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Stable Numerical Methods of Approaching Quantum Mechanical Molecular Force Fields to Experimental Data

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Applied Inverse Problems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 48))

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Abstract

This paper presents mathematical background of data processing in vibrational spectroscopy. Regularizing algorithms of molecular force fields calculation based on the joint treatment of experimental and quantum mechanical data have been proposed within the frame of theory of regularization of nonlinear ill-posed problems. Different models of molecular force fields have been implemented in our SPECTRUM software package.

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References

  1. E.B. Wilson, J.C. Decius and P.C. Cross: Molecular vibrations. McGraw-Hill, New York (1955).

    Google Scholar 

  2. M.V. Volkenstein, L.A. Gribov, M.A. El’yashevich and B.I. Stepanov: Vibrations of molecules. Nauka, Moscow (1972).

    Google Scholar 

  3. L.M. Sverdlov, M.A. Kovner and E.P. Krainov: Vibrational spectra of polyatomic molecules. Wiley, New York (1973).

    Google Scholar 

  4. P.C. Peinter, M.M. Coleman and J.L. Koenig: The theory of vibrational spectroscopy and its application to polymeric materials. Wiley, New York (1982).

    Google Scholar 

  5. L.A. Gribov and W.J. Orwille-Thomas: Theory and methods of calculation of molecular spectra. Wiley, Chichester, New York (1988).

    Google Scholar 

  6. H.J. Hadamard: Le probleme de Cauchy et les equations aux derivees partielles lineaires hyperbolique. Hermann, Paris (1932).

    Google Scholar 

  7. I.V. Kochikov, G.M. Kuramshina and A.G. Yagola: Stable numerical methods of solving certain inverse problems of vibrational spectroscopy. USSR Comput. Maths. Math. Phys. 27: 33–40 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  8. A.G. Yagola, I.V. Kochikov, G.M. Kuramshina and Yu.A. Pentin: Inverse problems of vibrational spectroscopy. VSP Publishers, The Netherlands (1999).

    MATH  Google Scholar 

  9. A.V. Goncharsky, A.S. Leonov and A.G. Yagola: A generalized discrepancy principle for the case of operators specified with an error. Dokl. Akad. Nauk SSSR. 203: 1238–1239 (1972).

    MathSciNet  Google Scholar 

  10. A.V. Goncharsky, A.S. Leonov and A.G. Yagola: A generalized discrepancy principle. USSR Comput. Maths. Math. Phys. 13: 294–302 (1973).

    Google Scholar 

  11. A.G. Yagola: The generalized discrepancy method in reflexive spaces. Dokl. Akad. Nauk SSSR. 249: 71–73 (1979).

    MathSciNet  Google Scholar 

  12. A.G. Yagola: Choice of the regularization parameter when solving ill-posed problems in reflexive spaces. USSR Comput. Maths. Math. Phys. 20: 586–596 (1980).

    Article  MathSciNet  Google Scholar 

  13. A.N. Tikhonov, A.S. Leonov and A.G. Yagola: Nonlinear ill-posed problems. Nauka, Moscow (1995); Chapman & Hall, London (1997).

    Google Scholar 

  14. A.B. Bakushinsky and A.V. Goncharsky: Ill-posed problems: Theory and applications. Kluwer, Dordrecht (1994).

    Book  Google Scholar 

  15. G.M. Vainikko and A.Yu. Veretennikov: Iterative procedures in ill-posed problems. Nauka, Moscow (1986).

    Google Scholar 

  16. A.M. Fedotov: Ill-posed problems with random errors. Nauka, Novosibirsk (1990).

    MATH  Google Scholar 

  17. V.V. Vasin and A.L. Ageev: Ill-posed problems with a priori information. VSP, Utrecht (1995).

    Book  MATH  Google Scholar 

  18. H.W. Engl, M. Hanke and A. Neubauer: Regularization of inverse problems. Kluwer, Dordrecht (1996).

    Book  MATH  Google Scholar 

  19. A.S. Leonov and A.G. Yagola: Can an ill-posed problem be solved if the data error is unknown? Moscow Univ. Phys. Bull. 50: 25–28 (1995).

    MATH  Google Scholar 

  20. A.S. Leonov: On solving linear ill-posed problems on the base of a modified quasi optimality criterion. Mat. USSR Sbornik. 122(164): 405–415 (1983).

    Google Scholar 

  21. G.M. Kuramshina, F. Weinhold, I.V. Kochikov, A.G. Yagola and Yu. A. Pentin: Joint treatment of ab initio and experimental data in molecular force field calculations with Tikhonov’s method of regularization. J. Chem. Phys. 100: 1414–1424 (1994).

    Article  Google Scholar 

  22. G.M. Kuramshina and A.G. Yagola: A priori constraints in the force field calculations of polyatomic molecules. J. Struct. Chem. 38(2): 181–194 (1997).

    Article  Google Scholar 

  23. G.M. Kuramshina and F. Weinhold: Constraints on the values of force constants for molecular force field models based on ab initio calculations. J. Mol. Struct. 410–411: 457–462 (1997).

    Google Scholar 

  24. I.V. Kochikov, G.M. Kuramshina and A.V. Stepanova: New approach for the correction of ab initio molecular force fields in cartesian coordinates. Int. J. Quant. Chem. 109: 28–33 (2009).

    Article  Google Scholar 

  25. G.M. Kuramshina and E. Osawa: Predicting vibrational spectra of large molecules within combined approach based on the joint use of theoretical and empirical methods. Proceedings of 13th Conference on Current trends of computational chemistry, Jackson, Miss.: 96–99 (2004).

    Google Scholar 

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Acknowledgements

The authors are grateful to Visby program and Russian Foundation on Basic Research for their partial financial support (Projects No. 11-03-00040-a and 11-01-97020-r_povolzh’e_a).

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    Gulnara Kuramshina, Igor Kochikov & Anatoly Yagola

Authors
  1. Gulnara Kuramshina
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  2. Igor Kochikov
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  3. Anatoly Yagola
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Corresponding author

Correspondence to Anatoly Yagola .

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Editors and Affiliations

  1. Department of Mathematical Sciences, Chalmers University of Technology Gothenburg University, Gothenburg, Sweden

    Larisa Beilina

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Kuramshina, G., Kochikov, I., Yagola, A. (2013). Stable Numerical Methods of Approaching Quantum Mechanical Molecular Force Fields to Experimental Data. In: Beilina, L. (eds) Applied Inverse Problems. Springer Proceedings in Mathematics & Statistics, vol 48. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7816-4_10

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