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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