Ab initio simulation of the IR spectra of pyrope, grossular, and andradite

IR spectra of pyrope Mg₃Al₂Si₃O ₁₂, grossular Ca₃Al₂Si₃O ₁₂ and andradite Ca₃Fe₂Si₃O ₁₂ garnets were simulated with the periodic ab initio CRYSTAL code by adopting an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. Two sets of 17 F_1u Transverse Optical (TO) and Longitudinal Optical (LO) frequencies were generated, together with their intensities. Because the generation of LO modes requires knowledge of the high frequency dielectric constant ε^∞ and Born effective charges, they were preliminary evaluated by using a finite field saw-tooth model and well localized Wannier functions, respectively. As a by-product, the static dielectric constant ε⁰ was also obtained. The agreement of the present calculated wavenumbers (i.e. peak positions) with the available experimental data is excellent, in that the mean absolute difference for the full set of data smaller than 8 cm^-1. Missing peaks in experimental spectra were found to correspond to modes with low calculated intensities. Correspondence between TO and LO modes was established on the basis of the overlap between the eigenvectors of the two sets and similarity of isotopic shifts; as result, the so called LO-TO splitting could be determined. Animation of the normal modes was employed to support the proposed pairing.