Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-consistent DFT+$U$+$V$ study of oxygen vacancies in SrTiO$_3$   Contradictory theoretical results for oxygen vacancies in SrTiO$_3$ (STO)
were often related to the peculiar properties of STO, which is a $d^0$
transition metal oxide with mixed ionic-covalent bonding. Here, we apply, for
the first time, density functional theory (DFT) within the extended Hubbard
DFT+$U$+$V$ approach, including on-site as well as inter-site electronic
interactions, to study oxygen-deficient STO with Hubbard $U$ and $V$ parameters
computed self-consistently via density-functional perturbation theory. Our
results demonstrate that the extended Hubbard functional is a promising
approach to study defects in materials with electronic properties similar to
STO. Indeed, DFT+$U$+$V$ provides a better description of stoichiometric STO
compared to standard DFT or DFT+$U$, the band gap and crystal field splitting
being in good agreement with experiments. In turn, also the description of the
electronic properties of oxygen vacancies in STO is improved, with formation
energies in excellent agreement with experiments as well as results obtained
with the most frequently used hybrid functionals, however at a fraction of the
computational cost. While our results do not fully resolve the contradictory
findings reported in literature, our systematic approach leads to a deeper
understanding of their origin, which stems from different cell sizes, STO
phases, the exchange-correlation functional, and the treatment of structural
relaxations and spin-polarization.

16
The categories of this paper are: stat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc