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Theoretical computation of normalised radii, density and global hardness as a function of orbital exponent

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Abstract

The recent work has an aim to establish a pivotal role of orbital exponent in the normalized atomic radii, atomic density and atomic hardness. These three periodic descriptors help to understand the real scenario of an element. Concerning the effective nuclear charge, screening constant and effective principal quantum number, we have developed a new relation between these periodic properties and invoked a new formula by which we can compute the normalized radii, density and global atomic hardness in terms of the orbital exponent. With comparison to the existing famous formulae originating from different concepts, we can conclude that our empirical computation has an inherent efficacy to predict periodicity.

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References

  1. D. Ghosh, R. Biswas, Theoretical calculation of absolute radii of atoms and ions. Part 1. The atomic radii. Int. J. Mol. Sci. 3(2), 87–113 (2002)

    Article  CAS  Google Scholar 

  2. S.T.K. Gazi, D.C. Ghosh, Computation of the atomic radii through the conjoint action of the effective nuclear charge and the ionisation energy. Mol. Phys. 108(16), 2081–2092 (2010)

    Article  CAS  Google Scholar 

  3. L. Pauling, The Nature of the Chemical Bond, vol. 260 (Cornell University Press, Ithaca, 1960), pp. 3175–3187

    Google Scholar 

  4. B. Cordero, V. Gómez, A.E. Platero-Prats, M. Revés, J. Echeverría, E. Cremades, S. Alvarez, Covalent radii revisited. Dalton Trans. 21, 2832–2838 (2008)

    Article  CAS  Google Scholar 

  5. R.T. Shannon, C.T. Prewitt, Effective ionic radii in oxides and fluorides. Acta Crystallogr. Sect. B Struct. Crystallogr. Cryst. Chem. 25(5), 925–946 (1969)

    Article  CAS  Google Scholar 

  6. R.D. Shannon, Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. Section A Cryst. Phys. Diffract. Theor. General Crystallogr 32(5), 751–767 (1976)

    Article  Google Scholar 

  7. J.T. Waber, D.T. Cromer, Orbital radii of atoms and ions. J. Chem. Phys. 42(12), 4116–4123 (1965)

    Article  CAS  Google Scholar 

  8. P. Politzer, R.G. Parr, D.R. Murphy, Relationships between atomic, chemical potentials, electrostatic potentials, and covalent radii. J. Chem. Phys. 79(8), 3859–3861 (1983)

    Article  CAS  Google Scholar 

  9. B.M. Deb, P.K. Chattaraj, New quadratic nondifferential Thomas-Fermi-Dirac-type equation for atoms. Phys. Rev. A 37(10), 4030 (1988)

    Article  CAS  Google Scholar 

  10. S. Nath, S. Bhattacharya, P.K. Chattaraj, Density functional calculation of a characteristic atomic radius. J. Mol. Struct. (Thoechem) 331(3), 267–279 (1995)

    Article  CAS  Google Scholar 

  11. J.E. Huheey, E.A. Keiter, R.L. Keiter, O.K. Medhi, Inorganic Chemistry: Principles of Structure and Reactivity (Pearson Education, India, 2006).

    Google Scholar 

  12. R.T. Sanderson, The covalent radius of xenon. Inorg. Chem. 2(3), 660–661 (1963)

    Article  CAS  Google Scholar 

  13. R.T. Sanderson, The covalent radius of radon and the electronegativities of gold, mercury, thallium, lead, and bismuth. J. Inorg. Nuclear Chem. 7, 288 (1958)

    Article  CAS  Google Scholar 

  14. T.L. Meek, Electronegativities of the noble gases. J. Chem. Educ. 72(1), 17 (1995)

    Article  CAS  Google Scholar 

  15. A. Bondi, van der Waals volumes and radii. J. Phys. Chem. 68(3), 441–451 (1964)

    Article  CAS  Google Scholar 

  16. P.G. Ashmore, R.M. Noyes, L. Valentine, N. Miller, G.C. Bond, J.S. Rowlinson, F.S. Dainton, General and physical chemistry. Ann. Rep. Progress Chem. 52, 7–92 (1955)

