Skip to main content
SpringerLink
Log in

Electron population of Bader’s interatomic surfaces: relevance of estimates based on the electron density function values at critical points

  • Full Articles
  • Published:
Russian Chemical Bulletin Aims and scope

Abstract

The possibility to estimate the electron population of Bader’s interatomic surfaces using the electron density function values at the (3, −1) critical points is discussed taking the results of quantum chemical calculations of three model sets of isolated atomic aggregates as examples. A relevant method based on the approximation of normal distribution of the electron density over the interatomic surface is proposed and verified. The range of applicability of this approximation is considered using the results of calculations for a new model set.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. R. F. W. Bader, Chem. Rev., 1991, 91, 893; DOI: https://doi.org/10.1021/cr00005a013.

    Article  CAS  Google Scholar 

  2. R. F. W. Bader, J. Chem. Phys., 1980, 73, 2871; DOI: https://doi.org/10.1063/1.440457.

    Article  ADS  MathSciNet  CAS  Google Scholar 

  3. R. F. W. Bader, Int. J. Quant. Chem., 1995, 56, 409; DOI: https://doi.org/10.1002/qua.560560427.

    Article  CAS  Google Scholar 

  4. R. F. W. Bader, P. Becker, Chem. Phys. Lett., 1988, 148, 452; DOI: https://doi.org/10.1016/0009-2614(88)87203-8.

    Article  ADS  CAS  Google Scholar 

  5. S. Srebrenik, R. F. W. Bader, J. Chem. Phys., 1975, 63, 3945; DOI: https://doi.org/10.1063/1.431834.

    Article  ADS  MathSciNet  CAS  Google Scholar 

  6. F. W. Biegler-König, R. F. W. Bader, T.-H. Tang, J. Comp. Chem., 1982, 3, 317; DOI: https://doi.org/10.1002/jcc.540030306.

    Article  Google Scholar 

  7. R. F. W. Bader, Phys. Rev. B, 1994, 49, 13348; DOI: https://doi.org/10.1103/PhysRevB.49.13348.

    Article  ADS  CAS  Google Scholar 

  8. A. M. Pendás, E. Francisco, M. A. Blanco, C. Gatti, Chem. Eur. J., 2007, 13, 9362; DOI: https://doi.org/10.1002/chem.200700408.

    Article  PubMed  Google Scholar 

  9. P.-O. Löwdin, J. Mol. Spectrosc., 1959, 3, 46; DOI: https://doi.org/10.1016/0022-2852(59)90006-2.

    Article  ADS  Google Scholar 

  10. R. F. W. Bader, P. M. Beddall, J. Chem. Phys., 1972, 56, 3320; DOI: https://doi.org/10.1063/1.1677699.

    Article  ADS  CAS  Google Scholar 

  11. A. A. Anisimov, I. V. Ananyev, Int. J. Quant. Chem., 2023, 123, e27082; DOI: https://doi.org/10.1002/qua.27082.

    Article  CAS  Google Scholar 

  12. A. A. Anisimov, I. V. Ananyev, J. Comput. Chem., 2020, 41, 2213; DOI: https://doi.org/10.1002/jcc.26390.

    Article  CAS  PubMed  Google Scholar 

  13. A. Romanova, K. Lyssenko, I. Ananyev, J. Comput. Chem., 2018, 39, 1607; DOI: https://doi.org/10.1002/jcc.25235.

    Article  CAS  PubMed  Google Scholar 

  14. V. A. Karnoukhova, I. V. Fedyanin, E. V. Dubasova, A. A. Anisimov, I. V. Ananyev, Mendeleev Commun., 2023, 33, 353; DOI: https://doi.org/10.1016/j.mencom.2023.04.018.

    Article  CAS  Google Scholar 

  15. I. V. Ananyev, V. A. Karnoukhova, A. O. Dmitrienko, K. A. Lyssenko, J. Phys. Chem. A, 2017, 121, 4517; DOI: https://doi.org/10.1021/acs.jpca.7b01495.

    Article  CAS  PubMed  Google Scholar 

  16. P. L. A. Popelier, Comput. Phys. Commun., 1998, 108, 180; DOI: https://doi.org/10.1016/S0010-4655(97)00121-5.

    Article  ADS  CAS  Google Scholar 

  17. E. S. Zhilin, I. V. Ananyev, A. N. Pivkina, L. L. Fershtat, Dalton Trans., 2022, 51, 14088; DOI: https://doi.org/10.1039/D2DT02445D.

