Ab initio molecular force fields fitted in Cartesian coordinates to experimental frequencies of isotopic species using symmetry constraints: application to indole and pyrrole molecules

  • I. V. Kochikov
  • A. V. Stepanova
  • G. M. KuramshinaEmail author
Original Research


We present the new computational procedure for the fitting ab initio molecular force fields represented in Cartesian coordinates to the experimental frequencies with inclusion data for isotopic species and symmetry constraints. This procedure is based on the original numerical algorithms developed within theory of regularization of ill-posed problems and included in the software package SPECTRUM. New procedure allows organize the synthesis of molecular force field of the target molecule from the matrices in Cartesian coordinates of corresponding patterns and to avoid difficulties with introducing internal coordinates for a case of complicated molecules, so appears beneficial for fitting vibrational spectra of the large molecular systems, when only moderately accurate quantum chemistry methods may be applied. In this work, an earlier suggested algorithm for scaling force matrices in Cartesian coordinates has been extended to allow direct reduction by symmetry and simultaneous use of the experimental data on several isotopic species of a molecule. The molecules of pyrrole and indole (typical fragments of biological molecules) were chosen to demonstrate the efficiency of scaling procedure in Cartesian coordinates with symmetry constraints.


Molecular force field Cartesian coordinates Scaling factors Indole Pyrrole 



This work was partially supported by the Russian Foundation for Basic Research grant.

No 18-03-00412a

Supplementary material

11224_2018_1262_MOESM1_ESM.docx (37 kb)
ESM 1 (DOCX 36 kb)


