Superposed atoms

Fig. 11. The Iso-, state of the H2+ system, (a) Binding charge. The dashed line shows the binding charge obtained from the superposed atomic density. The SA value is 0.5 e. (b) CEDs. Positive value means the inside of the nucleus. The SA values are 0.0,0.75, and -0.75 for the total, binding, and antibinding CEDs, respectively. (Reproduced from Koga et al., 1980.)...

Figure 10 (a) Schematic structure of the molecule Ni(C4N4H2)2 and (b)-(d) difference electron densities obtained by subtracting superposed atomic densities from the molecular density, (b), (c), and (d) were obtained from experiment, from Hartree-Fock calculations, andfrom LDA calculations, respectively (Reproduced by permission of the American Chemical Society from ref. 56)... 

Elastic interaction occurs when the displacement fields from steps substantially superpose. Atoms located in the vicinity of steps tend to relax stronger compared to those farther away. The resulting displacements or lattice distortions decay with increasing distance perpendicular to the steps. Atoms situated in between two steps experience two opposite forces and cannot fully relax to an energetically more favorable position as would be the case with quasiisolated steps. The line dipoles at steps are due to Smoluchowski smoothing [160] and interact electronically. Only dipole components perpendicular to the vicinal surface lead to repulsion whereas parallel components would lead to attractive interaction. The dipole-dipole interaction seems to be weaker than the elastic one. For instance, steps on vicinal Ag(lll) have weak dipoles as was shown in a theoretical study [161]. Entropic interaction is due to the condition that steps may not cross and leads to an effective repulsive potential, the weakest interaction type. This contribution is always present and results from the assumption that cavities under the surface are unstable. Experiments and theory investigating steps on surfaces were recently reviewed [162]. 

For highly excited states, we let an electron in the form of a wave packet be accepted in a rather weU-delined region far from the nucleus. For t = 0, we need to superpose atomic orbitals with aU kinds of n, f, and m quantum numbers. For t > 0, an electron will move almost classically if the principal quantum number is high, at least for some time. The limit motion is planetary motion according to Newton s equations. 

Fig. 32 Nanoring formed from Aui 2W similar to the construction of AU21W2 as shown in the upper parts. The lower part shows the nanoring as well as the difference in the electron density between that of the nanoring and that of the superposed atoms. Reproduced with permission of American Chemical Society from ref 107. 

Figure 15 The difference, Ao (r), between the radial charge density of the crystal, o(,yaai(r), and the superposed atomic radial charge density, O(uperposed(r), in the muffin-tin sphere t plotted versus the distance r from the center of the muffin-tin sphere t in atomic units [see Eq. (5)]. Full curves, nonmetal sphere broken curves, metal sphere. Rx and R are the radii of the respective muffin-tin spheres around the non-metal atom X (X = C, N) and around the metal atom M (M = T, V), respectively. (From Refs. 18 and 19. Reproduced with the permission of the Berichte der Bunsen-GeseUschaft, Berichte der Bunsen-Gesellschaft.)...

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