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The variable cell optimization of Bi2Te3
Date: 2017/06/15 19:51
Name: huiyuan geng

Dear Prof. Ozaki,

It is reported that the vdw correction is essential to the cell optimization of Bi2Te3.

And the openmx3.8 manual says: "The variable cell optimization is supported for only the collinear calculations including the plus U method, while, however, the cell optimization for the DFT-D2 and DFT-D3 methods for vdW interaction is not supported."
It seems like that openmx is not suitable for the optimization of Bi2Te3.

But in a pnas paper "Pressure-induced superconductivity in topological parent compound Bi2Te3", the authors successfully optimized the lattice constants and internal atom sites using openmx. The obtained lattice constants are very close to the experimental ones.
And in another paper (, the same authors claimed that "Spin-orbit coupling is included during the optimization procedure."

So, it seem like that openmx is suitable for the optimization of BieTe3?
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Re: The variable cell optimization of Bi2Te3 ( No.1 )
Date: 2017/06/16 02:07
Name: Chris Latham


In the paper you cited, the authors have calculated the total energy of a unit cell with openmx, varying the volume of the unit cell, with fixed c/a, and optimized the atom positions separately, with fixed lattice parameters at each pressure. So, this is not a fully-automatic optimization of the cell parameters.

However, it is also important to understand that the authors also used a GGA functional, which does not necessarily perform well for this type of laminar system with weak interlayer bonds. It may be better to use the LDA. To understand why, see the article by Nekovee et al., Phys. Rev. B, 68, 235108 (2003) doi: 10.1103/PhysRevB.68.235108, where it shown by QMC calculations that errors introduced by the LDA are made worse by including gradients for an artificial system comprising sheets of charge.

Moreover, a more careful examination of this system may reveal that the weak interlayer bonding is a consequence of the band structure of the system, rather than London dispersion forces. The bands are certainly not flat, which suggests there could be overlap of orbitals, and hence there are bonds in the "weak-bonding gap" between the layers. You would need to investigate how the electrons and holes are redistributed around the Brillouin zone for distortions of the crystal which have prismatic components, and how this relates to the corresponding elastic parameters, in order to work out exactly what is going on.

That should keep you busy for a while! :-) Good luck with the calculations!

Re: The variable cell optimization of Bi2Te3 ( No.2 )
Date: 2017/06/16 09:33
Name: huiyuan geng

Dear Chris,

Many thanks for your suggestion!!! It is really helpful.
I'd like to study the prb paper you mentioned. Indeed, it is reported in another prb paper(doi:10.1103/PhysRevB.86.184111) that LDA results are closer to experiment.

Best regards,

Re: The variable cell optimization of Bi2Te3 ( No.3 )
Date: 2017/06/17 02:49
Name: Chris Latham


Consider Fig. 6 in the article which you cited [PRB 86, 184111 (2012) doi:10.1103/PhysRevB.86.184111] (which shows the electronic band structure). The bands are not flat anywhere, so the origin of the weak interlayer binding is probably not from London dispersion forces, as in solidified noble gases, which do have flat bands. Instead, the band structure implies that there must be overlap of orbitals in the interlayer gap giving long, weak bonds. These bonds will respond differently to strains with prismatic components from the simple pairwise interactions of London dispersion forces.

It should be possible to calculate the elastic parameters with OpenMX, and I think you should find that their values given by the LDA are quite close to those observed in experiments.

Please let us know how you get on!
Re: The variable cell optimization of Bi2Te3 ( No.4 )
Date: 2017/06/17 07:24
Name: genghuiyuan

Dear Prof. Latham,

Good morning! The result is amazing! Thank you again.

Here is the Openmx-LDA optimised results:
a=4.368, c=30.317, c/a= 6.940

And the exp. result:
a=4.392,c=30.477, c/a=6.940

The error is within 0.5%!

And the openmx-pbe result is quite bad, unphysical. The simulation cannot converge.

