Periodic Hartree-Fock total-energy calculations on two-dimensional sla
bs have been used to study the symmetry-conserving relaxation of the n
onpolar (1010BAR) surface of ZnO. We find that it is energetically fav
orable for the Zn-O surface dimers to tilt slightly (by 2.3-degrees) a
nd move downwards towards the slab, and for the dimer bond to shorten
significantly. Our results agree fairly well with those of a recent de
nsity-functional calculation, but disagree with empirical tight-bindin
g theory which predicts surface bonds to shorten only slightly while t
he surface dimers undergo a large tilt (18-degrees). The available exp
erimental data lies between the ab initio and tight-binding results wi
th large error bars. We have tested the effects of several refinements
of our Hartree-Fock calculation, including improvements of the orbita
l basis set and precision tolerances, the use of thicker slabs in appr
oximating the semi-infinite crystal, and post-self-consistent-field de
nsity-functional correlation corrections to the total energy. None of
these refinements significantly changed our results. We discuss possib
le reasons for the disagreement between our results and those of tight
-binding theory.