Editing Electronegativity (section)

===Pauling electronegativity===
{{Anchor|Pauling electronegativity}}

[[Linus Pauling|Pauling]] first proposed<ref name="paulingJACS"/> the concept of electronegativity in 1932 to explain why the [[covalent bond]] between two different atoms (A–B) is stronger than the average of the A–A and the B–B bonds. According to [[valence bond theory]], of which Pauling was a notable proponent, this "additional stabilization" of the [[heteronuclear]] bond is due to the contribution of [[Ionic bond|ionic]]  [[Resonance (chemistry)|canonical form]]s to the bonding.

The difference in electronegativity between atoms A and B is given by:
<math display="block">|\chi_{\rm A} - \chi_{\rm B}| = ({\rm eV})^{-1/2} \sqrt{E_{\rm d}({\rm AB}) - \frac{E_{\rm d}({\rm AA}) + E_{\rm d}({\rm BB})} 2}</math>
where the [[Bond dissociation energy|dissociation energies]], ''E''<sub>d</sub>, of the A–B, A–A and B–B bonds are expressed in [[electronvolt]]s, the factor (eV)<sup>−{{frac|1|2}}</sup> being included to ensure a dimensionless result. Hence, the difference in Pauling electronegativity between hydrogen and [[bromine]] is 0.73 (dissociation energies: H–Br, 3.79&nbsp;eV; H–H, 4.52&nbsp;eV; Br–Br 2.00&nbsp;eV)

As only differences in electronegativity are defined, it is necessary to choose an arbitrary reference point in order to construct a scale. Hydrogen was chosen as the reference, as it forms covalent bonds with a large variety of elements: its electronegativity was fixed first<ref name="paulingJACS"/> at 2.1, later revised<ref name="Allred">{{cite journal
 |author= Allred, A. L.
 |year= 1961
 |journal= Journal of Inorganic and Nuclear Chemistry
 |volume= 17
 |issue= 3–4
 |pages= 215–221
 |title= Electronegativity values from thermochemical data
 |doi= 10.1016/0022-1902(61)80142-5}}</ref> to 2.20. It is also necessary to decide which of the two elements is the more electronegative (equivalent to choosing one of the two possible signs for the square root). This is usually done using "chemical intuition": in the above example, [[hydrogen bromide]] dissolves in water to form H<sup>+</sup> and Br<sup>−</sup> ions, so it may be assumed that bromine is more electronegative than hydrogen. However, in principle, since the same electronegativities should be obtained for any two bonding compounds, the data are in fact overdetermined, and the signs are unique once a reference point has been fixed (usually, for H or F).

To calculate Pauling electronegativity for an element, it is necessary to have data on the dissociation energies of at least two types of covalent bonds formed by that element. A. L. Allred updated Pauling's original values in 1961 to take account of the greater availability of thermodynamic data,<ref name="Allred"/> and it is these "revised Pauling" values of the electronegativity that are most often used.

The essential point of Pauling electronegativity is that there is an underlying, quite accurate, semi-empirical formula for dissociation energies, namely:
<math display="block">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}</math>
or sometimes, a more accurate fit
<math display="block">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}</math>

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 approximate, 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 in fact relatively 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 [[standard enthalpy of formation|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.

{{Periodic table (electronegativities)}}