I'm a beginning QE user. I would like to perform a calculation of TiO2 surface with O-vacancy. Since two of the surface Ti's will most likely have 3+ charge, there will be two unpaired electrons in the system. Unfortunately the QE manual is very unclear about it, and one needs to set several keywords like "nspin" and "starting magnetization". I want to actually check in the beginning if the closed shell and spin polarized calculations converge to the same of different minima, to be sure what to do in further steps. Do you have any ideas for a proper set of settings in the input file? What about the DFT+U correction?
Thanks in advance for help!
Hi! The "nspin=2" option switches QE to spin-polarized DFT. This option is also requires some additional input to specify if we deal with
Hi Sergei! Many thanks for your detailed answer! I think I start to undestand these keywords now.
Just to make sure - you wrote in point 1. that we have starting magnetization 0.5 and -0.5 on the Ti3+ ions (so tot_magnetization = 0). I had a feeling that in point 2. (ferromagnetic) then we would have magnetization 0.5 on each of the Ti3+ ions (is that right?). Wouldn't it be in this case tot_magnetization = 1 in the triplet state? I'm still not 100% if I understand these keywords correctly and how to determine them :). I ran several options (also with tot_magnetization equal to 2 and to 1) to see how and where it converges.
What about the DFT+U correction? I found a JPCC paper recently where the authors considered the U = 3.5 eV for TiO2 with some bulk O-vacancies. Then I guess probably I should use this set of keywords:
lda_plus_u = .TRUE.,
lda_plus_u_kind = 0,
Hubbard_U(i), i=1,ntyp ?
Is there anything else I should be cautious about?
Thanks in advance!
Rafał
Hi! The "tot_magnetization = n" value is constraint for 2Sz, it is not connected with starting_magnetization(i) array which is provided to make some proper initial guess. Therefore, tot_magnetization = 2 is always for triplet. Remember that tot_magnetization = Na - Nb. You may find that starting_magnetization(1) = 0.1, starting_magnetization(2) = 0.1 together with tot_magnetization = 2 may also converge SCF to the same desired triplet state.
The tot_magnetization = 1 constraint will give you spin density half singlet half triplet.
Simple DFT+U correction (lda_plus_u_kind = 0) is penalty function for total energy: E(DFT+U) = E(DFT) + U/2*ni*(1-ni). When the electron occupation number ni is fractional, i.e. when electron is artificially delocalized over 2 or more Ti ions, the addendum becomes positive non-zero, making conductive electron-delocalized solution higher in energy, than localized one (ni = 1 or 0). For some U value insulating localized solution will be the ground state. Now if you are know in advance, that system under consideration is really insulator, but pure DFT makes it conductive, you may want to apply DFT+U scheme to select proper ground state. The energy of the electronic state selected this way as you may make sure of is independent on U.
Therefore, triplet state where electrons are already localized do not require DFT+U scheme. However, there is an ambiguity with calculating an occupation number. Localized orbitals for which occupation numbers are calculated is not orthogonal to each other (default case in QE) therefore +U correction affects other orbitals, such as Ti-O bonds etc. This cause energy dependence on the applied U term. Many researchers use this "feature" as an additional fit of the theory to experiment, unfortunately. More rigorous method is applying DFT+U scheme on the orthogonal set of localized orbitals, such is maximally localized Wannier functions, but QE still has no possibility to do geometry optimization with them.
Anyway, just remember that DFT+U scheme is not a fit, but a scheme to select proper electronic state.
Good luck!
Hi Sergei! Now everything is clear. Thank you very much for your patience and for the detailed explanation!
Rafał