Historically, optical properties have played a key role in our understanding of the electronic structure of matter. An obvious example comes from early studies of the optical excitations in the hydrogen atom, which led to the development of the quantum theory of electronic states, first by Bohr and later by Heisenberg and Schrödinger. Indeed, the initial validation of the quantum theory centered on describing the spectral lines of a hydrogen atom and later many-electron atoms. This is reflected by the historical spectroscopic notation of atomic states by s, p, d and f. The letters refer to the hydrogen spectral lines characterized as "sharp," "principal," "diffuse," and "fine," respectively. This mode of discovery has continued over the last century or so. For example, most of our current understanding of the electronic structure of atoms, molecules and solids comes from examining the optical and dielectric properties of these systems. As a more recent example, the energy band structures of semiconductors were first established by using optical properties as the input for electronic structure calculations [Cohen 1989]. Unfortunately, examining optical excitations based on contemporary quantum mechanical methods can be especially challenging because accurate methods for structural energies, such as DFT, are often not well suited for excited state properties. This requires new methods designed for predicting excited states and new algorithms for implementing them.