Skip to main content
SpringerLink
Log in

An analysis of the torquoselectivity effect in a ring-opening reaction through Fermi–Dirac’s entropy: revealing the origin of the stereoselectivity.

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The manuscript discusses Information Theory, introduced by Shannon, deals with understanding communication between systems and quantifying information using the concept of entropy. Shannon’s entropy is a measure of uncertainty in a system and has similarities with the entropy in thermodynamics. On the other hand, Torquoselectivity is a concept in organic chemistry that refers to the preference of a chemical reaction to occur with a specific relative stereochemistry around a torsional bond. It is also relevant in electrocyclic reactions, where it describes the preference for inward or outward rotation of substituents during the reaction. In this vein, this work mentions the development of a new informational entropy called Fermi–Dirac’s entropy and its application to study the torquoselectivity in a specific reaction involving 3-cyancyclobutene (3-CN-cyclobutene). Overall, our results show that beyond the bond-breaking process in this reaction, a specific atom is responsible for the stereoselectivity observed in this reaction.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. Worthwhile to mention that there is a difference between our calculations and the calculations of Ref. [63], which is the basis set; in Ref. [63], the authors used 6-31g(d,p) basis set, while in this work we used \(6-31+G^{**}\) basis set, and also the operative systems and the processors used in booth works are different.

