Abstract
The inverse problem of molecular force fields calculation is considered within the theory of regularization.
In our strategy, we choose the stabilizing matrix
Dedicated to Professor Anatoly Yagola on the occasion of his 75th birthday
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 18-03-00412a
Funding statement: Gulnara M. Kuramshina was supported by the RFBR (Grant No. 18-03-00412a).
References
[1] N. V. Anikeeva, I. V. Kochikov, G. M. Kuramshina and A. G. Yagola, Regularizing algorithms for constructing intermolecular potentials on the basis of experimental data, Vychisl. Metody Programm. 4 (2003), no. 1, 200–206. Search in Google Scholar
[2] J. Ceponkus, G. Karlstrom and B. Nelander, Intermolecular vibrations of the water trimer, a matrix isolation study, J. Phys. Chem. 109A (2005), 7859–7864. 10.1021/jp052096vSearch in Google Scholar
[3] G. Fogarashi and P. Pulay, Ab initio calculation of force fields and vibrational spectra, Vibrational Spectra and Structure, Elsevier, Amsterdam (1985), 125–217. Search in Google Scholar
[4] J. B. Foresman and M. J. Frisch, Exploring Chemistry with Electronic Structure Methods, 3rd ed., Gaussian, Wallingford, 2015. Search in Google Scholar
[5] M. J. Frisch, G. W. Trucks and H. B. Schlegel, Gaussian 09, Revision D.01, Gaussian, Wallingford, 2013. Search in Google Scholar
[6] W. J. Hehre, L. Radom and P. V. R. Schlegel, Ab Initio Molecular Orbital Theory, Wiley, New York, 1985. Search in Google Scholar
[7] B. J. Howard and T. R. Dyke, The molecular beam spectrum and the structure of hydrogen bonded water dimer, J. Chem. Phys. 60 (1974), 2929–2930. 10.1063/1.1681463Search in Google Scholar
[8] A. R. Hoy and P. R. Bunker, A precise solution of the rotation behinding Schrodinger equation for a triatomic molecule with application to the water molecule, J. Molecular Spectroscopy 74 (1979), 1–8. 10.1016/0022-2852(79)90019-5Search in Google Scholar
[9] F. N. Keutsch, J. D. Cruzan and R. J. Saykally, The water trimer, Chem. Rev. 103 (2003), 2533–2577. 10.1021/cr980125aSearch in Google Scholar
[10] I. V. Kochikov and G. M. Kuramshina, A complex of programs for the force field calculations of polyatomic molecules by the Tikhonov regularization method, Vest. Mosk. Univ. Ser. 2 Khimia 26 (1985), no. 4, 354–358. Search in Google Scholar
[11] I. V. Kochikov, G. M. Kuramshina, I. A. Pentin and A. G. Iagola, Regularizing algorithm of the inverse vibrational problem solution, Dokl. Akad. Nauk SSSR 261 (1981), no. 5, 1104–1106. Search in Google Scholar
[12] I. V. Kochikov, G. M. Kuramshina, I. A. Pentin and A. G. Yagola, Calculation of force fields of polyatomic molecules by the Tikhonov regularization method, Dokl. Akad. Nauk SSSR 283 (1985), no. 4, 850–854. Search in Google Scholar
[13] I. V. Kochikov, G. M. Kuramshina and Y. A. Pentin, Application of Tikhonov’s regularization method to the calculation of force fields of polyatomic molecules, Russ. J. Phys. Chem. 61 (1987), no. 4, 451–457. Search in Google Scholar
[14] I. V. Kochikov, G. M. Kuramshina, Y. A. Pentin and A. G. Yagola, A stable method for the calculation of the force fields of polyatomic molecules in dependent coordinates, Theor. Exper. Chem. 20 (1984), no. 1, 66–72. 10.1007/BF00519791Search in Google Scholar
[15] I. V. Kochikov, G. M. Kuramshina, Y. A. Pentin and A. G. Yagola, Regularizing algorithms for molecular force field calculations, J. Mol. Struct. (Theochem) 272 (1992), 13–33. 10.1016/0022-2860(92)80022-ASearch in Google Scholar
[16] I. V. Kochikov, G. M. Kuramshina, A. V. Stepanova and A. G. Yagola, Regularized method of scaling factors for calculations of molecular force fields, Mosc. Univ. Phys. Bull. 5 (1997), 21–25. Search in Google Scholar
[17] I. V. Kochikov, G. M. Kuramshina and A. G. Yagola, Stable numerical methods of solving certain inverse problems of vibrational spectroscopy, USSR Comp. Math. Math. Phys. 27 (1987), no. 11–12, 33–40. 10.1016/0041-5553(87)90187-XSearch in Google Scholar
[18] I. V. Kochikov, A. V. Stepanova and G. M. Kuramshina, Ab initio molecular force fields fitted in Cartesian coordinates to experimental frequencies of isotopic species using symmetry constraints: Application to indole and pyrrole molecules, Struct. Chem. 30 (2019), no. 2, 605–614. 10.1007/s11224-018-1262-6Search in Google Scholar
