Electronegativity

Electronegativity is the most-used number in chemistry that nobody has ever measured.

Melting points are measured. Ionisation energies are measured. Electronegativity is not: no experiment takes an isolated atom and returns a value, because the quantity is defined only for an atom inside a bond, and an atom inside a bond is not separable from its partner. Every number in every electronegativity table is inferred from something else, and that is why there is more than one table.

Understanding where the numbers come from is what stops the concept being a list to memorise.

Where Pauling's numbers came from

Linus Pauling's 1932 definition — the power of an atom in a molecule to attract electrons to itself — came with a construction, and the construction is a piece of reasoning worth following once.

Pauling argued that if a bond between A and B were purely covalent, its strength ought to be around the average of the A–A and B–B bond strengths. Real A–B bonds are consistently stronger than that average, and he attributed the excess to partial ionic character arising from unequal electron attraction. The bigger the excess, the bigger the difference in electronegativity.

Take hydrogen chloride. The relevant bond energies, in kJ/mol, are H–H 436, Cl–Cl 242 and H–Cl 431.

Predicted purely covalent value = (436 + 242) ÷ 2 = 339
Excess, Δ = 431 − 339 = 92 kJ/mol

Pauling's relation, with Δ in kJ/mol, is:

|χ(Cl) − χ(H)| = 0.102 × √Δ
               = 0.102 × 9.59
               = 0.98

The tabulated values are 3.16 for chlorine and 2.20 for hydrogen, a difference of 0.96. The construction reproduces its own table, which is a good sign that it is a real relationship rather than a curve fit.

Notice what the method can and cannot give you. It produces differences only. To turn differences into a table of absolute values, Pauling fixed one element by hand — hydrogen, at 2.1 in the original work, later adjusted to 2.20. The scale therefore has an arbitrary zero point and no units at all. Electronegativity is dimensionless by construction.

Four scales, four definitions

Pauling's is the scale printed in textbooks, but three other serious constructions are in regular use, and they are answering slightly different questions.

Mulliken (1934) defines electronegativity as the average of an atom's ionisation energy and its electron affinity: how hard it is to take an electron away, averaged with how much it wants another. For fluorine, ionisation energy is 17.42 eV and electron affinity 3.40 eV, giving 10.41 eV. This has two attractions over Pauling's: both inputs are directly measured, and the quantity is defined for a free atom rather than only within a bond. Its drawback is that the result has energy units and must be rescaled by a fitted formula before it can be compared with Pauling values — and different authors have published different rescalings.

Allred–Rochow (1958) computes the electrostatic force that the effective nuclear charge exerts on an electron at the atom's covalent radius. It treats electronegativity as a straightforwardly physical pull, and it correlates well with Pauling's numbers for main-group elements.

Allen (1989) uses the average energy of the valence electrons in a free atom, taken from spectroscopic data. Allen called it "configuration energy" and argued it is the most fundamental of the four, being derived entirely from measured atomic spectra with no molecular input.

These are not competing attempts at the same measurement. They are four different operational definitions of a concept that has no single correct one, and they agree closely enough for most purposes that the disagreements are easy to overlook.

The noble gases the scales cannot agree on

The disagreements are sharpest where they are most interesting.

Pauling's scale traditionally leaves the noble gases blank, because they form so few bonds that there are almost no bond energies to work from. Values have since been assigned to krypton and xenon — around 3.00 and 2.60 — from their fluorides.

Allen's scale, which needs no bonds at all, assigns values to every noble gas and produces a striking result: neon comes out at 4.79 and helium at 4.16, against fluorine's 4.19. On that scale neon is the most electronegative element there is, and helium comes close.

Is that wrong? Not exactly. Neon holds its valence electrons more tightly than fluorine does — its ionisation energy is higher, and Allen's definition is a direct measure of that. What neon does not do is attract electrons in a bond, since it does not form bonds. The two scales disagree because Pauling's question is about behaviour in molecules and Allen's is about behaviour in an atom, and for the noble gases those come apart completely.

Is francium or cesium the least electronegative?

At the other end of the table there is a genuine unresolved question that most sources state with unwarranted confidence.

Pauling assigned francium 0.7 — the lowest value on his scale — and countless tables and quiz answers still list francium as the least electronegative element. But Pauling's 0.7 was an estimate by extrapolation, and it has never been revised, because no francium isotope survives longer than about 22 minutes and no bond energy for a francium compound has ever been measured. Cesium's value, originally also 0.7, was revised upward to 0.79 as better data arrived.

Meanwhile the relativistic effects that raise francium's ionisation energy above cesium's point the same way for electronegativity: francium should hold its outer electron more tightly, and therefore be slightly more electronegative than cesium, not less.

The honest position is that cesium is the least electronegative element for which a reliable value exists, that francium's tabulated 0.7 is an unrevised estimate now believed too low, and that reference works have not caught up. Where a question demands a single answer, give the one your course teaches and know why it is shaky.

The 1.7 cutoff, and hydrogen fluoride

The most common practical use of electronegativity is classifying bonds by the difference between two values, Δχ:

• below about 0.4 — essentially non-polar covalent
• 0.4 to 1.7 — polar covalent
• above 1.7 — ionic

The 1.7 boundary is not arbitrary. Pauling gave a formula for percent ionic character, 100 × (1 − e^(−0.25Δ²)), and at Δ = 1.7 that returns 51% — the point at which a bond is more ionic than covalent.

The rule nonetheless fails, and the failures are instructive rather than marginal.

Hydrogen fluoride has Δχ = 3.98 − 2.20 = 1.78, comfortably over the line. It should be an ionic solid. It is a molecular gas that condenses at 20 °C, unmistakably covalent, and one of the standard counterexamples to the whole scheme.

Sodium hydride goes wrong the other way. Δχ = 2.20 − 0.93 = 1.27 puts it in polar covalent territory, and sodium hydride is a genuinely ionic solid containing H⁻.

The reason is that bonding character depends on more than an electronegativity difference — ion sizes, polarisability and the resulting distortion of electron clouds all matter, which is why ionic bonding has to be argued through lattice energies rather than predicted from a subtraction. Treat Δχ as a first indication, never as a classification.

Carbon's electronegativity depends on what it is doing

The last simplification worth dismantling is that each element has one value.

A carbon atom's pull on electrons depends on its hybridisation. An sp carbon, as in an alkyne, holds shared electrons noticeably more tightly than an sp³ carbon, as in an alkane — roughly 3.3 against 2.5 on scales that resolve it. That difference has a visible consequence: terminal alkynes are weakly acidic and alkanes are not, purely because the sp carbon stabilises the resulting anion.

Oxidation state matters too. Iron in the +3 state is more electronegative than iron in the +2 state, since a more positively charged atom pulls harder on everything nearby.

Groups of atoms behave as units with their own effective values as well. The trifluoromethyl group, CF₃, is strongly electron-withdrawing, which is why it appears in so many pharmaceuticals as a way of tuning a molecule's electron distribution without changing its shape much.

None of this makes the table useless. It means the table lists a typical value for a neutral atom, and that in any situation where the atom's environment is unusual, the tabulated number is an approximation you should expect to be a few tenths out.