# [Pw_forum] error on phonon calculation (root not converged)

Liping YU lyu7 at ncsu.edu
Wed Apr 12 04:39:33 CEST 2006

```Paolo Giannozzi wrote:

>On Monday 10 April 2006 19:31, Liping YU wrote:
>
>
>
>>1x1x1 cell
>>Total energy: -275.21362101 ( *4= -1100.85448404 )
>>
>>
>
>
>
>>k = 0.0000 0.0000 0.0000 ( 1045 PWs) bands (ev):
>>
>>
>
>
>
>>-45.3707 [...]
>>
>>
>
>
>
>>2x2x1 super cell
>>Total energy: -1100.81820918
>>
>>
>
>
>
>>k = 0.0000 0.0000 0.0000 ( 4189 PWs) bands (ev):
>>
>>
>
>
>
>>-45.2796 -45.2775 -45.2775 -45.2757 [...]
>>
>>
>
>total energies per cell are not the same. Also eigenvalues are clearly
>not the same. Your 2x2x1 supercell is not 4 times a 1x1x1 cell.
>
>
Yes. The total energy difference between them is
-275.21362101 *4 - (-1100.81820918) = 0.03627486 ryd
What's the reason for this difference? Is it due to PP of Sr?
If this is true, then as paolo said, eigenvalues are not the same and
I guess band gaps of them might be either not same (need to check).
So can this possible bandgap difference cause to the big difference for
dielectric constant in xx and yy in two cells?

To check this for PTO, I did the same calculation for tetragonal PbTiO3
with k-point grid of 4*4*4 for 1x1x1 cell and 2*2*4 for 2x2x1 supercell,
using the same PPs of Ti and O as those in STO. I got that the total energy
difference between them is
-333.74323319*4 - (-1334.97293292) = 0.00000016 ryd
which is quite reasonable.

Here I attached the input files of STO.
1x1x1 unit cell,
========================================================
&CONTROL
title = 'relaxed cubic SrTiO3' ,
calculation = 'scf' ,
restart_mode = 'from_scratch' ,
outdir = './tmp/' ,
pseudo_dir = '../../pseudo/' ,
prefix = 'cb-st' ,
tstress = .true. ,
tprnfor = .true. ,
/
&SYSTEM
ibrav = 1,
celldm(1) = 7.27663673,
nat = 5,
ntyp = 3,
ecutwfc = 30 ,
ecutrho = 270 ,
/
&ELECTRONS
conv_thr = 1.D-8 ,
/
ATOMIC_SPECIES
Sr 87.62000 038-Sr-ca-sp-vgrp.uspp.UPF
Ti 47.86700 022-Ti-ca-sp-vgrp.uspp.UPF
O 16.00000 008-O-ca--vgrp.uspp.UPF
ATOMIC_POSITIONS crystal
Sr 0.000000000 0.000000000 0.000000000
Ti 0.500000000 0.500000000 0.500000000
O 0.000000000 0.500000000 0.500000000
O 0.500000000 0.000000000 0.500000000
O 0.500000000 0.500000000 0.000000000
K_POINTS automatic
4 4 4 0 0 0
=========================================================

2x2x1 supercell
=========================================================

&CONTROL
title = 'scf on cubic perovskite SrTiO3' ,
calculation = 'scf' ,
restart_mode = 'from_scratch' ,
outdir = './tmp/' ,
pseudo_dir = '../../pseudo/' ,
prefix = 'cb-st' ,
tstress = .true. ,
tprnfor = .true. ,
/
&SYSTEM
ibrav = 6,
celldm(1) = 14.55327346
celldm(3) = 0.5
nat = 20,
ntyp = 3,
ecutwfc = 30 ,
ecutrho = 270 ,
/
&ELECTRONS
conv_thr = 1.D-8 ,
/
ATOMIC_SPECIES
Sr 87.62000 038-Sr-ca-sp-vgrp.uspp.UPF
Ti 47.86700 022-Ti-ca-sp-vgrp.uspp.UPF
O 16.00000 008-O-ca--vgrp.uspp.UPF
ATOMIC_POSITIONS crystal
Sr 0.00 0.00 0.00
Sr 0.50 0.00 0.00
Sr 0.00 0.50 0.00
Sr 0.50 0.50 0.00
O 0.25 0.25 0.00
O 0.25 0.75 0.00
O 0.75 0.25 0.00
O 0.75 0.75 0.00
Ti 0.25 0.25 0.5
Ti 0.25 0.75 0.5
Ti 0.75 0.25 0.5
Ti 0.75 0.75 0.5
O 0.00 0.25 0.5
O 0.00 0.75 0.5
O 0.50 0.25 0.5
O 0.50 0.75 0.5
O 0.25 0.00 0.5
O 0.75 0.00 0.5
O 0.25 0.50 0.5
O 0.75 0.50 0.5
K_POINTS automatic
2 2 4 0 0 0

```