The geometric and electronic structure of the recently found new polymorph of tantalum oxynitride, gamma-TaON, and its structural stability were studied quantum-chemically at the density functional level. Results obtained by complementary quantum-chemical techniques with wavefunctions either expanded in atom-centered functions or in plane waves were compared, having employed pure density-functional functionals within the generalized gradient approximation as well as density-functional/Hartree-Fock hybrid methods. In particular, several plausible anion distributions were investigated and, in accordance with Pauling's second rule, it was found that the configuration in which nitrogen occupies crystallographic sites with highest coordination numbers is the most stable one. Theoretically generated local structural parameters were used to improve the accuracy of the experimentally derived information. The bonding situation in the most stable configuration was investigated by an analysis of the density of states.