If a unit cell of a solid is large enough, then a single point in *k*-space, the Γ
point,
is sufficient to specify the entire Brillouin zone. The secular determinant
for this point can be constructed by adding together the Fock matrix for
the central unit cell plus those for the adjacent unit cells. The periodic
boundary conditions are satisfied, and diagonalization yields the correct
density matrix for the Γ point.

At this point in the calculation, conventionally, the density matrix for each unit cell is constructed. Instead, the Γ-point density and one-electron density matrices are combined with "Γ-point-like" Coulomb and exchange integral strings to produce a new Fock matrix. The calculation can be visualized as being done entirely in reciprocal space, at the Γ point.

Most solid-state calculations take a very long time. These calculations, called "Cluster" calculations after the original publication, require between 1.3 and 2 times the equivalent molecular calculation.

A minor 'fudge' is necessary to make this method work. The contribution to the Fock matrix element arising from the exchange integral between an atomic orbital and all atomic orbitals which are more than half a unit cell away must be ignored.

The unit cell must be large enough that an atomic orbital in the center of the unit cell has an
insignificant overlap with the atomic orbitals at the ends of the unit
cell. In practice, a translation vector of more that about 7 or 8 Ångstrom is
sufficient. For one rare group of compounds a larger translation vector is
needed. Solids with delocalized * π*-systems, and solids with very
small band-gaps will require a larger translation vector, in order to
accurately sample *k*-space. For these systems, a translation vector in the
order of 15-20 Ångstroms is needed.