Here is my input file:

System.CurrrentDirectory ./ # default=./
System.Name bts-geo
level.of.stdout 1 # default=1 (1-3)
level.of.fileout 1 # default=1 (0-2)

Species.Number 2
Bi Bi8.0-s2p2d2f1 Bi_PBE13
Te Te7.0-s2p2d3 Te_PBE13

Atoms.Number 5
Atoms.SpeciesAndCoordinates.Unit FRAC # Ang|AU
1 Bi 0.4000 0.4000 0.4000 7.5 7.5
2 Bi 0.6000 0.6000 0.6000 7.5 7.5
3 Te 0.2097 0.2097 0.2097 8.0 8.0
4 Te 0.7903 0.7903 0.7903 8.0 8.0
5 Te 0 0 0 8.0 8.0

Atoms.UnitVectors.Unit Ang # Ang|AU
10.4732618332 0.0000000000 0.0000000000
9.5552938516 4.2878401131 0.0000000000
9.5552938516 2.0456578554 3.7684024166

scf.restart off # on|off,default=off
scf.SpinPolarization off # On|Off|NC
scf.ElectronicTemperature 300.0 # default=300 (K)
scf.energycutoff 600.0 # default=150 (Ry)
scf.maxIter 100 # default=40
scf.EigenvalueSolver Band # DC|GDC|Cluster|Band
scf.Kgrid 8 8 8 # means n1 x n2 x n3
scf.Mixing.Type rmm-diisk # Simple|Rmm-Diis|Gr-Pulay|Kerker|Rmm-Diisk
scf.Init.Mixing.Weight 0.01 # default=0.30
scf.Min.Mixing.Weight 0.01 # default=0.001
scf.Max.Mixing.Weight 0.100 # default=0.40
scf.Mixing.History 30 # default=5
scf.Mixing.StartPulay 10 # default=6
scf.Mixing.EveryPulay 1 # default=6
scf.criterion 1.0e-9 # default=1.0e-6 (Hartree)
scf.spinorbit.coupling off

MD.Opt.DIIS.History 5 # default=3
MD.Opt.StartDIIS 10 # default=5
MD.Opt.EveryDIIS 10000 # default=10
MD.maxIter 200 # default=1xsx
MD.Opt.criterion 0.0001 # default=1.0e-4 (Hartree/bohr)

Re: The variable cell optimization of Bi2Te3 ( No.5 )
Date: 2017/06/17 19:05
Name: Chris Latham


Good! Well done! Everything looks right. I see you have used a large cutoff radius for the atoms so that you get a good description of the orbital overlap in that critical gap region of the material, where you have long, weak bonds.

The LDA works because it overbinds slightly, but the PBE-GGA fails in this case because it overcompensates for the LDA overbinding, particularly for the weak "gap" bonds, for the reasons set out in the article by Nekovee et al., cited previously. Adding a so-called van der Waals correction appears to work because the parameters are chosen so that you are forced to get the right result, but it is for the wrong reasons. With sufficient parameters you can fit an elephant! :-)

Next, please use OpenMX to calculate the elastic parameters for the material using the LDA, and examine closely what happens to the band structure for strains with prismatic components, where you should be able to identify changes to particular features in the parts of the Brillouin zone which account for the weak interlayer bonds. If London dispersion forces were responsible for the long, weak interlayer bonds, which is the assumption made for the van der Waals methodology, then there ought to be very little change to the band structure when the crystal is compressed along its prismatic axis, or sheared in the basal plane. You will need to use a very dense k-point mesh for both the calculation and the analysis, because the critical part of the Brillouin zone is likely quite small, because the bonds we are interested in are weak, implying small, but not negligible overlap.

Again, tell us the result!
Re: The variable cell optimization of Bi2Te3 ( No.6 )
Date: 2017/06/18 14:24
Name: Huiyuan Geng  <>

Dear Prof. Latham,
Thank you very much for you suggestions:-)

I'd like to study the transport properties of Bi-Te-Se disordered crystals under different strain status. This is why I choose openmx. I will report the electric structures as you suggested.

Best regards,

Re: The variable cell optimization of Bi2Te3 ( No.7 )
Date: 2017/06/18 20:38
Name: Chris Latham


I am glad to be of help, but can't take any credit for the ideas: this is all standard textbook and literature material. I agree that OpenMX is a suitable tool for your proposed project.

I will be very interested to see what you find, especially for the elastic parameters, and especially those with prismatic components to the strain. If these are in agreement with experimental measurements, then it shows that the bonding and band structure is likely correct, and thus you can have greater confidence in your calculations of transport properties, because these will, of course, be sensitive to the band structure.

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