Hi,

    It depends on whether you are interested in structural or electronic properties. If only structural properties are concerned, DFT+U may not be necessary. The DFT-optimized geometry with a 4f-in-core pseudopotential basis for Lu could lead to a better agreement with experiments than that obtained with 4f-in-valence pseudopotential basis for Lu. Please refer to the attached paper for more details.

Best regards,

Lixin Ning

Dear Prof. Ning,

Thanks for the valuable suggestion and the nice paper.

Best wishes,

Yongchao

Pure DFT XC-functionals will most likely lead to a strong delocalisation of the 4f orbitals due to self-interaction. You may then get spurious covalent interactions with your coordinating species. A hybrid functional will help alleviate this to some extent. The issue with DFT+U is what value of U should you use? Depending on the physical property of interest, a different value of U may be appropriate. As Lixin Ning suggests, the 4f-in-core ECP's developed by the Dolg group may well be the best choice.

Indeed, freezing the 4f in the core state seems to be the suitable way. However, for other rare earth ions, like Ce3+ and Eu2+ ions, problems still exist, especially we need the information of 4f state.

Yes, for Ce3+ explicit 4f orbitals will probably be necessary, but here self-interaction should be less problematic since there is only 1 4f electron and so GGA or preferably a hybrid such as PBE0 may be suitable. For Eu2+, there may be two problems. One is the self-interaction as mentioned above will again be important, suggesting DFT+U or a hybrid if you need the explicit electronic structure. The second is the electronic configuration of Eu2+: are you sure that you would expect a 4f^n configuration as opposed to 4f^n-1 5d^1? Coordination complexes of divalent lanthanides can exhibit these different occupancies which would again make DFT+U difficult to apply. See recent work by the Evans group at UC Irvine.

The way I see it, for energetics involved in finding equilibrium lattice constants, optimize crystal structure, and bulk modulus DFT w/o U is the way to go. I would be careful with 4f in the core (standard rare-earth model) because the bulk modulus could be substantially overestimated in this model. Perhaps structural relaxations work. In order to reproduce electronic spectra a U must be applied, but DFT+U is probably not good for the energetics. Bottom line: try both and see what seems to be most appropriate for your study. We wrote a recent paper on the DFT and rare-earth metals that you may find helpful; Per Söderlind et al 2014 J. Phys.: Condens. Matter 26 416001

Thanks for the suggestion, Andrew.

For the Ce3+ ions, the GGA functional fails to explicitly describe the Ce4f state (from the result I have obtained.) At present, I utilize the " +U " method. Still, the U value is hard to determined. The hybrid functional is not tested.

For the Eu2+ ions, I am sorry that I do not understand your mean clearly. Do you mean that the configure (4f7 for ground state, or 4f65d1 for excited state) of Eu2+ will meet some problem in the DFT + U method?

Thanks for the sharing the idea and paper, Per.

Dear all,

Here I have obtained the electronic band structure of LuAG, with and without freezing the 4f electron in the core state.

The band gap with Lu 25e-psp (not freeze the 4f electron in the core) is 4.79298eV, while the value is 5.03974eV. The former is an indirect gap, and the latter is a direct one.

Both of the calculations use the structure geometry from experiment data.

From the results, it seems that the role of 4f electron will make an effect on the CBM and VBM. Therefore, I believe that we should consider the Lu 4f electron in the electronic band structure.

What do you think about the above results?

Best wishes,

Yongchao Jia