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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