Overlap of s orbitals

Figure 3.11. The overlap of s orbitals gives rise to an s band and the overlap of p orbitals gives rise to a p band. The s and p orbitals of the atoms can be so widely spaced that there is a bandgap. In many cases the separation is less and the bands overlap.

A A sigma bond is a single bond that is formed from the overlap of s orbitals. A diatomic hydrogen molecule falls under this category. 

The formation of single, double, and triple bonds in a molecule depends upon the types of hybridized orbitals that are sharing electrons. For example, when two hydrogen atoms bond to form H2(g), there is an overlap of s orbitals as shown in Figure 5.13. 

Figure 1.3. Bond formation H2 molecule, (a) Separate s orbitals. (b) Overlap of s orbitals, (c) and (ci) The a bond orbital.

The overlap of the p orbitals is qualitatively similar to the overlap of s orbitals and the bonding MO is designated... 

The complexes of group 4B elements under optimum conditions can serve as catalysts for the dimerization and oligomerization of ethylene (115—1221. Note that Ti(IV), Zr(lV), and Hf(IV) do not have any 3d, 4d, and 5d electrons, respectively, to coordinate strongly with the olefin. One possibility is that the olefin behaves simply as a weak base with a lone pair electrons. Consequently, the alkene is only weakly bonded, probably by overlap of s orbitals of the metal with the -it orhitals of the alkene [123]. This may he an important requirement for catalysis as distinct from compound formation. The weak coordination allows the olefins to rotate to form a nonpolar transition state, which is conducive to catalytic reactions. 

The overlap of s-orbitals ulbonding axis, while the Py, Pz orbitals perpendicular to the lxis form tt bonds. For every MO orbital type there is a bonding (9, 9 or simply <7, it) and an antibonding (9, if or 0, tt ) level. 

We said in Section 1.5 that chemists use two models for describing covalent bonds valence bond theory and molecular orbital theory. Having now seen the valence bond approach, which uses hybrid atomic orbitals to account for geometry and assumes the overlap of atomic orbitals to account for electron sharing, let s look briefly at the molecular orbital approach to bonding. We ll return to the topic in Chapters 14 and 15 for a more in-depth discussion. 

What accounts for the stability of conjugated dienes According to valence bond theory (Sections 1.5 and 1.8), the stability is due to orbital hybridization. Typical C—C bonds like those in alkanes result from a overlap of 5p3 orbitals on both carbons. In a conjugated diene, however, the central C—C bond results from conjugated diene results in part from the greater amount of s character in the orbitals forming the C-C bond. 

It is thus evident that the reaction path is controlled by the frontier-orbital interaction. The position of reaction will be determined by the rule of maximum overlapping of frontier orbitals, that is, HO and LU MO s of the two reacting molecules. Sometimes SO takes the place of HO or LU in radicals or excited molecules. Hence, the general orientation principle would be as follows ... 

Sigma (o) bonds are formed by the end to end overlap of two orbitals. This overlap can take place between s orbitals, p orbitals or hybrid orbitals. 

The requirements necessary for the occurrence of aromatic stabilisation, and character, in cyclic polyenes appear to be (a) that the molecule should be flat (to allow of cyclic overlap of p orbitals) and (b) that all the bonding orbitals should be completely filled. This latter condition is fulfilled in cyclic systems with 4n + 2n electrons (Huckel s rule), and the arrangement that occurs by far the most commonly in aromatic compounds is when m = 1, i.e. that with 6k electrons. IOti electrons ( = 2) are present in naphthalene [12, stabilisation energy, 255 kJ (61 kcal)mol ], and 4n electrons (n = 3) in anthracene (13) and phenanthrene (14)—stabilisation energies, 352 and 380 kJ (84 and 91 kcal) mor respectively ... 

Electrons near the Fermi level are mobile and give rise to electrical conductivity. The band formed from overlap of p atomic orbitals is called the p band. The overlap of andp orbitals produces andp bands. If separation between andp atomic orbitals is large, the separation between s and p bands in metal is large. There is a bandgap in this case (Fig. 3.11). When the s-p separation is smaller, the bands overlap. 

Tin (in its most stable room temperature form) and lead, although in the same group as silicon and germanium, are metals. For these elements the atomic s-p energy separation is greater and the overlap of s and p orbitals is much less than in silicon and germanium. For tin, the tetrahedral structure would have two s-p bands but the band gap is almost zero. Below 291 K, tin undergoes a transition to the diamond structure, but above this temperature, it is more stable for tin to adopt a... 

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. 

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