Vibrational spectra of distorted structure Macro & Nano molecules: An algebraic approach

Srinivasa Rao Karumuri^1*, J. Vijayasekhar², Velagapudi Uma Maheswara Rao², Ganganagunta Srinivas⁴, Aappikatla Hanumaiah⁵

¹Department of Electronics & Instrumentation, Lakireddy Bali Reddy College of Engineering, Mylavaram, India.
²Department of Mathematics, GITAM University, Hyderabad, India.
²Department of Applied Mathematics, Andhra University, Vishakhapatnam, India.
⁴Department of Physics, KL University, Guntur, India.
⁵Department of Sciences & Humanities, Lara Vigyan Institute of Science & Technology, Vadlamudi, India.

DOI: 10.4236/jbpc.2012.33031                

Abstract

Using the Lie algebraic method the vibrational frequencies of 97 resonances Raman lines (A_1g + B_1g + A_2g + B_2g) and 38 infrared bands (E_u) of octaethylporphyrinato-Ni (II) and its mesodeuterated and ¹⁵N-substituted derivates and Fullerenes C₆₀ and Cv₇₀ of 7 vibrational bands are calculated using U(2) algebraic Hamiltonian with four fitting algebraic parameters. The results obtained by the algebraic technique have been compared with experimental data; and they show great accuracy.

Keywords

Lie Algebra; Vibrational Spectra; Ni (OEP); Ni (OEP)-d₄ & Ni (OEP)-N₄ and Fullerenes

