Skip to main content
Log in

Atomic electronegativity based on hardness and floating spherical gaussian orbital approach

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

Abstract

Electronegativity (χ) is an important property of any chemical species as it helps to predict the pattern of physico-chemical interactions. In the present work, we have suitably studied this property and suggested a new model to compute atomic electronegativity based on atomic hardness using the Floating spherical Gaussian orbital model. Using this method, we have developed a new scale of electronegativity which provides atomic values for 54 elements. Our electronegativity data not only follows the periodic trend but is found to be well related to some electronegativity scales also. It also correlates well with other periodic properties. Our scale effectively establishes the Electronegativity equalization principle. Invoking our computed electronegativity values, we have been able to calculate internuclear bond distances of some molecular species and our prediction is quite satisfactory in terms of its correlation with experimental counterparts.

Graphical abstract

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. R.G. Parr, R.A. Donnelly, M. Levy, W.E. Palke, Electronegativity: the density functional viewpoint. J. Chem. Phys. 68(8), 3801–3807 (1978)

    Article  CAS  Google Scholar 

  2. K. Ruthenberg, J.C.M. González, Electronegativity and its multiple faces: persistence and measurement. Found. Chem. 19(1), 61–75 (2017)

    Article  CAS  Google Scholar 

  3. D.P. Upadhyay, Electronegativity and hardness: linear isoelectronic trends. Curr. Phys. Chem. 7(2), 118–125 (2017)

    Article  CAS  Google Scholar 

  4. A.A. Akhkubekov, S.N. Akhkubekova, A.M. Bagov, M.F. Bagova, T.K. Tamaev, Relation of effective charges to atom electronegativity. Bull. Russ. Acad. Sci. Phys. 81(5), 637–640 (2017)

    Article  CAS  Google Scholar 

  5. P. Politzer, J.S. Murray, Electronegativity—a perspective. J. Mol. Model. 24(8), 214–220 (2018)

    Article  PubMed  Google Scholar 

  6. A. Qteish, Electronegativity scales and electronegativity-bond ionicity relations: a comparative study. J. Phys. Chem. Solids 124, 186–191 (2019)

    Article  CAS  Google Scholar 

  7. R.A. Miranda-Quintana, M.M. González, P.W. Ayers, Electronegativity and redox reactions. Phys. Chem. Chem. Phys. 18(32), 22235–22243 (2016)

    Article  CAS  PubMed  Google Scholar 

  8. M. Rahm, T. Zeng, R. Hoffmann, Electronegativity seen as the ground-state average valence electron binding energy. J. Am. Chem. Soc. 141(1), 342–351 (2018)

    Article  PubMed  Google Scholar 

  9. H.L. Accorinti, Incompatible models in chemistry: the case of electronegativity. Found. Chem. 21(1), 71–81 (2019)

    Article  CAS  Google Scholar 

  10. J. Sánchez-Márquez, V. García, D. Zorrilla, M. Fernández, On electronegativity, hardness, and reactivity descriptors: a new property-oriented basis set. J. Phys. Chem. A 124(23), 4700–4711 (2020)

    Article  PubMed  Google Scholar 

  11. H. Tandon, T. Chakraborty, V. Suhag, A scale of atomic electronegativity in terms of atomic nucleophilicity index. Found. Chem. 22(2), 335–346 (2020)

    Article  CAS  Google Scholar 

  12. J. Mullay, Estimation of atomic and group electronegativities, in Electronegativity. Structure and bonding. ed. by K.D. Sen, C.K. Jørgensen (Springer, Berlin, 1987), pp. 1–25

    Google Scholar 

  13. R.G. Pearson, Electronegativity scales. Acc. Chem. Res. 23(1), 1–2 (1990)

    Article  CAS  Google Scholar 

  14. G. Sproul, Electronegativity and bond type. 2. Evaluation of electronegativity scales. J. Phys. Chem. 98(27), 6699–6703 (1994)

    Article  CAS  Google Scholar 

  15. M. Rahm, R. Cammi, N.W. Ashcroft, R. Hoffmann, Squeezing all elements in the periodic table: electron configuration and electronegativity of the atoms under compression. J. Am. Chem. Soc. 141(26), 10253–10271 (2019)