    Article  Google Scholar 

  17. V.M. Goldschmidt, T. Barth, G. Lunde, W.H. Zachariasen, Geochemical distribution law of the elements. VII. Summary of the chemistry of crystals. Skr. Nor. Vidensk. Akad 1, 1–117 (1926)

    Google Scholar 

  18. V.M. Goldschmidt, Crystal structure and chemical correlation. Ber. Deut. Chem. Ges. 60, 1263–1296 (1927)

    Article  Google Scholar 

  19. V.M. Goldschmidt, The distribution of the chemical elements 1. Nature 124, 15–17 (1929)

    Article  CAS  Google Scholar 

  20. L.H. Ahrens, The significance of the chemical bond for controlling the geochemical distribution of the elements-part 1. Phys. Chem. Earth 5, 1–54 (1964)

    Article  CAS  Google Scholar 

  21. D. Robert Hay, P.D. Parikh, Valence bond interpretation of elastic anisotropy in BCC transition metals. Phil. Mag. 20(166), 753–758 (1969)

    Article  Google Scholar 

  22. W.H. Zachariasen, A set of empirical crystal radii for ions with inert gas configuration. Zeitschrift für Kristallographie-Cryst. Mater. 80(1–6), 137–153 (1931)

    Article  CAS  Google Scholar 

  23. W.H. Zachariasen, Crystal radii of the heavy elements. Phys. Rev. 73(9), 1104 (1948)

    Article  CAS  Google Scholar 

  24. W.L. Bragg, XVIII The arrangement of atoms in crystals. Lond. Edinburgh Dublin Philos. Mag. J. Sci. 40(236), 169–189 (1920)

    Article  CAS  Google Scholar 

  25. J.K. Nagle, Atomic polarizability and electronegativity. J. Am. Chem. Soc. 112(12), 4741–4747 (1990)

    Article  CAS  Google Scholar 

  26. J.C. Slater, Atomic radii in crystals. J. Chem. Phys. 41(10), 3199–3204 (1964)

    Article  CAS  Google Scholar 

  27. J.C. Slater, Quantum Theory of Molecules and Solids: Symmetry and Energy Bands in Crystals, vol. 2 (McGraw-Hill, New York, 1963).

    Google Scholar 

  28. D.R. Hartree, The calculation of atomic structures (1957).

  29. E. Clementi, D.L. Raimondi, Atomic screening constants from SCF functions. J. Chem. Phys. 38(11), 2686–2689 (1963)

    Article  CAS  Google Scholar 

  30. D. Liberman, J.T. Waber, D.T. Cromer, Self-consistent-field Dirac-Slater wave Functions for atoms and ions. I. Comparison with previous calculations. Phys. Rev. 137(1), A27 (1965)

    Article  Google Scholar 

  31. C. Froese, Hartree—Fock parameters for the atoms helium to radon. J. Chem. Phys. 45(5), 1417–1420 (1966)

    Article  CAS  Google Scholar 

  32. E. Clementi, D.L. Raimondi, W.P. Reinhardt, Atomic screening constants from SCF functions. II. Atoms with 37 to 86 electrons. J. Chem. Phys. 47(4), 1300–1307 (1967)

    Article  CAS  Google Scholar 

  33. C. Fisk, S. Fraga, Atomic Radii. In Anales de fisica . Facultad de fisica quimica ciudad univ, 3 Madrid, vol. 65, ( Real Soc Espan Quimica, Spain), p. 135 (1969).

  34. A. C. Larson, J. T. Waber. Self-consistent field Hartree Calculations for Atoms and Ions (No. LA- 4297). Los Alamos Scientific Lab., N. Mex (1969).

