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An alternative approach to compute atomic hardness

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Abstract

Atomic hardness is an important periodic descriptor which can govern chemical reactivity and stability. A number of theoretical models are available to compute atomic hardness. In this report, we have suggested a new and simple approach to compute atomic hardness. Considering periodic relationship of atomic hardness with nucleophilicity index, effective nuclear charge and atomic radius, this model is derived to compute hardness of 103 elements of the periodic table. Our proposed scale satisfies all sine qua non of the periodic table. Characteristic periodic properties viz. lanthanide contraction, chemical inertness of noble gases, relativistic effect is quite distinct in our computed result. We have also calculated molecular hardness invoking Hardness Equalization Principle. A strong correlation between our computed data and their experimental counterparts justifies our study.

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References

  1. Parr RG, Pearson RG (1983) J Am Chem Soc 105:7512. https://doi.org/10.1021/ja00364a005

    Article  CAS  Google Scholar 

  2. Parr RG, Donnelly RA, Levy M, Palke W (1978) J Chem Phys 68:3801. https://doi.org/10.1063/1.436185

    Article  CAS  Google Scholar 

  3. Parr RG, Yang W (1984) J Am Chem Soc 106:4049. https://doi.org/10.1021/ja00326a036

    Article  CAS  Google Scholar 

  4. Islam N, Ghosh DC (2011) Mol Phys 109:1533. https://doi.org/10.1080/00268976.2011.569513

    Article  CAS  Google Scholar 

  5. Pearson RG (1997) Chemical hardness: application from molecules to solid. Wiley-VCH, Weinheim

    Book  Google Scholar 

  6. Mulliken RS (1952) J Am Chem Soc 74:811. https://doi.org/10.1021/ja01123a067

    Article  CAS  Google Scholar 

  7. Pearson RG (1963) J Am Chem Soc 85:3533. https://doi.org/10.1021/ja00905a001

    Article  CAS  Google Scholar 

  8. Pearson RG (1966) Science 151:172. https://www.jstor.org/stable/1717293

  9. Klopman G (1964) J Am Chem Soc 86:1463. https://doi.org/10.1021/ja01062a001

    Article  CAS  Google Scholar 

  10. Klopman G (1968) J Am Chem Soc 90:223. https://doi.org/10.1021/ja01004a002

    Article  CAS  Google Scholar 

  11. Pearson RG (1999) J Chem Edu 76:267. https://doi.org/10.1021/ed076p267

    Article  CAS  Google Scholar 

  12. Pearson RG (1986) Proc Natl Acad Sci 83:8440. https://doi.org/10.1073/pnas.83.22.8440

    Article  CAS  PubMed  Google Scholar 

  13. Pearson RG (1988) Inorg Chem 27:734. https://doi.org/10.1021/ic00277a030

    Article  CAS  Google Scholar 

  14. Tozer DJ, Proft FD (2005) J Phys Chem A 109:8923. https://doi.org/10.1021/jp053504y

    Article  CAS  PubMed  Google Scholar 

  15. Geerlings P, Proft FD, Langenaeker W (2003) Chem Rev 103:1793. https://doi.org/10.1021/cr990029p

    Article  CAS  PubMed  Google Scholar 

  16. Pearson RG (1987) J Chem Educ 64:561. https://doi.org/10.1021/ed064p561

    Article  CAS  Google Scholar 

  17. Chattaraj PK, Sengupta S (1996) J Phys Chem 100:16126. https://doi.org/10.1021/jp961096f

    Article  CAS  Google Scholar 

  18. Noorizadeh S (2005) THEOCHEM 713:27. https://doi.org/10.1016/j.theochem.2004.09.029

    Article  CAS  Google Scholar 

  19. Kaya S, Kaya C (2015) Mol Phys 113:1311. https://doi.org/10.1080/00268976.2014.991771

    Article  CAS  Google Scholar 

  20. Cardenas C, Heidar-Zadeh F, Ayers PW (2016) Phys Chem Chem Phys. 18:25721. https://doi.org/10.1039/C6CP04533B

    Article  CAS  PubMed  Google Scholar 

  21. Reed JL (1997) J Phys Chem A 101:7396. https://doi.org/10.1021/jp9711050

    Article  CAS  Google Scholar 

  22. Parr RG, von Szentpaly L, Liu S (1999) J Am Chem Soc 121:1922. https://doi.org/10.1021/ja983494x

    Article  CAS  Google Scholar 

  23. Chattaraj PK, Maiti B (2001) J Phys Chem A 105:169. https://doi.org/10.1021/jp0019660

    Article  CAS  Google Scholar 

  24. Gordy W (1946) Phys Rev 69:604. https://doi.org/10.1103/PhysRev.69.604

    Article  CAS  Google Scholar 

  25. Tandon H, Chakraborty T, Suhag V (2019) Int J Quant Struct Prop Relationsh 4:99. http://sci-hub.tw/10.4018/ijqspr.2019070104