    Article  CAS  PubMed  Google Scholar 

  16. G.D. Sproul, Evaluation of electronegativity scales. ACS Omega 5(20), 11585–11594 (2020)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. A. Campero, J.A. Díaz Ponce, Averaged scale in electronegativity joined to physicochemical perturbations. Consequences of periodicity. ACS Omega 5(40), 25520–25542 (2020)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. D.C. Ghosh, T. Chakraborty, Gordy’s electrostatic scale of electronegativity revisited. J. Mol. Struct. (Thoechem) 906(1–3), 87–93 (2009)

    Article  CAS  Google Scholar 

  19. D.C. Ghosh, T. Chakraborty, B. Mandal, The electronegativity scale of allred and rochow: revisited. Theoret. Chem. Acc. 124(3), 295–301 (2009)

    Article  CAS  Google Scholar 

  20. H. Tandon, M. Labarca, T. Chakraborty, A scale of atomic electronegativity based on floating spherical gaussian orbital approach. ChemistrySelect 6(22), 5622–5627 (2021)

    Article  CAS  Google Scholar 

  21. L. Pauling, The nature of the chemical bond. IV. The energy of single bonds and the relative electronegativity of atoms. J. Am. Chem. Soc. 54, 3570–3582 (1932)

    Article  CAS  Google Scholar 

  22. R.S. Mulliken, A new electroaffinity scale; together with data on valence states and on valence ionization potentials and electron affinities. J. Chem. Phys. 2(11), 782–793 (1934)

    Article  CAS  Google Scholar 

  23. W. Gordy, A new method of determining electronegativity from other atomic properties. Phys. Rev. 69(11–12), 604 (1946)

    Article  CAS  Google Scholar 

  24. A.L. Allred, E.G. Rochow, A scale of electronegativity based on electrostatic force. J. Inorg. Nucl. Chem. 5(4), 264–268 (1958)

    Article  CAS  Google Scholar 

  25. R.P. Iczkowski, J.L. Margrave, Electronegativity. J. Am. Chem. Soc. 83(17), 3547–3551 (1961)

    Article  CAS  Google Scholar 

  26. G. Simons, M.E. Zandler, E.R. Talaty, Nonempirical electronegativity scale. J. Am. Chem. Soc. 98(24), 7869–7870 (1976)

    Article  CAS  Google Scholar 

  27. S.G. Bratsch, Revised Mulliken electronegativities: I. Calculation and conversion to Pauling units. J. Chem. Educ. 65(1), 34–41 (1988)

    Article  CAS  Google Scholar 

  28. R.G. Parr, R.G. Pearson, Absolute hardness: companion parameter to absolute electronegativity. J. Am. Chem. Soc. 105(26), 7512–7516 (1983)

    Article  CAS  Google Scholar 

  29. R.G. Pearson, Absolute electronegativity and hardness: application to inorganic chemistry. Inorg. Chem. 27(4), 734–740 (1988)

    Article  CAS  Google Scholar 

  30. R.G. Pearson, Absolute electronegativity and hardness: applications to organic chemistry. J. Org. Chem. 54(6), 1423–1430 (1989)

    Article  CAS  Google Scholar 

  31. M.I. Trofimov, E.A. Smolenskii, Application of the electronegativity indices of organic molecules to tasks of chemical informatics. Russ. Chem. Bull. Int. Edn. 54(9), 2235–2246 (2005)

    Article  CAS  Google Scholar 

  32. M.E. Arroyo-De Dompablo, M. Armand, J.M. Tarascon, U. Amador, On-demand design of polyoxianionic cathode materials based on electronegativity correlations: an exploration of the Li2MSiO4 system (M= Fe, Mn Co, Ni). Electrochem. Commun. 8(8), 1292–1298 (2006)

    Article  CAS  Google Scholar 

  33. A.A. Frost, Floating spherical Gaussian orbital model of molecular structure. I. Computational procedure. LiH as an example. J. Chem. Phys. 47(10), 3707–3713 (1967)

    Article  CAS  Google Scholar 

  34. A.A. Frost, Floating spherical Gaussian orbital model of molecular structure. II. One-and two-electron-pair systems. J. Chem. Phys. 47(10), 3714–3716 (1967)

    Article  CAS  Google Scholar 

  35. A.A. Frost, The floating spherical gaussian method, in Methods of electronic structure theory. ed. by H.F. Schaefer (Plenum Press, New York, 1977), pp. 29–49

