  A translationally invariant formulation of the Hartree-Fock (HF)
$\Gamma$-point approximation is presented. This formulation is achieved through
introduction of the Minimum Image Convention (MIC) at the level of primitive
two-electron integrals, and implemented in a periodic version of the ONX
algorithm [J. Chem. Phys, {\bf 106} 9708 (1997)] for linear scaling computation
of the exchange matrix. Convergence of the HF-MIC $\Gamma$-point model to the
HF ${\bf k}$-space limit is demonstrated for fully periodic magnesium oxide,
ice and diamond. Computation of the diamond lattice constant using the HF-MIC
model together with the hybrid PBE0 density functional [Theochem, {\bf 493} 145
(1999)] yields $a_0=3.569$\AA with the 6-21G* basis set and a $3\times3\times3$
supercell. Linear scaling computation of the HF-MIC exchange matrix is
demonstrated for diamond and ice in the condensed phase
