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cubic-diamond Ge band structure issue
Date: 2023/01/12 01:10
Name: Marc Tunica   <>

Dear all,  
I am trying to reproduce the electronic band structure of cubic-diamond Ge with LDA and different basis sets (Ge7.0-s2p2d2, Ge7.0-s3p2d2f1, and Ge7.0-s3p3d3f2). After optimizing the lattice parameter by hand (by calculating the total energy as a function of different values of the lattice constant), I calculated the band structure with the optimized lattice parameter. For all the considered basis sets, results show an energy splitting between the first and second valence bands at Gamma (figure  

This result is in contrast with respect to VASP calculations and other results presented in the literature (see for example figure 2.6 in, or figure 2 in  

The LDA band structure of cubic Ge should not present such kind of energy splitting in the valence band. It is important to point out that this splitting persists if we use the experimental lattice parameter.  

A related point to consider is that, in the case of GGA, several papers reported such valence band splitting (see for example the same figure 2.6 in, though its magnitude is smaller than what I calculate in my simulations. Moreover, as is shown in the database webpage of openmx, if we use the experimental lattice constant (5.658 Ang) it disappears.  

I would like to ask if someone has an explanation for such discrepancy and if there is a way to improve it or overcome it. Any help or suggestions would be greatly appreciated.  

Thank you so much for your time.  
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Re: cubic-diamond Ge band structure issue ( No.1 )
Date: 2023/01/12 15:22
Name: T. Ozaki


The band structure in the materials project can be found at
The energy splitting between the first and second valence bands at Gamma is about 0.4 eV,
which is slightly larger than one you presented.
Since the geometrical structures shown in the materials project were optimized using GGA-PBE,
your result is found to be consistent with it.

Could you show us your input file to see if your calculation converged or not w.r.t basis function and cutoff energy?


Re: cubic-diamond Ge band structure issue ( No.2 )
Date: 2023/01/12 23:01
Name: Marc Tunica  <>

Dear prof. Ozaki, 

Thank you very much for your answer and your help. 

The input I am using for the LDA calculation: 

System.CurrrentDirectory        ./   
System.Name                      Ge    
level.of.stdout                  1    
level.of.fileout                  1    
Species.Number      1
  Ge    Ge7.0-s3p3d3f2      Ge_CA19

DATA.PATH /opt/DFT/openmx-latest/DFT_DATA19

Atoms.Number        2
Atoms.SpeciesAndCoordinates.Unit  Frac 
  1  Ge    0.00000000000000    0.00000000000000    0.00000000000000    4.0    0.0
  2  Ge    0.25000000000000    0.25000000000000    0.25000000000000    4.0    0.0
Atoms.UnitVectors.Unit            Ang 
0.000000000000  2.8200000000 2.8200000
2.82000000000 0.000000000000  2.8200000 
2.820000000000 2.820000000000 0.000000000000

scf.XcType                LDA    
scf.SpinPolarization        off        
scf.SpinOrbit.Coupling      off        
scf.ElectronicTemperature  300.0       
scf.energycutoff          100.0       
scf.maxIter                  300        
scf.EigenvalueSolver      band        
scf.Kgrid                  10 10 10       
scf.Mixing.Type          rmm-diisk    
scf.Init.Mixing.Weight    0.20        
scf.Min.Mixing.Weight      0.001       
scf.Max.Mixing.Weight      0.500      
scf.Mixing.History          7          
scf.Mixing.StartPulay      7          
scf.Mixing.EveryPulay      1          
scf.criterion            1.0e-8     

MD.Type                      nomd      
MD.maxIter                    100        
MD.TimeStep                  1       
MD.Opt.criterion        1.0e-8     

Band.dispersion            on        
5.64  0.00  0.00
0.00  5.64  0.00
0.00  0.00  5.64

Band.Nkpath                  6
  100  1.0 0.5 0.0  0.5 0.5 0.5    W L
  100  0.5 0.5 0.5  0.0 0.0 0.0    L G
  100  0.0 0.0 0.0  1.0 0.0 0.0    G X
  100  1.0 0.0 0.0  1.0 0.5 0.0    X W
  100  1.0 0.5 0.0  0.75 0.75 0.0  W K
  100 0.75 0.75 0.0  0.0 0.0 0.0    K G

Looking at different references, LDA calculations should not present such kind of splitting (see, for instance, where the authors used VASP). 
Though the energy splitting in my simulations is lower for LDA than for GGA (around half), it is still significant if I compare it with the literature (where no splitting is reported for LDA).

So my questions are:
1) Is there any parameter I could check more carefully to get a LDA band structure of Ge with no splitting between the first and the second valence band?
2) In the case of GGA, I agree with you that my results are qualitatively consistent with literature. However, the valence band splitting I calculate is almost twice the value reported with plane-waves calculations. Do you have any idea on the origin of this difference?   

Thank you very much for your time, I sincerely appreciate your help.

Best regards,

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