Large unit cell calculations of the properties of charged point defects in insulators largelyneglect dielectric polarization of the crystal, because the periodically repeatedcells are so small. Embedded quantum cluster calculations with shell-modelcrystals, representing a single defect in a large crystal, are able to representthe polarization more realistically. For such embedded quantum clusters, weevaluate the optical excitation energy for the nitrogen vacancy in charge state(+3):vN3+ in AlN. This is done with and without dielectric polarization of the embedding crystal. Adiscrepancy of a few per cent is found, when both ground and excited state orbitals arewell-localized within the vacancy. We show that the discrepancy rises rapidly as the excitedstate becomes more diffuse. We conclude that an embedded cluster approach will berequired for transitions that involve even somewhat diffuse states. The investigation isbased on a new model for AlN that shows promise for quantitative accuracy.