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 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

REFERENCES

Abrashev, M.V., Zlateva, G.A., Iliev, M.N. & Gyulmerov, M. 1994. Optical phonons in Nd2BaMO5 (M=Zn,Cu). Phys. Rev. B 49: 11783-17788.

Arguello, C.A., Rousseau, D.L. & Porto, S.P.S. 1969. First-order Raman effect in Wurtzite-type crystals. Phys. Rev. 181: 1351-1363.

Cusco, R., A-Llado, E., Ibanez, J., Artus, L., Jimenez, J., Wang, B. & Callahan, M.J. 2007. Temperature dependence of Raman scattering in ZnO. Phys. Rev. B 75: 165202-165212.

Devi, V.R., Madhavi, M.B., Srihari, E.L., Shrivastava, K.N. & Boolchand, P. 2005. Ab initio calculation of vibrational frequencies of GeSIglass. J. Non-Cryst. Solids 351: 489-494.

Hohenberg, P. & Kohn, W. 1964. Inhomogeneous electron gas. Phys. Rev. 136: B864-B871.

Jemali, N.A., Kassim, H.A., Devi, V.R. & Shrivastava, K.N. 2008. Ab initio calculation of vibrational frequencies of GeSe flass. J. Non-Cryst. Solids 354: 1744-1750.

Kassim, H.A., Ithnin, A.J., Yusof, N., Devi, V.R. & Shrivastava, K.N. 2007. Ab initio calculation of vibrational frequencies of GexPxS1-2x glass, J. Non-Cryst. Solids 353: 111-118.

Kohn, W. 1999. Nobel lecture: Electronic structure of matter-wave functions and density functionals. Rev. Mod. Phys. 71(5): 1253-1266.

Kohn, W. & Sham, L.J. 1965. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140: A 1133-A 1138.

Lucas, M., Wang, Z.L. & Riedo, E. 2007. Growth direction and morphology of ZnO nanobelts revealed by combining in situ atomic force microscopy and polarized Raman spectroscopy. Phys. Rev. B 81: 045415-045419.

Rosli, A.N., Zabidi, N.A., Kassim, H.A. & Shrivastava, K.N. 2010a. Ab initio calculation of vibrational frequencies of AsO glass. J. Non-Cryst. Solids 356: 428-433.

Rosli, A.N., Kassim, H.A. & Shrivastava, K.N. 2010b. Ab initio calculation of vibrational frequencies in a glassy state of Selenium. Sains Malaysiana 39(2): 281-283.

Rosli, A.N., Zabidi, N.A., Kassim, H.A. & Shrivastava, K.N. 2010c. DFT calculations of vibrational frequencies of carbon-nitrogen clusters: Raman spectra of carbon-nitrides. J. Cluster Sci. 21: 197-210.

Samanta, K., Bhattacharya, P. & Katiyar, R.S. 2007. Temperature dependent E2 Raman modes in the ZnCoO ternary alloy. Phys. Rev. B 75: 035208-035212.

Zabidi, N.A., Rosli, A.N., Kassim, H.A., Shrivastava, K.N., Venkateswara, R.P. & Devi, V.R. 2007. Adsorption of atoms on Thymine: Density functional theory. Malaysian Journal of Science 26(2): 99-109.

 

 

*Corresponding author; email: anazrul84@yahoo.com

 

 

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