We have calculated the octopole and hexadecapole moment and the dipole-quadrupole (A) and dipole-octopole (E) polarizability of the tetrahedral (CdS)(4) and (CdSe)(4) clusters using all-electron ab initio and density functional theory calculations and systematic sequences of purpose-oriented basis sets. Both clusters are characterized by very large octopole and small hexadecapole moments. Our estimates for the polarizabilities are A/e(2)a(0)(3)E(h)(-1) = 56.6 +/- 5.7, E/e(2)a(0)(4)E(h)(-1) = -1732 +/- 346 for (CdS)(4) and A/e(2)a(0)(3)E(h)(-1) = -140.7 +/- 14.0, E/e(2)a(0)(4)E(h)(-1) = -2252 +/- 450 for (CdSe)(4). (C) 2008 Elsevier B.V. All rights reserved.