Geometry of the Kevan model of the solvated electron (red: oxygen, white: hydrogen, dark grey: ghost atom representing the localized electron). A sketch of the two possible electronic states for the model system, with the electron localized either in the void at the center of the water cluster (left) or on the isolated atom (right) is also shown.
Sketch of the expected fractional-charge plots for (a) an isolated atom X (top left), (b) the Kevan structure (bottom left), and (c) the complex (right). q X corresponds to the excess charge on the isolated atom. Note that we define the excess charge on the Kevan structure as 1 − q X , even if the heteroatom is not present. This makes the overall charge of the system −q X for the atom, −1 + q X for the Kevan structure, and constant −1 at any q X for the complex. For a given value of q X the energies in plots (a) and (b) add to give the energy in plot (c).
Plot of the fully-numerical LSDA electronic energy as a function of fractional charge for the Kevan structure. These results are compared with the cubic interpolation, which depends only on the electronic energies and orbital eigenvalues using integer occupations.
Excess charge on the isolated atom, obtained with each of the four DFT methods, as a function of their electron affinity, relative to that of the Kevan structure.
Plot of the electronic energy as a function of fractional charge for the aluminium atom, Kevan structure, and sulphur atom (a)–(c). Also shown are plots of the electronic energy as a function of fractional charge transfer between the isolated aluminium atom (d) or sulphur atom (e) and the water cluster. q X = 0 indicates a neutral atom and anionic cluster, while q X = 1 indicates an atomic anion and neutral cluster. Fractional-charge energies were obtained using cubic interpolation.
Plots of the Kevan-structure electron density, in one of the planes bisecting the octahedron of water molecules, using the selected methods.
NCI plots for the water cluster, using an s = 0.5 a.u. isosurface. The plots are: (a) aluminium atom with LC-ωPBE, q X = 0; (b) aluminium atom with BHandHLYP, q X = 0.23; (c) phosphorus atom with BHandHLYP, q X = 0.39; (d) silicon atom with BHandHLYP, q X = 0.53; (e) sulphur atom with BHandHLYP, q X = 0.75; (f) sulphur atom with LC-ωPBE, q X = 1.
NCI isosurface (s = 0.5 a.u., left) and charge distribution (right) for the bis(15-crown-5)-cesium electride. Bader charges have been color-mapped onto the atoms (red: positive, blue: negative, the colour-scale limits are [− 1, 1]).
Calculated atomic charges for the Kevan model system a function of the heteroatom X. The electron affinities of each heteroatom, relative to that of the Kevan structure (ΔEA in eV from LC-ωPBE and used as the x axis in Figure 4 ) are also shown. The charge-transfer energy errors (E ct ) for dissociation into minimum-energy fragments, in kcal/mol, are also reported for each functional.
Bader charge analysis for the Kevan structure, showing the total charge contained within the void and the density at the resulting non-nuclear maxima.
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