    Article  CAS  PubMed  Google Scholar 

  18. A. A. Larin, D. D. Degtyarev, I. V Ananyev, A. N. Pivkina, L. L. Fershtat, Chem. Eng. J., 2023, 470, 144144; DOI: https://doi.org/10.1016/j.cej.2023.144144.

    Article  CAS  Google Scholar 

  19. A. A. Larin, A. N. Pivkina, I. V. Ananyev, D. V. Khakimov, L. L. Fershtat, Front. Chem., 2022, 10, 1012605; DOI: https://doi.org/10.3389/fchem.2022.1012605.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  20. R. F. W. Bader, H. Essén, J. Chem. Phys., 1984, 80, 1943; DOI: https://doi.org/10.1063/1.446956.

    Article  ADS  CAS  Google Scholar 

  21. E. Espinosa, C. Lecomte, E. Molins, Chem. Phys. Lett., 1999, 300, 745; DOI: https://doi.org/10.1016/S0009-2614(98)01399-2.

    Article  ADS  CAS  Google Scholar 

  22. E. Espinosa, E. Molins, C. Lecomte, Chem. Phys. Lett., 1998, 285, 170; DOI: https://doi.org/10.1016/S0009-2614(98)00036-0.

    Article  ADS  CAS  Google Scholar 

  23. R. F. W. Bader, T. S. Slee, D. Cremer, E. Kraka, J. Am. Chem. Soc., 1983, 105, 5061; DOI: https://doi.org/10.1021/ja00353a035.

    Article  CAS  Google Scholar 

  24. P. L. A. Popelier, Coord. Chem. Rev., 2000, 197, 169; DOI: https://doi.org/10.1016/S0010-8545(99)00189-7.

    Article  CAS  Google Scholar 

  25. M. A. Spackman, Cryst. Growth Des., 2015, 15, 5624; DOI: https://doi.org/10.1021/acs.cgd.5b01332.

    Article  CAS  Google Scholar 

  26. R. F. W. Bader, J. Phys. Chem. A, 2009, 113, 10391; DOI: https://doi.org/10.1021/jp906341r.

    Article  CAS  PubMed  Google Scholar 

  27. L. J. Farrugia, C. Evans, M. Tegel, J. Phys. Chem. A, 2006, 110, 7952; DOI: https://doi.org/10.1021/jp061846d.

    Article  CAS  PubMed  Google Scholar 

  28. C. Foroutan-Nejad, S. Shahbazian, R. Marek, Chem. Eur. J., 2014, 20, 10140; DOI: https://doi.org/10.1002/chem.201402177.

    Article  CAS  PubMed  Google Scholar 

  29. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, D. J. Fox, Gaussian 09, D.01, Wallingford, USA, Gaussian Inc., 2016.

    Google Scholar 

  30. G. E. Scuseria, C. L. Janssen, H. F. Schaefer III, J. Chem. Phys., 1988, 89, 7382; DOI: https://doi.org/10.1063/1.455269.

    Article  ADS  CAS  Google Scholar 

  31. C. Adamo, V. Barone, J. Chem. Phys., 1999, 110, 6158; DOI: https://doi.org/10.1063/1.478522.

    Article  ADS  CAS  Google Scholar 

  32. J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865; DOI: https://doi.org/10.1103/PhysRevLett.77.3865.

    Article  ADS  CAS  PubMed  Google Scholar 

  33. R. Krishnan, J. A. Pople, Int. J. Quant. Chem., 1978, 14, 91; DOI: https://doi.org/10.1002/qua.560140109.

    Article  CAS  Google Scholar 

  34. R. Krishnan, M. J. Frisch, J. A. Pople, J. Chem. Phys., 1980, 72, 4244; DOI: https://doi.org/10.1063/1.439657.

    Article  ADS  CAS  Google Scholar 

  35. T. H. Dunning, J. Chem. Phys., 1989, 90, 1007; DOI: https://doi.org/10.1063/1.456153.

    Article  ADS  CAS  Google Scholar 

  36. D. E. Woon, T. H. Dunning, J. Chem. Phys., 1993, 98, 1358; DOI: https://doi.org/10.1063/1.464303.

    Article  ADS  CAS  Google Scholar 

  37. T. D. Keith, AIMAll, Version 19.10.12, Overland Park KS, USA, TK Gristmill Software, 2019.

    Google Scholar 

  38. L. A. Terrabuio, T. Q. Teodoro, C. F. Matta, R. L. A. Haiduke, J. Phys. Chem. A, 2016, 120, 1168; DOI: https://doi.org/10.1021/acs.jpca.5b10888.

