Symmetry and vibration of LiCAF crystal

The LiCaAlF6 salt crystallizes in the trigonal space group PMc (D d) with lattice constants a = 4.996 A and c = 9.636 A [9]. All the metal cations of the crystal are 

In considering the vibronic side-bands to be expected in the optical spectra when we augment the static crystal field model by including the electron-phonon interaction, we must know the frequencies and symmetries of the lattice phonons at various critical points in the phonon density of states. We shall be particularly interested in those critical points which occur at the symmetry points T, A and at the A line in the Brillouin zone. Using the method of factor group for crystals we have  

From these normal vibrations, three of symmetry A2u + Eu at the T point are acoustic vibrations and the others are optical vibrations. 

LOW-LYING ENERGY LEVELS IN STATIC CRYSTAL FIELD MODEL 

The ground-state absorption spectrum of the Cr3+ impurity incorporated in LiCAF crystals consists of two absorption bands occurring at 15 873 and 23 255 cm-1 due to 4,42j, — 4T2g and 4A2g — 4T ig transitions, respectively, as well as two sharp features near 15 413 and 16 408 cm-1 which arise from 2Eg and 2Tlg excited states [5]. The emission spectra are typical for the 4T2g 4A 2g transition, with the peak situated near 13 200 cm-1 and the full-width half-maximum of about 2000 cm-1 [5]. 

---