Mulliken electronegativity (${\chi }_{\mathrm{M}}$)

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 isThe free electron's energy is the zero reference. Here $I$ is the ionization energy and $A_{\mathrm{ea}}$ is the electron affinity, positive for exothermic attachment. If attachment is instead tabulated as the signed energy change $\Delta E_{\mathrm{attach}}=E(X^{-})-E(X)$, the same expression is $(I-\Delta E_{\mathrm{attach}})/2$. 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.^[ref]

Mulliken electronegativity has energy units before any additional rescaling. With $I$ and $A_{\mathrm{ea}}$ in electronvolts per chemical atom, ${\chi }_{\mathrm{M}}$ is in electronvolts; with both in $\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, it is a molar energy. For hydrogen, the RSC ground-state inputs are $I=1312.05$ and $A_{\mathrm{ea}}=72.769\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, giving ${\chi }_{\mathrm{M}}=692.4095\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}\approx 7.176\mathrm{eV}$ per chemical atom. For chlorine, $I=1251.186$ and $A_{\mathrm{ea}}=348.575\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ give $799.8805\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}\approx 8.290\mathrm{eV}$. These are calculated ground-state Mulliken electronegativities, not the RSC's tabulated Pauling electronegativities.^[ref][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.

Electron affinity measures how strongly an isolated neutral species binds an additional electron. In the spectroscopic convention used here, it is the positive energy required to detach that electron from a bound anion. With the free electron at rest assigned zero energy,The quantum states of $X$ and $X^{-}$ must be specified, usually their ground states. Positive $A_{\mathrm{ea}}$ means that attachment lowers the energy; a signed attachment energy is then negative. This convention agrees with the IUPAC definition and with the atomic tables used for Mulliken electronegativity.^[ref]

For chlorine, a published photodetachment threshold is $A_{\mathrm{ea}}/(hc)=29138.59(22)\mathrm{c}{\mathrm{m}}^{-1}$, approximately $3.612725\mathrm{eV}$ per chemical atom. Here $h$ is the Planck constant, $c$ the speed of light, and the inverse-length unit expresses an energy through a spectroscopic wavenumber. The parentheses give the reported uncertainty in the last digits, not a range of possible sign conventions.^[ref]

An electron affinity is neither an electronegativity nor a lattice energy. The first describes a specified isolated-species energy difference, electronegativity compares attraction for electron density in a chemical bond, and lattice energy refers to an entire ionic crystal and separated gaseous ions. A stable anion can therefore help explain ionic bonding without describing the full energy balance for making a salt.

An electron attachment enthalpy is the signed molar enthalpy change for a stated attachment reaction,For favourable attachment such as chlorine's first attachment, the electron attachment enthalpy is negative. Its leading isolated-ground-state energy contribution is $-N_{\mathrm{A}}{A}_{\mathrm{ea}}$, where $N_{\mathrm{A}}$ is the Avogadro constant. At finite temperature, consistent thermal populations, translational contributions and the $pV$ term in enthalpy must also be included, together with the same gaseous-electron reference used in the corresponding ionization energy term. Consequently a measured spectroscopic electron affinity is not automatically an exact $298.15\mathrm{K}$ attachment enthalpy with a minus sign. A Born-Haber cycle must use compatible enthalpies throughout.

Photodetachment removes an electron from an anion using a photon. For chlorine, the reaction is ${\mathrm{Cl}}^{-}(g)+\gamma ⟶\mathrm{Cl}(g)+e^{-}$. Measuring the minimum photon energy for the specified final quantum state gives a photodetachment threshold and hence an electron affinity.

In the published chlorine experiment, negative ions were accelerated and mass-selected, then overlapped with a tunable laser beam. A downstream electric field deflected charged ions; neutral chemical atoms continued to a plate, whose secondary electrons were counted. Scanning the laser frequency produced an onset in this neutral-atom signal. The apparatus therefore inferred an electron affinity from a threshold, rather than measuring the heat of attachment.^[ref]

Reversing the laser direction and averaging the two thresholds corrected the first-order Doppler shift. A Fabry–Pérot interferometer and reference spectral lines calibrated the frequency. Finite laser bandwidth, unresolved quantum state splitting and shifts of the calibration lines limited the inference; the authors included these effects in fitting and the error estimate. The level diagram shows only the extracted gap, not a measured signal curve.^[ref]

An electronvolt is $1.602176634\times 10^{-19}\mathrm{J}$. One electronvolt per particle corresponds to approximately $96.485\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$.^[ref]