Wrong bandgap calculated for Cu2O using DFT+U

[yasheng]

Hi All,

I want to calculate the bandgap of Cu2O using DFT+U in ATK. I used the script generator. The calculation uses spin polarized PBE with U=7 eV and FHI basis sets. However, I calculated a direct bandgap of 0.62 eV, which is not consistent with the experimental indirect bandgap of 1.4 eV.

I attached my script (results are too big to be attached). I really appreciate if you look at my input files and give me suggestions on how to get a correct bandgap. (Except the suggetions of going to hybrid functionals).

Thank you,
Yasheng

[Jess Wellendorff]

I do not know your experimental reference, but to me it looks like Cu2O is supposed to have a direct gap at the Gamma point, just like your calculation suggests: https://arxiv.org/pdf/1508.00499.pdf

[yasheng]

I was referring to the article here: http://pubs.rsc.org/en/Content/ArticleLanding/2006/CP/b611969g#!divAbstract   It is written in the abstract.

[yasheng]

Sorry, here in this article (http://scitation.aip.org/content/aip/journal/jcp/131/12/10.1063/1.3231869)  state that 'Cuprous oxide (Cu 2 O)
(Cu2O) is an abundant, low cost, nontoxic semiconductor material with a direct band gap of 2.17 eV'  (first sentence of the Introduction).

In any case, 0.62 eV of bandgap I calculated seems bit small.

[Umberto Martinez]

2.17 eV is the exp. band gap.
0.62 eV is the calculated one which reproduce previous VASP calculations as reported in table 1 of your reference, 0.67 eV.

You can try MGGA as implemented in ATK to get a better description of the band gap if you need it.

[yasheng]

Yes, in the first reference (http://pubs.rsc.org/en/Content/ArticleLanding/2006/CP/b611969g#!divAbstract ), it is shown that PBE+U (U=7) gives 1.48 eV band gap.

In the second reference (http://scitation.aip.org/content/aip/journal/jcp/131/12/10.1063/1.3231869) PBE+U yields 0.67 eV and argued that PBE+U method fails to predict the correct band gap.

I am surprised by the inconsistencies in literature. The lesson learned is that never trust the literature, trust your own calculation.

[zh]

It is well known that the band gap predicted by the DFT+U method is dependent strongly on the U value.  Even the same U value, the use of different basis set (e.g., plane wave and local atomic orbital) may also give a slight difference for the predicted band gap value, because the occupied electron number for the atomic orbital may be affected by the locality of orbital.

[yasheng]

I agree with you. But the difference between bandgaps 0.6 eV and 1.4 eV is not a slight difference.

[zh]

The DFT+U may easily give different electron state for  the orbital that is applied by U.  In the practice of DFT+U calculations, the occupancy of orbital should be initialized. For example, if the U is applied on a d orbital,   the occupation number for  dxy, dz2, dxz, dyz, dx2-y2  should be initialized. In most cases, an average value estimated from the occupation number of d orbital that takes. But this couldn't guarantee the convergence of calculation to the global solution of electronic configurations.  In a word, in the use of DFT+U  there are many subtle ticks that usually aren't written in the published paper. 

For the discrepancy in the literature, it is difficult to figure out the clear reason without communication with the authors of literature sources.

[yasheng]

Hi Zh,

what you are saying about initializing the occupation numbers make complete sense. I really wish to learn about these subtle tricks. Can you please demonstrate these tricks in a tutorial? (I can see that you are a member of Quantumwise support team).



Umberto Martinez suggested that  MGGA may give better band gap. I have never done calculations using MGGA.
What is the performance of MGGA method in terms of computational speed compared to normal DFT ?

Thanks,

Yasheng




   

[zh]

Please see the manual for the initialization of spin
http://www.quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/chap.atkdft.html#sect2.atkdft.hubbardU

You can tune the setup of spin configuration by the following two parameters:
filling_method = Anisotropic
number_of_spins=

For the performance of meta-GGA exchange, I suggest to refer to the literature.
http://scitation.aip.org/content/aip/journal/jcp/124/22/10.1063/1.2213970
Specially for its citation.

[Anders Blom]

In general, the overhead for MGGA-TB09 is very small compared to LDA/GGA.

[neerajkumar]

The value of U can be varied but is there any way to change the value of exchange parameter J?

[Anders Blom]

Actually the parameter in ATK is U-J, if you compare to other codes, so what you cannot do is modify U and J separately.

[neerajkumar]

Thanks for the clarification.