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Kroto, H.W., Heath, J.R., Brien, S.C.O., Curl, R.F. and Smalley, R.E. (1985) C60: Buckminsterfullerene. Nature, 318, 162-163. doi:10.1038/318162a0
[2]	Treubig, J.M.Jr. and Brown, P.R. (2002) Analysis of C60 and C70 fullerenes using high-performance liquid chromatography—Fourier transform infrared spectroscopy. Journal of Chromatography A, 960, 135-142.
[3]	Levine, R.D. (1982) Representation of one-dimensional motion in a morse potential by a quadratic Hamiltonian. Chemical Physics Letters, 95, 87-90. doi:10.1016/0009-2614(83)85071-4
[4]	Iachello, F. and Levine, R.D. (1982) Algebraic approach to molecular rotation—vibration spectra. I. Diatomic molecules. Journal of Chemical Physics, 77, 3046-3055. doi:10.1063/1.444228
[5]	Roosmalen, O.S.van, Dieperink, A.E.L. and Iachello, F. (1982) A unified algebraic model description for interacting vibrational modes in ABA molecules. Chemical Physics Letters, 85, 32-36. doi:10.1016/0009-2614(82)83455-6
[6]	Roosmalen, O.S.van, Iachello, F., Levine, R.D. and Dieperink, A.E.L. (1983), The geometrical-classical limit of algebraic Hamiltonians of molecular vibrational spectra, Chemical Physics Letters, 79, 2515. doi:10.1063/1.446164
[7]	Sarkar, N.K., Choudhury, J. and Bhattacharjee, R. (2006) An algebraic approach to the study of the vibrational spectra of HCN. Molecular Physics, 104, 3051-3055. doi:10.1080/00268970600954235
[8]	Sarkar, N.K., Choudhury, J., Karumuri, S.R. and Bhattacharjee, R. (2008) An algebraic approach to the comparative study of the vibrational spectra of monofluoroacetylene (HCCF) and deuterated acetylene (HCCD). Molecular Physics, 106, 693-702. doi:10.1080/00268970801939019
[9]	Sarkar, N.K., Choudhury, J. and Bhattacharjee, R. (2008) Study of vibrational spectra of some linear triatomic molecules. Indian Journal of Physics, 82, 767.
[10]	Choudhury, J., Karumuri, S.R., Sarkar, N.K. and Bhattacharjee, R. (2008) Vibrational spectroscopy of CCl4 and SnBr4 using lie algebraic approach. Physics and Astronomy, 71, 439-445. doi:10.1007/s12043-008-0123-z
[11]	Choudhury, J., Karumuri, S.R. and Bhattacharjee, R., (2008) Algebraic approach to analyze the vibrational spectra of tetrahedral molecules. Indian Journal of Physics, 82, 561-565.
[12]	Karumuri, S.R., Sarkar, N.K., Choudhury, J. and Bhattacharjee, R. (2008) Vibrational spectroscopy of Cm-H, C?-C? stretching vibrations of Nickel metalloporphyrins. Molecular Physics, 106, 1733-1738. doi:10.1080/00268970802248998
[13]	Karumuri, S.R., Choudhury, J., Sarkar, N.K. and Bhattacharjee, R. (2008) Analysis of resonance raman spectra of nickeloctaethyl porphyrin using lie algebra. Journal of Environmental Research and Development, 3, 250-256.
[14]	Karumuri, S.R., Sarkar, N.K., Choudhury, J. and Bhattacharjee, R. (2009) Study of vibrational spectra of Nickel metalloporphyrins: An algebraic approach. Pramana—Journal of Physics, 72, 517-525.
[15]	Karumuri, S.R., Sarkar, N.K., Choudhury, J. and Bhattacharjee, R. (2009) Vibrational spectroscopy of stretching and bending modes of nickel tetraphenyl porphyrin: An algebraic approach. Chinese Physics Letters, 26, 093- 301. doi:10.1088/0256-307X/26/9/093301
[16]	Karumuri, S.R., Sarkar, N.K., Choudhury, J. and Bhattacharjee, R. (2009) U(2) algebraic model applied to vibrational spectra of Nickel Metalloporphyrins. Journal of Molecular Spectroscopy, 255, 183-188. doi:10.1016/j.jms.2009.03.014
[17]	Karumuri, S.R., Choudhury, J., Sarkar, N.K. and Bhattacharjee, R. (2010) Vibrational Spectroscopy of Cm-C/ Cb-Cb stretching vibrations of Copper Tetramesityl Porphyrin Cu (TMP): An algebraic approach. Pramana—Journal of Physics, 74, 57-66. doi:10.1007/s12043-010-0007-x
[18]	Karumuri, S.R. (2010) Calculation of vibrational spectra by an algebraic approach: Applications to Copper Tetramesityl Porphyrins and its Cation radicals. Journal of Molecular Spectroscopy, 259, 86-92. doi:10.1016/j.jms.2009.11.005
[19]	Iachello, F. and Levine, R.D. (1995) Algebraic theory of molecules. Oxford University Press, Oxford.
[20]	Iachello, F. and Oss, S. (2002), Algebraic methods in quantum mechanics: From molecules to polymers. Physics and Astronomy, 19, 307-314. doi:10.1140/epjd/e20020089
[21]	Child, M.S. and Halonen, L.O. (1984) Overtone frequencies and intensities in the local mode picture. Advances in Chemical Physics, 57, 1. doi:10.1002/9780470142813.ch1
[22]	Wood, B.R., Stoddart, P.R. and McNaughton, D. (2007) Molecular imaging of red blood cells by raman spectroscopy. Australian Journal of Chemistry, 387, 1691.
[23]	Phuber, K. and Herzberg, G., (1979) Molecular spectra and molecular structure IV: Constants of diatomic molecules. Van Nostrand Reinhold Co., New York.
[24]	Kitagawa, T., Abe, M. and Ogoshi, H. (1978) Resonance Raman spectra of octaethylporphyrinato—Ni(II) and meso—deuterated and 15N substituted derivatives. II. A normal coordinate analysis, Journal of Chemical Physics, 69, 4526. doi:10.1063/1.436450
[25]	Schettino, V., Pagliai M. and Cardini, G. (2002) The infrared and raman spectra of fullerene C70. DFT calculations and correlation with C60. The Journal of Physical Chemistry A, 106, 1815-1823. doi:10.1021/jp012680d.