Orbitals Hybridization Molecular

We 11 expand our picture of bonding by introducing two approaches that grew out of the idea that electrons can be described as waves—the valence bond and molecular orbital models In particular one aspect of the valence bond model called orbital hybridization, will be emphasized... 

Generally speaking the three models offer complementary information Organic chemists use all three emphasizing whichever one best suits a particular feature of struc ture or reactivity Until recently the Lewis and orbital hybridization models were used far more than the molecular orbital model But that is changing... 

Section 2 22 Lewis structures orbital hybridization and molecular orbital descriptions of bonding are all used m organic chemistry Lewis structures are used the most MO descriptions the least All will be used m this text... 

FIGURE 3.16 Three common hybridization schemes shown as outlines of the amplitude of the wavefunction and in terms of the orientations of the hybrid orbitals, (a) An s-orbital and a p-orbital hybridize into two sp hybrid orbitals that >oint in opposite direc tions, forming a linear molecular shape, (b) An s-orbital and two p-orbitals can blend together to give three ip hybrid orbitals that point to the corners of an equilateral triangle, (c) An s-orbital and three p-orbitals can blend together to give four sp hybrid orbitals that point to the corners of a tetrahedron. 

Although orbital hybridizations and molecular shapes for hypovalent metal hydrides of the early transition metals and the normal-valent later transition metals are similar, the M—H bonds of the early metals are distinctly more polar. For example, metal-atom natural charges for YH3 (+1.70), HfH4 (+1.75), and TaHs (+1.23) are all significantly more positive than those (ranging from +0.352 to —0.178) for the homoleptic hydrides from groups 6-10. Indeed, the empirical chemistry of early transition-metal hydrides commonly reveals greater hydricity than does that of the later transition-metal hydrides. 

The GHO basis can therefore provide a localised, directional set of orbitals (hybrids) which do not have the principal qualitative disadvantage of the usual hybrid sets they can be mutually orientated in any directions. What is more the directions taken up by the GHOs can be decided variationally and not by the unitary properties of a hybridisation matrix . This conclusion means that the use of a GHO basis provides both a localised bonding picture and simultaneously a theoretical validation of the VSEPR rules. Thus, it is not necessary, for example, to contrast the hybrid method and the VSEPR method for molecular geometries (30) they are complementary. 

There exists no uniformity as regards the relations between localized orbitals and molecular symmetry. Consider for example an atomic system consisting of two electrons in an (s) orbital and two electrons in a (2px) orbital, both of which are self-consistent-field orbitals. Since they belong to irreducible representations of the atomic symmetry group, they are in fact the canonical orbitals of this system. Let these two self-consistent-field orbitals be denoted by Cs) and (2p), and let (ft+) and (ft ) denote the two digonal hybrid orbitals defined by... 

A conglomerate of three hexagons contains one central atom and 12 atoms around it. A conglomerate of seven hexahedrons comprises 12 external and 12 internal (common) atoms. In these two cases geometric centers of hybridized molecular orbitals of each hexahedron are equidistant from such nearest centers of a conglomerate. This, apparently, explains the experimental fact that polyhedrons of carbon clusters represent an icosahedron - 12-apex crystalline structure each apex of which is connected with five other apexes. 

The VSEPR theory is only one way in which the molecular geometry of molecules may be determined. Another way involves the valence bond theory. The valence bond theory describes covalent bonding as the mixing of atomic orbitals to form a new kind of orbital, a hybrid orbital. Hybrid orbitals are atomic orbitals formed as a result of mixing the atomic orbitals of the atoms involved in the covalent bond. The number of hybrid orbitals formed is the same as the number of atomic orbitals mixed, and the type of hybrid orbital formed depends on the types of atomic orbital mixed. Figure 11.7 shows the hybrid orbitals resulting from the mixing of s, p, and d orbitals. 

A second common type of orbital hybridization involves the 2s orbital and only two of the three 2p orbitals (2a). This process is therefore referred to as sp hybridization. The result is three equivalent sp hybrid orbitals lying in one plane at an angle of 120° to one another. The remaining 2px orbital is oriented perpendicular to this plane. In contrast to their sp counterparts, sp -hybridized atoms form two different types of bond when they combine into molecular orbitals (2b). The three sp orbitals enter into a bonds, as described above. In addition, the electrons in the two 2px orbitals, known as n electrons, combine to give an additional, elongated n molecular orbital, which is located above and below the plane of the a bonds. Bonds of this type are called double bonds. They consist of a a bond and a n bond, and arise only when both of the atoms involved are capable of sp hybridization. In contrast to single bonds, double bonds are not freely ro-... 

Figure 2. Rearrangement in molecular orbital hybridization and geometry of the carbon atom undergoing a first-order nucleophilic substitution (or Sn1) reaction.

Like 17th-eentury meehanieal atomism, modem atomism also reeognizes the importanee of shape—at the level of individual atoms in terms of the eoncept of orbital hybridization and direetional bonding—and at the molecular level in terms of the loek and key model of intermolecular interaetions. 

The other electron-pair geometries that are listed in Table 9-2 are also related to specific hybrid molecular orbitals, but they are more complicated because they involve midp. In every case, the ami/ orbitals are of the same priflfap l( BMlSqis%mfeehySflffMftrofif feg... 

E More on Hybrid Bond Orbitals and Molecular Geometry... 

There is no unequivocal answer to the question as to which is the better method. Calculations by the VB method are likely to be more reliable than those by the MO method, but in practice are much more difficult to carry out. For many-electron molecules the MO procedure is simpler to visualize because we combine atomic orbitals into molecular orbitals and then populate the lower-energy orbitals with electrons. In the VB method, atomic orbitals are occupied, but the electrons of different atoms are paired to form bonds, a process that requires explicit consideration of many-electron wave functions. To put it another way, it is easier to visualize a system of molecular orbitals containing N electrons than it is to visualize a hybrid wave function of N electrons. 

It is important to realize that methane is not tetrahedral because carbon has sp3, hybrid orbitals. Hybridization is only a model—a theoretical way of describing the bonds that are needed for a given molecular structure. Hybridization is an interpretation of molecular shape shape is not a consequence of hybridization. 

You might be wondering how hybridization relates to molecular orbitals. Hybridization is a part of valence-bond theory and is used in molecular orbital theory only in special cases. In molecular orbital theory, molecular orbitals are constructed from all the raw (unhybridized) atomic orbitals that are available. 

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