A hybrid density functional approach with very large basis sets was used for studying Ca-2 through Ca-19 and Zn-3 through Zn-11 neutral clusters and their cluster anions. Energetics, structure, and vibrational analysis of all these neutral clusters and cluster anions are reported. The calculated electron affinities are in excellent agreement with experiment displaying a characteristic kink at Ca-10 and Zn-10. This kink occurs because the 10-atom neutral cluster is very stable whereas the cluster anion is not. Additionally, the electron detachment binding energies (BEs) up to Ca-6(-) and Zn-6(-) were identified by analyzing the ground and excited states of the cluster anions and of their corresponding size neutral clusters. The theoretical BE is in very good agreement with experiment for both calcium and zinc cluster anions. The three main peaks in the spectrum correspond to BEs from the ground state of the cluster anion (doublet) to the ground state of the neutral cluster (singlet) and to the first triplet and quintet excited states of the neutral cluster. The calculated energy gap from the lowest BE peak to the second peak is in excellent agreement with experiment. The calculation reproduces very well the energy gap observed in Ca-4(-) and Zn-4(-), which is larger than those for other sizes and is indicative of the strong stability of the anion and neutral tetramers.