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<p class="MsoNormal"><span style="font-size:11.0pt">Dear Wien2k experts,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">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].<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">[1] <a href="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</a><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">So I performed a systemic study using U=3, 5, 8, 10 eV as in [1] and obtained the following:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">U=3 a=4.650 c=2.985 vs U=3 a=4.671 c=3.012 [1]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">U=5 a=4.649 c=2.995 vs U=5 a=4.687 c=3.042 [1]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">U=8 a=4.652 c=3.011 vs U=8 a=4.709 c=3.081 [1]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">U=10 a=4.655 c=3.021 vs U=10 a=4.725 c=3.108 [1]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I have checked the band gaps and they are comparable with the reported results.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">U=3 2.24 eV vs U=3 2.15 eV [1]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">U=5 2.42 eV vs U=5 2.3 eV [1]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">U=8 2.72 eV vs U=8 2.7 eV [1]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">U=10 2.98 eV vs U=10 2.92 eV [1]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">For your information, I have copied the input files case.inorb and case.indm and the top portion of the structure file.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> 1 1 0 nmod, natorb, ipr<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">PRATT 1.0 BROYD/PRATT, mixing<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> 1 1 2 iatom nlorb, lorb<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> 1 nsic 0..AMF, 1..SIC, 2..HFM<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> 0.44 0.00 U J (Ry) Note: you can also use U_eff = U-J and J=0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">-12. Emin cutoff energy<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">1 number of atoms for which density matrix is calculated<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">1 1 2 index of 1st atom, number of L's, L1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">0 0 r-index, (l,s)index
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">TiO2
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">P 2
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> RELA<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> 8.788126 8.788126 5.669865 90.000000 90.000000 90.000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">ATOM -1: X=0.00000000 Y=0.00000000 Z=0.00000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> MULT= 2 ISPLIT= 8<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> -1: X=0.50000000 Y=0.50000000 Z=0.50000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Ti NPT= 781 R0=0.00005000 RMT= 1.7800 Z: 22.00000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> 0.7071068 0.7071068 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> -0.7071068 0.7071068 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> 0.0000000 0.0000000 1.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">ATOM -2: X=0.30509790 Y=0.30509790 Z=0.00000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> MULT= 4 ISPLIT= 8<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> -2: X=0.69490210 Y=0.69490210 Z=0.00000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> -2: X=0.19490210 Y=0.80509790 Z=0.50000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> -2: X=0.80509790 Y=0.19490210 Z=0.50000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">O NPT= 781 R0=0.00010000 RMT= 1.6100 Z: 8.00000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> 0.0000000-0.7071068 0.7071068<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> 0.0000000 0.7071068 0.7071068<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> -1.0000000 0.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> 16 NUMBER OF SYMMETRY OPERATIONS<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I am not sure if I have errored using pbe+U and if so, where, but I would very much appreciate your advice.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Sincerely,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Ken Park<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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