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Dear ABINIT users,

As a part of the research at my institute I have been trying to produce “ab inito” band structure calculations for Hg(1-x)Cd_(x)Te, where the Hg-Cd contribution is to be replaced with a virtual crystal approximation (VCA). The calculations for CdTe and HgTe are similar to those produced by WIEN2K, but when performing the Hg_(0.72)Cd_(0.28)Te calculations via VCA some peculiar problems arise.

I have been using projector augmented waves (PAW), and have derived the pseudo-potentials by using ATOMPAW v.2.2 with the LDA-PW XC-functional (input files are given at the end of this post). The attached plots are the band structures for CdTe, HgTe and HgCdTe (I am sorry for the low resolution), all of them are without LDA+U, but I do intend to apply it later on for the high lying d-orbitals. As you can see the bands for CdTe and HgTe are about as expected, but not HgCdTe.

I was just wondering if anyone has any experience with doing VCA in calculating eg. AlGaAs or anything like that, and knows how to avoid this problem. I suppose the problem could lie at the use of ATOMPAW. Also attached are the input files I used for Cd, Hg, Te and MC(the Hg-Cd VCA). When using ATOMPAW I noticed that the generator would only accept integer atom numbers and not fractional atom numbers which I wish to do. I think it only is meant to be used for generating “pure” atoms, and not VCA atoms, do anyone know anything more about this?

Here are the ATOMPAW input files:

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Cd(Cd.atompaw.input):

Cd 48 ! Definition of material
LDA-PW scalarrelativistic loggrid 2000 ! All-electrons calc.: LDA+scalar-relativstic - log.grid with 2000 pts
5 5 4 0 0 0 ! Max. n per angular momentum: 5s 5p 4d
4 2 10 ! Partially occupied states: 4d: occ=10
5 1 0 ! 5p: occ=0
5 0 2 ! 5s: occ=2
0 0 0 ! End of occupation section
c ! 1s: core state
c ! 2s: core state
c ! 3s: core state
c ! 4s: core state
v ! 5s: valence state
c ! 2p: core state
c ! 3p: core state
c ! 4p: core state
v ! 5p: valence state
c ! 3d: core state
v ! 4d: valence state
2 ! Max. l for partial waves basis
2.3 ! r_PAW radius
y ! Do we add an additional s partial wave ? yes
0. !Ref. energy
n ! Do we add an additional s partial wave ? no
y ! Do we add an additional p partial wave ? yes
0. !Ref. energy
n ! Do we add an additional p partial wave ? no
y ! Do we add an additional d partial wave ? yes
0. !Ref. energy
n ! Do we add an additional d partial wave ? no
bloechl ! Scheme for PS partial waves and projectors
3 0. troulliermartins ! Scheme for pseudopotential (l_loc=3, E_loc=0Ry)
0 ! End of file

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Hg(Hg.atompaw.input):

Hg 80 ! Definition of material
LDA-PW scalarrelativistic loggrid 2000 ! All-electrons calc.: LDA+scalar-relativstic - log.grid with 2000 pts
6 6 5 4 0 0 0 ! Max. n per angular momentum: 6s 6p 5d 4f
4 3 14 ! Partially occupied states: 4f: occ=14
5 2 10 ! 5d: occ=10
6 1 0 ! 6p: occ=0
6 0 2 ! 6s: occ=2
0 0 0 ! End of occupation section
c ! 1s: core state
c ! 2s: core state
c ! 3s: core state
c ! 4s: core state
c ! 5s: core state
v ! 6s: valence state
c ! 2p: core state
c ! 3p: core state
c ! 4p: core state
c ! 5p: core state
v ! 6p: valence state
c ! 3d: core state
c ! 4d: core state
v ! 5d: valence state
v ! 4f: valence state
3 ! Max. l for partial waves basis
2.9 ! r_PAW radius
n ! Do we add an additional s partial wave ? no
y ! Do we add an additional p partial wave ? yes
0. !Ref. energy
n ! Do we add an additional p partial wave ? no
y ! Do we add an additional d partial wave ? yes
0. !Ref. energy
n ! Do we add an additional d partial wave ? no
n ! Do we add an additional f partial wave ? no
bloechl ! Scheme for PS partial waves and projectors
3 0. troulliermartins ! Scheme for pseudopotential (l_loc=3, E_loc=0Ry)
0 ! End of file

