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A new method to derive electronegativity from resonant inelastic x-ray scattering
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Image of FIG. 1.
FIG. 1.

Left panel: Schematic of the polarized-x-ray emission spectrometer used for RIXS measurements. Inset: Simplified representation of the RIXS process studied. (See text for details.) Right panel (upper): Experimental and calculated x-ray absortpion spectra of HCl.37 In solid lines (dashed line) are indicated the 2p 3/2 and 2p 1/2 spin-orbit states where the 2p hole is in the Cl 2p xy (Cl 2p z ) atomic orbital. Right panel (lower): Theoretical KL RIXS spectra obtained at θ = 0° (left) and θ = 90° (right) at the top of the resonance, compared to experiment. Cl 2p z components of interest are in grey colour.

Image of FIG. 2.
FIG. 2.

Pictorial description of the relationship between absolute electronegativities in free atoms/radicals and the electronegativity scale derived in the present work. G1 and G2 refer to different geometries of the same radical.

Image of FIG. 3.
FIG. 3.

Calculated Hartree-Fock Mulliken charge, Q Cl (in red), in the ground state and electronic population (Pop(Cl) LUMO ) on chlorine in the core-excited state (in blue) vs % spin-orbit population.

Image of FIG. 4.
FIG. 4.

Pictorial description of the relationship between various chemical properties: (i) electronegativity scale derived in the present work; (ii) singlet-triplet exchange (STE) interactions and LUMO electron-density surfaces (0.04e/Å3) for 2p −1LUMO1 core-excited states of three different Cl-R molecules; (iii) calculated polarized-RIXS KL spectra (θ = 0) for NaCl, CF3Cl, and Cl-F from Eq. (27). Comparison is made with the experimental spectrum for CF3Cl. Incoming photon bandwidth, γ p = 0.2 eV, and spectrometer resolution, γ s = 0.25 eV, as half width half maximum (HWHM) have been used for the calculations.

Image of FIG. 5.
FIG. 5.

Experimental 2p 3/2/2p 1/2 spin-orbit intensity ratios (circles) from CF3Cl KL RIXS spectra as a function of the angle θ between the polarization vectors of the incident and scattered photons, compared to calculated values (solid curve). Insets: Theoretical KL RIXS spectra obtained at θ = 0° (left) and θ = 90° (right), compared to experiment.

Image of FIG. 6.
FIG. 6.

Atomic Cl 2p z populations as a function of the singlet-triplet exchange energy ΔST.

Image of FIG. 7.
FIG. 7.

Pauling electronegativities versus present RIXS electronegativities. The linear fit gives χ(Pauling) = 1.0446× χ(RIXS)+0.061.

Image of FIG. 8.
FIG. 8.

Pauling electronegativities versus Pearson electronegativities for atoms. Calculated electronegativities of CH3 for planar (free radical) configuration and umbrella geometry in CH3Cl. Linear fit between χ(Pauling) against χ(Pearson) for several atomic species have been considered.


Generic image for table
Table I.

Calculated (this work) and experimental36,37,39,40 populations (in %) of the singlet Cl LUMO1 component in the Cl LUMO1 spin-orbit state. Hartree-Fock singlet-triplet energy differences (ΔST), molecular-field splittings (MF) (E2p xy -E2p z ) in the ground state (GS) and Mulliken Cl elect. pop. Pop(Cl) LUMO on the LUMO in the Cl LUMO1 final state. Mulliken Q Cl and on chlorine in GS and LUMO1 core-excited states.

Generic image for table
Table II.

Calculated IP, EA, electronegativity, and hardness (η), in eV, at the equilibrium geometries of the t-C4 H 9, SiH3, and CH3 free radicals, compared to their frozen geometries in t-C4 H 9Cl, SiH3Cl, and CH3Cl molecules. Charges on the chlorine centers (Q) are calculated using Eq. (14), χ, and η of Cl (8.31 eV, 4.70 eV). The Coulombic interaction (J ClG ) is calculated by considering the distance between chlorine and the center of mass of the group G. Experimental values are shown in parentheses.5

Generic image for table
Table III.

Calculated net charges on Cl using the Rappe-Goddard (RG) charge-equilibration model,17 compared with present HF/DFT-B3LYP/Mulliken charges for t-C(1)-(C(2)H3)3Cl, SiH3Cl, and CH3Cl.

Generic image for table
Table IV.

Calculated –ε2p KT (in eV) within the Frozen-core approximation (Koopmans Theorem (KT)) as derived from HF ground-state calculations. Calculated ΔSCF core-binding energy (in eV). Calculated ΔV and ΔR (see text, in eV).a CH3Cl is chosen as reference. Calculated Kohn-sham (ΔKS) core binding energies with B3LYP50,51 exchange-correlation functional. Δ corr =B3LYP/ΔKS – ΔSCF (in eV). Measured Cl 2p3/2 core binding energies from Ref. 26. DFT/B3LYP valence-shell electronic transfer (CT) from the ligand to the core-ionized(excited) chlorine. Calculated LUMO (Mulliken) electronic population of chlorine () in the core-excited state.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A new method to derive electronegativity from resonant inelastic x-ray scattering