Sains Malaysiana 42(5)(2013): 649–654

DFT Calculation of Vibrations in the Clusters of Zinc and Oxygen Atoms

(Pengiraan Getaran bagi Kluster Atom Zink dan Oksigen dengan DFT)

Ahmad Nazrul Rosli*

Faculty of Science and Technology, Universiti Sains Islam Malaysia, 71800 Nilai, Negeri Sembilan, Malaysia

Hasan Abu Kassim & Keshav N. Shrivastava

Department of Physics, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received: 4 October 2011/Accepted: 24 October 2012

ABSTRACT

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 ZnO_n and continue with Zn₂O_n, Zn₃O_n and Zn₄O_n 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.

Keywords: Cluster; density functional theory; Raman spectrum, vibrational frequency; ZnO

ABSTRAK

Kluster bersaiz nanometer selalu wujud dalam ZnO. Kami telah membuat pengiraan frekuensi getaran bagi zink oksida menggunakan teori fungsi ketumpatan. Kluster ZnO dibentuk daripada ZnO_n dan diikuti pula oleh Zn₂O_n, Zn₃O_n dan Zn₄O_n dengan n = 1, 2, 3 dan 4. Apabila tenaga persamaan Schrödinger diminimumkan, kami dapat mengukur panjang ikatan dan frekuensi getaran bagi setiap kluster. Perbandingan antara data pengiraan ini dengan spektrum Raman hasil daripada keputusan eksperimen dibuat untuk mengesan kluster yang wujud dalam bahan ZnO₄. Teori fungsi ketumpatan dalam penghampiran ketumpatan (LDA) digunakan bersama set asas nombor berganda. Hasil daripada pengiraan ini, kami menemui panjang ikatan bagi kluster ZnO₄ dengan simetri tetrahedron (Td) adalah 1.923 Å dan frekuensi getaran adalah 94.4 cm^-1 dan 440.4 cm^-1 dengan 3 ulangan setiap satu. Kami menghasilkan beberapa kluster menggunakan atom zink dan oksigen dengan frekuensi getaran, ulangan dan keamatan telah dikira untuk setiap kes.

Kata kunci: Getaran frekuensi; kluster; spektrum Raman; teori fungsi ketumpatan; ZnO

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*Corresponding author; email: anazrul84@yahoo.com