We report calculations of the electronic structure in the neighborhood
of the (001) surface of CuAuI using the self-consistent-field, linear
muffin-tin orbital method within the atomic sphere approximation, wit
h a slab geometry and including the surface dipole terms. We focus our
attention on the vicinity of the (M) over bar point in the surface Br
illouin zone and we identify the two (Tamm-type) surface states report
ed recently in photoemission measurements. The overall agreement betwe
en the theoretically determined dispersions of these states and those
observed experimentally is very good and provides strong support for o
ur calculational scheme. We show also that measurements of the surface
core level shifts should allow a determination of the termination.