[QE-users] Translated orbitals in periodic calculation

[Phillip Thomas]

Dear QE team,

I have an issue regarding orbitals generated from QE 7.0 runs on two
different translated variants of a Silicon lattice. I am using a primitive
cubic cell containing 8 atoms instead of the simplest 2-atom unit cell (as
I need to pass the output orbitals to another program which only accepts a
tetragonal cell geometry).

Here is the input file for 'pw.x' for the first variant:
--------------------------------
&control
   prefix = 'silicon'
   calculation = 'scf'
   tstress = .true.
   etot_conv_thr = 1d-5
   forc_conv_thr = 1d-4
/
&system
   ibrav = 1
   celldm(1) = 10.173697855629921
   nat = 8
   ntyp = 1
   nbnd = 32
   ecutwfc = 80.0
/
&electrons
   electron_maxstep = 100
   conv_thr = 1.0d-8
   mixing_mode = 'plain'
   mixing_beta = 0.7
   mixing_ndim = 8
   diagonalization = 'david'
   diago_david_ndim = 4
   diago_full_acc = .true.
/
&ions
/
ATOMIC_SPECIES
  Si  28.086  Si.pw-mt_fhi.UPF
ATOMIC_POSITIONS alat
  Si  0.00  0.00  0.00
  Si  0.00  0.50  0.50
  Si  0.50  0.00  0.50
  Si  0.50  0.50  0.00
  Si  0.25  0.25  0.25
  Si  0.75  0.75  0.25
  Si  0.25  0.75  0.75
  Si  0.75  0.25  0.75
K_POINTS automatic
4 4 4 0 0 0
--------------------------------
The second variant has the same input file except that the coordinates of
the atoms are shifted to:

  Si  0.125  0.125  0.125
  Si  0.125  0.625  0.625
  Si  0.625  0.125  0.625
  Si  0.625  0.625  0.125
  Si  0.375  0.375  0.375
  Si  0.875  0.875  0.375
  Si  0.375  0.875  0.875
  Si  0.875  0.375  0.875

Both calculations give the same total energy, -63.52598191 Ry, as I would
expect, and the same band structure (except that three additional symmetry
equivalent bands are printed out in the latter case); the bands for
matching KPOINTS are also the same in both runs, all as expected. Here are
the bands for the 0 0 0 KPOINT for reference:
--------------------------------
     End of self-consistent calculation

          k = 0.0000 0.0000 0.0000 ( 12797 PWs)   bands (ev):

    -5.8606  -1.6207  -1.6207  -1.6207  -1.6207  -1.6207  -1.6207   3.3705
     3.3706   3.3706   3.3706   3.3706   3.3706   6.2827   6.2827   6.2827
     6.8712   6.8712   6.8712   6.8712   6.8712   6.8712   8.8517   8.8517
     8.8517   9.6765  14.0241  14.0783  14.0783  16.4618  16.4618  16.4618
--------------------------------
Now I would like to generate the orbitals for the 0 0 0 KPOINT in cube file
format, so here is my input to ''pp.x':
--------------------------------
 &inputpp
 prefix='silicon'
 plot_num=7
 kband(1)=1
 kband(2)=          32
 kpoint=1
 lsign=.true.
 /
 &plot
 iflag=3
 output_format=6
 /
--------------------------------

When I visually inspect the orbitals, I find that many of the orbitals are
qualitatively different for the two translated variants of the lattice;
they are not simply translated variants of the same orbital as I would
expect. I have attached plots of the highest occupied orbital (#16) as
examples.

So I am curious, is there a mistake in my inputs or procedure that would
cause differences like these? If not, then is there a way in QE that I can
generate the orbitals such that they are translationally invariant? Many
thanks for looking into this!

Kind regards,

Phillip Thomas, Ph.D.
National Energy Research Scientific Computing Center
Lawrence Berkeley National Laboratory
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