The multiplet structure of the tetrahedrally coordinated Cr4+ in Y3Al5O12 [yttrium aluminum garnet (YAG)] was calculated by the ab initio electronic-structure calculation method. The authors examined the dependence of the multiplet structures on the size of cluster models, with the use of (CrO4)(4-) (without point charges), (CrO4)(4-) (with point charges), (CrY6Al4O44)(54-), and (CrY18Al42O148)(112-) models. The covalency of the impurity-level molecular orbitals was analyzed, and it was revealed that the wave functions of the atoms outside the CrO4 tetrahedron should not be neglected. The validity of the assignment of the peaks in the absorption spectrum written in the literature was evaluated by the calculated magnitude of the spin-orbit splittings and the oscillator strengths of the transitions, which were obtained by the fully relativistic many-electron calculation. The effect of the codopant on the transition probability was also estimated by (CrCaY5Al4O44)(55-) models. It was indicated that the nearest Cr-Ca pairs would reduce the symmetry, and could produce some satellite peaks. The mixing of the wave functions of the triplet states was numerically analyzed, and the results were correlated with the transition probability. The traditional nephelauxetic parameter was estimated, and the value 0.51 was obtained. It was confirmed from first principles that the magnitude of the nephelauxetic parameter in some literature was appropriate.