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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
Diserahkan: 4 Oktober 2011/Diterima: 24 Oktober 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 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.
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 ZnOn dan diikuti pula oleh Zn2On, Zn3On dan Zn4On 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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*Pengarang untuk surat-menyurat; email: anazrul84@yahoo.com
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