  An extensive theoretical investigation of the nonpolar (10$\bar{1}$0) and
(11$\bar{2}$0) surfaces as well as the polar zinc terminated (0001)--Zn and
oxygen terminated (000$\bar{1}$)--O surfaces of ZnO is presented. Particular
attention is given to the convergence properties of various parameters such as
basis set, k--point mesh, slab thickness, or relaxation constraints within LDA
and PBE pseudopotential calculations using both plane wave and mixed basis
sets. The pros and cons of different approaches to deal with the stability
problem of the polar surfaces are discussed. Reliable results for the
structural relaxations and the energetics of these surfaces are presented and
compared to previous theoretical and experimental data, which are also
concisely reviewed and commented.
