In this article, we present a computational study of the structure and vibrational properties of the species formed by the interaction between Cr sites of Phillips catalyst and probe molecules (CO, N-2). The vibrational properties of these surface species, intensively investigated in the past, form a very rich and ideal set of experimental data to test computational approaches. By adopting the X4Si2O3Cr (X = H, OH, F) cluster as a simplified model of the ( SiO)(2)Cr(II) species present at the surface of the real catalyst, we found that the B3LYP hybrid functional (containing 20% of Hartree-Fock exchange), when applied to this model, is unable to reproduce with reasonable accuracy the Currently available experimental data (principally coming from IR spectroscopy). Better agreement is obtained when the percentage of Hartree-Fock exchange is increased (up to 35-40%).