The vibrational spectrum of alpha-AlOOH diaspore has been calculated at the B3LYP level of theory with a double-zeta quality Gaussian-type basis set by using the periodic ab initio CRYSTAL code. Harmonic frequencies at the Gamma point and the corresponding 48 normal modes are analyzed and classified in terms of simple models (octahedra modes, hydrogen stretching, bending, rotations) by direct inspection of eigenvectors, graphical representation, and isotopic substitution. Hydrogen modes are fully separated from the octahedra modes appearing under 800 cm(-1); bending modes are located in the range of 1040-1290 cm(-1), whereas stretching modes appear at 3130-3170 cm(-1). The available experimental IR and Raman spectra are characterized by broad bands, in some cases as large as 800 cm(-1), and individual peaks are obtained by decomposing these bands in terms of Lorentz-Gauss product functions; such a fitting procedure is affected by a relatively large degree of arbitrariness. The comparison of our calculated data with the most complete sets of experimental data shows, nevertheless, a relatively good agreement for all but the H modes; the mean absolute differences for modes not involving H are 10.9 and 7.2 cm(-1) for the IR and the Raman spectra, respectively, the maximum differences being 15.5 and 18.2 cm(-1). For the H bending modes, differences increase to 30 and 37 cm(-1), and for the stretching modes, the calculated frequencies are about 200 cm(-1) higher than the experimental ones; this is not surprising, as anharmonicity is expected to red shift the OH stretching by about 150 cm(-1) in isolated OH groups and even more when the latter is involved in strong hydrogen bonds, as is the case here.