References

  1. C.E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948)

  2. A. Rényi, Proc. Fourth Berkeley Symp. Math. Stat. Prob. 1, 547 (1961)

    Google Scholar 

  3. S. Kullback, R.A. Leibler, Ann. Math. Stat. 22, 79 (1951)

    Google Scholar 

  4. E.T. Jaynes, Phys. Rev. 106, 620 (1957)

    Google Scholar 

  5. E.T. Jaynes, Phys. Rev. 108, 171 (1957)

    Google Scholar 

  6. P.A. Sant’ana, I.J. Taneja, J. Inf. Sci. 35, 145 (1985)

    Google Scholar 

  7. C. Tsallis, J. Stat. Phys. 52, 479 (1988)

    Google Scholar 

  8. I.J. Taneja, Adv. Electron. Electron Phys. 76, 327 (1989)

    Google Scholar 

  9. R.A. Fisher, Proc. Camb. Philos. Soc. 22, 700 (1925)

    Google Scholar 

  10. C.F. Weizsäcker, Z. Phys. 96, 431 (1935)

    Google Scholar 

  11. K.D. Sen, F. De Proft, A. Borgoo, P. Geerlings, Chem. Phys. Lett. 410(1–3), 70 (2005)

    CAS  Google Scholar 

  12. P. Ziesche, Int. J. Quantum Chem. 1995 56(4), 363 (1995)

    CAS  Google Scholar 

  13. P. Gersdorf, W. John, J. Perdew, P. Ziesche, Int. J. Quantum Chem. 61(6), 935 (1997)

    CAS  Google Scholar 

  14. A. Grassi, Int. J. Quantum Chem. 108(4), 774 (2008)

    CAS  Google Scholar 

  15. A. Grassi, Int. J. Quantum Chem. 111(10), 2390 (2011)

    CAS  Google Scholar 

  16. G.T. Smith, H.L. Schmider, V.H. Smith Jr., Phys. Rev. A. 65, 032508-1 (2002)

  17. A.D. Gottlieb, N.J. Mauser, Phys. Rev. Lett. 95, 123003-1 (2005)

  18. L.D. Site, Int. J. Quantum Chem. 115(19), 1396 (2015)

    Google Scholar 

  19. N. Flores-Gallegos, Chem. Phys. Lett. 666, 62 (2016)

    CAS  Google Scholar 

  20. N. Flores-Gallegos, Chem. Phys. Lett. 692, 61 (2018)

    CAS  Google Scholar 

  21. P. Ziesche, V.H. Smith Jr., M. Hô, S.P. Rudin, P. Gersdorf, M. Taut, J. Chem. Phys. 110(13), 6135 (1999)

    CAS  Google Scholar 

  22. N. Flores-Gallegos, J. Theor. Comput. Chem. 16(2), 1750051–1 (2017)

    CAS  Google Scholar 

  23. N. Flores-Gallegos, Chem. Phys. Lett. 650, 57 (2016)

    CAS  Google Scholar 

  24. N. Flores-Gallegos, Chem. Phys. Lett. 692, 61 (2018)

    CAS  Google Scholar 

  25. A.J. Thakkar, AIP Conf. Proc. 1504, 586 (2012)

    CAS  Google Scholar 

  26. A. Kerbert, R. Laude, M. Meringer, C. Rücker, Comput. Chem. Jpn. 3, 85 (2004)

    Google Scholar 

  27. N. Flores-Gallegos, Chem. Phys. Lett. 676, 1 (2017)

    CAS  Google Scholar 

  28. R.F. Nalewajski, P. Gurdek, J. Math. Chem. 49, 1226 (2011)

    CAS  Google Scholar 

  29. R.F. Nalewajski, J. Math. Chem. 43, 780 (2007)

    Google Scholar 

  30. R.F. Nalewajski, P. Gurdek, Struct. Chem. 23, 1383 (2012)

    CAS  Google Scholar 

  31. R.F. Nalewajski, J. Math. Chem. 43, 265 (2006)

    Google Scholar 

  32. R.F. Nalewajski, J. Math. Chem. 49, 2308 (2011)

    CAS  Google Scholar 

  33. R.F. Nalewajski, J. Math. Chem. 49, 371 (2011)

    CAS  Google Scholar 

  34. R.F. Nalewajski, J. Math. Chem. 52, 42 (2014)

    CAS  Google Scholar 

  35. R.F. Nalewajski, J. Math. Chem. 52, 1292 (2014)

    CAS  Google Scholar 

  36. R.F. Nalewajski, J. Math. Chem. 53, 1 (2015)

    CAS  Google Scholar 

  37. D. Szczepanik, J. Mrozek, J. Math. Chem. 49, 562 (2011)

    CAS  Google Scholar 

  38. R.F. Nalewaski, Entropy 22, 749 (2020)

    Google Scholar 

  39. R.F. Nalewajski, Appl. Sci. 9, 1262 (2019)

    CAS  Google Scholar 

  40. D.S. Sabirov, I.S. Shepelevich, Entropy 23, 1240 (2021)

    CAS  PubMed  PubMed Central  Google Scholar 

  41. N. Flores-Gallegos, J. Math. Chem. 61, 723 (2023)

    CAS  Google Scholar 

  42. N. Flores-Gallegos, J. Math. Chem. 60, 1405 (2022)

    CAS  Google Scholar 

  43. N. Flores-Gallegos, J. Math. Chem. 61, 712 (2023)

    CAS  Google Scholar 

  44. N. Flores-Gallegos, L. Flores-Gómez, J. Math. Chem. 61, 1726 (2023)

    CAS  Google Scholar 

  45. D. Sabirov, A.A. Tukhbatullina, I.S. Shepelevich, J. Mol. Gr. Model. 110, 108052 (2022)

    CAS  Google Scholar 

  46. D.S. Sabirov, Comput. Theor. Chem. 1123, 169 (2018)

