Hybridization and overlap

Transition metals are characterized by a fairly tightly bound d band of width W that overlaps and hybridizes with a broader nearly-free-electron sp band as illustrated in Fig. 7.4. This difference in behaviour between the valence sp and d electrons arises from the d shell lying inside the outer valence s shell, thereby leading to small overlap between the d orbitals in the bulk. 

The foregoing observation does not, of course, constitute a criticism of the computational methods that have to be used. It does, however, bear upon the question of what we are to think about the theory of chemical forces as a whole. In the last resort these depend simply upon the Coulomb electrostatic law, the condition of minimum energy consistent with acceptable solutions of the wave equation, and the Pauli principle in its generalized form. All the other principles, such as maximum overlapping and hybridization, are really auxiliaries introduced for the purposes of practical calculation. Used with discretion they are also helpful in permitting us to construct certain naive pictures of molecules and atoms, which, however, must not be taken too literally. 

A further consequence of 5f-Sf overlap and hybridization in metallic actinides is a reduction of the importance of valence as a useful concept. In most of the light actinide metallic materials there is no clear separation between Sf electrons and bonding electrons. Unlike 4f electrons, the 5f electrons may enter into the bonding. There are, however, cases where the concept of actinide valence is useful, particularly when the magnetism has a local-moment character. Many properties of each system must be examined and reconciled before simplifying concepts such as localized magnetism and valence can be used correctly. Chan and Lam [19]... 

Figure 19.18 Schematic representation of the orbital overlaps leading to M-CO bonding (a) a overlap and donation from the lone-pair on C into a vacant (hybrid) metal orbital to form a u M <—C bond, and (b) 7T overlap and the donation from a filled d or dj orbital on M into a vacant antibonding n orbital on CO to form a tt M—> C bond.

When two sp-hybridized carbon atoms approach each other, sp hybrid orbitals on each carbon overlap head-on to form a strong sp-sp a bond. In addition, the pz orbitals from each carbon form a pz-pz it bond by sideways overlap and the py orbitals overlap similarly to form a py-py tt bond. The net effect is the sharing of six electrons and formation of a carbon-carbon triple bond. The two remaining sp hybrid orbitals each form a bond with hydrogen to complete the acetylene molecule (Figure 1.16). 

The electronic structure of benzyne, shown in Figure 16.19, is that of a highly distorted alkyne. Although a typical alkyne triple bond uses sp-hybridized carbon atoms, the benzyne triple bond uses sp2-hybridized carbons. Furthermore, a typical alkyne triple bond has two mutually perpendicular it bonds formed bv p-p overlap, but the benzyne triple bond has one tt bond formed by p-p overlap and one tt bond formed by sp2 sp2 overlap. The latter tt bond is in the plane of the ring and is very weak. 

The valence atomic orbitals which are available to form the orbitals of a CC single bond, directed along the x axis, are the 2s and 2px atomic orbitals on each carbon atom. Their admixture—in proportions which depend on the number of neighbors at each carbon and on the subsequent hybridization—creates two (s, p ) hybrids on each atom. One of these hybrids points away from the other atom and can be used for bonding to additional atoms. The pair of hybrids which point at each other overlap and interact in the conventional fashion [we symbolize the non-interacting orbitals by an interruption of the bond axis (Fig. 1)]. The two bond orbitals which are formed in this manner both have [Pg.3]

First, the VB part of the description of benzene. Each C atom is sp2 hybridized, with one electron in each hybrid orbital. Each C atom has a p.-orbital perpendicular to the plane defined by the hybrid orbitals, and it contains one electron. Two sp2 hybrid orbitals on each C atom overlap and form cr-bonds with similar orbitals on the two neighboring C atoms, forming the 120° internal angle of the benzene hexagon. The third, outward-pointing sp2 hybrid orbital on each C atom forms a hydrogen atom. The resulting cr-framework is the same as that illustrated in Fig. 3.20. 

To visualize bond formation by an outer atom other than hydrogen, recall the bond formation in HF. One valence p orbital from the fluorine atom overlaps strongly with the hydrogen 1 S orbital to form the bond. We can describe bond formation for any outer atom except H through overlap of one of its valence p orbitals with the appropriate hybrid orbital of the inner atom. An example is dichloromethane, CH2 CI2, which appears in Figure 10-11. We describe the C—H bonds by 5 -I S overlap, and we describe the C—Cl bonds by 5 - 3 p... 

