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

A quantum-mechanical calculation of the zone-centre phonon spectrum of beryl has been per- formed, 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 frequen- cies (Raman, IR-TO and IR-LO) less than 5 cm–1 on average. In the few cases where a relatively large dis- agreement between calculated and experimental data is observed, an explanation can be found which attri- butes the reason of the discrepancies to the experi- mental data rather than to the calculated ones. The calculation (i) allows the identification, in the experi- mental spectra, of the peaks corresponding to funda- mental 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 corre- sponding to each normal mode.