The performance of five different density functionals (LDA, PBE, PBESOL, B3LYP and PBE0) in describing the infrared spectrum of a crystalline periodic system with a large unit cell (spessartine, 80 atoms in the primitive cell) is studied by using the periodic ab initio CRYSTAL09 code and an all electron basis set. The transverse (TO) and longitudinal (LO) optical branches of the 17 IR active modes are evaluated together with the oscillator strengths and the high frequency dielectric tensor epsilon(infinity). These ingredients permit to compute the dielectric function epsilon(nu), and then the reflectance spectrum R(nu), which is compared with experiment. (C) 2010 Elsevier B.V. All rights reserved.