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Te(Te.atompaw.input):

Te 52 ! Definition of material
LDA-PW scalarrelativistic loggrid 2000 ! All-electrons calc.: LDA+scalar-relativstic - log.grid with 2000 pts
5 5 4 0 0 0 ! Max. n per angular momentum: 5s 5p 4d
4 2 10 ! Partially occupied states: 4d: occ=10
5 1 4 ! 5p: occ=4
5 0 2 ! 5s: occ=2
0 0 0 ! End of occupation section
c ! 1s: core state
c ! 2s: core state
c ! 3s: core state
c ! 4s: core state
v ! 5s: valence state
c ! 2p: core state
c ! 3p: core state
c ! 4p: core state
v ! 5p: valence state
c ! 3d: core state
v ! 4d: valence state
2 ! Max. l for partial waves basis
2.4 ! r_PAW radius
y ! Do we add an additional s partial wave ? yes
0. !Ref. energy
n ! Do we add an additional s partial wave ? no
y ! Do we add an additional p partial wave ? yes
0. !Ref. energy
n ! Do we add an additional p partial wave ? no
y ! Do we add an additional d partial wave ? yes
0. !Ref. energy
n ! Do we add an additional d partial wave ? no
bloechl ! Scheme for PS partial waves and projectors
3 0. troulliermartins ! Scheme for pseudopotential (l_loc=3, E_loc=0Ry)
0 ! End of file

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

HgCd VCA(MC.atompaw.input):

MC 71 ! Definition of material
LDA-PW scalarrelativistic loggrid 2000 ! All-electrons calc.: LDA+scalar-relativstic - log.grid with 2000 pts
6 5 5 4 0 0 0 ! Max. n per angular momentum: 6s 5p 5d 4f
4 3 10.0625 ! Partially occupied states: 4f: occ=10.0625
5 2 7.1875 ! 5d: occ=7.1875
5 1 4.3125 ! 5p: occ=4.3125
6 0 1.4375 ! 6s: occ=1.4375
0 0 0 ! End of occupation section
c ! 1s: core state
c ! 2s: core state
c ! 3s: core state
c ! 4s: core state
v ! 5s: valence state
v ! 6s: valence state
c ! 2p: core state
c ! 3p: core state
c ! 4p: core state
v ! 5p: valence state
c ! 3d: core state
v ! 4d: valence state
v ! 5d: valence state
v ! 4f: valence state
2 ! Max. l for partial waves basis
2.3 ! r_PAW radius
n ! Do we add an additional s partial wave ? no
y ! Do we add an additional p partial wave ? yes
0. !Ref. energy
n ! Do we add an additional p partial wave ? no
y ! Do we add an additional d partial wave ? yes
0. !Ref. energy
n ! Do we add an additional d partial wave ? no
bloechl ! Scheme for PS partial waves and projectors
3 0. troulliermartins ! Scheme for pseudopotential (l_loc=3, E_loc=0Ry)
0 ! End of file

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Kind Regards
Bjornar Karlsen

Dear Bjornar,

Two quick answers:

- I may be wrong but, if I remember correctly, a more recent version of Atompaw (3.0...) should accept real coocupation numbers; to be tested, at least.

- Note that the VCA approximation in ABINIT is anly available for norm-conserving pseudopotentials and not PAW;
VCA for PAW is not immediate because you have to mix atomic quantities while preserving the orthogonality properties of the PAW partial wave basis...

Dear Torrent,

Thanks for taking the time to respond! It was kind of what I feared, so I will have to do some major revisions.
Hopefully this option in ABINIT will be available in the future.

Kind regards
Bjornar