Dear Giacomo,
If the supercell is charge neutral which is the default, then one aims at
simulating a neutral substitutional defect with respect to Ti. In this case V
in 4+ oxidation state which corresponds in the naive fully ionic picture to V
losing 4 of its valence electrons to oxygen and retaining the last one as you
said. The question arises whether this electron is localized on the V site
and it is really in 4+ oxidation state. The other alternative is that the
electron delocalizes and the supercell contains V in 5+ oxidation state and an
extra "free" electron. In my opinion the best way to analyze this problem is
to start from the most positive oxidation state and systematically reduce it.
In the case of V you can do 6 separate relaxation simulations starting from
tot_charge=+1 which corresponds to V on 5+ oxidation state, all the way to
tot_charge=-4 which corresponds to V in 0 oxidation state. After these 6
simulations are done you can track the changes in the charge density and spin
density when you go from the oxidation state q to the oxidation state q-1. In
my experience V in oxides such as TiO2 can take oxidation states from 5+ to 2+.
If you compare 1+ and 2+ you will notice that the extra electron you add to 2+
to achieve 1+ never localizes on V and as such 2+ is likely the lowest
oxidation state for V in these oxides.
If you do not want to do this lengthy analysis and you just want to check
whether you have 4+ or not , check the spin density. V4+ will likely have a net
magnetic moment close to 1 Bohr Mag.
Also there are many cases in literature where achieving certain oxidation state
never happens because of electron (hole) delocalization. For example, if you
try to model neutral hydrogen interstitial in ZnO or ZrO2, you will get
interstitial proton and a free delocalized electron. See for example:
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.85.1012
A final word of caution, analyzing the oxidation states of transition metal
dopants and their changes by adding or removing electrons requires very dense
and accurate grids for representing the charge (and spin) density. The reason
is that the change of the localized charge (if any) on the transition metal
defect while going from formal oxidation state q to q-1 is usually very low (in
my experience in the order of 0.1 e). This observation was discussed in this
article: http://www.nature.com/nature/journal/v453/n7196/full/nature07009.html
(It is also fun and instructive to follow the debate that this paper raised in
literature!)
Best Regards,
Mostafa Youssef
MIT
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