We study the optical and electronic properties of carbon-based quantum dots using first-principles calculations. Based on time-dependent density functional theory we calculated absorption and emission of carbon quantum dots, we focus on the influence of surface (edge) functional groups. We can show that nitrogen groups on the carbon edges are decisive for the emission properties of small carbon quantum dots and could give rise to charge-carrier multiplication which has been suggested by recent experiments. Moreover, we explain the stability, with regard to the absorption in the optical range, of carbon quantum dots under ambient conditions. Here, we demonstrate that surface oxidation does only influence the absorption in the visible light range but does give rise to variation in the UV absorption.