F// hybrid orbitals

In cesium chloride, CsC , where each atom is surrounded by eight equivalent neighbors, the orbitals of the elementary cells are built from the four p and p orbitals of chlorine atom, as well as from the eight sp d f hybrid orbitals of the neighboring cesium atoms, pointing toward the chlorine atom. 

The structure of ethylene, C2H4, is shown in Fig. 8-2. The molecule is planar, and each carbon is bonded to two hydrogens and to the other carbon, With three groups attached to each carbon, we use a set of s-f hybrid orbitals for v bonding. 

How are the three s-f" hybrid orbitals needed to form BH3 arranged in space Your intuition may well give you the answer. They are directed so that electrons in them will be as far as possible from one another. The angle between them is 120°, and they are aimed toward the corners of a triangle (Fig. 2.6). An s- carbon and the three atoms surrounding it lie in the same plane. 

The carbon atoms are sp hybridized. The six C—H bonds are formed from the sp hybrid orbitals on C with the Is atomic obitals from the hydrogen atoms. The carbon-carbon bond is formed from an s/f hybrid orbital on each C atom. 

Each carbon of ethylene uses two of its sp hybrid orbitals to form a bonds to two hydrogen atoms, as illustrated in the first par-f of Figure 2.17. The remaining sp orbitals, one on each carbon, overlap along the internuclear- axis to give a a bond connecting the two carbons. 

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The hybrid orbital has cylindrical symmetry, and accordingly the introduction of d character and f character in the axial bond itself does not lead to an interaction dependent on the relative azimuthal orientation of the two groups. 

Atoms in the second row (such as C, N, O, and F) have one s orbital and three p orbitals in the valence shell. These orbitals are usually mixed together to give us hybridized orbitals (sp, sp, and sp). We get these orbitals by mixing the properties of i and p orbitals. What do we mean by mixing ... 

Figure 8.7 Diborane, BaH. (a) Contour map of pb in the plane of the terminal hydrogens, (b) Contour map of pb in the plane of the bridging hydrogens, (c) Calculated geometry, (d) Experimental geometry. (e) Interatomic H-H distances, (f) Ionic model, (g) Resonance structures, (h) Protonated doublebond model, (i) VSEPR domain model showing the two three-center, two-electron bridging domains, (j) Hybrid orbital model.

The orbitals containing the bonding electrons are hybrids formed by the addition of the wave functions of the s-, p-, d-, and f- types (the additions are subject to the normalization and orthogonalization conditions). Formation of the hybrid orbitals occurs in selected symmetric directions and causes the hybrids to extend like arms on the otherwise spherical atoms. These arms overlap with similar arms on other atoms. The greater the overlap, the stronger the bonds (Pauling, 1963). 

The strength of a Lewis acid is a measure of its ability to attract a pair of electrons on a molecule that is behaving as a Lewis base. Fluorine is more electronegative than chlorine, so it appears that three fluorine atoms should withdraw electron density from the boron atom, leaving it more positive. This would also happen to some extent when the peripheral atoms are chlorine, but chlorine is less electronegative than fluorine. On this basis, we would expect BF3 to be a stronger Lewis acid. However, in the BF3 molecule, the boron atom uses sp2 hybrid orbitals, which leaves one empty 2p orbital that is perpendicular to the plane of the molecule. The fluorine atoms have filled 2p orbitals that can overlap with the empty 2p orbital on the boron atom to give some double bond character to the B-F bonds. 

The Cl—F and Cl—Cl bonds in the cation are then formed by the overlap of the half-filled sp3 hybrid orbitals of the central chlorine atom with the half-filled p-orbitals of the terminal Cl and F atoms. Thus, by using sp3 hybridization, we end up with the same bent molecular geometry for the ion as that predicted by VSEPR theory (when the lone pairs on the central atom are ignored)... 

Still another aspect of the Li and F valence orbitals is modified by ionic-bond formation. In an isolated ionic or neutral species, each NAO retains the characteristic angular shape of the pure s and p hydrogenic orbitals shown in Fig. 1.1, reflecting the full rotational symmetry of atoms. However, in the presence of another atom or ion this symmetry is broken, and the optimal valence orbitals acquire sp hybrid form (assumed for simplicity to include only valence s and p orbitals), as represented mathematically by... 

The significance of term A was defined in section 1.17.1. Factor f is analogous (ratio A/ defines the polarity of the bond) and parameters e and s describe the hybridization state of the orbitals. Because cos e = 0.093 (Duncan and Pople, 1953), molecular hybrid orbitals ) and are composed essentially of the wave functions of atomic orbitals 2p of oxygen and D of hydrogen. The value 0.578 obtained for cos s also indicates that orbitals (0 and are essentially of type sp. Figure 8.1C shows the formation of hybrid MOs... 

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 ... 

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