903 -0.000 -0.000 -0.000 -0.000
 -0.000  0.888 -0.000  0.000 -0.037
 -0.000 -0.000  0.888 -0.037 -0.000
 -0.000  0.000 -0.037  0.863  0.000
 -0.000 -0.037 -0.000  0.000  0.863
   spin  2
    eigenvalues:
  0.053  0.053  0.084  0.148  0.148
    eigenvectors:
  0.000  0.000  1.000  0.000  0.000
  0.513  0.000  0.000  0.269  0.218
  0.000  0.513  0.000  0.218  0.269
  0.000  0.487  0.000  0.230  0.284
  0.487  0.000  0.000  0.284  0.230
    occupations:
  0.084 -0.000 -0.000 -0.000 -0.000
 -0.000  0.099 -0.000  0.000  0.047
 -0.000 -0.000  0.099  0.047 -0.000
 -0.000  0.000  0.047  0.101  0.000
 -0.000  0.047 -0.000  0.000  0.101
atomic mag. moment =     3.920354

The eigenvectors correctly describe the superposition of symmetrized d
orbitals (with the exception of dz^2) and the occupation matrix is
almost diagonal. However the occupations are quite far from 0 or 1 (thus
indicating that that projection scheme is not very accurate).

Now I want to compare a ferromagnetic and an antiferromagnetic solution
(obtained with the same value for U).

However the differences in the total energies are of the same order of
magnitude of the difference of the Hubburd energy contributions, i.e.

FM:
Hubbard energy            =       0.27813179 Ry
Total energy              =     -1798.78355984 Ry

AFM:
Hubbard energy            =       0.28726541 Ry
Total energy              =     -1798.79322285 Ry

I believe that it is possible to compare the two total energies but I
think that spurious contributions arising from the different projections
should be negligible. Is this correct?

I can use the poor man wannier tool to possibly reduce the size of the
Hubburd contribution but it will always be comparable with the energy
difference that I'm trying to characterize.

Concluding, what is the correct way to handle this problem?

Thanks in advances,
Pietro Bonfa'


-- 
Pietro Bonfa'
Dipartimento di Fisica e Scienze della Terra "Macedonio Melloni"
Viale delle Scienze 7A
43124 Parma - Italy