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[Pio Baettig <baettigp@gmx.net>]

Dear Abinit-users,

I have a small problem using PAW implemented in Abinit.
I downloaded the Al-PAWs (LDA and GGA) from
http://www.wfu.edu/%7Enatalie/papers/pwpaw/periodictable/periodictable.html
and started doing convergence tests with respect to number of K-points and
the cutoff-energy. I am using Abinit 5.3.4

The first thing I noticed, is that the convergence with respect to the
energy-cutoff is quite slow, for Al around 35 Ha are needed to converge the
energy to one mHa. (8*8*8 k-points seem also to be sufficient.)

I tried the same calculations for a cubic unit cell
(a=4.05Angst, pos. 0.0 0.0 0.0;0.0 0.5 0.5;0.5 0.0 0.5;0.5 0.5;0.0 , nband=40)
and for a rhombohedral unit cell
(a=4.05/SQRT(2), alpha=60 deg, pos:0.0 0.0 0.0, nband=10)
and then took the difference of
E(cubic)-(4*E(rhomb)) which should converge to zero quite fast. (even though
the number of k-points in the irreducible Brillouin-zone is not the same
for the same mesh in the full BZ, the convergence should still be good),
but the energy-difference converges to about 0.28 Ha, which I interpret,
that I cannot compare energies of different structures.

I did not yet repeat the same calculations with another element in order to
check whether the problem is with the Al-PAWs or with the method. I hope not
to have forgotten something important in the inputs.

Please find attached the inputs used for the cubic and the rhombohedral case.
I also attach a table with the energies. Lines are for the different k-point-
meshes, columns for the different cutoff energies.
First comes LDA, then GGA,
for each I put a table with the energies of the cubic unit cell, then the
rhombohedral unit cell, then the difference (c-4r)

If someone has some insight into the behaviour, I would be very grateful

Best regards,

Pio Baettig


Al LDA      All Energies in Hartree
Cubic cell, 4 Atoms per cell
pawecutdg 50

                10 Ha        15 Ha        20 Ha        25 Ha        30 Ha     
   35 Ha        40 Ha
2*2*2     -323.818405  -325.507127  -325.547488  -325.556193  -325.563865  
-325.565574  -325.565747
4*4*4     -323.859252  -325.489153  -325.530181  -325.538974  -325.546555  
-325.548254  -325.548420
6*6*6     -323.822893  -325.495309  -325.536682  -325.545438  -325.553077  
-325.554773  -325.554938
8*8*8     -323.840451  -325.497445  -325.538481  -325.547271  -325.554878  
-325.556571  -325.556736
10*10*10  -323.832626  -325.497161  -325.538138  -325.546904  -325.554532  
-325.556224  -325.556389
12*12*12  -323.837675  -325.497580  -325.538388  -325.547160  -325.554784  
-325.556475  -325.556640
14*14*14  -323.834228  -325.498300  -325.539150  -325.547930  -325.555543  
-325.557237  -325.557402

Rhombohedral cell, 1 Atom per cell
                10 Ha        15 Ha        20 Ha        25 Ha        30 Ha     
   35 Ha        40 Ha
2*2*2      -80.915799   -81.338517   -81.348628   -81.350809   -81.352730   
-81.353157   -81.353200
4*4*4      -80.902754   -81.310862   -81.321181   -81.323385   -81.325284   
-81.325709   -81.325750
6*6*6      -80.887276   -81.306179   -81.316589   -81.318785   -81.320698   
-81.321123   -81.321164
8*8*8      -80.889724   -81.304854   -81.315185   -81.317389   -81.319295   
-81.319719   -81.319760
10*10*10   -80.887267   -81.304314   -81.314631   -81.316829   -81.318740   
-81.319164   -81.319205
12*12*12   -80.888190   -81.304104   -81.314380   -81.316580   -81.318490   
-81.318914   -81.318955
14*14*14   -80.887086   -81.303973   -81.314260   -81.316462   -81.318369   
-81.318794   -81.318834

4Atom-(4*1Atom)LDA
                10 Ha        15 Ha        20 Ha        25 Ha        30 Ha     
   35 Ha        40 Ha
2*2*2       -0.155210    -0.153059    -0.152976    -0.152958    -0.152946    
-0.152945    -0.152945
4*4*4       -0.248235    -0.245706    -0.245458    -0.245432    -0.245420    
-0.245418    -0.245418
6*6*6       -0.273791    -0.270591    -0.270325    -0.270298    -0.270284    
-0.270281    -0.270281
8*8*8       -0.281555    -0.278029    -0.277741    -0.277715    -0.277700    
-0.277697    -0.277697
10*10*10    -0.283558    -0.279907    -0.279614    -0.279588    -0.279571    
-0.279568    -0.279569
12*12*12    -0.284914    -0.281164    -0.280866    -0.280840    -0.280823    
-0.280820    -0.280821
14*14*14    -0.285882    -0.282407    -0.282110    -0.282082    -0.282066    
-0.282063    -0.282064




Al GGA cubic unitcell, 4 atoms per cell
                10 Ha        15 Ha        20 Ha        25 Ha        30 Ha     
   35 Ha        40 Ha
2*2*2     -324.221240  -325.913822  -325.953945  -325.963125  -325.971014  
-325.972678  -325.972859
4*4*4     -324.262114  -325.896183  -325.937010  -325.946272  -325.954064  
-325.955718  -325.955893
6*6*6     -324.225793  -325.902285  -325.943454  -325.952680  -325.960533  
-325.962184  -325.962357
8*8*8     -324.243307  -325.904338  -325.945162  -325.954425  -325.962245  
-325.963893  -325.964067
10*10*10  -324.235510  -325.904054  -325.944818  -325.954056  -325.961898  
-325.963545  -325.963719
12*12*12  -324.240541  -325.904466  -325.945061  -325.954305  -325.962142  
-325.963789  -325.963962
14*14*14  -324.237230  -325.905400  -325.946050  -325.955299  -325.963124  
-325.964774  -325.964948

