Time-dependent density functional theory with linear and quadratic response technology is used to calculate electronic structure, spectra, and spin-orbit coupling effects for analysis, of the main mechanism for phosphorescence of the recently synthesized iridium complex [bis(2-phenylpyridine)(2-carboxy-4-dimethyl-aminopyridine)iridium(III)]. This compound exhibits strong green phosphorescence which is used in solution processable organic light-emitting diode devices (OLEDs) to overcome the efficiency limit imposed by the formation of triplet excitons. Attempting to foresee new structure-property relations that can guide an improved design of OLED devices based on phosphorescence of the lowest triplet state, we have conducted a theoretical analysis of the photophysical properties of a series of iridium cyclometalated complexes.