  We report on a first-principles study of the structure of O/Rh(001) at half a
monolayer of oxygen coverage, performed using density-functional theory. We
find that oxygen atoms sit at the center of the black squares of a chess-board,
$c(2\times 2)$, pattern. This structure is unstable against a rhomboid
distortion of the black squares, which shortens the distance between an O atom
and two of the four neighboring Rh atoms, while lengthening the distance with
respect to the other two. We actually find that the surface energy is further
lowered by allowing the O atom to get off the short diagonal of the rhombus so
formed. We predict that the latter distortion is associated with an
order-disorder transition, occurring below room temperature. The above rhomboid
distortion of the square lattice may be seen as a rotation of the empty, white,
squares. Our findings are at variance with recent claims based on STM images,
according to which it is instead the black squares which would rotate. We argue
that these images are indeed compatible with our predicted reconstruction
pattern.
