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Localized electron model

The localized-electron model or the ligand-field approach is essentially the same as the Heitler-London theory for the hydrogen molecule. The model assumes that a crystal is composed of an assembly of independent ions fixed at their lattice sites and that overlap of atomic orbitals is small. When interatomic interactions are weak, intraatomic exchange (Hund s rule splitting) and electron-phonon interactions favour the localized behaviour of electrons. This increases the relaxation time of a charge carrier from about 10 s in an ordinary metal to 10 s, which is the order of time required for a lattice vibration in a polar crystal. [Pg.287]

Localized d or/electrons retain their one-atom manifolds, except that states arising from different d or f are split by crystal field and spin-orbit coupling. Multiplet splittings due to spin-orbit coupling are larger than crystal-field splittings of Af levels the converse is the case for 3d levels. The difference in energy between d (f) and d (/ 1) manifolds corresponds to the amount of free atom U that is decreased due to interatomic interaction in the solid. [Pg.287]

The localized-electron model has the advantage that it can predict the insulating [Pg.287]

The need to use a much more complete Hamiltonian was discussed in great detail by several authors (see [28] and references therein). In some cases, the problem includes a large number of independent parameters because all ion states are taken into account [29]. Actually, it seems always possible to reduce their number by some convenient approximations or local symmetry considerations. In other cases, the effective Hamiltonian is determined within the framework of the strong crystal-field scheme [30-32]. [Pg.59]

The last two terms are relative to the anisotropy effects on sites i and j, and so can be regarded as extra-contributions to the crystal-field the first one is the exchange interaction term whose the parameter is usually written as  [Pg.59]

This way, we take into account the intraionic transfers between degenerate states as well as interionic transfers. [Pg.59]

A similar effect arises when a half filled orbital overlaps a completely filled one. In this case, one has to consider the intermediate spin configuration of the ion which emits the electron. The metal-metal interaction is then introduced from the Anderson Hamiltonian [26]  [Pg.60]

within Anderson s framework, singly polarized states are involved together with unpolarized ones, the effective exchange Hamiltonian can be written as [Pg.60]


The physical description of strongly pressure dependent magnetic properties is the object of considerable study. Edwards and Bartel [74E01] have performed the more recent physical evaluation of strong pressure and composition dependence of magnetization in their work on cobalt and manganese substituted invars. Their work contrasts models based on a localized-electron model with a modified Zener model in which both localized- and itinerant-electron effects are incorporated in a unified model. Their work favors the latter model. [Pg.122]

The Lewis model of the chemical bond assumes that each bonding electron pair is located between the two bonded atoms—it is a localized electron model. However, we know from the wave-particle duality of the electron (Sections 1.5-1.7) that the location of an electron in an atom cannot be described in terms of a precise position, but only in terms of the probability of finding it somewhere in a region of... [Pg.229]

Several models based on the electronic properties of mixtures of metals and molten salts have been proposed, i.e., the localized electron model, the free electron model and the band model. A model which gives a good description of the properties of alkali metal-alkali halide mixtures at low metal concentrations is the model of trapped electrons or the so-called model of F-centers [76,77], An F-center may be regarded as a localized state, and the electron is then trapped in a cavity with octahedral coordination with the neighboring cations. On average, the F-center may be considered as an M65+ species. [Pg.490]

Describing a Molecule with the Localized Electron Model... [Pg.660]

Carbon occurs in the allotropes (different forms) diamond, graphite, and the fullerenes. The fullerenes are molecular solids (see Section 16.6), but diamond and graphite are typically network solids. In diamond, the hardest naturally occurring substance, each carbon atom is surrounded by a tetrahedral arrangement of other carbon atoms, as shown in Fig. 16.26(a). This structure is stabilized by covalent bonds, which, in terms of the localized electron model, are formed by the overlap of sp3 hybridized atomic orbitals on each carbon atom. [Pg.785]

Hydrogen bridges between the beryllium atoms produce a polymeric structure for BeH2, as shown in Fig. 18.6. The localized electron model describes this bonding by assuming that only one electron pair is available to bind each Be—H—Be cluster. This is called a three-center bond, since one electron pair is shared among three atoms. Three-center bonds have also been postulated to explain the bonding in other electron-deficient compounds (compounds where there are fewer electron pairs than bonds), such as the boron hydrides (see Section 18.5). [Pg.877]

Compare the description of the localized electron model (Lewis structure) with that of the molecular orbital model for the bonding in NO, NO+, and NO-. Account for any discrepancies between the two models. [Pg.925]

By this point in your study of chemistry, you no doubt recognize that the localized electron model, although very simple, is a very useful model for describing the bonding in molecules. Recall that a central feature of the model is the formation of hybrid atomic orbitals that are used for sharing electron pairs to form cr bonds between atoms. This same model can be used to account for the bonding in complex ions, but there are two important points to keep in mind. [Pg.955]

Although the localized electron model can account in a general way for metal-ligand bonds, it is rarely used today because it cannot predict important properties of complex ions, such as magnetism and color. Thus we will not pursue the model any further. [Pg.957]

The main reason that the localized electron model cannot fully account for the properties of complex ions is that in its simplest form it gives no information about how the energies of the d orbitals are affected by complex ion formation. This is critical because, as we will see, the color and magnetism of complex ions result from changes in the energies of the metal ion d orbitals caused by the metal-ligand interactions. [Pg.957]

The simplest member of the saturated hydrocarbons, which are also called the alkanes, is methane (CH4). As discussed in Section 14.1, methane has a tetrahedral structure and can be described in terms of a carbon atom using an sp-J hybrid set of orbitals to bond to the four hydrogen atoms (see Fig. 22.1). The next alkane, the one containing two carbon atoms, is ethane (C2H6), as shown in Fig. 22.2. Each carbon in ethane is surrounded by four atoms and thus adopts a tetrahedral arrangement and sp3 hybridization, as predicted by the localized electron model. [Pg.1013]

A special class of cyclic unsaturated hydrocarbons is known as the aromatic hydrocarbons. The simplest of these is benzene (C6H6), which has a planar ring structure, as shown in Fig. 22.11(a). In the localized electron model of the bonding in benzene, resonance structures of the type shown in Fig. 22.11(b) are used to account for the known equivalence of all the carbon-carbon bonds. But as we discussed in Section 14.5, the best description of the benzene molecule assumes that sp2 hybrid orbitals on each carbon are used to form the C—C and C—H a bonds, while the remaining 2p orbital on each carbon is used to form 77 molecular orbitals. The delocalization of these 1r electrons is usually indicated by a circle inside the ring [Fig. 22.11(c)]. [Pg.1024]

Alternatively, the process of intrinsic electronic disordering can be represented within the framework of localized electrons model, for example ... [Pg.48]


See other pages where Localized electron model is mentioned: [Pg.99]    [Pg.287]    [Pg.290]    [Pg.81]    [Pg.163]    [Pg.279]    [Pg.10]    [Pg.650]    [Pg.650]    [Pg.651]    [Pg.653]    [Pg.655]    [Pg.657]    [Pg.659]    [Pg.661]    [Pg.663]    [Pg.665]    [Pg.786]    [Pg.881]    [Pg.3]    [Pg.4]    [Pg.58]    [Pg.59]   
See also in sourсe #XX -- [ Pg.287 ]




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Electronic models

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