  Using first-principles calculations, we analyze the structural properties of
tungsten trioxide WO3 . Our calculations rely on density functional theory and
the use of the B1-WC hybrid functional, which provides very good agreement with
experimental data. The hypothetical high-symmetry cubic reference structure
combines several ferroelectric and antiferrodistortive (antipolar cation
motions, rotations and tilts of oxygen octahedra) structural instabilities. The
instability related to antipolar W motions combines with those associated to
oxygen rotations and tilts to produce the biggest energy reduction, yielding a
P21/c ground state. This non-polar P21/c phase is only different from the
experimentally reported Pc ground state by the absence of a very tiny
additional ferroelectric distortion. The calculations performed on a
stoichiometric compound so suggest that the low temperature phase of WO3 is not
intrinsically ferroelectric and that the reported ferroelectric character might
arise from extrinsic defects such as oxygen vacancies. Independently, we also
identify never observed R3m and R3c ferroelectric phases with large
polarizations and low energies close to the P 21/c ground state, which makes
WO3 a potential antiferroelectric material. The relative stability of various
phases is discussed in terms of the couplings between different structural
distortions, highlighting a very complex interplay involving improper-like
couplings up to fourth order in the energy expansion in the cubic phase.
