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cubic-diamond Ge band structure issue Date: 2023/01/12 01:10 Name: Marc Tunica   <marc.tunica-i-rosich@universite-paris-saclay.fr> 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 https://ibb.co/GF7mjg1).   This result is in contrast with respect to VASP calculations and other results presented in the literature (see for example figure 2.6 in https://doi.org/10.3990/1.9789036528733, or figure 2 in https://doi.org/10.1103/PhysRevB.48.17791).   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 https://doi.org/10.3990/1.9789036528733), 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.   Marc

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Re: cubic-diamond Ge band structure issue ( No.1 ) Date: 2023/01/12 15:22 Name: T. Ozaki Hi, The band structure in the materials project can be found at https://materialsproject.org/materials/mp-32?chemsys=Ge 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? Regards, TO  Re: cubic-diamond Ge band structure issue ( No.2 ) Date: 2023/01/12 23:01 Name: Marc Tunica  <marc.tunica-i-rosich@universite-paris-saclay.fr> 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 <Definition.of.Atomic.Species   Ge    Ge7.0-s3p3d3f2      Ge_CA19 Definition.of.Atomic.Species> DATA.PATH /opt/DFT/openmx-latest/DFT_DATA19 Atoms.Number        2 Atoms.SpeciesAndCoordinates.Unit  Frac  <Atoms.SpeciesAndCoordinates            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.SpeciesAndCoordinates>   Atoms.UnitVectors.Unit            Ang  <Atoms.UnitVectors                      0.000000000000  2.8200000000 2.8200000 2.82000000000 0.000000000000  2.8200000  2.820000000000 2.820000000000 0.000000000000 Atoms.UnitVectors> 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         <Band.KPath.UnitCell 5.64  0.00  0.00 0.00  5.64  0.00 0.00  0.00  5.64 Band.KPath.UnitCell> Band.Nkpath                  6 <Band.kpath   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 Band.kpath> Looking at different references, LDA calculations should not present such kind of splitting (see, for instance, https://doi.org/10.1016/j.commatsci.2014.11.026 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, Marc

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