Rhombohedral cell, 1 Atom per cell
                10 Ha        15 Ha        20 Ha        25 Ha        30 Ha     
   35 Ha        40 Ha
2*2*2      -81.016061   -81.439727   -81.449781   -81.452077   -81.454050   
-81.454466   -81.454511
4*4*4      -81.002915   -81.412074   -81.422350   -81.424667   -81.426615   
-81.427029   -81.427073
6*6*6      -80.987461   -81.407435   -81.417806   -81.420114   -81.422076   
-81.422490   -81.422534
8*8*8      -80.989922   -81.406143   -81.416437   -81.418752   -81.420707   
-81.421120   -81.421163
10*10*10   -80.987482   -81.405626   -81.415908   -81.418216   -81.420176   
-81.420589   -81.420633
12*12*12   -80.988412   -81.405432   -81.415674   -81.417984   -81.419942   
-81.420356   -81.420399
14*14*14   -80.987317   -81.405312   -81.415565   -81.417877   -81.419833   
-81.420246   -81.420290

4Atom-(4*1Atom)GGA
                10 Ha        15 Ha        20 Ha        25 Ha        30 Ha     
   35 Ha        40 Ha
2*2*2       -0.156995    -0.154916    -0.154821    -0.154816    -0.154816    
-0.154814    -0.154814
4*4*4       -0.250454    -0.247887    -0.247612    -0.247603    -0.247605    
-0.247602    -0.247602
6*6*6       -0.275948    -0.272544    -0.272229    -0.272226    -0.272227    
-0.272223    -0.272223
8*8*8       -0.283621    -0.279767    -0.279414    -0.279416    -0.279419    
-0.279413    -0.279414
10*10*10    -0.285581    -0.281552    -0.281187    -0.281192    -0.281194    
-0.281188    -0.281189
12*12*12    -0.286894    -0.282737    -0.282365    -0.282370    -0.282372    
-0.282366    -0.282367
14*14*14    -0.287963    -0.284151    -0.283791    -0.283791    -0.283794    
-0.283789    -0.283789


# Al element test
# Convergence with respect to the number of k points and e_cut.

#datasets
ndtset 49 udtset 7 7 

#Definition of the k-point grids
kptopt 1          # Option for the automatic generation of k points, taking
                  # into account the symmetry
ngkpt?1 2 2 2
ngkpt?2 4 4 4
ngkpt?3 6 6 6
ngkpt?4 8 8 8
ngkpt?5 10 10 10
ngkpt?6 12 12 12
ngkpt?7 14 14 14


#Definition of the planewave basis set
ecut1? 10.0         # Maximal kinetic energy cut-off, in Hartree
ecut2? 15.0
ecut3? 20.0
ecut4? 25.0
ecut5? 30.0
ecut6? 35.0
ecut7? 40.0

pawecutdg 50

getwfk 0         # restarting from previous wavefunctions

#Definition of the unit cell
acell 4.05 4.05 4.05 angstrom
angdeg 90.0 90.0 90.0
chkprim 0

#Definition of the atom types
ntypat 1
znucl 13

nband 40


#Definition of the atoms
natom 4
typat 1 1
xred
0.0 0.0 0.0
0.5 0.5 0.0
0.5 0.0 0.5
0.0 0.5 0.5

#Definition of the SCF procedure
nstep 100          # Maximal number of SCF cycles
toldfe 1.0d-8     # Convergence Criterion (Hartree)
#diemac  #does not need to be set, default is metallic

#DOS
#prtdos 2 #smearing=1, tetrahedron=2

#magnetism
nsppol 1

# Al element test
# Convergence with respect to the number of k points and e_cut.

#datasets
ndtset 49 udtset 7 7 

#Definition of the k-point grids
kptopt 1          # Option for the automatic generation of k points, taking
                  # into account the symmetry
ngkpt?1 2 2 2
ngkpt?2 4 4 4
ngkpt?3 6 6 6
ngkpt?4 8 8 8
ngkpt?5 10 10 10
ngkpt?6 12 12 12
ngkpt?7 14 14 14

#Definition of the planewave basis set
ecut1? 10.0         # Maximal kinetic energy cut-off, in Hartree
ecut2? 15.0
ecut3? 20.0
ecut4? 25.0
ecut5? 30.0
ecut6? 35.0
ecut7? 40.0

pawecutdg 50

getwfk 0         # restarting from previous wavefunctions

#Definition of the unit cell
acell 2.8637825 2.8637825 2.8637825 angstrom
angdeg 60.0 60.0 60.0
#chkprim 0

#Definition of the atom types
ntypat 1
znucl 13
nband 10

#Definition of the atoms
natom 1
typat 1
xred
0.0 0.0 0.0

#Definition of the SCF procedure
nstep 100          # Maximal number of SCF cycles
toldfe 1.0d-8     # Convergence Criterion (Hartree)
#diemac  #does not need to be set, default is metallic

#DOS
#prtdos 2 #smearing=1, tetrahedron=2

#magnetism
nsppol 1