  We present an efficient first-principles approach for calculating Fermi
surface averages and spectral properties of solids, and use it to compute the
low-field Hall coefficient of several cubic metals and the magnetic circular
dichroism of iron. The first step is to perform a conventional first-principles
calculation and store the low-lying Bloch functions evaluated on a uniform grid
of k-points in the Brillouin zone. We then map those states onto a set of
maximally-localized Wannier functions, and evaluate the matrix elements of the
Hamiltonian and the other needed operators between the Wannier orbitals, thus
setting up an ``exact tight-binding model.'' In this compact representation the
k-space quantities are evaluated inexpensively using a generalized
Slater-Koster interpolation. Because of the strong localization of the Wannier
orbitals in real space, the smoothness and accuracy of the k-space
interpolation increases rapidly with the number of grid points originally used
to construct the Wannier functions. This allows k-space integrals to be
performed with ab-initio accuracy at low cost. In the Wannier representation,
band gradients, effective masses, and other k-derivatives needed for transport
and optical coefficients can be evaluated analytically, producing numerically
stable results even at band crossings and near weak avoided crossings.
