T Heoretical D Ivision, Los a L Am Os N Ational Laboratory, Los a L Am Os, N Ew M Exico 87545

A translationally invariant form ulation ofthe Hartree-Fock (HF) -point approxim ation is presented.Thisform ulation isachieved through introduction oftheM inim um Im ageConvention (M IC) atthe levelofprim itive two-electron integrals,and im plem ented in a periodic version ofthe O NX algorithm [J.Chem .Phys,106 9708 (1997)]for linear scaling com putation ofthe exchange m atrix.Convergence ofthe HF-M IC -pointm odelto the HF k-space lim itisdem onstrated forfully periodic m agnesium oxide,ice and diam ond. Com putation ofthe diam ond lattice constant using the HF-M IC m odeltogetherwith the hybrid PBE0 density functional[Theochem ,493 145 (1999)] yieldsa0 = 3:569 A with the6-21G * basissetand a 3 3 3 supercell.Linearscaling com putation ofthe HF-M IC exchange m atrix isdem onstrated fordiam ond and ice in the condensed phase. K eyw ords:Self-consistenteld,linear-scaling,periodic system s,exact-exchange,m inim um im age convention