Do you understand the concepts such as "Brillouin zone" and "first Brillouin zone"? If yes, it will easy for you to understand the answer why k is usually taken from -0.5 to 0.5. If no, please take a look at the "Solid state physics" textbook first.
The k point can be given in the Cartesian coordinate or in the fractional coordinate. For the former case, the unit of k point is 1/unit of length. Usually, the unit of length in electronic structure calculations are Bohr radius (a.u.) or Angstrom. As you know, 1 a.u.=0.529177 Angstrom. For the latter case, the unit of k point is 2[tex]\pi[/tex]/a, where a is the lattice constant of the lattice, and the value of k is less than 1.0. Further, we can consider only the k points in the first Brillouin zone due to the symmetry (i.e., the k-space periodicity). Hence the value of k point is usually taken from -0.5 to 0.5.
Due to the periodicity along the directions perpendicular to the transport direction, the above discussion for the k point used in transmission calculations is also right.