  35. C.F. Fischer, Average-energy-of-configuration Hartree-Fock results for the atoms helium to radon charlotte Froese Fischer. Atom. Data Nucl. Data Tabl. 12, 301–399 (1972)

    Article  Google Scholar 

  36. C.W. Kammeyer, D.R. Whitman, Quantum mechanical calculation of molecular radii. I. Hydrides of elements of periodic groups IV through VII. J. Chem. Phys. 56(9), 4419–4421 (1972)

    Article  CAS  Google Scholar 

  37. S. Fraga, J. Karwowski, K.M.S. Saxena, Hartree-Fock values of coupling constants, polarizabilities, susceptibilities, and radii for the neutral atoms, helium to nobelium. At. Data Nucl. Data Tables 12(5), 467–477 (1973)

    Article  CAS  Google Scholar 

  38. C.F. Fischer. Atom. Data 4 (1972) 301. Atom. Data Nucl. Data, 12, 87 (1973).

  39. J.P. Desclaux, Atomic Data Nucl. Data Tables 12(4), 311 (1973)

    Article  CAS  Google Scholar 

  40. R.J. Boyd, The relative sizes of atoms. J. Phys. B At. Mol. Phys. 10(12), 2283 (1977)

    Article  CAS  Google Scholar 

  41. B.M. Deb, R. Singh, N. Sukumar, A universal density criterion for correlating the radii and other properties of atoms and ions. J. Mol. Struct. (Thoechem) 259, 121–139 (1992)

    Article  Google Scholar 

  42. D. Ghosh, R. Biswas, Theoretical calculation of absolute radii of atoms and ions. Part 1. The atomic radii. Int. J. Mol. Sci. 3(2), 87–113 (2002)

    Article  CAS  Google Scholar 

  43. M.V. Putz, N. Russo, E. Sicilia, Atomic radii scale and related size properties from density functional electronegativity formulation. J. Phys. Chem. A 107(28), 5461–5465 (2003)

    Article  CAS  Google Scholar 

  44. P. Pyykko, S. Riedel, M. Patzschke, Chem. Eur. J.11: 3511 (2005).

  45. D.C. Ghosh, R. Biswas, T. Chakraborty, N. Islam, S.K. Rajak, J. Mol. Struct. (Theochem) 865, 60 (2008)

    Article  CAS  Google Scholar 

  46. T. Chakraborty, K. Gazi, D.C. Ghosh, Computation of the atomic radii through the conjoint action of the effective nuclear charge and the ionisation energy. Mol. Phys. 108(16), 2081–2092 (2010)

    Article  CAS  Google Scholar 

  47. J.C. Slater, Atomic shielding constants. Phys. Rev. 36(1), 57 (1930)

    Article  CAS  Google Scholar 

  48. R.T. Sanderson, The covalent radius of radon and the electronegativities of gold, mercury, thallium, lead, and bismuth. J. Inorg. Nucl. Chem. 7, 288 (1958)

    Article  CAS  Google Scholar 

  49. A. Bondi, Vander Waals volumes and radii. J. Phys. Chem. 68(3), 441–451 (1964)

    Article  CAS  Google Scholar 

  50. W.H. Zachariasen, A set of empirical crystal radii for ions with inert gas configuration. Zeitschriftfür Kristallographie-Crystall. Mater. 80(1–6), 137–153 (1931)

    Article  CAS  Google Scholar 

  51. P.W. Atkins, R.S. Friedman, Molecular Quantum Mechanics, 3rd edn. (Oxford University Press, Oxford, 1997).

    Google Scholar 

  52. T. Brinck, J.S. Murray, P. Politzer, J. Chem. Phys. 98, 4305 (1993)

    Article  CAS  Google Scholar 

  53. S. Hati, D. Dutta, J. Phys. Chem. 98, 10451 (1994)

    Article  CAS  Google Scholar 

  54. E.M. Purcell, Berkley Physics Course, TMH Edition, Vol. 2, (Tata McGraw-Hill Publishing Company, Bombay) (1963).

  55. O. Roberto, On weak interactions as short-distance manifestations of gravity. Mod. Phys. Lett. A 28, 1350022 (2013)

    Article  Google Scholar 

  56. U.V.S. Seshavatharam, S. Lakshminarayana, Role of four gravitational constants in nuclear structure. Mapana J. Sci. 18(1), 21–46 (2019)

