= Pauling electronegativity
{c}
{title2=$\chi_{\rm P}$}
= Pauling scale
{c}
{synonym}
<Pauling electronegativity> is a relative, <dimensionless> scale motivated by <bond-dissociation energies>. The interesting observation is that a <chemical bond> between unlike <chemical atoms> can be stronger than a simple baseline inferred from the corresponding like-atom <chemical bonds>. An empirical excess <energy> can then be associated with an <electronegativity> difference. The 1932 paper <The Nature of the Chemical Bond. IV. The Energy of Single Bonds and the Relative Electronegativity of Atoms> built such a map; its original coordinates used <hydrogen> as zero, so those coordinates should not be mistaken for the modern tabulated <Pauling electronegativities>.<The Nature of the Chemical Bond. IV. The Energy of Single Bonds and the Relative Electronegativity of Atoms by Linus Pauling>[pp. 3576–3578, equation (1), Table III: H 0.00, Cl 0.94]{ref}
One arithmetic-baseline version of the <Pauling scale> relation is
$$
\Delta_D=D_{AB}-\frac{D_{AA}+D_{BB}}{2},\qquad
\left|\chi_{\rm P}(A)-\chi_{\rm P}(B)\right|\approx\sqrt{\frac{\Delta_D}{1\,\mathrm{eV}}}.
$$
Here $D_{AB}$, $D_{AA}$ and $D_{BB}$ are consistently defined <bond-dissociation energies> per <molecule>, and the <arithmetic mean> is the chosen baseline. With molar <energies> instead, write $\sqrt{\Delta_D/(96.485\,\mathrm{kJ\,mol^{-1}})}$, approximately $0.102\sqrt{\Delta_D/(1\,\mathrm{kJ\,mol^{-1}})}$. The denominator makes the result <dimensionless>; the factor $0.102$ is not a unit-independent magic constant. This is an empirical relation with a specified baseline, not a definition valid for every <chemical bond>.<Energy Electronegativity and Chemical Bonding by Stepan S. Batsanov>[§1 equation (1), coefficients for eV, kcal/mol and kJ/mol; §2.2, dependence on other bond properties]{ref}
For an explicitly synthetic example, suppose $D_{AA}=D_{BB}=300\,\mathrm{kJ\,mol^{-1}}$ and $D_{AB}=396.485\,\mathrm{kJ\,mol^{-1}}$ with the same temperature and dissociation convention. Then $\Delta_D=96.485\,\mathrm{kJ\,mol^{-1}}$ and the model gives an <electronegativity> difference of $1$. Replacing $D_{AB}$ by $300\,\mathrm{kJ\,mol^{-1}}$ gives zero; a negative excess would make this real square-root model inapplicable, not produce a negative <electronegativity> difference. These invented inputs illustrate the formula and are not measurements of named <chemical substances>.
Only differences appear, so adding the same constant to every <Pauling electronegativity> leaves this relation unchanged. A reference value must fix the origin. The <bond-dissociation energies> alone also do not tell which endpoint attracts <electron density> more strongly, because interchanging $A$ and $B$ leaves the formula unchanged. Chemical comparisons fix that direction. Thus <Pauling electronegativity> is useful as a compact ordering, while the underlying measured <energies> and approximations remain essential.
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