= Mulliken electronegativity
{c}
{title2=$\chi_{\rm M}$}
= Mulliken scale
{c}
{synonym}
<Mulliken electronegativity> uses both the cost of removing an <Electron> and the <energy> released by accepting an <Electron>. For specified isolated-atom states, the common ground-state convention is
$$
\chi_{\rm M}=\frac{I+A_{\rm ea}}{2},\qquad
I=E(X^+)-E(X),\qquad A_{\rm ea}=E(X)-E(X^-).
$$
The free <Electron>'s <energy> is the zero reference. Here $I$ is the <ionization energy> and $A_{\rm ea}$ is the <electron affinity>, positive for exothermic attachment. If attachment is instead tabulated as the signed <energy> change $\Delta E_{\rm attach}=E(X^-)-E(X)$, the same expression is $(I-\Delta E_{\rm attach})/2$. Stating the sign convention prevents adding the wrong quantities. The 1934 original treated suitable valence states, which are not automatically the ground states used in this example.<A New Electroaffinity Scale; Together with Data on Valence States and on Valence Ionization Potentials and Electron Affinities by Robert S. Mulliken>{ref}
<Mulliken electronegativity> has <energy> units before any additional rescaling. With $I$ and $A_{\rm ea}$ in <electronvolts> per <chemical atom>, $\chi_{\rm M}$ is in <electronvolts>; with both in $\mathrm{kJ\,mol^{-1}}$, it is a molar <energy>. For <hydrogen>, the RSC ground-state inputs are $I=1312.05$ and $A_{\rm ea}=72.769\,\mathrm{kJ\,mol^{-1}}$, giving $\chi_{\rm M}=692.4095\,\mathrm{kJ\,mol^{-1}}\approx7.176\,\mathrm{eV}$ per <chemical atom>. For <chlorine>, $I=1251.186$ and $A_{\rm ea}=348.575\,\mathrm{kJ\,mol^{-1}}$ give $799.8805\,\mathrm{kJ\,mol^{-1}}\approx8.290\,\mathrm{eV}$. These are calculated ground-state <Mulliken electronegativities>, not the RSC's tabulated <Pauling electronegativities>.<Periodic Table by Royal Society of Chemistry/Hydrogen — Element information, properties and uses>{ref}<Periodic Table by Royal Society of Chemistry/Chlorine — Element information, properties and uses>{ref}
Both schemes place <chlorine> above <hydrogen> here, but their numerical differences cannot be subtracted from one another or equated. Dividing a molar <Mulliken electronegativity> by an <energy> conversion factor changes units; it does not transform it into a <Pauling electronegativity>. A further empirical mapping would require its own calibration and stated domain.
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