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["Lukas Thulin" <lthulin@nanoptek.com>]

Hello,

 

I am trying to calculate the work function of anatase titania.  To do this I am using a slab/vacuum supercell, where I get the vacuum potential using the prt1dm command and the HOMO energy comes from a band structure plot.  I’m having some problems with the bands calculation/interpretation. 

 

1)      Despite high k-sampling (8,8,1), highly converged (toldfde=1e-9) scf run, high energy cutoffs, etc. I can’t converge the iscf run to tolwfr=1e-12.  Even for nstep=500 the calculation stops at tolwfr=6.8e-11.  Is this ok, or should I expect better convergence?

2)      Even without any vacuum the simple tetragonal supercell bands calculation doesn’t quite agree with the bulk (body centered tetragonal) bands.  There is some difference especially around the gamma point and some additional bands (blue in the plot) are found in the supercell case.

3)      As I increase the layers of vacuum I get some occupied states (green in plot) within the gap.  I don’t understand why these states appear, and for the work function calculation, should I ignore these for the HOMO energy value.

 

Thanks for any suggestions,

Luke Thulin

Nanoptek Corp

 

I am using Abinit v5.8.4 with the following input files:

 

# Crystalline anatase titania

#Geometry optimization parameters, none for this case.
ionmov 0

#Use to get a vacuum potential reference
prt1dm 1

#Definition of the unit cell;
acell 3.802 3.802 9.68411/2 angstrom    # a,a,c/2

#Orient the vacuum above the (001) plane.
rprim   1.0            0.0              0.0  
        0.0            1.0              0.0  
        0.0            0.0              6.5 
chkprim 0   # This input variable allows to use non-primitive unit cells.

#Definition of the atom types
ntypat 2          # There are two types of atoms: Ti and O
znucl 22 8

#Definition of the atoms
natom 18           # There are 18 atoms in our supercell.
typat 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2  
xangst              
   0.000  0.000  0.0000000000E+00   #layer 1
   0.000  1.901  2.4210275000E+00
   0.000  0.000 -2.0020593599E+00
   0.000  0.000  2.0020593599E+00
   0.000  1.901  4.1896814012E-01   
   0.000  1.901  4.4230868599E+00
   1.901  1.901  4.8420550000E+00   #layer 2
   1.901  3.802  7.2630825000E+00
   1.901  1.901  2.8399956400E+00
   1.901  1.901  6.8441143600E+00
   1.901  3.802  5.2610231400E+00
   1.901  3.802  9.2651418600E+00
   0.000  0.000  9.6841100000E+00   #layer 3
   0.000  1.901  1.2105137500E+01
   0.000  0.000  7.6820506400E+00
   0.000  0.000  1.1686169360E+01
   0.000  1.901  1.0103078140E+01
   0.000  1.901  1.4107196860E+01

#Definition of the planewave basis set
ecut  24.0         # Maximal kinetic energy cut-off, in Hartree
pawecutdg 60.0

#Definition of the k-point grid;
kptopt 1
kptrlatt  8  0  0
          0  8  0
          0  0  1 
shiftk 0.5 0.5 0.0

#Definition of the SCF procedure
iscf 17          
nstep 150         # Maximal number of SCF cycles
toldfe 1.0d-9     # Will stop when, twice in a row, the difference
                  # between two consecutive evaluations of energy
                  # differ by less than toldfe (in Hartree)
#SCF preconditioner
iprcel 45         # Inhomogeneous systems work better with RPA method.
diemix 0.7        # Default for PAW

 

 

Band structure calculation input file:

# Crystalline anatase titania
#
# Computation of the band structure.
# Abinit automatically looks for density from a previous run, file #Slabi_DEN, proceeds with non-SCF band structure calculation.

#The band structure
iscf    -2     #Perform a non-scf calculation
kptopt  -1     #Use one segment and rely on kptbounds and ndivk
nband   90     #The number of bands
ndivk   22     #The number of samples for each segment
                   
kptbounds    0.0  0.0  0.0  #Gamma
             1/2  1/2  0.0  #X

tolwfr  1.0d-12       # Tolerance of the wavefunction squared residual
enunit  1             # Will output the eigenenergies in eV
prteig  1             # Will outupt the eigenenergies to a separate file

#Definition of the unit cell;
acell 3.802 3.802 9.68411/2 angstrom    # a,a,c/2

#Alter rprim, oriented with vacuum above the (001) plane.
rprim   1.0            0.0              0.0  
        0.0            1.0              0.0  
        0.0            0.0              6.5 
chkprim 0   # This input variable allows to use non-primitive unit cells.

#Definition of the atom types
ntypat 2          # There are two types of atoms
znucl 22 8                     

#Definition of the atoms
natom 18           # There are 18 atoms in our supercell
typat 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2
xangst               
   0.000  0.000  0.0000000000E+00   #layer 1
   0.000  1.901  2.4210275000E+00
   0.000  0.000 -2.0020593599E+00
   0.000  0.000  2.0020593599E+00
   0.000  1.901  4.1896814012E-01   
   0.000  1.901  4.4230868599E+00
   1.901  1.901  4.8420550000E+00   #layer 2
   1.901  3.802  7.2630825000E+00
   1.901  1.901  2.8399956400E+00
   1.901  1.901  6.8441143600E+00
   1.901  3.802  5.2610231400E+00
   1.901  3.802  9.2651418600E+00
   0.000  0.000  9.6841100000E+00   #layer 3
   0.000  1.901  1.2105137500E+01
   0.000  0.000  7.6820506400E+00
   0.000  0.000  1.1686169360E+01
   0.000  1.901  1.0103078140E+01
   0.000  1.901  1.4107196860E+01

#Definition of the planewave basis set
ecut  24.0         # Maximal kinetic energy cut-off, in Hartree
pawecutdg 60.0

nstep 250         # Maximal number of non-SCF cycles

 

 

 

Attachment: Bulk Bands.jpg
Description: JPEG image

Attachment: ST supercell bands no vacuum.jpg
Description: JPEG image

Attachment: Three layer supercell with vacuum.jpg
Description: JPEG image