    Article  CAS  Google Scholar 

  57. R.S. Mulliken, Electronic population analysis on LCAO–MO molecular wave functions I. J. Chem. Phys. 23(10), 1833–1840 (1955)

    Article  CAS  Google Scholar 

  58. 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 

  59. 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 

  60. 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 

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

    Article  CAS  PubMed  Google Scholar 

  62. P. Geerlings, F. De Proft, W. Langenaeker, Conceptual density functional theory. Chem. Rev. 103(5), 1793–1874 (2003)

    Article  CAS  PubMed  Google Scholar 

  63. R.G. Parr, R.G. Pearson, J. Am. Chem. Soc. 105, 7512 (1983)

    Article  CAS  Google Scholar 

  64. R.G. Pearson, J. Chem. Educ. 64, 561 (1987)

    Article  CAS  Google Scholar 

  65. R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989).

    Google Scholar 

  66. R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lecture on Physics, Addison– Wesley: Mass., Vol. II., (1964).

  67. P.B. Janardhan, B. Sivasankar, A Text-Book of Inorganic Chemistry (Oxford and IBH, New Delhi, 1978).

    Google Scholar 

  68. D.C. Ghosh, N. Islam, Semiempirical evaluation of the global hardness of the atoms of 103 elements of the periodic table using the most probable radii as their size descriptors. Int. J. Quantum Chem. 110(6), 1206–1213 (2010)

    Article  CAS  Google Scholar 

  69. D.C. Ghosh, R. Biswas, Theoretical calculation of absolute radii of atoms and ions. Part 1. The atomic radii. Int. J. Mol. Sci 3(2), 87–113 (2002)

    Article  CAS  Google Scholar 

  70. R.P. Shalini, T. Chakraborty, Theoretical Computation of Periodic Descriptors Invoking Periodic Properties, in Chemical Science and Engineering Technology. ed. by C.A. Suresh, C. Tanmoy (Apple Academic Press, Waretown, 2019), pp. 31–40

    Chapter  Google Scholar 

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Acknowledgements

Dr. Tanmoy Chakraborty is thankful to Sharda University for providing computational resources and research facility.

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Authors and Affiliations

  1. Department of Chemistry, Alankar P.G. Girls College, Jaipur, Rajasthan, 302034, India

    Shalini Chaudhary

  2. Department of Chemistry, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India

    Shalini Chaudhary

  3. Department of Computer Science Engineering, Vellore Institute of Technology, Amaravati, Andhra Pradesh, 522237, India

    Abhay Chaudhary

  4. Department of Chemistry, Dumkal College, Murshidabad, West Bengal, 742406, India

    Sandip Kumar Rajak

  5. Department of Pharmacy Health Services Vocational School, Sivas Cumhuriyet University, Sivas, 58140, Turkey

    Savaş Kaya

  6. Faculty of Education, Sivas Cumhuriyet University, Sivas, 58140, Turkey

    Mustafa Elik

  7. Department of Chemistry and Biochemistry, School of Basic Sciences and Research, Sharda University, Uttar Pradesh, Knowledge Park III, Greater Noida, 201310, India

    Tanmoy Chakraborty

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  1. Shalini Chaudhary
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Shalini Chaudhary, Chaudhary, A., Rajak, S.K. et al. Theoretical computation of normalised radii, density and global hardness as a function of orbital exponent. J Math Chem 59, 1014–1028 (2021). https://doi.org/10.1007/s10910-021-01224-8

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