Most of peoples use the U value, which gives the best agreement with experiment. I myself never performed calculations using the DFT+U formalism.

All best wishes,

Roberts

I never described the f states in my works, but if you don't have the 4f-VBM experimental value, a good approximation is evaluate 0

Thank you, Roberts.

Thank you, Nadia.

In the publication, some people use the Ueff = 6.0 eV. I don't know whether I should use a similar value in my work or not.

Depending on the size of your system you might want to do a hybrid functional calculation. Use that  bang gap as a point of reference for determining the U value. 

Thanks for the suggestion, Isaac.

You mean:

firstly,  we use a hybrid functional method to get the band structure of Ce doped compound (we can determine the 4f energy level in the band structure).

And then, we use the information (maybe 4f -VBM) to decide the "U" value in the normal DFT calculation (I mean, just the LDA or GGA functional).

am I right?

Here, I have a question:

can we be sure that the hybrid functional method can provide a accurate information about the 4f state of Ce3+ in the band structure?

Best wishes,

yongchao

About the value Ueff = 6.0 eV, if you have found it in some papers, you should verify the origin of information, why they decided use this values and in what condition. Probably should be good also for you.

You may try to determine also the U value for Eu or Ce pure and verify your method whith experimental results.

Some paper report U= 5.0 eV for Ce(4f)

Hello Jia.  I am experimentalist but I know my collaborators use the method by M. Cococcioni and S. de Gironcoli to estimate U. If useful for you please look at

Phys. Rev. B 71, 035105 (2005)

Ideally U values would be calculated "ab initio". Several groups have published approaches to this, including the linear response method [1], and more recently, using constrained RPA [2]. A third technique that has been more widely used is to statisfy "generalized Koopmans condition" [3,4]. 

If the U value is fitted to reproduce external data (e.g. from hybrid DFT calculations or experiment) then one must be careful to fit to parameters that are directly affected by the U term. The direct effect of applying U to e.g. CeO2 is to open up an energy gap between occupied and unoccupied Ce f states. A side-effect is to open up the fundamental band gap. However I would not recommend *fitting* to the band gap, because this is the energy (if we ignore hybridisation for the moment) between unoccupied Ce 4+ states that dominate the conduction band minimum, and the occupied O 2p states that dominate the valence band maximum. Applying U only affects the O 2p states indirectly (by driving rehybridization of the valence and conduction band states) so has a relatively opaque effect on the O 2p – Ce 4f states. This is why some earlier papers fitted U values to the experimental splitting between occupied and unoccupied states *on the same atom species* in n-type or p-type samples (e.g. [5]).

If fitting to other theoretical values, such as band energy differences from hybrid DFT, there are additional issues. The results from a hybrid DFT calculation depend on (at a minimum) the proportion of HF exchange included in the functional, and selecting an appropriate %HF-xc leads us back to the original problem: how to tune a parameter in the functional to give the correct electronic structure? Even if a hybrid functional chosen does give e.g. the correct fundamental band gap, there is no a priori reason it should give the correct energy difference for occupied–unoccupied rare-earth metal states (and equally U fitted to reproduce one of these values can not be assumed to reproduce the other).

With these issues in mind, a simpler approach might seem to use values from the literature, which would (in principle) allow direct comparisons between two sets of calculations. Even here however care should be taken to ensure that other calculation parameters are also kept the same. In particular, the effect of a given U term depends strongly on the choice of projection operators used to define the occupation matrices. Where different codes use different projection operators values of U *cannot* be simply transferred between calculations.

Ultimately, if one is being cautious, a range of U values would be used to assess the sensitivity of any specific result to the chosen U. If the results change drastically with small changes in U then strong claims about the predicted behaviour are probably not recommended, and good experimental data or higher level theory would be necessary to decide whether your results constitute "realistic" behaviour.

[1] Cococcioni, M., & de Gironcoli, S. (2005). Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Physical Review B, 71(3), 035105. doi:10.1103/PhysRevB.71.035105

[2] Setvin, M., Franchini, C., Hao, X., Schmid, M., Janotti, A., Kaltak, M., et al. (2014). Direct View at Excess Electrons in TiO2 Rutile and Anatase. Physical Review Letters, 113, 086402. doi:10.1103/PhysRevLett.113.086402

[3] Lany, S., & Zunger, A. (2009). Polaronic hole localization and multiple hole binding of acceptors in oxide wide-gap semiconductors. Physical Review B, 80(8), 085202. doi:10.1103/PhysRevB.80.085202

[4] Morgan, B. J., & Watson, G. W. (2009). Polaronic trapping of electrons and holes by native defects in anatase TiO2. Physical Review B, 80(23), 233102.

[5] Morgan, B. J., & Watson, G. W. (2007). A DFT+U description of oxygen vacancies at the TiO2 rutile (110) surface. Surface Science, 601(21), 5034–5041. doi:10.1016/j.susc.2007.08.025