What is the source of this band structure and DOS inconsistency?

Question

Using VASP, I have conducted DOS and BS calculations of a Ti-doped $\ce{MoI3}$ monolayer using the following:

POSCAR:

MoI3                                    
   1.00000000000000     
    14.4854649408170939   -0.0007532821817704    0.0005796963007335
    -7.2434972127101211   12.5459583006560749   -0.0041326374435996
     0.0032311730240303   -0.0104455455087482   18.1668086991713693
   Mo   I    Ti
     7    24     1
Direct
  0.3330971891338734  0.1665736841755603  0.5001910329994956
  0.8338455665356221  0.1665137499446203  0.5000335513376868
  0.8337203761162328  0.6672255720968678  0.4997592499121311
  0.1668628879574570  0.3324368411586676  0.4996237331998330
  0.1666184313766692  0.8342365889988201  0.5005685048525947
  0.6670249562338242  0.3334898971870714  0.4998774696965782
  0.6677440326294573  0.8338841744313470  0.4999147964603026
  0.3185958390353250  0.4990001196708960  0.4083710595595704
  0.3224440807443472  0.0000730839056828  0.4107381054445298
  0.8230113583266387  0.5002725798922327  0.4102414939751000
  0.8236284250252481  0.0001794556197936  0.4101278084079425
  0.1768491044609064  0.1760019495846450  0.4100411439620828
  0.1791796302185205  0.6795166206652183  0.4106424776233766
  0.6779141980430552  0.1774485021457863  0.4105289952472475
  0.6775027972865217  0.6773950436894296  0.4105178207308171
  0.0001120659225933  0.3223358259823073  0.4106311815782249
  0.0001845604753541  0.8236045013874786  0.4101885057831041
  0.4998608569263183  0.3222287852645920  0.4106355330682092
  0.5000851739820860  0.8214457178196923  0.4109122177341433
  0.1768409869017873  0.0007345664211797  0.5903431383554363
  0.1791385851876157  0.4996356126462445  0.5893403090229796
  0.6778624449165420  0.0001609976698589  0.5893797531545246
  0.6779724716073687  0.5003694678926749  0.5893281968251074
  0.3231945670457677  0.3230001036273578  0.5895971617382969
  0.3183718014933135  0.8193577758142965  0.5918113350629071
  0.8228303391782177  0.3225522091477657  0.5895183779090090
  0.8235858965414664  0.8233930983732023  0.5897716811696228
  0.0002009070245350  0.1765762143626333  0.5897595904439115
  0.9997867292834854  0.6776268821436702  0.5893750036233527
  0.5002106990392505  0.1777406882794708  0.5893809980283820
  0.5001248011394424  0.6786600597049599  0.5890115938959326
  0.3319993862111303  0.6658919222959270  0.5000070991975392
 
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00
  0.00000000E+00  0.00000000E+00  0.00000000E+00

SCF INCAR:

NCORE = 2
#KPAR = 5
# Self Consistent Calculation step:
ISTART = 0
ICHARG = 2
IBRION = -1
NSW = 0
LORBIT = 11

#Electronic Relaxation:
ENCUT = 600 eV
EDIFF = 1.0E-6
PREC = Accurate
LREAL = .FALSE.
ALGO = Normal
ADDGRID=.TRUE.

#Relaxation:
ISMEAR = -5
SIGMA = 0.1
EDIFFG = -0.01
GGA COMPAT = .FALSE.

