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I tried to calculate the bandgap of the TiO2-Rutile bulk phase, DFT(not +U) calculation shows the bandgap is about 1.8eV, which is roughly the same as the 1.78eV on the Material Project. When calculating the TiO2-Rutile -110 slab, whether +U or not +U, the bandgap is about 1.3eV, which is 0.5eV smaller than the bulk. After checking some literature, there are also many cases where the slab band gap is obviously smaller than bulk.

But for TiO2, a lot of literature show the bandgap of the slab is 2eV-3eV with the DFT+U method, and the U value given is not very large, between 4-6, but I can’t reproduce similar results. When I increase U to 6, the bandgap of Rutile-110-slab is still around 1.3,eV which has not increased significantly, let alone reached the experimental level of 3eV.

my question is: Generally speaking, can the bandgap of slab be reduced by about 20%-40% compared to bulk? Can +U make the bandgap change from 1.3eV to 3eV? The slab calculation results given in the literature, using the DFT+U method to obtain a bandgap as large as 3eV, is it credible?

As the following DOS diagram shows, pseudohydrogen does reduce the density of state near VBM and CBM, but it also causes the Fermi energy to fall below the VBM, which makes the material turn into a conductor.

enter image description here

I checked the charge density of my result, the charge from H.66 moves to H1.33.

enter image description here

Here are the VASP input files:
KPOINTS

K-Spacing Value to Generate K-Mesh: 0.040
0
Gamma
   8   4   1
0.0  0.0  0.0

INCAR:

Global Parameters
ISTART =  1            (Read existing wavefunction; if there)
ISPIN  =  2            (Non-Spin polarised DFT)
# ICHARG =  11         (Non-self-consistent: GGA/LDA band structures)
LREAL  = .FALSE.       (Projection operators: automatic)
ENCUT  =  520        (Cut-off energy for plane wave basis set, in eV)
PREC   =  Normal       (Precision level)
LWAVE  = .TRUE.        (Write WAVECAR or not)
LCHARG = .TRUE.        (Write CHGCAR or not)
ADDGRID= .TRUE.        (Increase grid; helps GGA convergence)
# LVTOT  = .TRUE.      (Write total electrostatic potential into LOCPOT or not)
# LVHAR  = .TRUE.      (Write ionic + Hartree electrostatic potential into LOCPOT or not)
# NELECT =             (No. of electrons: charged cells; be careful)
# LPLANE = .TRUE.      (Real space distribution; supercells)
# NPAR   = 4           (Max is no. nodes; don't set for hybrids)
# Nwrite = 2           (Medium-level output)
# KPAR   = 2           (Divides k-grid into separate groups)
# NGX    = 500         (FFT grid mesh density for nice charge/potential plots)
# NGY    = 500         (FFT grid mesh density for nice charge/potential plots)
# NGZ    = 500         (FFT grid mesh density for nice charge/potential plots)
 
Static Calculation
ISMEAR =  0            (gaussian smearing method)
SIGMA  =  0.05         (please check the width of the smearing)
LORBIT =  11           (PAW radii for projected DOS)
NEDOS  =  2001         (DOSCAR points)
NELM   =  60           (Max electronic SCF steps)
EDIFF  =  1E-04        (SCF energy convergence; in eV)
 

POSCAR

TiO2_mp-2657_slab_unitcell             
   1.0000000000000000     
     2.9691998959000001    0.0000000000000000    0.0000000000000000
     0.0000000000000000    6.5806999206999999    0.0000000000000000
     0.0000000000000000    0.0000000000000000   38.4453010559000035
   Ti   O    H1.33   H.66
     8    16     1     1
Selective dynamics
Direct
  0.5000000000168399  0.4999999999468159  0.1635600030510105   F   F   F
  0.5000000000168399  0.0000000000000000  0.2491499930530523   F   F   F
  0.5000000000168399  0.4999999999468159  0.3347299993122306   F   F   F
  0.5000000000168399  0.0000000000000000  0.4203200042185671   F   F   F
  0.0000000000000000  0.0000000000000000  0.1635600030510105   F   F   F
  0.0000000000000000  0.4999999999468159  0.2491499930530523   F   F   F
  0.0000000000000000  0.0000000000000000  0.3347299993122306   F   F   F
  0.0000000000000000  0.4999999999468159  0.4203200042185671   F   F   F
  0.5000000000168399  0.8045799732252163  0.1635600030510105   F   F   F
  0.5000000000168399  0.3045800030624690  0.2491499930530523   F   F   F
  0.5000000000168399  0.8045799732252163  0.3347299993122306   F   F   F
  0.5000000000168399  0.3045800030624690  0.4203200042185671   F   F   F
  0.5000000000168399  0.1954199970363035  0.1635600030510105   F   F   F
  0.5000000000168399  0.6954200267671808  0.2491499930530523   F   F   F
  0.5000000000168399  0.1954199970363035  0.3347299993122306   F   F   F
  0.5000000000168399  0.6954200267671808  0.4203200042185671   F   F   F
  0.0000000000000000  0.4999999999468159  0.1301099955941751   F   F   F
  0.0000000000000000  0.0000000000000000  0.2157000005265246   F   F   F
  0.0000000000000000  0.4999999999468159  0.3012799918554023   F   F   F
  0.0000000000000000  0.0000000000000000  0.3868699967877447   F   F   F
  0.0000000000000000  0.4999999999468159  0.1970099955775382   F   F   F
  0.0000000000000000  0.0000000000000000  0.2825999856055930   F   F   F
  0.0000000000000000  0.4999999999468159  0.3681800067430530   F   F   F
  0.0000000000000000  0.0000000000000000  0.4537700116754024   F   F   F
  0.0000000000000000  0.0000000000000000  0.1179976847000919   T   T   T
  0.0000000000000000  0.4999999999468159  0.1034677544189809   T   T   T
$\endgroup$
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  • $\begingroup$ Did you perform a structural relaxation of the atom positions for the slab case? $\endgroup$ Jan 16, 2022 at 11:06
  • 1
    $\begingroup$ I am not an expert on the physics of your system, but usage of DFT+U is anything but trivial and you probably did not give enough information in your question to enable someone to answer your question. Besides being material-dependent U values also depend on the DFT implementation because they are interpreted in different ways. Also DFT+U stabilizes electronic configurations during the SCF process because it moves occupied states down and unoccupied states up. If you start with an unphysical solution it stabilizes it. Is the band structure beyond the gap okay? $\endgroup$ Jan 16, 2022 at 11:58
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    $\begingroup$ Are you passivating the surface? Regardless, I recommend plotting the PDOS, looking particularly for 2 things: 1) the Ti d-states (to which any Hubbard U would be applied); and 2) the surface states (top Ti, O and any passivation). In the case of (1), if the states aren't anywhere near the gap, then applying a Hubbard U won't change the band-gap. $\endgroup$ Jan 16, 2022 at 23:19
  • 2
    $\begingroup$ Where's the (pseudo-)hydrogen in this system? I can only see Ti and O in your inset and PDOS. (The yellow is also rather hard to see!) The system looks to have a large band-gap, so there's no problem with metallisation here, at least. $\endgroup$ Jan 19, 2022 at 0:08
  • 1
    $\begingroup$ @Jack The input you provided doesn't allow relaxation of the system and doesn't include +U corrections. Too many atoms are frozen. You also need to set NSW = 100 or something. Try U = 6 eV to see if there is any change in band gap. $\endgroup$
    – che_kid
    Jan 25, 2022 at 20:56

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