  Nickel and Rhodium (001) surfaces display a similar - as from STM images -
clock reconstruction when half a monolayer of C/Ni, N/Ni or O/Rh is adsorbed;
no reconstruction is observed instead for O/Ni. Adsorbate atoms sit at the
center of the black squares of a chess-board, $c(2\times 2)$, pattern and two
different reconstructions are actually compatible with the observed STM images
- showing a $(2\times 2)p4g$ pattern - according to whether a rotation of the
black or white squares occurs. We report on a first - principles study of the
structure of X/Ni(001) and X/Rh(001) surfaces (X=C,N,O) at half a monolayer
coverage, performed using density-functional theory. Our findings are in
agreement with all available experimental information and shed new light on the
mechanisms responsible for the reconstructions. We show that the same substrate
may display different reconstructions - or no reconstruction - upon adsorption
of different atomic species, depending on the relative importance of the
chemical and steric factors which determine the reconstruction.
