[Wien] Optimized lattice constants using pbe+U

[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

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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