Calculate U for LSDA+U: Difference between revisions

Revision as of 17:44, 8 August 2019

Task

In this exercise you will calculate the U parameter for the LSDA+U treatment of Ni d-electrons in NiO using the linear response ansatz of Cococcioni et al..^[1]

POSCAR

For this calculation we will use a 2×2×2 supercell of AFM-II NiO:

AFM  NiO
   4.03500000 
 2.0000000000   1.0000000000   1.0000000000 
 1.0000000000   2.0000000000   1.0000000000 
 1.0000000000   1.0000000000   2.0000000000 
  1 15   16 
Direct
 0.0000000000   0.0000000000   0.0000000000 
 0.2500000000   0.2500000000   0.2500000000 
 0.0000000000   0.0000000000   0.5000000000 
 0.2500000000   0.2500000000   0.7500000000 
 0.0000000000   0.5000000000   0.0000000000 
 0.2500000000   0.7500000000   0.2500000000 
 0.0000000000   0.5000000000   0.5000000000 
 0.2500000000   0.7500000000   0.7500000000 
 0.5000000000   0.0000000000   0.0000000000 
 0.7500000000   0.2500000000   0.2500000000 
 0.5000000000   0.0000000000   0.5000000000 
 0.7500000000   0.2500000000   0.7500000000 
 0.5000000000   0.5000000000   0.0000000000 
 0.7500000000   0.7500000000   0.2500000000 
 0.5000000000   0.5000000000   0.5000000000 
 0.7500000000   0.7500000000   0.7500000000 
 0.1250000000   0.1250000000   0.1250000000 
 0.3750000000   0.3750000000   0.3750000000 
 0.1250000000   0.1250000000   0.6250000000 
 0.3750000000   0.3750000000   0.8750000000 
 0.1250000000   0.6250000000   0.1250000000 
 0.3750000000   0.8750000000   0.3750000000 
 0.1250000000   0.6250000000   0.6250000000 
 0.3750000000   0.8750000000   0.8750000000 
 0.6250000000   0.1250000000   0.1250000000 
 0.8750000000   0.3750000000   0.3750000000 
 0.6250000000   0.1250000000   0.6250000000 
 0.8750000000   0.3750000000   0.8750000000 
 0.6250000000   0.6250000000   0.1250000000 
 0.8750000000   0.8750000000   0.3750000000 
 0.6250000000   0.6250000000   0.6250000000 
 0.8750000000   0.8750000000   0.8750000000

Atoms 1-16 are Ni and atoms 17-32 are O.

Note that the Ni atoms are split into two groups: atom 1, and atom 2-15. This trick breaks the symmetry of the Ni sub-lattice and allows us to treat atom 1 differently from atom 2-15. Our POTCAR file has to reflect the fact that we now formally have 3 "species" (2 ×Ni + 1×O), i.e., we concatenate two Ni POTCAR files and one O POTCAR file:

cat Ni/POTCAR Ni/POTCAR O/POTCAR > POTCAR

KPOINTS

Gamma only
 0
Monkhorst
 1 1 1 
 0 0 0

$U = \chi^{-1}-\chi_0^{-1} \approx \frac{1}{0.131333}-\frac{1}{0.492333} = 5.58 \; eV$

References

↑ M. Cococcioni and S. de Gironcoli, Phys. Rev. B 71, 035105 (2005).

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[cococcioni:2005-1] M. Cococcioni and S. de Gironcoli, Phys. Rev. B 71, 035105 (2005).

[1]

@@ Line 51: / Line 51: @@
 Note that the Ni atoms are split into two groups: atom 1, and atom 2-15.
 This trick breaks the symmetry of the Ni sub-lattice and allows us to treat atom 1 differently from atom 2-15.
-Our {{FILE|POTCAR}} file has to reflect the fact that we now formally have 3 "species" (2 &times;Ni + 1&times;O):
+Our {{FILE|POTCAR}} file has to reflect the fact that we now formally have 3 "species" (2 &times;Ni + 1&times;O),
+''i.e.'', we concatenate two Ni {{FILE|POTCAR}} files and one O {{FILE|POTCAR}} file:
   cat Ni/POTCAR Ni/POTCAR O/POTCAR > POTCAR