Hybrid orbitals for

In most metals the electron behaves as a particle having approximately the same mass as the electron in free space. In the Group IV semiconductors, dris is usually not the case, and the effective mass of electrons can be substantially different from that of the electron in free space. The electronic sUmcture of Si and Ge utilizes hybrid orbitals for all of the valence elecU ons and all electron spins are paired within this structure. Electrons may be drermally separated from the elecU on population in dris bond structure, which is given the name the valence band, and become conduction elecU ons, creating at dre same time... 

Self-Test 3.7B Suggest a structure in terms of hybrid orbitals for each carbon atom in ethyne, C2H2. 

In triaziridine 23, the o-relaxation is appreciable due to the lone pair effect (Sect. 2.1.4) as is the case with triphosphirane 14 which has almost the same SE as tetra-phosphetane 15. Triaziridine 23 has lower SE (31.8 kcal moF ) than tetraazetidine 24 (SE = 33.4 kcal moF ) (Scheme 12) [12]. Lone pairs on nitrogen atoms have high s-character. The hybrid orbitals for the N-N bonds have lower s-character (sp ) in 23 than that (sp ) in triazane 25 [12]. The geminal a-a interaction is less antibonding in 23 (IBP, = -0.004) than in 25 (IBP. = -0.014). The geminal... 

In general, lone pairs occupy hybridized orbitals. For example, consider the lone pair on the nitrogen atom in the following compound ... 

Any hybrid orbital is named from the atomic valence orbitals from which It Is constmcted. To match the geometry of methane, we need four orbitals that point at the comers of a tetrahedron. We construct this set from one s orbital and three p orbitals, so the hybrids are called s p hybrid orbitais. Figure 10-8a shows the detailed shape of an s p hybrid orbital. For the sake of convenience and to keep our figures as uncluttered as possible, we use the stylized view of hybrid orbitals shown in Figure 10-8Z). In this representation, we omit the small backside lobe, and we slim down the orbital in order to show several orbitals around an atom. Figure 10-8c shows a stylized view of an s p hybridized atom. This part of the figure shows that all four s p hybrids have the same shape, but each points to a different comer of a regular tetrahedron. 

Constmct the a bonding framework using hybrid orbitals for inner atoms and atomic orbitals for outer atoms, as described in Section 10-1. Any hybrid orbitals not used to form a bonds contain lone pairs of electrons. 

Ozone, which has 18 valehce electrohs, exemplifies bent molecules. Another example is the hitrite ahioh, the subject of Extra Practice Exercise. The bohdihg of NO2 can be represented using s p hybrid orbitals for the inner nitrogen atom and one set of delocalized n orbitals. 

The coefficients must be normalized, i.e. af + pf + yf + 8f = 1. Their values determine the preferential directions of the hybrid orbitals. For example, the functions... 

For example, we can construct hi and h2, two hybrid orbitals for describing the bonds in the water molecule, by taking the two combinations... 

When the number of electrons in the d orbitals is four, as in the case of Mn3+, there exists more than one possible type of hybrid orbital. For example, if the electrons remain unpaired in the d orbitals, there is only one orbital in the set that is empty. As a result, if an octahedral complex is formed, making... 

We now use a Pauling-like approach to show how hybrid orbitals for a variety of combinations of s, p, and d orbitals may be formulated.10 We assume that the radial dependences of the s, p, d orbitals are similar so that they can be neglected. The angular parts of the orbital wavefunctions are given by the following expressions (in the usual spherical coordinates 9, ) ... 

Hybridization concepts can also be applied to atoms other than carbon. Here, we look at how we can understand the properties of oxygen and nitrogen compounds by considering hybrid orbitals for these atoms. 

A pioneering work for their qualitative understanding was the covalent treatment of the 5f-6d hybridization due to FriedeP Like p orbitals, f orbital are antisymmetric (il)(— R) = — tl)(R)) thus by linear combination with symmetric d orbitals, they give rise to highly directive hybrid orbitals (like s-p hybrids). Thus in Pa, U, Np and Pu metals each atom has four nearest neighbours more or less coplanar and at 90°. Let s take the example of a-U and put the nearest neighbours along the x and z axes. Necessary hybrid orbitals for such positions are ... 

In valence bond theory, the strength of the bond depends on the degree of overlap. The greater the overlap, the stronger the bond. One feature of the bond valence theory is that the orbitals may combine to produce hybrid orbitals. For example, an s and three p orbital may combine to form four sp hybrid orbitals. 

In equations (1.4) and (1.5), the sums run over the number of hybridized orbitals. For any pair of hybrid orbitals, A, and hj, the following relationship exists ... 

In Table 11-3.1 hybrid orbitals for a selection of geometries are tabulated. 

So far we have only considered which AOs are required for the construction of hybrid orbitals of the appropriate symmetry. We now will show how we can obtain explicit mathematical expressions for the hybrid orbitals which will allow us to see exactly how much each AO contributes. Though hybrid orbitals are most frequently used in qualitative discussions of bonding, they do have their quantitative use when one carries out an exact MO calculation and when one deals with coordination compounds, where it is often necessary to use hybrid orbitals for evaluating overlap integrals which are often related to bond strengths in these situations the explicit expressions are required. 

Hybrid orbitals for nickel tet-racarbonyi have been discussed by G. Giacometti, J. Chem. Phys. 23, 2068 (1955), who reaches the conclusion that with dtp hybrid orbitals the bondB can have as much as 75 percent of double-bond character. 

What s, p, and d orbitals of a central atom can be used to form a hybrid orbitals for an AB8 molecule having a square antiprism structure ... 

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