Pauling's formula, from the electronegativity difference alone
The only input that matters is ΔEN, the difference in electronegativity between the two bonded atoms. Pauling fit this curve to hundreds of measured dipole moments in 1935, and it is still the standard classroom method.
ΔEN is just |ENA − ENB|. A difference of 0 gives 0% (a pure covalent bond); the value rises steeply and then flattens, approaching 100% but never reaching it.
Electronegativity difference → percent ionic
| ΔEN | % ionic (Pauling) | Bond type |
|---|---|---|
| 0.0 | 0% | Nonpolar covalent |
| 0.5 | 6% | Nonpolar / weakly polar |
| 1.0 | 22% | Polar covalent |
| 1.5 | 43% | Polar covalent |
| 1.7 | 51% | Ionic threshold |
| 2.0 | 63% | Ionic |
| 2.5 | 79% | Ionic |
| 3.0 | 89% | Ionic |
The 50% mark falls near ΔEN = 1.7, which is why that value is the usual dividing line between polar covalent and ionic.
Common bonds, and why the formula overstates
| Bond | ΔEN | Pauling % | Measured % |
|---|---|---|---|
| H–H | 0.00 | 0% | 0% |
| C–O | 0.89 | 18% | ~25% |
| H–Cl | 0.96 | 20% | ~18% |
| Na–Cl | 2.10 | 67% | ~67% |
| Cs–F | 3.19 | 92% | ~95% |
Two things people get wrong: ΔEN > 2 does not mean 100% ionic (NaCl is only ~67%), and a polar bond does not make a polar molecule — CO&sub2; has two polar C=O bonds but is nonpolar overall because they cancel by symmetry.
Common questions
How do you calculate percent ionic character?
Take the electronegativity difference between the two atoms, square it, multiply by 0.25, and use it in Pauling's formula: percent ionic = 100 times (1 minus e to the power of minus 0.25 times the difference squared). For HCl the difference is 0.96, which gives about 19 percent.
What electronegativity difference counts as an ionic bond?
The common rule of thumb is that a difference above roughly 1.7 to 2.0 is treated as ionic, which corresponds to more than about 50 percent ionic character. Below 0.5 the bond is essentially nonpolar covalent, and in between it is polar covalent.
Is any bond 100 percent ionic?
No real bond reaches 100 percent. Even sodium chloride, a textbook ionic compound, is only about 67 percent ionic by dipole measurement. Some electron sharing always remains, so the calculated value approaches but never hits 100.
