The structural parameters, energies, and spectroscopic characteristics of singlet and triplet titanium porphyrin pi-complexes Ti(P)(pi-L) (P = C20H12N4) with the axial ligands L = C2H2, C2H4, N2H2, HCN, C6H6, N-2, and C-60 coordinated to the Ti atom through C-C, C-N, and N-N multiple bonds have been calculated by the density functional theory B3LYP method. The changes in the calculated properties of the pi-complexes as compared with the properties of the isolated (uncoordinated) Ti(P) and L molecules have been examined. The activation of multiple bonds on coordination to the titanium atom is manifested in (i) their sharp weakening and elongation by 0.10-0.20 angstrom or more, (ii) a long-wavelength shift of their stretching modes by 300-500 cm(-1) or more, (iii) considerable electron density transfer from the porphyrin ring (P ring) to the ligand and the corresponding ligand distortion and polarization, (iv) a strong displacement (0.5-0.6 angstrom) of the Ti atom from the P ring plane toward the pi-ligand and the dome distortion of the P ring. For the Ti(P)(pi-L) systems, the addition of the second axial pi-ligand to form six-coordinate pi-complexes is not typical. In the Ti(P)(pi-L)(2) with identical ligands, the Ti atom is strongly displaced out of the P ring plane toward one of the ligands and the second ligand is repulsed from the P ring and actually removed from the metal coordination sphere. In the Ti(P)(pi-L) (pi-L') complexes with different ligands, according to the relative strength of the Ti-L and Ti-L' bonds, which decreases in the series N2H2 > C2H2 > HCN > C-60 > C2H4 > C6H6 > N-2, the weaker ligand is forced out by the stronger ligand (acetylene is pushed out of the coordination sphere by diimine; ethylene, by acetylene and fullerene; fullerene, by hydrogen cyanide; etc.). In mixed pi sigma-complexes Ti(P)(pi-L)(CO) in the singlet state, acetylene pushes out the CO group; conversely, in the triplet state, acetylene is pushed out by carbonyl. There is a trend in the behavior of the activation effects along the series of the above ligands and with a change in the electronic state multiplicity of the complexes.