[Wien] Optimized lattice constants using pbe+U

fabien.tran at vasp.at fabien.tran at vasp.at
Mon Aug 28 10:01:13 CEST 2023


As Peter mentioned, U is applied only inside the atomic spheres. In 
general, the details of the implementation of DFT+U depends on the basis 
set, which can lead to disagreements between codes that are more 
important than for plain LDA or GGA (see 
https://doi.org/10.1063/1.4945608).

You wrote that you used the default k-mesh and gmax. You should also 
test these parameters.


On 25.08.2023 18:48, Peter Blaha wrote:
> Hard to say without repeating the calculations, but:
> 
> a) I see nothing wrong in your calculation setups/procedure
> b) I've seen previously VERY wrong PBE+U results using VASP in other
> cases. VASP potentials have been optimized for PBE (and probably for
> HSE), and those results are usually ok, but I don't know about PBE+U.
> c) At the time when the rutile/anatase stability problem came up, I
> let a student try if PBE+U could fix it. It did not do it. But this is
> long time ago.
> 
> Maybe repeat one U value with a significantly larger RMT for Ti. Note
> that the Hubbard-U is applied only within the spheres in WIEN2k and
> since the Ti-3d states are not too localized, there might be an
> effect.
> 
> Am 24.08.2023 um 17:55 schrieb Park, Ken:
>> Dear Wien2k experts,
>> 
>> I have been studying the effect of the Hubbard U on various phases of 
>> TiO2 using wien2k 23.2. I have observed that some calculated 
>> properties are different from those reported in literature (mostly 
>> with pseudopotential) and would like to get your suggestions to see if 
>> I have made a mistake.
>> 
>> For rutile TiO2 using pbe, my optimized lattice constants are a=4.648 
>> Å and c=2.966Å, which are close to the published result of 4.650 and 
>> 2.968 [1]. However, after I added U= 6eV and ran the optimization, I 
>> obtained a=4.655 Å and c=3.000Å, in contrast to a=4.687Å and c=3.042Å 
>> for U=5 eV in [1].
>> 
>> [1] 
>> https://pubs.aip.org/aip/jcp/article/135/5/054503/190719/DFT-U-calculations-of-crystal-lattice-electronic 
>> <https://pubs.aip.org/aip/jcp/article/135/5/054503/190719/DFT-U-calculations-of-crystal-lattice-electronic>
>> 
>> So I performed a systemic study using U=3, 5, 8, 10 eV as in [1] and 
>> obtained the following:
>> 
>> U=3        a=4.650                c=2.985                vs U=3    
>>                a=4.671                c=3.012 [1]
>> 
>> U=5        a=4.649                c=2.995                 vs 
>> U=5                   a=4.687                c=3.042 [1]
>> 
>> U=8        a=4.652                c=3.011                vs 
>> U=8                   a=4.709                c=3.081 [1]
>> 
>> U=10     a=4.655                c=3.021                vs 
>> U=10                a=4.725                c=3.108 [1]
>> 
>> The lattice constant a is nearly constant or expanded very little 
>> despite the increasing U whereas the constant c shows a similar 
>> increase albeit by smaller amount. In rutile, c is the direction of 
>> the Ti-Ti short chain.
>> 
>> I have checked the band gaps and they are comparable with the reported 
>> results.
>> 
>> U=3        2.24 eV                 vs U=3                  2.15 eV [1]
>> 
>> U=5        2.42 eV                 vs U=5                   2.3 eV  
>> [1]
>> 
>> U=8        2.72 eV                 vs U=8                   2.7 eV [1]
>> 
>> U=10     2.98 eV                 vs U=10                2.92 eV [1]
>> 
>> For your information, I have copied the input files case.inorb and 
>> case.indm and the top portion of the structure file.
>> 
>>    1  1  0                     nmod, natorb, ipr
>> 
>> PRATT  1.0                    BROYD/PRATT, mixing
>> 
>>    1 1 2                          iatom nlorb, lorb
>> 
>>    1                              nsic 0..AMF, 1..SIC, 2..HFM
>> 
>>     0.44 0.00        U J (Ry)   Note: you can also use U_eff = U-J and 
>> J=0
>> 
>> -12.                      Emin cutoff energy
>> 
>> 1                       number of atoms for which density matrix is 
>> calculated
>> 
>> 1  1  2      index of 1st atom, number of L's, L1
>> 
>> 0 0           r-index, (l,s)index
>> 
>> TiO2
>> 
>> P                            2
>> 
>>               RELA
>> 
>>    8.788126  8.788126  5.669865 90.000000 90.000000 90.000000
>> 
>> ATOM  -1: X=0.00000000 Y=0.00000000 Z=0.00000000
>> 
>>            MULT= 2          ISPLIT= 8
>> 
>>        -1: X=0.50000000 Y=0.50000000 Z=0.50000000
>> 
>> Ti         NPT=  781  R0=0.00005000 RMT=    1.7800   Z:  22.00000
>> 
>>                       0.7071068 0.7071068 0.0000000
>> 
>>                      -0.7071068 0.7071068 0.0000000
>> 
>>                       0.0000000 0.0000000 1.0000000
>> 
>> ATOM  -2: X=0.30509790 Y=0.30509790 Z=0.00000000
>> 
>>            MULT= 4          ISPLIT= 8
>> 
>>        -2: X=0.69490210 Y=0.69490210 Z=0.00000000
>> 
>>        -2: X=0.19490210 Y=0.80509790 Z=0.50000000
>> 
>>        -2: X=0.80509790 Y=0.19490210 Z=0.50000000
>> 
>> O          NPT=  781  R0=0.00010000 RMT=    1.6100   Z:   8.00000
>> 
>>                       0.0000000-0.7071068 0.7071068
>> 
>>                       0.0000000 0.7071068 0.7071068
>> 
>>                      -1.0000000 0.0000000 0.0000000
>> 
>>    16      NUMBER OF SYMMETRY OPERATIONS
>> 
>> I optimized the structure with ‘runsp_lapw -p -orb -min -ec 0.00001 
>> -cc 0.0001 -fc 1’ (or smaller fc) using rkmax 9 (or 10 to check for 
>> convergence) and default values such as k-mesh and gmax. I also used 
>> two different ways to check the optimization: one varying volume and 
>> varying c/a, and the second varying a and c. Both methods yielded the 
>> same or consistent results.
>> 
>> I am not sure if I have errored using pbe+U and if so, where, but I 
>> would very much appreciate your advice.
>> 
>> Sincerely,
>> 
>> Ken Park
>> 
>> 
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