= Experimental inputs to electronegativity scales
The contrast between <Pauling electronegativity> and <Mulliken electronegativity> becomes clearer by following the measurements into the formulas. A <Pauling bond-energy excess> compares three compatible <bond-dissociation energies>; <Mulliken electronegativity> takes the <arithmetic mean> of an <ionization energy> and an <electron affinity>. The former asks how much stronger an unlike-atom <chemical bond> is than a stipulated baseline; the latter combines two different isolated-species <energy> gaps.
Actual readouts precede those model choices. In the <nitrogen dissociation threshold from fragment images>, fitted squared image radii versus assigned excitation <energies> reveal a threshold after accounting for the product <quantum states>. In the <chlorine> <photodetachment threshold> experiment, mass-selected <anions> overlap a tunable <laser>, and neutral-atom counts reveal the onset of <Electron> detachment. Opposite <laser> directions control the <Doppler shift>. That second threshold supplies an <electron affinity>, not an <electronegativity>; the <Mulliken scale> still needs an independent <ionization energy>.<Accurate measurements of the bond dissociation energies of 14N2, 14N15N and 15N2 by Liya Lu and others>[§1, recoil-energy/image-radius equation; §3.2, Figure 5, squared image sizes versus term energies; §3.2, threshold channel assignment]{ref}<Isotope shift in the electron affinity of chlorine by U. Berzinsh and others>[§2, printed pp. 2–4, Figure 1: mass selection and neutral counting; §2.1, direction reversal]{ref}
For an original arithmetic comparison, stipulate isolated-species $I=(8,7,6)\,\mathrm{eV}$ and positive attachment-release $A_{\rm ea}=(0.5,3,3)\,\mathrm{eV}$ for fictitious species $A,B,C$. Their <Mulliken electronegativities> are $(4.25,5,4.5)\,\mathrm{eV}$. The largest <ionization energy> belongs to $A$, while the largest <Mulliken electronegativity> belongs to $B$: accepting an <Electron> matters as well as retaining one. Using signed attachment <energies> $(-0.5,-3,-3)\,\mathrm{eV}$ in $(I-\Delta E_{\rm attach})/2$ gives exactly the same results.
\Image[/electronegativity-scale-inputs-and-orderings.png]
{title=Stipulated inputs to <Mulliken electronegativity> and arithmetic-baseline <Pauling electronegativity>: different <energies>, units and orderings}
{id=image-electronegativity-scale-inputs-and-orderings}
Independently stipulate $D_{RR}=300$ and $D_{XX}=(200,300,450)\,\mathrm{kJ\,mol^{-1}}$ for $X=A,B,C$, with unlike-atom values
$$
D_{RX}=\frac{D_{RR}+D_{XX}}{2}+96.485\,s_X^2\,\mathrm{kJ\,mol^{-1}},\qquad
(s_A,s_B,s_C)=(0.5,1,1.5).
$$
Thus $D_{RX}=(274.12125,396.485,592.09125)\,\mathrm{kJ\,mol^{-1}}$, and the <Pauling scale> differences from $R$ are $(0.5,1,1.5)$. If all three fictitious species are placed above $R$ on that scale, their ordering is $A<B<C$, whereas the stipulated <Mulliken scale> gives $A<C<B$. The <bond-dissociation energies> and isolated-species <energies> were invented independently: this demonstrates what the formulas do, not a measured disagreement for actual <chemical elements>. A unit conversion cannot force these two input models to agree.
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