    CAS  Google Scholar 

  47. L.I.U. Shu-Bin, Acta Phys. Chim. Sin. 32, 98 (2016)

    Google Scholar 

  48. C. Rong, B. Wang, D. Zhao, S. Liu, WIREs Comput. Mol. Sci. 10(2), e1461 (2019)

    Google Scholar 

  49. C. Rong, D. Zhao, X. He, S. Liu, J. Phys. Chem. Lett. 48, 11191 (2022)

    Google Scholar 

  50. N. Flores-Gallegos, J. Math. Chem. 61, 1453 (2023)

    CAS  Google Scholar 

  51. A.E. Reed, R.B. Weinstock, F. Weinhold, J. Chem. Phys. 83, 735 (1985)

    CAS  Google Scholar 

  52. C.W. Jefford, G. Bernardinelli, Y. Wang, D.C. Spellmeyer, A. Buda, K.N. Houk, J. Am. Chem. Soc. 114, 1157

  53. A.J. Frontiera, C. Collison, Tetrahedron 61, 7577 (2005)

    Google Scholar 

  54. H.M. Frey, Trans. Faraday Soc. 60, 83 (1965)

    Google Scholar 

  55. M.J. Curry, I.D.R. Stevens, J. Chem. Soc. Perkin Trans. 2, 1391 (1980)

    Google Scholar 

  56. W.R. Dolbier, H. Koroniak, K.N. Houk, C. Sheu, Acc. Chem. Res. 29, 471 (1996)

    CAS  Google Scholar 

  57. C. Hulot, S. Amiri, G. Blond, P.R. Schreiner, J. Suffert, J. Am. Chem. Soc. 131, 16587 (2009)

    CAS  Google Scholar 

  58. N.L. Bauld, J. Cessac, J. Am. Chem. Soc. 99, 23 (1977)

    CAS  Google Scholar 

  59. J.E. Baldwin, M.C. McDaniel, J. Am. Chem. Soc. 89, 1537 (1967)

    CAS  Google Scholar 

  60. S. Sakai, S. Takane, J. Phys. Chem. A 103, 2878 (1999)

    CAS  Google Scholar 

  61. R.B. Woodward, R. Hoffmann, J. Am. Chem. Soc. 87, 395 (1965)

    CAS  Google Scholar 

  62. W. Kirmse, N.G. Rondan, K.N. Houk, J. Am. Chem. Soc. 106, 7989 (1984)

    CAS  Google Scholar 

  63. A. Morales-Bayuelo, J. Sánchez-Márquez, Heliyon 7, e06675 (2021)

    CAS  PubMed  PubMed Central  Google Scholar 

  64. H. Eyring, M. Polanyi, Z. Phys. Chem. Abt. B 1931(12), 279 (1939)

    Google Scholar 

  65. H. Eyring, Chem. Rev. 17, 65 (1935)

    CAS  Google Scholar 

  66. A. Morales-Bayuelo, Int. J. Quantum Chem. 113, 1534 (2013)

    CAS  Google Scholar 

  67. A. Morales-Bayuelo, J. Sánchez-Márquez, Heliyon 7, e06675 (2021)

    CAS  PubMed  PubMed Central  Google Scholar 

  68. R. Momen, A. Azizi, A. Morales-Bayuelo, M. Pazhoohesh, X. Ji, J. Chem. Phys. 155, 204305 (2021)

    CAS  PubMed  Google Scholar 

  69. Gaussian 09, Revision E.01, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, 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, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian, Inc., Wallingford CT (2013)

  70. K. Fukui, J. Phys. Chem. 74(23), 4161 (1970)

    CAS  Google Scholar 

  71. K. Fukui, Acc. Chem. Res. 14(12), 363 (1981)

    CAS  Google Scholar 

  72. A. Morales-Bayuelo, S. Pan, J. Caballero, P.K. Chattaraj, Phys. Chem. Chem. Phys. 17, 2310 (2015)

    Google Scholar 

Download references

Acknowledgements

N. Flores-Gallegos wishes to thank the CONAHCYT, the PRODEP-SEP program for support. AMB many thanks to the Fundación universitaria tecnológico Comfenalco by the support.

Author information

Authors and Affiliations

  1. Centro Universitario de los Valles, Universidad de Guadalajara, Carretera Guadalajara - Ameca Km. 45.5, C.P. 46600, Ameca, Jalisco, Mexico

    N. Flores-Gallegos

  2. Process Research Center of Tecnológico Comfenalco (CIPTEC), Industrial Engineering Program., Fundación Universitaria Tecnológico Comfenalco, Cartagena, Colombia

    Alejandro Morales-Bayuelo

Authors
  1. N. Flores-Gallegos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alejandro Morales-Bayuelo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Flores-Gallegos.

Ethics declarations

Conflict of interest

The authors declared that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Flores-Gallegos, N., Morales-Bayuelo, A. An analysis of the torquoselectivity effect in a ring-opening reaction through Fermi–Dirac’s entropy: revealing the origin of the stereoselectivity.. J Math Chem 62, 62–72 (2024). https://doi.org/10.1007/s10910-023-01519-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-023-01519-y

Keywords

Search

Navigation