The effects of peripheral substituents and axial ligands (L) on the electronic structure and properties of cobalt tetraphenylporphyrin (CoTPP) have been studied using DFT methods. Various density functionals were tested, and the ground state of each system was determined by considering several possible low-lying states. The ground states of the fully fluorinated CoTPPF28(L)(2) complexes with L == THF, Py, and Im were identified to be high-spin (E-4(g)) by the meta-GGA functional tau-HCTH, which contains the kinetic energy density tau, in agreement with experimental measurements. All the pure GGA functionals, including the recently developed mPBE, OPBE, and HCTH/407, show more or less overestimation of the relative energies of the high-spin states. The energy gap between the (2)A(1g) and E-4(g) states is insignificant (similar to 0.1 eV) and varies in the order L = Py < L = THF < L = Im. The results and their trend are consistent with F-19 NMR studies which show partial population of the E-4(g) state in CoTPPF28(THF)(2) and CoTPPF28(Py)(2) and a complete conversion to the high-spin state in CoTPPF28(1-Melm)(2). Upon coordination by two very strong field axial CO ligands, CoTPPF28(CO)(2) becomes low-spin, as in unligated (CoTPPFx. The influence of the peripheral substituents and axial ligands on the ionization potentials, electron affinities, and CoTPPFx-(L)(2) binding strength was also investigated in detail.