    Article  CAS  PubMed  Google Scholar 

  39. R. Glaser, R. F. Waldron, K. B. Wiberg, J. Phys. Chem., 1990, 94, 7357; DOI: https://doi.org/10.1021/j100382a009.

    Article  Google Scholar 

  40. A. M. Pendás, M. A. Blanco, A. Costales, P. M. Sénchez, V. Luaña, Phys. Rev. Lett., 1999, 83, 1930; DOI: https://doi.org/10.1103/PhysRevLett.83.1930.

    Article  ADS  Google Scholar 

  41. D. R. Alcoba, L. Lain, A. Torre, R. C. Bochicchio, Chem. Phys. Lett., 2005, 407, 379; DOI: https://doi.org/10.1016/j.cplett.2005.03.078.

    Article  ADS  CAS  Google Scholar 

  42. L. A. Terrabuio, T. Q. Teodoro, M. G. Rachid, R. L. A. Haiduke, J. Phys. Chem. A, 2013, 117, 10489; DOI: https://doi.org/10.1021/jp406992q.

    Article  CAS  PubMed  Google Scholar 

  43. J. A. Platts, J. Overgaard, C. Jones, B. B. Iversen, A. Stasch, J. Phys. Chem. A, 2011, 115, 194; DOI: https://doi.org/10.1021/jp109547w.

    Article  CAS  PubMed  Google Scholar 

  44. A. Azizi, R. Momen, T. Xu, S. R. Kirk, S. Jenkins, Phys. Chem. Chem. Phys., 2018, 20, 24695; DOI: https://doi.org/10.1039/C8CP05214J.

    Article  CAS  PubMed  Google Scholar 

  45. B. M. ter Haar Romeny, Front-End Vision and Multi-Scale Image Analysis (Computational Imaging and Vision, Vol. 27), Springer, Dordrecht, Netherlands, 2003.

    Google Scholar 

  46. I. V. Ananyev, M. G. Medvedev, S. M. Aldoshin, I. L. Eremenko, K. A. Lyssenko, Russ. Chem. Bull., 2016, 65, 1178; DOI: https://doi.org/10.1007/s11172-016-1474-0.

    Article  CAS  Google Scholar 

  47. A. A. Kovalenko, Yu. V. Nelyubina, A. A. Korlyukov, K. A. Lyssenko, I. V. Ananyev, Z. fur Krist.—Cryst. Mater., 2018, 233, 317; DOI: https://doi.org/10.1515/zkri-2017-2085.

    Article  CAS  Google Scholar 

Download references

Funding

This work was carried out within the State Assignment to the N. D. Zelinsky Institute of Organic Chemistry, Russian Academy of Sciences (Research Direction FFZZ-2022-0003, Project No. 122041100187-9).

Author information

Authors and Affiliations

  1. N. D. Zelinsky Institute of Organic Chemistry, Russian Academy of Sciences, 47 Leninsky prosp., 119991, Moscow, Russian Federation

    I. V. Ananyev & L. L. Fershtat

Authors
  1. I. V. Ananyev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. L. Fershtat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. V. Ananyev.

Ethics declarations

Animal Testing and Ethics

No human or animal subjects were used in this research.

Conflict of Interest

The authors declare no competing interests.

Additional information

Dedicated to Academician of the Russian Academy of Sciences M. P. Egorov on the occasion of his 70th birthday.

Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, Vol. 73, No. 1, pp. 110–116, January, 2024.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ananyev, I.V., Fershtat, L.L. Electron population of Bader’s interatomic surfaces: relevance of estimates based on the electron density function values at critical points. Russ Chem Bull 73, 110–116 (2024). https://doi.org/10.1007/s11172-024-4122-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11172-024-4122-0

Key words

Search

Navigation