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

[Stefano de Gironcoli]

The level occupations are not negative as seen from the eigenvalues. 
Some of the matrix elements are negative but this only tells the relative sign of the atomic orbitals components in the occupied states

stefano 
(sent from my phone)

> On 22 Mar 2016, at 07:54, Mostafa Youssef <myoussef at mit.edu> wrote:
> 
> 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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