HSE Functional for Band Structures in VASP

Related Reading

VASP the GUIDE: Hartree-Fock (HF) type and hybrid functional calculations
VASPwiki: Tutorial on hybrid functionals
Related discussion: How can I calculate the DOS by using HSE06 in vasp?

These instructions are taken from the Vasp forum

Band structures using hybrid functionals have to be calculated the following way:

  1. First perform a selfconsistent Hartree-Fock/HSE calculation using a conventional KPOINTS file.

  2. Copy the IBZKPT file to KPOINTS, and explicitely add all desired k-points along high-symmetry lines of the BZ that are needed for the bandstructure plot. Add the points at the end of the KPOINTS file, but set the weights of these added k-points to 0.

  3. Do not forget to set the number of k-points in KPOINTS correctly (to the number of the k-points used in the standard mesh PLUS the number of the k-points along the lines), such that all k-points are used for the calculations.

  4. NKRED can not be used.

  5. Perform a second VASP run:
    It is recommended to use the Davidson algorithm, since it converges that eigen energies at the new k-points fastest. Since VASP terminates when the total energy is converged to a certain threshold, it is important to force VASP to do a minimum number of steps, so that the orbitals at the new k-points are fully converged (note: since their weight is zero, they do not contribute to the total energy). This can be done using e.g.

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    ALGO = N ; NELMIN = 5 ! Davidson, minimum 5 scf-steps
    IMIX = 1 ! Use simple charge mixer, since

    Pulay might blow up

  6. The KS-eigenvalues of the states along the high-symmetry lines are written in OUTCAR, EIGENVAL, vasprun.xml; please cut the k-points required for the bandstructure from one of these files and proceed as usual (using p4vasp or any other graphics tool you usually use to produce bandstructure-plots)

Note: A Hartee-Fock calculation can NOT be continued from an existing CHGCAR file, since the non-local exchange is not determined by the charge density but by the density matrix and/or the KS-orbitals.

HSE06 calculated records

1. Gamma-scf

After structural optimization opt[1]

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cp -rf opt Gamma-scf

INCAR

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SYSTEM=x
ISTART=0
ENCUT=350
EDIFF=1E-5
IBRION=2
POTIM=0.25
NSW=0
EDIFFG=-1E-2
ISMEAR=0
SIGMA=0.05
PREC=ACCURATE
ISIF=2
NPAR=4
#LWAVE=FALSE
#LCHARG=FALSE
LREAL=Auto
#IALGO=48
ISYM=0

KPOINTS

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auto
0
Gamma
1 1 1
0 0 0

POSCAR

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cp ../opt/CONTCAR POSCAR

2. 1hse-scf

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cp -rf Gamma-scf 1hse-scf

INCAR

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SYSTEM=x
ISTART=1
ENCUT=350
EDIFF=1E-5
IBRION=2
POTIM=0.25
NSW=0
EDIFFG=-1E-2
ISMEAR=0
SIGMA=0.05
PREC=ACCURATE
ISIF=2
NPAR=4
#LWAVE=FALSE
#LCHARG=FALSE
LREAL=Auto
#IALGO=48
ISYM=0
LHFCALC=.TRUE.
HFSCREEN=0.2
ALGO=Damped
TIME=0.4

3. 2hse-scf

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cp -rf 1hse-scf 2hse-scf

INCAR

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SYSTEM=x
ISTART=1
ENCUT=350
EDIFF=1E-5
IBRION=2
POTIM=0.25
NSW=0
EDIFFG=-1E-2
ISMEAR=0
SIGMA=0.05
PREC=ACCURATE
ISIF=2
NPAR=4
#LWAVE=FALSE
#LCHARG=FALSE
LREAL=Auto
#IALGO=48
ISYM=0
LHFCALC=.TRUE.
HFSCREEN=0.2
#ALGO=Damped
#TIME=0.4

4. Hseband

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cp -rf 2hse-scf hseband

INCAR

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SYSTEM=x
ISTART=1
ICHARG=11
LORBIT=10
ENCUT=350
EDIFF=1E-5
IBRION=2
POTIM=0.25
NSW=0
EDIFFG=-1E-2
ISMEAR=0
SIGMA=0.05
PREC=ACCURATE
ISIF=2
NPAR=4
LWAVE=FALSE
#LCHARG=FALSE
LREAL=Auto
#IALGO=48
ISYM=0
LHFCALC=.TRUE.
HFSCREEN=0.2
#ALGO=Damped
#TIME=0.4

KPOINTS

  1. Use script gk.x and file syml to output file inp.kpt. If the file has a few lines of zero, then delete.
  2. Add the contents of inp.kpt at the end of the IBZKPT file, set the weights of these added k-points to 0.
  3. Set the number of k-points correctly. For this example, the number is 1 + rows of file ink.kpt.
  4. Copy the IBZKPT file to KPOINTS.
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Automatically generated mesh
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Reciprocal lattice
0.00000000000000 0.00000000000000 0.00000000000000 1
0.000000 0.000000 0.000000 0
0.025000 0.000000 0.000000 0
0.050000 0.000000 0.000000 0
0.075000 0.000000 0.000000 0
0.100000 0.000000 0.000000 0
0.125000 0.000000 0.000000 0
... ... ...

Submit the job, then the EIGENVAL file will generate after the calculation. Modify the contents of the EIGENVAL: Remove high symmetry points whose weights are not zero and set the number of k-points correctly.

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120 120 1 1
0.4622031E+02 0.1284000E-08 0.1040630E-08 0.4151000E-08 0.2500000E-15
1.000000000000000E-004
CAR
GeS@SnS
600 80 364
0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
1 -15.982521
2 -15.834306
3 -15.615449
4 -15.458326
5 -15.457173
6 -15.366968
. ....

Use script pbnf.x to output file bnd.dat and highk.dat. Import the data into origin and plot band structure.

NOTE: There is a problem. In the step Hseband, the ICHARG parameter in the INCAR file needs to be set to 11 or 2? This needs to be tested.
Related discussion: http://muchong.com/t-3723568-1 http://muchong.com/t-4232787-1

Reference

[1] VASP Band Calculation and Drawing

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