Density functional theory (DFT) electronic structure calculations were carried out to predict the triplet Jahn-Teller distorted structures and energetics for zinc complexes of porphyrin (ZnP), tetraazaporphyrin, tetrabenzoporphyrin, and phthalocyanine. The D-4h square planar structures in the ground state are found to distort along the b(1g) mode leading to the D-2h rectangle structures in the lowest triplet state. Time-dependent DFT calculations were also carried out to interpret the observed triplet-triplet spectra and to quantify the effects of meso-tetraaza substitutions and tetrabenzo annulations on ZnP. The computed triplet-triplet excitation energies and oscillator strengths are in good agreement with experiment. The effects of meso-tetraaza substitutions and tetrabenzo annulations on the triplet excited state structures and spectra are discussed in detail.