An ab initio perturbed ion (aiPI) study using X-ray diffraction data has been carried out for pure and doped calcium aluminum silicate garnet, Ca3Al2Si3O12 (grossularite, GROS), and yttrium aluminum garnet, Y-3-Al5O12 (YAG); crystal structures. Different clusters containing from 55 to 139 ions have been built up, using large Slater type orbitals (STOs)to represent each atomic center. Basis sets and geometry optimizations have been performed with the aim of determining the relative stability, cell parameters, force constants, and vibrational frequencies of radial displacements associated with the local relaxation for pure and doped structures. Numerical results are compared with experimental data, and the geometrical cell parameters of different structures obtained by computer simulation are found to be similar to the experimental results. This comparison validates the aiPI methodology used in the theoretical characterization of the local properties of complex ionic systems. For GROS, the substitution of Cr3+ for Al3+ at the octahedral site is energetically favorable while the substitution of Cr4+ for Si4+ at the tetrahedral site is unstable. For YAG, the substitution of Cr3+ for Al3+ at octahedral or tetrahedral sites is energetically unfavorable. The differences between the ionic radii reported by Shannon and Prewitt for the species concerned in the doping process are capable of explaining the relaxation of crystal lattice parameters for tetrahedral sites. However, the relaxation in octahedral sites is lower than the differences in ionic radii. The doping process produces a decrease of force constant (k) values associated with the breathing fundamental vibrational mode for YAG garnet while an opposite effect appears in GROS. The k associated with the radial displacement in octahedral substitution in grossularite is especially high. The bulk modulus of the pure structures has also been theoretically calculated, GROS being less compressible than YAG.