The application of theoretical models of complex shape to the fitting of experimental spectra having closely overlapping bands

Abstract

The problem of the uniqueness of parameters obtained during fitting of experimental spectra containing closely overlapping bands has been evaluated, since conventional methods of fitting do not produce reliable results. It is here shown that, despite the difficulties inherent in both the formal mathematical problem and its numerical solutions, typical and representative spectra can be resolved unambiguously within a reasonably chosen theoretical model. Reliable values of the parameters of the model, including parameters of band shape, can also be obtained. A random search method of global minimisation of a function with a significant number of arguments is derived. A program and algorithm to implement this method for spectra decomposition have been developed. The program allows the microdynamics of liquids to be obtained directly upon performing numerical Fourier transformations on a model (theoretical) time correlation function together with using model spectra obtained thereby in each fitting step. A model spectrum for any desired accuracy and frequency range can hence be generated without the unavoidable errors inherent in conventional methods. The apparatus function of the spectrophotometer is also now readily incorporated. Using the algorithm, the parameters of the microdynamics of acetonitrile molecules are obtainable for the first time upon decomposition of its ν₂ Raman vibration, and a value of 0.069 was obtained for the dimensionless modulation speed in liquid acetonitrile. This method has also enabled for the first time the detection of molecules in the second solvation shell around Li⁺ in acetonitrile, from within its Raman spectrum.

References

1. M. Besnard, M. I. Cabaco and J. Yarwood, Chem. Phys. Lett., 1992, 198, 207.
2. I. Vuchkov, L. Boyadzhieva and E. Solakov, Applied Linear Regression Analysis, Financy i statistika, Moscow, 1987.
3. D. S. Konyaev, S. A. Merny and Yu. V. Kholin, New software for studying of equilibrium of complexes formation, XIV Ukrainian Conference on Inorganic Chemistry, 1996.
4. O. N. Kalugin, D. A. Nerukh, I. N. Vunnik, E. G. Otlejkina, Yu. N. Surov and N. S. Pivnenko, J. Chem. Soc., Faraday Trans., 1994, 90, 297.
5. R. Kubo, J. Phys. Soc. Jpn., 1962, 17, 1100.
6. R. J. Le Roy, J. Mol. Spectrosc., 1998, 191, 223.
7. D. M. Himmelblau, Applied Nonlinear Programming, McGraw-Hill, New York, 1972.
8. A. G. Zhilinskas, Global Optimisation: Axiomatics of Statistical Models, Algorithms, Applications, Mokslas, Vilnjus, 1986.
9. A. A. Zhiglyavsky, Mathematical Theory of Global Random Search, LGU, Leningrad, 1985.
10. A. A. Avdeenko, V. V. Eremenko, N. I. Gorbenko, P. V. Zinoviev, D. A. Nerukh, A. T. Pugachev, N. B. Silaeva, Yu. A. Tiunov and N. P. Churakova, Sverkhtverdye Materialy, 1997, 3, 54.
11. O. N. Kalugin, D. A. Nerukh, S. A. Eremenko, A. V. Vankevich and A. G. Nerukh, Zh. Neorg. Khim., 1996, 41, 261.
12. D. A. Nerukh, PhD Thesis, Kharkov, 1996.
13. S. Hashimoto, T. Ohba and S. Ikawa, Chem. Phys., 1989, 138, 63.
14. A. Sugitani, S. Ikawa and S. Konaka, Chem. Phys., 1990, 142, 423.
15. K. Tanabe and J. Haraishi, Spectrochim. Acta, 1980, A36, 665.
16. G. Fini and P. Mirone, Spectrochim. Acta, 1976, A32, 439.
17. M. I. S. Sastry and S. Singh, J. Raman Spectrosc., 1984, 15, 80.
18. M. I. S. Sastry and S. Singh, Can. J. Chem., 1985, 63, 1351.
19. I. M. Strauss and M. C. R. Symons, J. Chem. Soc., Faraday Trans., 1978, 74, 2146.
20. R. Kubo, in Fluctuations, Relaxation, and Resonance in Magnetic Systems, ed. D. Ter Haar, Plenum, New York, 1962, p. 27.
21. M. Maroncelli, J. Chem. Phys., 1991, 94, 2084.
22. W. G. Rothschild, J. Chem. Phys., 1976, 65, 455.
23. I. S. Perelygin, A. S. Krauze and I. G. Itkulov, Chem. Phys., 1993, 12, 404.
24. S. A. Eremenko, O. N. Kalugin and D. A. Nerukh, Proc. Kharkov. Univ., Chem., 1997, 1, 34.