  1. 1.
    Tikhonov AN, Leonov AS, Yagola AG (1998) Nonlinear Ill-posed Problems. Chapman & Hall, London (Original Russian language edition: (1993) Nonlinear Ill-posed Problems. Nauka, Moscow)Google Scholar
  2. 2.
    Kochikov IV, Kuramshina GM, Pentin IA, Iagola AG (1981) Regularizing algorithm of the inverse vibrational problem solution. Dokl Akad Nauk SSSR 261:1104–1106Google Scholar
  3. 3.
    Kochikov IV, Kuramshina GM (1985) A complex of programs for the force-field calculations of polyatomic molecules by the Tikhonov regularization method. Vestnik Moskovskogo universiteta seria 2 Khimiia 26:354–358Google Scholar
  4. 4.
    Kochikov IV, Kuramshina GM, Yagola AG (1987) Stable numerical methods of solving certain inverse problems of vibrational spectroscopy. USSR Comput Math Math Phys 27:33–40CrossRefGoogle Scholar
  5. 5.
    Kuramshina GM, Weinhold FA, Kochikov IV, Pentin YA, Yagola AG (1994) Joint treatment of ab initio and experimental data within Tikhonov regularization method. J Chem Phys 100:1414–1424CrossRefGoogle Scholar
  6. 6.
    Kochikov IV, Kuramshina GM, Stepanova AV, Yagola AG (1997) Regularized scaling factor method for calculating molecule force fields. Moscow University Physics Bulletin c/c of Vestnik – Moskovskii Universitet Fizika I Astronimiia 52: 28–33 . ALLERTON PRESS, INC.Google Scholar
  7. 7.
    Kuramshina GM, Weinhold F, Pentin YA (1998) Ab initio and regularized force fields of haloethanes: CH3CH2Cl, CH3CHCl2, CH3CF2Cl, and CH3CFCl2. J Chem Phys 109:7286–7299CrossRefGoogle Scholar
  8. 8.
    Yagola AG, Kochikov IV, Kuramshina GM, Pentin YA (1999) Inverse problems of vibrational spectroscopy. VSP, ZeistCrossRefGoogle Scholar
  9. 9.
    Kochikov IV, Tarasov YI, Kuramshina GM, Spiridonov VP, Yagola AG, Strand TG (1998) 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 445:243–258CrossRefGoogle Scholar
  10. 10.
    Kochikov IV, Tarasov YI, Spiridonov VP, Kuramshina GM, Yagola AG, Saakjan AS, Popik MV, Samdal S (1999) 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 485-486:421–443CrossRefGoogle Scholar
  11. 11.
    Kochikov IV, Tarasov YI, Spiridonov VP, Kuramshina GM, Rankin DWH, Saakjan AS, Yagola AG (2001) The equilibrium structure of thiophene by the combined use of electron diffraction, vibrational spectroscopy and microwave spectroscopy guided by theoretical calculations. J Mol Struct 567-568:29–40CrossRefGoogle Scholar
  12. 12.
    Kochikov IV, Tarasov YI, Vogt N, Spiridonov VP (2002) Large-amplitude motion in 1,4-cyclohexadiene and 1,4-dioxin. J Mol Struct 607:163–174CrossRefGoogle Scholar
  13. 13.
    Khaikin LS, Kochikov IV, Grikina OE, Tikhonov DS, Baskir EG (2015) IR spectra of nitrobenzene and nitrobenzene-15 N in the gas phase, ab initio analysis of vibrational spectra and reliable force fields of nitrobenzene and 1,3,5-trinitrobenzene. Investigation of equilibrium geometry and internal rotation. Struct Chem 26:1651–1687CrossRefGoogle Scholar
  14. 14.
    Khaikin LS, Vogt N, Rykov AN, Grikina OE, Demaison J, Vogt J, Kochikov IV, Shishova YD, Ageeva ES, Shishkov IF (2018) The equilibrium molecular structure of 4-cyanopyridine according to a combined analysis of gas-phase electron diffraction and microwave data and coupled-cluster computations. Russ J Phys Chem A 92:1970–1974CrossRefGoogle Scholar
  15. 15.
    Blom CE, Slingerland PJ, Altona C (1976) Application of self-consistent-field ab initio calculations to organic molecules. I. Equilibrium structure and force constants of hydrocarbons. Mol Phys 31:1377–1391CrossRefGoogle Scholar
  16. 16.
    Pulay P, Fogarasi G, Pongor G, Boggs JE, Vargha A (1983) Combination of theoretical ab initio and experimental information to obtain reliable harmonic force constants. Scaled quantum mechanical (QM) force fields for glyoxal, acrolein, butadiene, formaldehyde, and ethylene. J Am Chem Soc 105:7037–7047CrossRefGoogle Scholar
  17. 17.
    Fogarasi G, Zhou X, Taylor PW, Pulay P (1992) The calculation of ab initio molecular geometries: efficient optimization by natural internal coordinates and empirical correction by offset forces. J Am Chem Soc 114:8191–8201CrossRefGoogle Scholar
  18. 18.
    Kochikov IV, Kuramshina GM, Stepanova AV, Yagola AG (2004) Numerical aspects of the calculation of scaling factors from experimental data. Numerical Methods and Programming 5:281–290. Google Scholar
  19. 19.
    Pulay P, Zhou X, Fogarasi G (1993) Development of an ab initio based database of vibrational force fields for organic molecules. R Fausto (ed) Recent experimental and computational advances in molecular spectroscopy. Cluver Academic Publishers, pp 99–111Google Scholar
  20. 20.
    Kochikov IV, Kuramshina GM, Stepanova AV (2009) New approach for the correction of ab initio molecular force fields in Cartesian coordinates. Int J Quant Chem 109:28–33CrossRefGoogle Scholar
  21. 21.
    Kochikov IV, Kuramshina GM, Stepanova AV (2009) Scaled ab initio molecular force fields in Cartesian coordinates: application to benzene, pyrazine and isopropylamine molecules. Аsian. Chem Lett 13:143–154Google Scholar
  22. 22.
    Collier WB (1988) Vibrational frequencies for polyatomic molecules. I. Indole and 2,3-benzofuran spectra and analysis. J Chem Phys 88:7295–7306CrossRefGoogle Scholar
  23. 23.
    Geidel E, Billes F (2000) Vibrational spectroscopic study of pyrrole and its deuterated derivatives: comparison of the quality of the applicability of the DFT/Becke3P86 and the DFT/Becke3LYP functionals. J Mol Struct (THEOCHEM) 507:75–87CrossRefGoogle Scholar
  24. 24.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, and Pople JA. GAUSSIAN03, Revision C.02 (Gaussian Inc., Wallingford CT), 2004Google Scholar
  25. 25.
    Becke AD (1993) Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys 98:5648–5652CrossRefGoogle Scholar
  26. 26.
    Yagola AG, Kochikov IV, Kuramshina GM, Pentin YA (2007) Inverse problems of vibrational spectroscopy. KURS, MoscowGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • I. V. Kochikov
    • 1
  • A. V. Stepanova
    • 2
  • G. M. Kuramshina
    • 2
    Email author
  1. 1.Scientific Research Computer CentreLomonosov Moscow State UniversityMoscowRussia
  2. 2.Department of Physical Chemistry, Faculty of ChemistryLomonosov Moscow State UniversityMoscowRussia

Personalised recommendations