By using quantum chemical calculation data obtained by the DFT method with the OPBE/TZVP and B3PW91/TZVP levels, the principal possibility of the existence of three heteroligand complexes of nickel, each of which was shown to contain in the inner coordination sphere either porphyrazine or di[benzo]- and tetra[benzo]porphyrazine, oxygen (O2−)2−) and fluorine (F−)−) ions. The data on the geometric parameters of the molecular structure of these complexes are presented; which shows that NiN4 chelate nodes, all metal-chelate and non-chelate cycles in each of these complexes, are strictly planar. The bond angles between two donor nitrogen atoms and a nickel atom are equal to 90∘∘, while the bond angles between donor atoms N, Ni, and O or F, in most cases, albeit insignificantly, differ from this value. Nevertheless, the bond angles formed by Ni, O and F atoms are exactly 180∘∘. NBO analysis data for these complexes are presented; it was noted that the ground state of all these complexes was a spin doublet. It has been shown that a good agreement between the data obtained using the above two versions of the DFT method occurs. Also, standard thermodynamic parameters of formation (standard enthalpy ΔH0f,298ΔH0f,298, entropy S0f,298S0f,298 and Gibbs’s energy ΔG0f,298)ΔG0f,298) for the macrocyclic compounds under consideration were calculated.