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about LDA band gap of bulk Si
Date: 2005/04/06 00:31
Name: Brighton Yan   <>


It's well known that the LDA band gap is always smaller than the experimental value.
However, during my calculation using OPENMX I've obtained those band gaps(about 1.15ev) of bulk crystalline silicon, very close to the experimental gap(1.17ev), even most of them(1.4ev or 1.5ev) are larger than this value.
I wonder whether the LDA gap has been corrected automatically in OPENMX code or some fatal errors have been made in my calculation.

In my input file, Si.dat, some of these main parameters are given by:
Si Si7.5-s22p22 Si_TM
scf.XcType LDA
scf.EigenvalueSolver band
scf.Kgrid 10 10 10
orderN.HoppingRanges 10.0
orderN.NumHoppings 2
orderN.RecursiveLevels 6
orderN.NumPoles 100
orderN.ChargeDeviation 1.0e-6
It should be noted that when different PAO is employed, quite different results are obtained as follows:
PAO Utot Band Gap
Si7.5-s22p22 -7.7816 1.15
Si7.0-s22p22 -7.9041 1.52
Si6.0-s22p22 -7.7702 1.37
By the way, does the origin(0.0ev) fo the energy in both DOS calculation and BAND dispersion correspond to the Fermi energy ?

Thanks !
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Re: about LDA band gap of bulk Si ( No.1 )
Date: 2005/04/07 18:02
Name: T.Ozaki

Thank you for your report.

I have found that the overestimated band gap is due to the lack of the non-local
part for the d-state in Si_TM.vps. It seems that Si_TM.vps does not provide
an appropriate potential to the conduction band for which the d-state contributes.
To improve it, new relativistic pseudo potentials (Si_LDA.vps, Si_GGA.vps) and
new basis functions have been generated including the d-states which are
downloadable from

The revised pseudo potential well reproduces a previously reported LDA gap of
bulk Si as well as the lattice constant (see the above web).
Please try the calculations using the pseudo potentials.
As for the basis set, Si7.0R and Si7.5R seem to be close to an overcomplete basis set,
maybe the best choice for the basis set is Si6.0R-s2p2d1 or Si6.5R-s2p2d1.

> By the way, does the origin(0.0ev) fo the energy in both DOS calculation and BAND
> dispersion correspond to the Fermi energy ?

You are right.

The following is just a remark.
When a unexpected band gap is obtained, there would be two reasons:

(1) less accurate basis set
A less accurate basis set (short cutoff and small number of basis functions)
overestimates eigenvalues of the conduction band, since the conduction band
usually more extends and more oscillates than the valence band in real space.

(2) less accurate pseudo potential
When the lower excited states are crucial to determine the band gap, it is
desirable to include the first excited state (polarization state) in the generation
of pseudo potential. The Si pseudo potential was the case.

Since the d-state is not included in the pseudo potential generation for the
other elements (P, S, Cl, Ge, As, Se, Br), I wonder that the band gap of materials
consisting of these elements is less reproduced. If someone reports any flaw in pseudo
potentials of these elements, I would appreciate the cooperations.


T. Ozaki
Re: about LDA band gap of bulk Si ( No.2 )
Date: 2005/04/10 12:21
Name: Brighton Yan

The same trouble has also been found for Ge case.
It seems that those pseudopotentials and PAOs should be revised.

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