[Wien] Optimized lattice constants using pbe+U

[Peter Blaha]

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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-- 
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300
Email: peter.blaha at tuwien.ac.at    WIEN2k: http://www.wien2k.at
WWW:   http://www.imc.tuwien.ac.at
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