Numerical aspects of the calculation of scaling factors from experimental data

Authors

  • I.V. Kolos
  • M.V. Kolos

Keywords:

краевые задачи
параболические уравнения
гиперболические уравнния
математическое моделирование
обобщенные функции
негативная норма

Abstract

New algorithms for finding molecular force field parameters expressed in terms of scaling factors are developed. A new formulation of the inverse vibrational problem (the so-called inverse scaling problem) is given and stable numerical methods are proposed. Examples include calculations of scaling factors for the molecules of methylsilane and perfluoroethane within different models.

New computational technologies

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Published

2004-10-07

Issue

Vol. 5 (2004): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biographies

I.V. Kolos

University of Russian Innovation Education

M.V. Kolos

Lomonosov Moscow State University,
Research Computing Center

References

  1. A.N. Tikhonov, A.S. Leonov, A.G. Yagola . Nonlinear ill-posed problems. London: Chapman & Hall, 1998 (Original Russian language edition: Nonlinear ill-posed problems. Moscow: Nauka, 1993).
  2. A.G. Yagola, I.V. Kochikov, G.M. Kuramshina, Yu.A. Pentin . Inverse problems of vibrational spectroscopy. Zeist (The Netherlands): VSP, 1999.
  3. G.M. Kuramshina, A.G. Yagola . A priori constraints in the force field calculations of polyatomic molecules // J. Struct. Chem. 1997. 38. 181-194.
  4. G.M. Kuramshina, F. Weinhold . Constraints on the values of force constants for molecular force field models based on ab initio calculations // J. Mol. Struct. 1997. 410, N 2. 457-462.
  5. G.M. Kuramshina, F.A. Weinhold, I.V. Kochikov, Yu.A. Pentin, A.G. Yagola . Joint treatment of ab initio and experimental data in molecular force field calculations with Tikhonov’s method of regularization // J. Chem. Phys. 1994. 100, N 2. 1414-1424.
  6. P. Pulay, G. Fogarasi, G. Pongor, J.E. Boggs, A. Vargha . Combination of theoretical ab initio and experimental information to obtain reliable harmonic force constants. Scaled quantum mechanical (SQM) force fields for glyoxal, acrolein, butadiene, formaldehyde, and ethylene // J. Am. Chem. Soc. 1983. 105. 7037-7047.
  7. T.I. Seidman, C.R. Vogel . Well-posedness and convergence of some regularization methods for nonlinear ill-posed problems // Inverse Problems. 1989. 5. 227-238.
  8. H.W. Engl, M. Hanke, A. Neubauer . Regularization of inverse problems. Dordrecht: Kluwer Academic Publishers, 1996.
  9. A.V. Stepanova, I.V. Kochikov, G.M. Kuramshina, A.G. Yagola . Regularizing scale factor method for molecular force field calculations // Computer Assistance for Chemical Research. International Symposium CACR-96. Moscow, 1996. 52.
  10. I.V. Kochikov, G.M. Kuramshina, A.V. Stepanova, A.G. Yagola . Regularizing scale factor method for molecular force field calculations // Moscow Univ. Bull. Ser. 3. Physics and Astronomy. 1997. 5. 21-25 (in Russian).
  11. I.V. Kochikov, Yu.I. Tarasov, V.P. Spiridonov, G.M. Kuramshina, A.G. Yagola, A.S. Saakyan, M.V. Popik, S. Samdal . Extension of a regularizing algorithm for the determination of equilibrium geometry and force field of free molecules from joint use of electron diffraction, molecular spectroscopy and ab initio data on systems with large-amplitude oscillatory motion // J. Mol. Struct. 1999. T. 485-486 . 421-443.
  12. I.V. Kochikov . Inverse problems of molecular structure and force field calculation on the basis of vibrational spectroscopy and electron diffraction experimental data // ISIP2001. International Symposium on Inverse Problems in Engineering Mechanics. 6-9 February 2001. Nagano City (Japan), 2001. 121-124.
  13. S. Kondo . Empirical improvement of the anharmonic ab initio force field of methyl fluoride // J. Chem. Phys. 1984. 81, N 12. 5945-5951.
  14. I.V. Kochikov, Yu.I. Tarasov, V.P. Spiridonov, G.M. Kuramshina, A.S. Saakyan, Yu.A. Pentin . The use of ab initio calculation results in electron diffraction studies of the equilibrium structure of molecules // Russian Journal of Physical Chemistry. 2001. 75, N 3. 395-400.
  15. I.V. Kochikov, Y.I. Tarasov, V.P. Spiridonov, G.M. Kuramshina, A.S. Saakyan, A.G. Yagola . The use of ab initio anharmonic force fields in experimental studies of equilibrium molecular geometry // J. Mol. Struct. 2000. T. 550-551 . 429-438.
  16. I.V. Kochikov, Yu.I. Tarasov, V.P. Spiridonov, G.M. Kuramshina, et al. The equilibrium structure of thiophene by the combined use of electron diffraction, vibrational spectroscopy and microwave spectroscopy guided by theoretical calculations // J. Mol. Struct. 2001. T. 567-568 . 29-40.
  17. M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Jonhson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Peterson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakhara, M. Chablacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogie, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Deflees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople . Gaussian 94, Revision C2. Gaussian Inc. Pittsburgh, 1995.
  18. R.W. Kilb, L. Pieree . Microwave spectrum, structure and internal barrier of methylsilane // J. Chem. Phys. 1957. 27. 108-112.
  19. wref 19 R.E. Wilde . The infrared spectrum of CH_3SiH3 and CH_3SiD3 // J. Mol. Spectr. 1962. 8, N 6. 427-454.
  20. A.J.F. Clark, J.E. Drake . The vibrational spectra of germane and silane derivatives. Vibrational spectra and normal co-ordinate analysis of the methylsilanes // Can. J. Chem. 1977. 22, N 4. 79-83.
  21. S.V. Syn’ko, G.M. Kuramshina, A.I. L’vov, Yu.A. Pentin, G.S. Gol’din . Vibrational spectra of CH_ 3 SiH_ 2 D and CH_3SiHD2 // Moscow Univ. Bull. Ser. 2. Chemistry. 1983. 24, N 4. 360-364 (in Russian).
  22. K.L.Gallaher, A.Yokozeki, S.H.Bauer . Reinvestigation of the structure of perfluoroethane by electron diffraction // J. Phys. Chem. 1974. 78, N 23. 2389-2395.
  23. I.M.Mills, W.B.Person, J.R.Scherer, B.Crawford, Jr. Vibrational intensities. IX. C_2F_6: extension and revision // J. Chem. Phys. 1958. 28, N 5. 851-853.