  We explore the oxidation of a single layer of black phosphorous using ab
initio density functional theory calculation. We search for the equilibrium
structures of phosphorene oxides, PO$_x$ with various oxygen concentrations $x$
($0{\le}x{\le}1$). By evaluating the formation energies with diverse
configurations and their vibrational properties for each of various $x$ values,
we identify a series of stable oxidized structures with $x$ and confirm that
the oxidation occurs naturally. We also find that oxidation makes some modes
from the P-O bonds P-P bonds IR-active implying that the infrared spectra can
be used to determine the degree of oxidation of phosphorene. Our electronic
structure calculation reveals that the fully oxidized phosphorene (PO) has a
direct band gap of 0.83 eV similar to the pristine phosphorene. Intriguingly,
the PO possesses two nonsymmorphic symmetries with the inversion symmetry
broken, guaranteeing a symmetry-protected band structures including the band
degeneracy and four-fold degenerate Dirac points. Our results may provide a
significant insight into the intriguing relations between symmetry of lattice
and band topology of electrons.