    Chapter  Google Scholar 

  36. N. Islam, D.C. Ghosh, Spectroscopic evaluation of the global hardness of the atoms. Mol. Phys. 109(12), 1533–1544 (2011)

    Article  CAS  Google Scholar 

  37. R.S. Mulliken, Molecular compounds and their spectra. II. J. Am. Chem. Soc. 74(3), 811–824 (1952)

    Article  CAS  Google Scholar 

  38. R.G. Pearson, Hard and soft acids and bases. J. Am. Chem. Soc. 85(22), 3533–3539 (1963)

    Article  CAS  Google Scholar 

  39. R.G. Pearson, Acids and bases. Science 151(3707), 172–177 (1966)

    Article  CAS  PubMed  Google Scholar 

  40. G. Klopman, A semiempirical treatment of molecular structures. I. Electronegativity and atomic terms. J. Am. Chem. Soc. 86(8), 1463–1469 (1964)

    Article  CAS  Google Scholar 

  41. G. Klopman, Chemical reactivity and the concept of charge-and frontier- controlled reactions. J. Am. Chem. Soc. 90(2), 223–234 (1968)

    Article  CAS  Google Scholar 

  42. R.G. Parr, P.K. Chattaraj, Principle of maximum hardness. J. Am. Chem. Soc. 113(5), 1854–1855 (1991)

    Article  CAS  Google Scholar 

  43. P.W. Ayers, The physical basis of the hard/soft acid/base principle. Faraday Discuss. 135, 161–190 (2007)

    Article  CAS  PubMed  Google Scholar 

  44. P.W. Ayers, R.G. Parr, Beyond electronegativity and local hardness: higher-order equalization criteria for determination of a ground-state electron density. J. Chem. Phys. 129(5), 054111 (2008)

    Article  PubMed  Google Scholar 

  45. D. Datta, Geometric mean principle for hardness equalization: a corollary of Sanderson’s geometric mean principle of electronegativity equalization. J. Phys. Chem. 90(17), 4216–4217 (1986)

    Article  CAS  Google Scholar 

  46. L. Komorowski, Electronegativity and hardness in the chemical approximation. Chem. Phys. 114(1), 55–71 (1987)

    Article  CAS  Google Scholar 

  47. J.L. Reed, Electronegativity: chemical Hardness I. J. Phys. Chem. A 101(40), 7396–7400 (1997)

    Article  CAS  Google Scholar 

  48. M.V. Putz, Absolute and chemical electronegativity and hardness (Nova Science Publishers, Inc, New York, 2008)

    Google Scholar 

  49. N. Islam, D.C. Ghosh, The electronegativity and the global hardness are periodic properties of atoms. J. Quantum Inf. Sci. 1(3), 135–141 (2011)

    Article  CAS  Google Scholar 

  50. D.C. Ghosh, N. Islam, Whether electronegativity and hardness are manifest two different descriptors of the one and the same fundamental property of atoms−A quest. Int. J. Quantum Chem. 111(1), 40–51 (2011)

    Article  CAS  Google Scholar 

  51. P.H. Blustin, J.W. Linnett, Applications of a simple molecular wavefunction Part 1.—Floating spherical Gaussian orbital calculations for propylene and propane. J. Chem. Soc. Faraday Trans. Mol. Chem. Phys. 70, 274–289 (1974)

    CAS  Google Scholar 

  52. J. Hinze, H.H. Jaffé, Electronegativity. I. Orbital electronegativity of neutral atoms. J. Am. Chem. Soc. 84(4), 540–546 (1962)

    Article  CAS  Google Scholar 

  53. M.V. Putz, Systematic formulations for electronegativity and hardness and their atomic scales within density functional softness theory. Int. J. Quantum Chem. 106(2), 361–389 (2006)

    Article  CAS  Google Scholar 

  54. R.T. Sanderson, An interpretation of bond lengths and a classification of bonds. Science 114(2973), 670–672 (1951)

    Article  CAS  PubMed  Google Scholar 

  55. R.T. Sanderson, Partial charges on atoms in organic compounds. Science 121(3137), 207–208 (1955)

    Article  CAS  PubMed  Google Scholar 

  56. R.G. Parr, L.J. Bartolotti, On the geometric mean principle for electronegativity equalization. J. Am. Chem. Soc. 104(14), 3801–3803 (1982)

