Interstitial electrons

The graph-theoretical 4N + 2 Hiickel rule analogy with the aromaticity of two-dimensional polygons requires that N = 0 in all the three-dimensional deltahedra. The Jemmis-Schleyer interstitial electron rule [55], originally introduced for nido half-sandwich species, also relates the 4N + 2 Hiickel rule to the delocalized deltahedra directly In this treatment, N is typically 1. 

In order to apply the Jemmis-Schleyer interstitial electron rule, the closo B H 2 dianions (their isoelectronic analogues are treated similarly) are dissected conceptually into two BH caps and one or two constituent (BH) rings. The BH- caps contribute three interstitial electrons each but the rings (which, formally, have zero electrons in the n MOs), contribute none. Hence, six electrons, described as interstitial, link the bonding symmetry-adapted cap and ring orbitals together perfectly. 

The interstitial electron rule can be applied more directly to pyramidal clusters than the graph-theoretical approximation since the latter breaks down by giving zero eigenvalues in Eq. (3) when applied to pyramids. The same ideas as those in the Jemmis-Schleyer method are needed to treat nido pyramids graph-theoretically. 

Aihara introduced the term, three dimensional aromaticity (featured in the tide of his paper), to discuss doso-borane dianions in 1978 [12]. Jemmis and Schleyer applied the term to nido systems with six interstitial electrons [55], but their treatment emphasized the Hiickel analogy, rather than the spherical character. 

Obviously, eight electrons can be accommodated in either the (n -C5H5)M or (q -C5H5)MH bonding scheme. However, the question of whether a six- or eight-electron interstitial electron count is more valid will depend on (a) whether the 2ai MO is occupied, and (b) if the 2aj MO is occupied whether it involves significant ring-M interaction. 

Interstitial electrons have been defined (3b) as electrons which bind ir-bonding ligands to a central atom. 

An alternative approach to aromaticity in some deltahedral boranes is based on the Jemmis and Schleyer [41] interstitial electron rule, originally introduced for nido half-sandwich species. This also relates aromaticity in deltahedral boranes to the 4A + 2 Hiickel mle, but for deltahedral boranes k is typically 0. 

The Jemmis-Schleyer interstitial electron rules [41] are directly applicable to 5-, 6-, and 7-vertex deltahedra (which have one ring), and to 10-, 11-, and 12-vertex deltahedra (which have two rings) but are less obvious for 8- and 9-vertex... 

The host-guest phase of Na is stable at room temperature to 190 GPa, where it transforms to a transparent insulating form, with a hexagonal hP4 structure which calculations suggest contains distinct pockets of interstitial electron density [5]. The same hP4 structure is observed in K at lower pressures [252]. The experimental... 

Unlike metals, the conductivity of semi-conductors and insulators is mainly due to the presence of interstitial electrons and positive holes in the solids due to imperfections. The conductivity of semiconductors and insulators increases with increase in temperature while that of metals decreases. 

Cyclopentadienyllithium. The tt charge in the aromatic cyclopentadienyl anion is distributed equally to all five carbon atoms. A lithium counterion should thus electrostatically favor a central location (Csv, 26a) over the tt face. The same conclusion is reached on the basis of MO considerations (46). The six interstitial electron interactions involving the three cyclopentadienyl TT orbitals and those of corresponding symmetry on lithium (one of these is shown in 26b) also favor structure 26a. 

The Interstitial-Electron Theory has been applied to the structure of metals, alloys and interstitial compounds, to their magnetic and superconducting properties, as well as to a range of surface phenomena. This work has seemingly not come to the attention of the wider scientific community perhaps because it was published only in Japanese journals. It merits wider recognition and a critical evaluation. 

Jemmis, E.D. and Schleyer, P.v.R. (1982) Aromaticity in three dimensions. 4. Influence of orbital compatibility on the geometry and stability of capped annu-lene rings with six interstitial electrons. J. Am. Chem. Soc., 104 (18), 4781-4788. 

Recent ab initio calculations by Schleyer and coworkers indicate that 4 is strongly stabilized by interaction of the empty 3p Si orbital with the Jt-orbital of one allylic double bond [5]. This interaction leads to a pyramidalized silicon center and relatively short Si-C(sp ) distances and stabilizes the cation 4 by 15.4 kcal moT compared to trimethylsilylium (at MP2/6-31G //MP2/ 6-3IG ). The bonding situation in 4 is best described in terms of three dimensional aromaticity with the 3p(Si) and the C=C double bond obeying the 4n+2 interstitial electron" rule. Due to the reduced positive charge at silicon, cations such as 4 should be also less reactive towards nucleophiles. A facile synthetic approach to this novel typ of silyl cation is outlined in Scheme 1. 

Zero-dimensional defects or point defects conclude the list of defect types with Fig. 5.87. Interstitial electrons, electron holes, and excitons (hole-electron combinations of increased energy) are involved in the electrical conduction mechanisms of materials, including conducting polymers. Vacancies and interstitial motifs, of major importance for the explanation of diffusivity and chemical reactivity in ionic crystals, can also be found in copolymers and on co-crystallization with small molecules. Of special importance for the crystal of linear macromolecules is, however, the chain disorder listed in Fig. 5.86 (compare also with Fig. 2.98). The ideal chain packing (a) is only rarely continued along the whole molecule (fuUy extended-chain crystals, see the example of Fig. 5.78). A most common defect is the chain fold (b). Often collected into fold surfaces, but also possible as a larger defect in the crystal interior. Twists, jogs, kinks, and ends are other polymer point defects of interest. 

The description of metal bonding by interstitial electrons was given in 1972. In the interstitial electron model, atoms in metals shed some of their valence electrons, which occupy interstitial holes in the metal ion lattice. Not all of the valence electrons are in the interstices. The more electrons that are removed from the atoms, the more electronegative the cations become and the less they tend to donate further electrons to the interstices. Thus some valence electrons stay behind on the metal ions. How many depends on the atom. 

Figure 2.24. The interstitial spaces in fee and bee lattices (I) The cubic fee lattice with an octahedral and a tetrahedral interstitial site indicated. In the interstitial electron model the valence electrons in fee metals occupy these sites. (II) The cubic bcc lattice a and the types of interstitial sites. The octahedral sites in one of the cube faces are shown as squares in b. The tetrahedral sites (triangles) are closely connected and form rings in the side planes and around the cube ribs as shown in c and d.

The way in which the interstitial electrons act as ligands to split the d-orbitals of the bcc metals chromium, tungsten, and iron is illustrated in Figure 2.25, which shows that the tungsten and chromium ions are spin-paired and the iron ions have a triplet ground state in the ligand field of the interstitial electrons and the other cations. 

Johnson s interstitial electron model has not been used by others, the dominant model for metallic bonding being the band model. Recently the interstitial view was revived because new ab initio calculations (calculated approximations without... 

Figure 2.25. Splitting of the valence electron levels on metal atoms by the ligand field of the interstitial electrons. The magnetic moments on the iron atoms are ferromagnetically coupled.

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