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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Electronegativity | 2/4 | https://en.wikipedia.org/wiki/Electronegativity | reference | science, encyclopedia | 2026-05-05T10:52:24.353764+00:00 | kb-cron |
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{\displaystyle E_{\rm {d}}({\rm {AB}})={\frac {E_{\rm {d}}({\rm {AA}})+E_{\rm {d}}({\rm {BB}})}{2}}+(\chi _{\rm {A}}-\chi _{\rm {B}})^{2}{\rm {eV}}}
or sometimes, a more accurate fit
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{\displaystyle E_{\rm {d}}({\rm {AB}})={\sqrt {E_{\rm {d}}({\rm {AA}})E_{\rm {d}}({\rm {BB}})}}+1.3(\chi _{\rm {A}}-\chi _{\rm {B}})^{2}{\rm {eV}}}
These are approximate equations but they hold with good accuracy. Pauling obtained the first equation by noting that a bond can be approximately represented as a quantum mechanical superposition of a covalent bond and two ionic bond states. The covalent energy of a bond is approximately, by quantum mechanical calculations, the geometric mean of the two energies of covalent bonds of the same molecules, and there is additional energy that comes from ionic factors, i.e. polar character of the bond. The geometric mean is approximately equal to the arithmetic mean—which is applied in the first formula above—when the energies are of a similar value, e.g., except for the highly electropositive elements, where there is a larger difference of two dissociation energies; the geometric mean is more accurate and almost always gives positive excess energy, due to ionic bonding. The square root of this excess energy, Pauling notes, is approximately additive, and hence one can introduce the electronegativity. Thus, it is these semi-empirical formulas for bond energy that underlie the concept of Pauling electronegativity. The formulas are approximate, but this rough approximation is good and gives the right intuition, with the notion of the polarity of the bond and some theoretical grounding in quantum mechanics. The electronegativities are then determined to best fit the data. In more complex compounds, there is an additional error since electronegativity depends on the molecular environment of an atom. Also, the energy estimate can be only used for single, not for multiple bonds. The enthalpy of formation of a molecule containing only single bonds can subsequently be estimated based on an electronegativity table, and it depends on the constituents and the sum of squares of differences of electronegativities of all pairs of bonded atoms. Such a formula for estimating energy typically has a relative error on the order of 10% but can be used to get a rough qualitative idea and understanding of a molecule.
=== Mulliken electronegativity ===
Robert S. Mulliken proposed that the arithmetic mean of the first ionization energy (Ei) and the electron affinity (Eea) should be a measure of the tendency of an atom to attract electrons:
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{\displaystyle \chi ={\frac {E_{\rm {i}}+E_{\rm {ea}}}{2}}}
As this definition is not dependent on an arbitrary relative scale, it has also been termed absolute electronegativity, with the units of kilojoules per mole or electronvolts. However, it is more usual to use a linear transformation to transform these absolute values into values that resemble the more familiar Pauling values. For ionization energies and electron affinities in electronvolts,
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0.187
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0.17
{\displaystyle \chi =0.187(E_{\rm {i}}+E_{\rm {ea}})+0.17\,}
and for energies in kilojoules per mole,
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1.97
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3
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0.19.
{\displaystyle \chi =(1.97\times 10^{-3})(E_{\rm {i}}+E_{\rm {ea}})+0.19.}
The Mulliken electronegativity can only be calculated for an element whose electron affinity is known. Measured values are available for 72 elements, while approximate values have been estimated or calculated for the remaining elements. The Mulliken electronegativity of an atom is sometimes said to be the negative of the chemical potential. By inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is possible to show that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i.e.,
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{\displaystyle \mu ({\rm {Mulliken)=-\chi ({\rm {Mulliken)={}-{\frac {E_{\rm {i}}+E_{\rm {ea}}}{2}}}}}}}
=== Allred–Rochow electronegativity ===
A. Louis Allred and Eugene G. Rochow considered that electronegativity should be related to the charge experienced by an electron on the "surface" of an atom: The higher the charge per unit area of atomic surface the greater the tendency of that atom to attract electrons. The effective nuclear charge, Zeff, experienced by valence electrons can be estimated using Slater's rules, while the surface area of an atom in a molecule can be taken to be proportional to the square of the covalent radius, rcov. When rcov is expressed in picometres,
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3590
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0.744
{\displaystyle \chi =3590{{Z_{\rm {eff}}} \over {r_{\rm {cov}}^{2}}}+0.744}
=== Sanderson electronegativity equalization ===
R.T. Sanderson has also noted the relationship between Mulliken electronegativity and atomic size and has proposed a method of calculation based on the reciprocal of the atomic volume. With a knowledge of bond lengths, Sanderson's model allows the estimation of bond energies in a wide range of compounds. Sanderson's model has also been used to calculate molecular geometry, s-electron energy, NMR spin-spin coupling constants and other parameters for organic compounds. This work underlies the concept of electronegativity equalization, which suggests that electrons distribute themselves around a molecule to minimize or equalize the Mulliken electronegativity. This behavior is analogous to the equalization of chemical potential in macroscopic thermodynamics.
=== Allen electronegativity ===
Perhaps the simplest definition of electronegativity is that of Leland C. Allen, who has proposed that it is related to the average energy of the valence electrons in a free atom,