Physics at the nanoscale has emerged as a field where discoveries of fundamental physical effects lead to a greater understanding of the solid state. Additionally, the field is believed to have a large potential for technological applications, which has driven a high pace of experimental achievements in fabrication and characterization. From the side of theoretical modeling—so successful in solid state physics in general, since the emergence of density functional theory—we must acknowledge a weak connection to state of the art experimental achievements in the realm of nanostructures. The cause for this partial disconnect resides in the difficulty of the matter, nanostructures being small in size but large in the number of atoms constituting them, and the relevant observables being accessible only through proper treatment of excitations. The large number of atoms and the need for excited state properties makes this a challenging task for theory and modeling.

In this contribution we will outline the framework, based on empirical pseudopotentials and configuration interaction, to obtain quantitative predictions of the excited state properties of semiconductor nanostructures using their experimental sizes, compositions and shapes. The methodology can be used to describe colloidal nanostructures of a few hundred atoms all the way to epitaxial structures requiring millions of atoms. The aim is to fill the gap existing between ab initio approaches and continuum descriptions. Based on the pseudopotential idea and the developments of empirical pseudopotentials for bulk materials in the early 1960s, the method has evolved into a powerful tool where the pseudopotential construction has lost some of its empirical character and is now based on modern density functional theory. We will present the construction of these potentials and the way the ensuing wavefunctions are used in a subsequent configuration interaction treatment of the excitation. We will illustrate the available capabilities by recent applications of the methodology to unveil new effects in the optics of nanostructures, quantum entanglement and wavefunction imaging.