To design nanocrystalline nanosystems, a theory for nanocrystals is needed
which can be: applied to nanocrystals with atomic-scale variations in compo
sition, structure and shape. We present an empirical tight-binding theory f
or nanocrystal heteronanostructures. Electronic structure and optical absor
ption spectra are obtained for CdS/HgS/CdS and ZnS/CdSZnS quantum-dot quant
um-well nanocrystals. Comparison with experiment shows that tight-binding t
heory provides a good description of nanosystems with monolayer variations
in composition. Issues for designing nanocrystal heteronanostructures are d
iscussed.