Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric, electronic and magnetic structure of Fe$_{x}$O$_{y}^{+}$
  clusters   Correlation between geometry, electronic structure and magnetism of solids is
both intriguing and elusive. This is particularly strongly manifested in small
clusters, where a vast number of unusual structures appear. Here, we employ
density functional theory in combination with a genetic search algorithm,
GGA$+U$ and a hybrid functional to determine the structure of gas phase
Fe$_{x}$O$_{y}^{+/0}$ clusters. For Fe$_{x}$O$_{y}$ cation clusters we also
calculate the corresponding vibration spectra and compare them with
experiments. We successfully identify Fe$_{3}$O$_{4}^{+}$, Fe$_{4}$O$_{5}^{+}$,
Fe$_{4}$O$_{6}^{+}$, Fe$_{5}$O$_{7}^{+}$ and propose structures for
Fe$_{6}$O$_{8}^{+}$. Within the triangular geometric structure of
Fe$_{3}$O$_{4}^{+}$ a non-collinear, ferrimagnetic and ferromagnetic state are
comparable in energy. Fe$_{4}$O$_{5}^{+}$ and Fe$_{4}$O$_{6}^{+}$ are
ferrimagnetic with a residual magnetic moment of 1~\muB{} due to ionization.
Fe$_{5}$O$_{7}^{+}$ is ferrimagnetic due to the odd number of Fe atoms. We
compare the electronic structure with bulk magnetite and find
Fe$_{4}$O$_{5}^{+}$, Fe$_{4}$O$_{6}^{+}$, Fe$_{6}$O$_{8}^{+}$ to be mixed
valence clusters. In contrast, in Fe$_{3}$O$_{4}^{+}$ and Fe$_{5}$O$_{7}^{+}$
all Fe are found to be trivalent.

13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas