The validity of hybrid and nonlocal DFT methods are tested on examples of systems which are difficult to model by way of quantum chemistry techniques. The electron affinities for the oxygen and fluorine atoms were calculated. The exothermicity, the barrier for the fluorine atom reaction with the hydrogen molecule, and the energy of the H-F bond and its distance were computed with DFT methods, as well as, with ROHF, MPn, and QCISD͑T͒ ab initio methods. The computations were performed by using various basis sets, with 6-311ϩϩG (3d f ,3pd) as the largest. The obtained results are compared with the experimental values. The results of the Becke3LYP hybrid method is in qualitative agreement with experimental results and in the majority of the cases reassembles the high cost QCISD͑T͒ calculation results. Considering the modest computational cost for DFT methods, Becke3LYP/6-311ϩG(2d,2p) is suggested as the standard theory model for computation, and Becke3LYP/6-311ϩϩG(3d f ,3pd) as the model for generating highly accurate results. They should be applicable to relatively sizable chemical systems.