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.

   1 2	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

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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

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Automatically generated mesh
       81
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
  ...       ...       ...

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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
[email protected]
   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
   .      ....

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