Abstract
Formal charge and oxidation state are two means of estimating the charge of an atom in a molecule. Though these concepts have very different origins—formal charge is derived from the ball-and-hook model of bonding and oxidation state is based on the ionic approximation of molecules—they are used to predict reactivity and other molecular properties through their properties as charges. In this submission, it is shown that formal charge and oxidation state are two extreme descriptions of bonding: formal charge represents zero charge transfer between atoms while oxidation state represents complete charge transfer in each bond. These ‘localised electron approximations’ form an incomplete picture of atomic charge. Electronegativity measures the extent of polarity in real bonds; this concept can be introduced to polarise bonds relative to the ‘equal sharing model’. It is shown that the various electronegativity models are fundamentally related. We chose two models to demonstrate numerically that polar bonds yield charges intermediate between the localised electron approximations: Pauling and Mulliken. It is shown that probabilistic interpretation of the Pauling scale (‘scaled Pauling’ method) and use of asymmetric chemical potential (‘modified Mulliken’ method) lead to atomic charges that closely approximate experimental values using simple ‘back of the envelope’ calculations. It is seen that formal charge, oxidation state, and electronegativity-interpolated charge lie on a continuum and are mathematically related. It is therefore concluded that electronegativity introduces (quantum) delocalisation to the localised (classical) picture of electron bonding.
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Chemical potentials and asymmetric chemical hardnesses (positive and negative) of the elements H—Xe are tabulated in the Supporting Information along with the method used to obtain them.
References
Allen, L.C.: Electronegativity is the average one-electron energy of the valence-shell electrons in ground-state free atoms. J. Am. Chem. Soc. 111, 9003–9014 (1989). https://doi.org/10.1021/ja00207a003
Allred, A.L., Rochow, E.G.: A scale of electronegativity based on electrostatic force. J. Inorg. Nucl. Chem. 5, 264–268 (1958). https://doi.org/10.1016/0022-1902(58)80003-2
Bader, R.F.W.: Atoms in Molecules: A Quantum Theory. Oxford University Press (1994)
Berzelius, J.J.: Suite des expériences sur les proportions déterminées, d’après lesquelles les éléments de la nature inorganique s’ unissent. Ann. Chim. 79, 233–264 (1811a)
Berzelius, J.J.: Essai sur la nomenclature chimique. J. Phys. Chim. d’histoire Nat. des arts. 73, 253–286 (1811b)
Brown, T.L., LeMay Jr., H.E., Bursten, B.E., Murphy, C.J., Woodward, P.M., Stoltzfus, M.W., Lufaso, M.W.: Chemistry: The Central Science. Pearson, New York, New York (2018)
Clementi, E., Raimondi, D.L.: Atomic screening constants from SCF functions. J. Chem. Phys. 38, 2686–2689 (1963)
Clementi, E., Raimondi, D.L., Reinhardt, W.P.: Atomic screening constants from SCF functions. II. Atoms with 37 to 86 electrons. J. Chem. Phys. 47, 1300–1307 (1967)
Dorato, M.: Truth, laws and the progress of science. Manuscrito. 34, 185–205 (2011). https://doi.org/10.1590/S0100-60452011000100009
Hati, S., Datta, D.: Hardness: a concept in inorganic chemistry. Some aspects. Proc. Indian Acad. Sci. - Chem. Sci. 108, 143–158 (1996). https://doi.org/10.1007/BF02870020
Hirshfeld, F.L.: Bonded-atom fragments for describing molecular charge densities. Theor. Chim. Acta. 44, 129–138 (1977). https://doi.org/10.1007/BF00549096
Hoffmann, R.: Marginalia: Hi O Silver. Am. Sci. 89, 311–313 (2001)
Johnson III, R.D. ed: NIST Computational Chemistry Comparison and Benchmark Database: NIST Standard Reference Database Number 101, http://cccbdb.nist.gov/, (2019)
Kaupp, M., von Schnering, H.G.: Formal oxidation state versus partial charge—a comment. Angew. Chemie Int. Ed. English. 34, 986–986 (1995). https://doi.org/10.1002/anie.199509861
Koopmans, T.: The distribution of wave function and characteristic value among the individual electrons of an atom. Physica. 1, 104–113 (1933)
Lewis, G.N.: The atom and the molecule. J. Am. Chem. Soc. 38, 762–785 (1916). https://doi.org/10.1021/ja02261a002
Lide, D.R. (ed.): CRC Handbook of Chemistry and Physics. CRC Press, Boca Raton, Florida (2003)
Manz, T.A., Limas, N.G.: Introducing DDEC6 atomic population analysis: part 1. Charge partitioning theory and methodology. RSC Adv. 6, 47771–47801 (2016). https://doi.org/10.1039/c6ra04656h
Nič, M., Jirát, J., Košata, B., Jenkins, A., McNaught, A. eds: IUPAC Compendium of Chemical Terminology. IUPAC, Research Triangle Park, NC (2009)
Mulliken, R.S.: A new electroaffinity scale; together with data on valence states and on valence ionization potentials and electron affinities. J. Chem. Phys. 2, 782–793 (1934). https://doi.org/10.1063/1.1749394
Mulliken, R.S.: Electronic population analysis on LCAO–MO molecular wave functions. I. J. Chem. Phys. 23, 1833–1840 (1955). https://doi.org/10.1063/1.1740588
Parkin, G.: Valence, oxidation number, and formal charge: three related but fundamentally different concepts. J. Chem. Educ. 83, 791 (2006). https://doi.org/10.1021/ed083p791
Parr, R.G., Pearson, R.G.: Absolute hardness: companion parameter to absolute electronegativity. J. Am. Chem. Soc. 105, 7512–7516 (1983). https://doi.org/10.1021/ja00364a005
Pauling, L.: 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). https://doi.org/10.1021/ja01348a011
Pauling, L.: The modern theory of valency. J. Chem. Soc. (1948). https://doi.org/10.1039/jr9480001461
Pauling, L.: The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry. Cornell University Press (1960)
Pearson, R.G.: Hard and soft acids and bases. J. Am. Chem. Soc. 85, 3533–3539 (1963). https://doi.org/10.1021/ja00905a001
Pearson, R.G.: Absolute electronegativity and hardness: application to inorganic chemistry. Inorg. Chem. 27, 734–740 (1988). https://doi.org/10.1021/ic00277a030
Reed, A.E., Weinstock, R.B., Weinhold, F.: Natural population analysis. J. Chem. Phys. 83, 735–746 (1985). https://doi.org/10.1063/1.449486
Šima, J.: Redox reactions: inconsistencies in their description. Found. Chem. 15, 57–64 (2013). https://doi.org/10.1007/s10698-011-9143-8
Slater, J.C.: Atomic shielding constants. Phys. Rev. 36, 57–64 (1930)
Wöhler, F.: Grundriss der Chemie: Unorganische Chemie. Duncker und Humblot, Berlin (1835)
Zener, C.: Analytic atomic wave functions. Phys. Rev. 36, 51–56 (1930)
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Viswanathan, B., Gulam Razul, M. Electronegativity provides the relationship between formal charge, oxidation state, and actual charge. Found Chem 25, 5–28 (2023). https://doi.org/10.1007/s10698-022-09447-6
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DOI: https://doi.org/10.1007/s10698-022-09447-6