Quantum-mechanical calculation of the vibrational spectrum of beryl (Al4Be6Si12O36) at the Γ point

Abstract

A quantum-mechanical calculation of the zone-centre phonon spectrum of beryl has been performed, by using an hybrid HF/DFT Hamiltonian (B3LYP). An excellent agreement with the experiment has been obtained, being the difference between the calculated and the experimental vibrational frequencies (Raman, IR-TO and IR-LO) less than 5 cm−1 on average. In the few cases where a relatively large disagreement between calculated and experimental data is observed, an explanation can be found which attributes the reason of the discrepancies to the experimental data rather than to the calculated ones. The calculation (i) allows the identification, in the experimental spectra, of the peaks corresponding to fundamental modes, overtones, combination bands and leakage; (ii) solves problems of band assignements due to the presence of LO–TO splitting in the IR spectra; (iii) provides the frequencies of silent modes; (iv) permits a full analysis of the atomic motion corresponding to each normal mode.