[Pw_forum] negative occupations in DFT+U for nonmagnetic semiconductor

[Mostafa Youssef]

Dear all,

I'm relaxing the structure of rutile TiO2 using ultrasoft pseudopotentials for Ti and O and PBEsol + U with U=5 eV on Ti.  For that purpose I use occupations = 'fixed'.  But I found that one of the Ti ions has negative occupations. To me this looks a bit strange since I'm not using any smearing.  The same result can be obtained by another set of PP. Improving the cutoffs or the k-point sampling does not resolve the problem. Any thoughts about the reason and possible remedies are appreciated.  I copy below the occupation matrices for the two Ti ions in the cell and the input file.


Thank you,
Mostafa Youssef
MIT

The matrices are:

atom    1   Tr[ns(na)] =   2.70769
    eigenvalues:
  0.142  0.177  0.182  0.417  0.436
    eigenvectors:
  0.675  0.000  0.000  0.325  0.000
  0.000  0.000  0.500  0.000  0.500
  0.000  0.000  0.500  0.000  0.500
  0.000  1.000  0.000  0.000  0.000
  0.325  0.000  0.000  0.675  0.000
    occupations:
  0.231  0.000  0.000  0.000 -0.129
  0.000  0.309 -0.127  0.000  0.000
  0.000 -0.127  0.309  0.000  0.000
  0.000  0.000  0.000  0.177  0.000
 -0.129  0.000  0.000  0.000  0.328
atom    2   Tr[ns(na)] =   2.70768
    eigenvalues:
  0.142  0.177  0.182  0.417  0.436
    eigenvectors:
  0.675  0.000  0.000  0.325  0.000
  0.000  0.000  0.500  0.000  0.500
  0.000  0.000  0.500  0.000  0.500
  0.000  1.000  0.000  0.000  0.000
  0.325  0.000  0.000  0.675  0.000
    occupations:
  0.231  0.000  0.000  0.000  0.129
  0.000  0.309  0.127  0.000  0.000
  0.000  0.127  0.309  0.000  0.000
  0.000  0.000  0.000  0.177  0.000
  0.129  0.000  0.000  0.000  0.328
N of occupied +U levels =    5.415371

The input file:
&CONTROL
   calculation =   'vc-relax'   ,
   verbosity = 'high' ,
   restart_mode = 'from_scratch' ,
   outdir='./' ,
   pseudo_dir = './' ,
   tstress = .true.  ,
   tprnfor= .true.  ,
   nstep = 2000 ,
   etot_conv_thr = 1.0D-7  ,
   forc_conv_thr = 4.0D-5 ,
 /
 &SYSTEM
   ibrav = 0 ,
    nat  =  6 ,
   ntyp  =  2 ,
   nbnd  = 48 ,
  ecutwfc  =  45 ,
  ecutrho  =  360 ,
  nosym =.true.
  occupations = 'fixed',
  lda_plus_u = .true.,
  Hubbard_U(1) = 5.0 ,
  Hubbard_U(2) = 0.0 ,
 /
 &ELECTRONS
                    diagonalization='david',
                    mixing_mode = 'plain' ,
                    mixing_beta = 0.7,
                    startingwfc = 'random',
                    conv_thr  =  1.0d-8  ,
  /
&ions
    ion_dynamics='bfgs'
/
&CELL
   cell_dynamics = 'bfgs' ,
   cell_dofree = 'shape',
   press_conv_thr = 0.5 ,
 /
CELL_PARAMETERS  angstrom
    4.6320252669841118    0.0000000000000000    0.0000000000000000
    0.0000000000000000    4.6320252669841118    0.0000000000000000
    0.0000000000000000    0.0000000000000000    2.9608930000414442
ATOMIC_SPECIES
  Ti   47.867   ti_pbesol_v1.4.uspp.F.UPF
  O    15.9994  o_pbesol_v1.2.uspp.F.UPF
ATOMIC_POSITIONS crystal
Ti   0.0000000000000000  0.0000000000000000  0.0000000000000000
Ti   0.5000000000000000  0.5000000000000000  0.5000000000000000
O    0.3048741584772117  0.3048741584772117  0.0000000000000000
O    0.6951258415227883  0.6951258415227883  0.0000000000000000
O    0.8048741584772117  0.1951258415227883  0.5000000000000000
O    0.1951258415227883  0.8048741584772117  0.5000000000000000
K_POINTS automatic
  4 4 6  1 1 1

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