The four carbon atoms of butadiene have steric number 3 and can be described using s hybridization. There are no lone pairs in the molecule, so all of the hybrid orbitals are used to form a bonds. There are three C—C bonds formed >y s p " -S p " overlap and six C—bonds formed by. y - 1 5 overlap. The a bonding system, which Figure 10-41 shows, has nine bonds that account for 18 of the 22 valence electrons, leaving 4 for the n system. 

Next, we half-fill the lone unhybridized 3p orbital on sulfur and the lone 2p orbital on the oxygen atom with a formal charge of zero (atom B). Following this, the 2p orbital of the other two oxygen atoms (atoms C and D), are filled and then lone pairs are placed in the sp2 hybrid orbitals that are still empty. At this stage, then, all 24 valence electrons have been put into atomic and hybrid orbitals on the four atoms. Now we overlap the six half-filled sp2 hybrid orbitals to generate the cr-bond framework and combine the three 2p orbitals (2 filled, one half-filled) and the 3p orbital (half-filled) to form the four 7t-molecular orbitals, as shown below ... 

The left-most C atom (in the structure drawn below) is sp3 hybridized, and the C-H bonds to that C atom are between the sp3 orbitals on C and the Is orbital on H. The other two C atoms are sp hybridized. The right-hand C-H bond is between the sp orbital on C and the Is orbital on H. The c a C triple bond is composed of one sigma bond formed by overlap of sp orbitals, one from each C atom, and two pi bonds, each formed by the overlap of two 2p orbitals, one from each C atom (that is a 2py—2py overlap and a 2pz—2pz overlap). 

A valuable feature of the overlapping PNHO hybrids hA and hB is that they allow the (hA A hB) NHO interaction elements to be estimated in terms of the corresponding PNHO overlap integral hA hB) by a Mulliken-type approximation49 of the form... 

Figure 3.5 Overlapping natural hybrids of Li2 (left) and Li2+ (right) at (a)...

In graphite, a different form of carbon, atoms are bonded to each other in such a way that a hexagonal structure is formed in a plane. Each carbon atom is bonded to three other carbon atoms with an angle of 120° between the bonds. The bonding involves sp2 - sp2 hybrid overlap and this gives rise to layers. 

Lithiacarboranes are obtained when 1,2,4-triboracyclopentanes and 1,3,5-triboracyclohexanes are reacted with elemental Li in donor solvents. In the contact ion pairs Li ions coordinate to B-B and B-C bonds depending on the number of methylene bridges in bis- and trishomoaromatic species (O, P). The 3c2e bonds in N, O are described as 7i,cr-distorted (indicated as dashed circles) and the overlapping sp3 hybrid orbitals in P practically yield a bonding (dashed triangle). Derivatives of N, O, and P fully characterized by X-ray structure analyses, are presented. 

Consider a fully delocalized symmetrical cyclobutadiene here each carbon atom is equivalent and sp hybridized this leaves four p-electrons to overlap and to form a 7U-system. Two electrons would then... 

The concepts which we need for understanding the structural trends within covalently bonded solids are most easily introduced by first considering the much simpler system of diatomic molecules. They are well described within the molecular orbital (MO) framework that is based on the overlapping of atomic wave functions. This picture, therefore, makes direct contact with the properties of the individual free atoms which we discussed in the previous chapter, in particular the atomic energy levels and angular character of the valence orbitals. We will see that ubiquitous quantum mechanical concepts such as the covalent bond, overlap repulsion, hybrid orbitals, and the relative degree of covalency versus ionicity all arise naturally from solutions of the one-electron Schrodinger equation for diatomic molecules such as H2, N2, and LiH. 

Fig. 4-10.—The effect of hybridization of a w orbital. At the left is shown the angular dependence of orbital strength for a pure pic orbital, px (z axis vertical). At the right is shown a 7r orbital with 4.5 percent d character. It is seen that the d character increases overlap of the orbital with a similar orbital to the right (bonding overlap) and decreases overlap with a similar orbital to the left (nonbonding overlap).

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