# Magnetism:
ISPIN= 2
MAGMOM = 7*5.0 24*0.6 1*0.6
LASPH = .TRUE.
LMAXMIX = 4
VOSKOWN = 1

#Mixer
#AMIX     = 0.2
#BMIX     = 0.00001
#AMIX_MAG = 0.8
#BMIX_MAG = 0.00001

GGA+U
  LDAU      = .TRUE.
  LDAUTYPE  = 2
  LDAUL     = 2 -1 2
  LDAUU     = 3.00 0.00 2.50
  LDAUJ     = 0.00 0.00 0.00
  LDAUPRINT = 2

DOS INCAR :

NCORE = 6
#KPAR = 5
# DOS
ICHARG = 11
IBRION = -1
NSW = 0
LORBIT = 11
NEDOS = 2001

#Electronic Relaxation:
ENCUT = 600 eV
EDIFF = 1.0E-6
PREC = Accurate
LREAL = .FALSE.
ALGO = Normal
ADDGRID=.TRUE.

#Relaxation:
ISMEAR = -5
#SIGMA = 0.1
EDIFFG = -0.01
GGA COMPAT = .FALSE.

# Magnetism:
ISPIN= 2
MAGMOM = 7*5.0 24*0.6 1*0.6
LASPH = .TRUE.
LMAXMIX = 4
VOSKOWN = 1

#Mixer
#AMIX     = 0.2
#BMIX     = 0.00001
#AMIX_MAG = 0.8
#BMIX_MAG = 0.00001

GGA+U
  LDAU      = .TRUE.
  LDAUTYPE  = 2
  LDAUL     = 2 -1 2
  LDAUU     = 3.00 0.00 2.50
  LDAUJ     = 0.00 0.00 0.00
  LDAUPRINT = 2

DOS statistics :

     +-------------------------- Summary ----------------------------+
            Spin Channel:     <UP>       <DOWN>      <TOTAL>
           Band Gap (eV):    1.3920      2.4001      1.3920
  Eigenvalue of VBM (eV):   -2.4897     -3.0363     -2.4897
  Eigenvalue of CBM (eV):   -1.0977     -0.6362     -1.0977
       Fermi Energy (eV):   -2.4852     -2.4852     -2.4852
               HOMO Band:       150       128         150
               LUMO Band:       151       129         151
    Location of VBM (UP):    0.0000      0.4615     -0.0000
    Location of CBM (UP):    0.0000      0.0000      0.0000
    Location of VBM (DW):    0.0000      0.0000      0.0000
    Location of CBM (DW):    0.0000      0.0000      0.0000
    Location of VBM (TO):    0.0000      0.4615     -0.0000
    Location of CBM (TO):    0.0000      0.0000      0.0000
 +---------------------------------------------------------------+
E-fermi = -2.485212

BS INCAR :

NCORE = 2
#KPAR = 5
# Self Consistent Calculation step:
ISTART = 0
ICHARG = 2
IBRION = -1
NSW = 0
LORBIT = 11

#Electronic Relaxation:
ENCUT = 600 eV
EDIFF = 1.0E-6
PREC = Accurate
LREAL = .FALSE.
ALGO = Normal
ADDGRID=.TRUE.

#Relaxation:
ISMEAR = 0
SIGMA = 0.1
EDIFFG = -0.01
GGA COMPAT = .FALSE.

# Magnetism:
ISPIN= 2
MAGMOM = 7*5.0 24*0.6 1*0.6
LASPH = .TRUE.
LMAXMIX = 4
VOSKOWN = 1

#Mixer
#AMIX     = 0.2
#BMIX     = 0.00001
#AMIX_MAG = 0.8
#BMIX_MAG = 0.00001

GGA+U
  LDAU      = .TRUE.
  LDAUTYPE  = 2
  LDAUL     = 2 -1 2
  LDAUU     = 3.00 0.00 2.50
  LDAUJ     = 0.00 0.00 0.00
  LDAUPRINT = 2

BS statistics :

