Electronic states in metallic slabs ordinarily involve multiple interp
lanar couplings even in a nearest-neighbor-atom-coupling approximation
, except for special cases such as (100) and (111) face-centered-cubic
surfaces. A tight-binding study with nonzero multiple interplanar cou
plings shows that there can be many, depending upon the orientation of
the slab, exponentially decaying states within the energy band. Their
existence is needed to satisfy the boundary conditions at the slab su
rface. The effect of multiple interplanar coupling is to cause phase s
hifts in the plane-wave states in the bulk of material. These phase sh
ifts produce an effective free-electron surface plane, independent of
energy to the extent that the bands are parabolic, and affect quantiza
tion rules and the energy spectrum in slabs. The corresponding effects
must also occur in more accurate representations of the electron stat
es.