### Im(eps) not zero for energies < band gap

Posted:

**Fri Dec 22, 2017 4:57 pm**Dear VASP support team,

Analyzing the result of the calculation of the dielectric function of a semiconductor (LOPTICS = .True.), I found that the imaginary part [Im(eps)] in not zero even at energies well below the band gap value. In fact, the imaginary part departs from zero as soon as the energy is > 0. This is, of course, unphysical, and can lead to erroneous results for quantities depending on the dielectric function. I found the inaccuracy both with PBE and HSE06.

The problem greatly reduced if one uses a CSHIFT much smaller than the default one, e.g., CSHIFT=0.01, instead of CSHIFT=0.1. I ran a test using a 21x21x21 k-point mesh using VASP version 5.4.4 (PBE calculation), comparing the result with both CSHIFTs. But the imaginary part of the dielectric function for CSHIFT=0.01, although small, is still not zero at energies > 0 below the band gap value. Also, the curve for CSHIFT=0.01 is not ideal, as it is jagged. In principle a higher density k-point mesh should solve this. However, performing a HSE06 calculation over such dense k-point meshes becomes computationally prohibitive, specially for systems such as the present one. This is unfortunate, because for a semiconductor one would like to use HSE06. I wonder how the calculations can be improved having hybrid functionals in mind.

The SCF calculation was done with the following INCAR and KPOINTS files:

INCAR

SYSTEM = Pb2SnSbO6.5

ENCUT = 450

PREC = Normal

ISMEAR = 0

SIGMA = 0.01

LREAL = Auto

EDIFF = 1.E-05

NSIM = 4

NBANDS = 120

NPAR = 120

KPAR = 2

LMAXMIX = 4

KPOINTS

Pb2SnSbO6.5

0 ! automatically generate k-points

Gamma !To generate k points via MP method

4 4 4 !the number of divisions along basic vector

0. 0. 0. !the shift

The dielectric function calculation was done with the following INCAR and KPOINTS files:

INCAR

SYSTEM = Pb2SnSbO6.5

ENCUT = 450

PREC = Normal

ISMEAR = 0

SIGMA = 0.01

LREAL = Auto

EDIFF = 1.E-08

NSIM = 4

NBANDS = 240

NPAR = 120

KPAR = 2

LMAXMIX = 4

LOPTICS = .TRUE.

CSHIFT = 0.01

NEDOS = 10000

KPOINTS

Pb2SnSbO6.5

0 ! automatically generate k-points

Gamma !To generate k points via MP method

21 21 21 !the number of divisions along basic vector

0. 0. 0. !the shift

The POTCARs used for the metals included the d electrons.

Best regards,

Rolando Saniz

Analyzing the result of the calculation of the dielectric function of a semiconductor (LOPTICS = .True.), I found that the imaginary part [Im(eps)] in not zero even at energies well below the band gap value. In fact, the imaginary part departs from zero as soon as the energy is > 0. This is, of course, unphysical, and can lead to erroneous results for quantities depending on the dielectric function. I found the inaccuracy both with PBE and HSE06.

The problem greatly reduced if one uses a CSHIFT much smaller than the default one, e.g., CSHIFT=0.01, instead of CSHIFT=0.1. I ran a test using a 21x21x21 k-point mesh using VASP version 5.4.4 (PBE calculation), comparing the result with both CSHIFTs. But the imaginary part of the dielectric function for CSHIFT=0.01, although small, is still not zero at energies > 0 below the band gap value. Also, the curve for CSHIFT=0.01 is not ideal, as it is jagged. In principle a higher density k-point mesh should solve this. However, performing a HSE06 calculation over such dense k-point meshes becomes computationally prohibitive, specially for systems such as the present one. This is unfortunate, because for a semiconductor one would like to use HSE06. I wonder how the calculations can be improved having hybrid functionals in mind.

The SCF calculation was done with the following INCAR and KPOINTS files:

INCAR

SYSTEM = Pb2SnSbO6.5

ENCUT = 450

PREC = Normal

ISMEAR = 0

SIGMA = 0.01

LREAL = Auto

EDIFF = 1.E-05

NSIM = 4

NBANDS = 120

NPAR = 120

KPAR = 2

LMAXMIX = 4

KPOINTS

Pb2SnSbO6.5

0 ! automatically generate k-points

Gamma !To generate k points via MP method

4 4 4 !the number of divisions along basic vector

0. 0. 0. !the shift

The dielectric function calculation was done with the following INCAR and KPOINTS files:

INCAR

SYSTEM = Pb2SnSbO6.5

ENCUT = 450

PREC = Normal

ISMEAR = 0

SIGMA = 0.01

LREAL = Auto

EDIFF = 1.E-08

NSIM = 4

NBANDS = 240

NPAR = 120

KPAR = 2

LMAXMIX = 4

LOPTICS = .TRUE.

CSHIFT = 0.01

NEDOS = 10000

KPOINTS

Pb2SnSbO6.5

0 ! automatically generate k-points

Gamma !To generate k points via MP method

21 21 21 !the number of divisions along basic vector

0. 0. 0. !the shift

The POTCARs used for the metals included the d electrons.

Best regards,

Rolando Saniz