[19] I. V. Kochikov, Y. D. Tarasov, G. M. Kuramshina, V. P. Spiridonov, A. G. Yagola and T. G. Strand, Regularizing algorithm for determination of equilibrium geometry and harmonic force field of free molecules from joint use of electron diffraction, vibrational spectroscopy and ab initio data with application to benzene, J. Mol. Struct. 445 (1998), 243–258. 10.1016/S0022-2860(97)00428-6Search in Google Scholar
[20] I. V. Kochikov, Y. I. Tarasov, V. P. Spiridonov, G. M. Kuramshina, D. W. H. Rankin, A. S. Saakjan and A. G. Yagola, The equilibrium structure of thiophene by the combined use of electron diffraction, vibrational spectroscopy and microwave spectroscopy guided by theoretical calculations, J. Mol. Struct. 567-568 (2001), 29–40. 10.1016/S0022-2860(01)00539-7Search in Google Scholar
[21] I. V. Kochikov, Y. I. Tarasov, V. P. Spiridonov, G. M. Kuramshina, A. S. Saakjan and A. G. Yagola, The use of ab initio anharmonic force fields in experimental studies of equilibrium molecular geometry, J. Mol. Struct. 550-551 (2000), 429–438. 10.1016/S0022-2860(00)00504-4Search in Google Scholar
[22] I. V. Kochikov, Y. I. Tarasov, V. P. Spiridonov, G. M. Kuramshina, A. G. Yagola, A. S. Saakjan, M. V. Popik and 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. 485-486 (1999), 421–443. 10.1016/S0022-2860(99)00185-4Search in Google Scholar
[23] I. V. Kochikov, A. G. Yagola, G. M. Kuramshina, V. M. Kovba and Y. A. Pentin, Force-fields and mean amplitudes of vibration of chromium, molybdenum and tungsten oxotetrafluorides, J. Mol. Struct. (Theochem) 15 (1984), no. 3–4, 355–360. 10.1016/0166-1280(84)85039-3Search in Google Scholar
[24] 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 (1997), 457–462. 10.1016/S0022-2860(96)09506-3Search in Google Scholar
[25] G. M. Kuramshina, F. Weinhold, I. V. Kochikov, A. G. Yagola and Y. 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 (1994), no. 2, 1414–1424. 10.1063/1.466619Search in Google Scholar
[26] G. M. Kuramshina and A. G. Yagola, A priori constraints in the force field calculations of polyatomic molecules, J. Struct. Chem. 38 (1997), no. 2, 181–194. 10.1007/BF02762644Search in Google Scholar
[27] G. M. Kuramshina and A. G. Yagola, Regularizing algorithms for solving nonlinear ill-posed problems of vibrational spectroscopy, Eurasian J. Math. Comp. Appl. 4 (2015), no. 2, 14–36. 10.32523/2306-6172-2016-4-4-14-36Search in Google Scholar
[28] G. M. Kuramshina and A. G. Yagola, Applications of regularizing algorithms in Structural Chemistry, Eurasian J. Math. Comp. Appl. 5 (2017), no. 3, 53–72. 10.32523/2306-6172-2017-5-3-53-72Search in Google Scholar
[29] R. G. Parr and W. Yang, Density-functional theory of atoms and molecules, Oxford University, Oxford, 1992. Search in Google Scholar
[30] A. V. Stepanova, I. V. Kochikov and G. M. Kuramshina, New approach for the correction of ab initio molecular force fields in Cartesian coordinates, Int. J. Quant. Chem. 109 (2009), 28–33. 10.1002/qua.21728Search in Google Scholar
[31] A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov and A. G. Yagola, Numerical Methods for the Solution of Ill-posed Problems, Springer, Heidelberg, 2013. Search in Google Scholar
[32] A. N. Tikhonov, A. S. Leonov and A. G. Yagola, Nonlinear Ill-Posed Problems, Chapman and Hall, London, 1998. 10.1007/978-94-017-5167-4Search in Google Scholar
[33] A. van der Avoird and K. Szalewicz, Water trimer torsional spectrum from accurate ab initio and semiempirical potentials, J. Chem. Phys. 128 (2008), Article ID 014302. 10.1063/1.2812556Search in Google Scholar PubMed
[34] M. Van Thiel, E. D. Becker and G. C. Pimentel, Infrared studies of hydrogen bonding of water by the matrix isolation technique, J. Chem. Phys. 27 (1957), 486–490. 10.1063/1.1743753Search in Google Scholar
[35] A. G. Yagola, I. V. Kochikov, G. M. Kuramshina and Y. A. Pentin, Inverse Problems of Vibrational Spectroscopy, Walter de Gruyter, Berlin, 2014. Search in Google Scholar
[36] Chemcraft Version 1.8 (build 486). http://www.chemcraftprog.com. Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