    Article  Google Scholar 

  26. Ghosh DC, Biswas R (2002) Int J Mol Sci 3:87. https://doi.org/10.3390/i3020087

    Article  CAS  Google Scholar 

  27. Chakraborty T, Gazi K, Ghosh DC (2010) Mol Phys 108:2081. https://doi.org/10.1080/00268976.2010.505208

    Article  CAS  Google Scholar 

  28. Ayers PW, Parr RG (2008). J Chem Phys. https://doi.org/10.1063/1.2957900

    Article  PubMed  Google Scholar 

  29. Yang W, Lee C, Ghosh SK (1985) J Phys Chem 89:5412. https://doi.org/10.1021/j100271a019

    Article  CAS  Google Scholar 

  30. Datta D (1986) J Phys Chem 90:4216. https://doi.org/10.1021/j100408a076

    Article  CAS  Google Scholar 

  31. Ghosh DC, Islam N (2011) Int J Quantum Chem 111:1961. https://doi.org/10.1002/qua.22508

    Article  CAS  Google Scholar 

  32. Kaya S, Kaya C (2015) Inorg Chem 54:8207. https://doi.org/10.1021/acs.inorgchem.5b00383

    Article  CAS  PubMed  Google Scholar 

  33. Tandon H, Chakraborty T, Suhag V (2019) Chem Biomol Eng 4:45. http://article.sciencepublishinggroup.com/pdf/10.11648.j.cbe.20190404.11.pdf

  34. Tandon H, Chakraborty T, Suhag V (2019) Res Med Eng Sci 7:791. https://crimsonpublishers.com/rmes/pdf/RMES.000668.pdf

  35. Tandon H, Ranjan P, Chakraborty T, Suhag V (2021) Mol Divers 25:249. https://doi.org/10.1007/s11030-020-10062-w

    Article  CAS  PubMed  Google Scholar 

  36. Waddington TC (1959) Adv Inorg Chem Radiochem 1:157. https://doi.org/10.1016/S0065-2792(08)60254-X

    Article  CAS  Google Scholar 

  37. Sen KD, Vinayagam SC (1988) Chem Phys Lett 144:178. https://doi.org/10.1016/0009-2614(88)87112-4

    Article  Google Scholar 

  38. Pyykkö P (2012) Annu Rev Phys Chem 63:45. https://doi.org/10.1146/annurev-physchem-032511-143755

    Article  CAS  PubMed  Google Scholar 

  39. Balasubramanian K (1997) Relativistic effects in chemistry: part A theory & techniques. John Wiley & Sons, New York

    Google Scholar 

  40. Balasubramanian K (1997) Relativistic Effects in Chemistry Part B: Applications. Wiley, New York

    Google Scholar 

  41. Thayer JS (2010) Challenges and advances in computational chemistry and physics. In: Barysz M, Ishikawa Y (eds) Relativistic methods for chemists, vol 10. Springer, Dordrecht, pp 63–97

    Chapter  Google Scholar 

  42. Balasubramanian K, Pitzer KS (1983) J Chem Phys 78:321. https://doi.org/10.1063/1.444504

    Article  CAS  Google Scholar 

  43. Balasubramanian K, Sumathi K, Dai D (1991) J Chem Phys 95:3494. https://doi.org/10.1063/1.460852

    Article  CAS  Google Scholar 

  44. Pearson RG (1988) Inorg Chem 27:734. https://doi.org/10.1021/ic00277a030

    Article  CAS  Google Scholar 

  45. Robles J, Bartolotti LJ (1984) J Am Chem Soc 106:3723. https://doi.org/10.1021/ja00325a003

    Article  CAS  Google Scholar 

  46. Szarek P, Grochala W (2014) J Phys Chem A 118:10281. https://doi.org/10.1021/jp507423p

    Article  CAS  PubMed  Google Scholar 

  47. Tandon H, Chakraborty T, Suhag V (2019) J Math Chem 57:2142. https://doi.org/10.1007/s10910-019-01055-8

    Article  CAS  Google Scholar 

  48. Pershina V (2014). In: Schädel M, Shaughnessy D (eds) The chemistry of superheavy elements. Springer, Heidelberg, pp 135–239

    Chapter  Google Scholar 

  49. Balasubramanian K (2001) Chem Phys Lett 341:607. https://doi.org/10.1016/S0009-2614(01)00413-4

    Article  Google Scholar 

Download references

Acknowledgements

This manuscript has been prepared for the Special Issue of the Theoretical Chemistry Accounts dedicated to celebrate 80th birth anniversary of renowned Theoretical and Computational Chemist Prof. (Dr.) Ramon Carbó-Dorca. Dr. Tanmoy Chakraborty is thankful to Sharda University, and Dr. Hiteshi Tandon is thankful to Manipal University Jaipur for providing computational resources and 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].

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Correspondence to Hiteshi Tandon or Tanmoy Chakraborty.

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Published as part of the special collection of articles "Festschrift in honour of Prof. Ramon Carbó-Dorca".

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Yadav, P., Tandon, H., Malik, B. et al. An alternative approach to compute atomic hardness. Theor Chem Acc 140, 60 (2021). https://doi.org/10.1007/s00214-021-02768-3

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