The nanometer size clusters are often present in ZnO. We have calculated the vibrational frequencies of zinc oxide by using the density-functional theory. We synthesized clusters of ZnO starting with ZnOn and continue with Zn2On, Zn3On and Zn4On with n = 1, 2, 3 and 4. By minimizing the energy of the Schrödinger equation, we found the bond lengths and the vibrational frequencies of each cluster. These calculated data are compared to the experimentally measured Raman spectra of ZnO4 to identify the clusters which exist in this material. The density-functional theory in the local density approximation (LDA) is used with double numerical basis set. From this calculation, we find that the bond length for the cluster of ZnO4 with tetrahedral symmetry (Td) is 1.923 Å and the vibrational frequencies are 94.4 cm-1 and 440.4 cm-1 with degeneracy of 3 each. We have made several clusters using zinc and oxygen atoms and have calculated the vibrational frequencies, degeneracies and intensities in each case.