    Article  CAS  Google Scholar 

  57. R.F. Nalewajski, A study of electronegativity equalization. J. Phys. Chem. 89(13), 2831–2837 (1985)

    Article  CAS  Google Scholar 

  58. N.K. Rayb, L. Samuelsc, R.G. Parr, Studies of electronegativity equalization. J. Chem. Phys. 70(8), 3680–3684 (1979)

    Article  Google Scholar 

  59. F.J. Lovas, E. Tiemann, Microwave spectral tables. I. Diatomic molecules. J. Phys. Chem. Ref. Data 3(3), 609–770 (1974)

    Article  CAS  Google Scholar 

  60. H. Tandon, P. Ranjan, T. Chakraborty, V. Suhag, Computation of absolute radii of 103 elements of the periodic table in terms of nucleophilicity index. J. Math. Chem. 58(5), 1025–1040 (2020)

    Article  CAS  Google Scholar 

  61. R.T. Sanderson, Electronegativities in inorganic chemistry. J. Chem. Educ. 29(11), 539–544 (1952)

    Article  CAS  Google Scholar 

  62. P. Zaleski-Ejgierd, P.M. Lata, Krypton oxides under pressure. Sci. Rep. 6(1), 18938 (2016)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  63. L. Khriachtchev, M. Pettersson, N. Runeberg, J. Lundell, M. Rӓsӓnen, A stable argon compound. Nature 406(6798), 874–876 (2000)

    Article  CAS  PubMed  Google Scholar 

  64. D.A. Dixon, T.H. Wang, D.J. Grant, K.A. Peterson, K.O. Christe, G.J. Schrobilgen, Heats of formation of krypton fluorides and stability predictions for KrF4 and KrF6 from high level electronic structure calculations. Inorg. Chem. 46(23), 10016–10021 (2007)

    Article  CAS  PubMed  Google Scholar 

  65. J.B. Mann, T.L. Meek, E.T. Knight, J.F. Capitani, L.C. Allen, Configuration energies of the d-block elements. J. Am. Chem. Soc. 122(21), 5132–5137 (2000)

    Article  CAS  Google Scholar 

  66. J. Kohler, M.H. Whangbo, Late transition metal anions acting as p-metal elements. Solid State Sci. 10(4), 444–449 (2008)

    Article  Google Scholar 

  67. C. Lee, M.H. Whangbo, J. Kohler, Analysis of electronic structures and chemical bonding of metal-rich compounds. 2. Presence of dimer (T−T)4− and isolated T2− anions in the polar intermetallic Cr5B3-type compounds AE5T3 (AE = Ca, Sr; T = Au, Ag, Hg, Cd, Zn). Z. Anorg. Allg. Chem. 636(1), 36–40 (2010)

    Article  CAS  Google Scholar 

  68. H. Tandon, T. Chakraborty, V. Suhag, A new model of atomic nucleophilicity index and its application in the field of QSAR. Int. J. Quant. Struct. Prop. Relat. 4(3), 99–117 (2019)

    Google Scholar 

Download references

Acknowledgements

Dr. Tanmoy Chakraborty is thankful to Sharda University and Dr. Hiteshi Tandon is thankful to Manipal University Jaipur for providing research facility.

Funding

Dr. Tanmoy Chakraborty would like to acknowledge the funding support from Science and Engineering Research Board (SERB), Department of Science and Technology, Government of India, under Grant No. CRG/2020/002951. Dr. Martín Labarca is thankful to Agencia Nacional de Promocíon Científica y Tecnológica (FONCyT) (Grant PICT-2018-04519), to Universidad de Buenos Aires (Grant UBACyT 20020190200097BA) and to Universidad Austral of Argentina.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Hiteshi Tandon, Martín Labarca or Tanmoy Chakraborty.

Ethics declarations

Conflict of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

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

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (PDF 463 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumari, V., Singh, T., Devi, S. et al. Atomic electronegativity based on hardness and floating spherical gaussian orbital approach. J Math Chem 60, 360–372 (2022). https://doi.org/10.1007/s10910-021-01306-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-021-01306-7

Keywords

Navigation