  Many physical quantities in solid-state physics are calculated from k-space
summation. For spectral functions, the frequency-dependent factor can be
decomposed into the energy-conserving delta function part and the
nondissipative principal value part. A very useful scheme for this k-space
summation is the tetrahedron method. Tetrahedron methods have been widely used
to calculate the summation of the energy-conserving delta function part such as
the imaginary part of the dielectric function. On the other hand, the
corresponding tetrahedron method for the nondissipative part such as the real
part of the dielectric function has not been used much. In this paper, we
address the technical difficulties in the tetrahedron method for the
nondissipative part and present an easy-to-implement, stable method to overcome
those difficulties. We demonstrate our method by calculating the static and
dynamical spin Hall conductivity of platinum. Our method can be widely applied
to calculate linear static or dynamical conductivity, self-energy of an
electron, and electric polarizability, to name a few.