 +-------------------------- Summary ----------------------------+
            Spin Channel:     <UP>       <DOWN>      <TOTAL>
           Band Gap (eV):    1.5015      2.4738      1.5015
  Eigenvalue of VBM (eV):   -2.5966     -3.0388     -2.5966
  Eigenvalue of CBM (eV):   -1.0951     -0.5650     -1.0951
       Fermi Energy (eV):   -2.0467     -2.0467     -2.0467
               HOMO Band:       150       128         150
               LUMO Band:       151       129         151
    Location of VBM (UP):   -0.2222      0.4444      0.0000
    Location of CBM (UP):    0.0000      0.0000      0.0000
    Location of VBM (DW):    0.0000      0.0000      0.0000
    Location of CBM (DW):    0.0000      0.0000      0.0000
    Location of VBM (TO):   -0.2222      0.4444      0.0000
    Location of CBM (TO):    0.0000      0.0000      0.0000
 +---------------------------------------------------------------+
    E-fermi = -2.046733

Also, when I draw BS and DOS I noticed that they are shifted from each other. I have also got this problem with some other materials. What might be my mistake?

@ChiKou In this case I think you should not use screenshots since it won't take much space to put these as text, and blind people who use screen readers can't know what's in the screenshots, and people with browsers that can't (quickly) load in-line images would also have a better time, and the text would be more searchable and look nicer. — Nike Dattani, Aug 23, 2021 at 18:40
Without knowing anything about your calculations I guess the obvious cause for differences are different k-point sets. What are the k-point sets for the two calculations? — Gregor Michalicek, Aug 23, 2021 at 19:38
That true Nike, I'll try to edit my post. @GregorMichalicek concerning DOS I have used "Gamma 13x13x1", but for BS I have used 2D KPATH generated by vaspkit. — Chi Kou, Aug 23, 2021 at 22:10

Nike Dattani · Accepted Answer · 2021-08-23 23:35:45Z

3

Neither the valence band maximum (VBM) nor the conduction band minimum (CBM) have to be at a k-point from the k-point set that you use for an SCF, DOS, or band structure calculation. I don't know what VASP reports as the Fermi level for insulators, but I guess that it is the energy of the highest occupied state within the used k-point set. Since it is not guaranteed that this is the real VBM you have to see this as an approximation. If you use a k-point mesh you can actually systematically converge this quantity by using finer and finer meshes. If you use a high-symmetry k-point path you cannot do that. The VBM is not guaranteed to be on that path. The same argument applies to the size of the band gap.

As a consequence these quantities differ when using different k-point sets.

edited Aug 23, 2021 at 23:35

Nike Dattani

33.6k4 gold badges95 silver badges237 bronze badges

answered Aug 23, 2021 at 23:20

Gregor Michalicek

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$\begingroup$ I saw that in many articles BS and DOS are consistent with each other. If the problem is k-points set, how to solve it then ? $\endgroup$
– Chi Kou
Aug 23, 2021 at 23:34
1

$\begingroup$ @ChiKou I think Gregor's answer has a sufficient level of detail for an appropriate answer to your original question (+1 by the way!). If after finding the source of the problem, you now want to know how to fix it, I suggest asking a new question about that! Alternatively, in 36 hours, you'll be able to offer a bounty if you think the answers here are insufficient or can be improved with the help of a bounty. $\endgroup$
– Nike Dattani
Aug 23, 2021 at 23:38
2

$\begingroup$ That is just a matter of correcting the Fermi level. In the last lines of your screenshot with the statistics there is actually a hint how to do that. $\endgroup$
– Gregor Michalicek
Aug 23, 2021 at 23:39
$\begingroup$ @NikeDattani I am still not sure that this is the source of the problem, and whether DOS or BS stats are the correct ones. $\endgroup$
– Chi Kou
Aug 23, 2021 at 23:45

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Chi Kou · Accepted Answer · 2021-08-24 20:10:45Z

2

Thanks to all who contributed to answer to this post.

I have found that the problem is that I have used ICHARG=11 in DOS to read the charge density from SCF calcualtion, but for BS I have used ICHARG=2 which doesn't allow the reading of charge density from SCF calcualtion. So DOS and BS doesn't start from the same charge density.

answered Aug 24, 2021 at 20:10

Chi Kou

5,6837 silver badges42 bronze badges

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