Maximum overlap, hybrid orbitals

Ethene has one double bond (H2C=CH2) and each carbon atom is coimected via three sp orbitals two spin pair with Ij hydrogen electrons and the third is shared with the other carbon atom, giving a total of five ct bonds in one plane. Each carbon atom has, at right angles to this plane, two further p orbitals, each with one electron and these orbitals take no part in the a hybridization. The p orbitals can overlap sideways and form a n orbital in the form of two dogbone or sausage shaped sections, one above the ct orbital plane and the other below (Figure 1.7) [5], where the plane represents a node for the n orbital. Maximum overlap of the p orbitals prevents rotation about the double bond. 

As we have pointed out many times previously, the columns of the standard tableaux functions are antisymmetrized, and the orbitals in a column may be replaced by any linear combination of them with no more than a change of an unimportant overall constant. In this case, consider a linear combination that has two hybrid orbitals that point directly at the H atoms in accord with Pauling s principle of maximum overlap. Using the parameter

[Pg.180]

To explain the bonding there would be two orbitals needed in carbon which should be concentrated strongly in opposite directions so that maximum overlap for the two bonds to hydrogen and to nitrogen would occur at an angle of 180°. On mathematical analysis of the problem it is found that one s and one p orbital can be hybridized to form two new hybrid orbitals, sp orbitals, to fulfill this requirement. Each new orbital is a mixture of one-half of an s orbital and one-half of a p orbital. The situation on nitrogen is quite similar, only here the second orbital would not be used in bond formation but would hold the lone pair. 

Analyze the interaction between the vacant p orbital of a carbocation and an unshared electron pair on an adjacent nitrogen. Assume sp3 hybridization for nitrogen, and the conformation in which the unshared pair has maximum overlap with the carbon/) orbital. 

The bonding between phosphorous atoms in the P4 molecule can be described by a simple bent bond model, which is formed by the overlap of sp3 hybrids of the P atoms. Maximum overlap of each pair of sp3 orbitals does not occur along an edge of the tetrahedron. Instead, the P-P bonds are bent, as shown in Fig. 15.3.1(b). In a more elaborate model, the P4 molecule is further stabilized by the d orbitals of P atoms which also participate in the bonding. 

The basis set used is Dunning s cc-pVDZ [16]. The CASSCF wave function was obtained with CAS(4,4). The geometries of the equilibrium and TS structures were determined with this basis set and active space. The orbitals were then localized in the active orbital space. The orbitals were transformed so as to have maximum overlap with two carbon sp2 orbitals and hydrogen Is orbitals. The sp1 orbitals were used with the fixed hybridization ratio of 2s to 2p orbitals (1 2) and with a fixed angle of 120° relative to the CO axis... 

You probably remember the solution to these problems from general chemistry. The 2s and the three 2p AOs are mathematically combined in a kind of averaging process to produce four equivalent hybridized AOs. Because they result from combining one s orbital and three p orbitals, the new AOs are said to be sp3 hybridized. The hybrid AOs are ideal for bonding. They are all equivalent, and they have tetrahedral geometry. In addition, each has a large lobe of the orbital pointed in the direction where the other atom of the bond will be and only a small lobe on the other side of the carbon. This directionality of the hybrid AO allows for maximum overlap when it interacts with another AO to fonn a MO. The hybridization process and the sp3 hybrid AOs are shown in Figure 3.6. 

In the spin-coupled description of a molecule such as SF6, the sulfur atom contributes six equivalent, nonorthogonal sp -like hybrids which delocalize onto the fluorine atoms. Each of these two-centre orbitals overlaps with a distorted F(2p) function and the perfect-pairing spin function dominates. Of course, using only 3s, 3px, 3p and 3pz atomic orbitals, we can at most form four linearly independent hybrid orbitals localized on sulfur, with a maximum occupancy of 8 electrons, as in the octet rule. However, the six sulfur+fluorine hybrids which emerge in the spin-coupled description are not linearly dependent, precisely because each of them contains a significant amount of F(2p) character. It is thus clear that the polar nature of the bonding is crucial. 

Fig. 12.12 JcH for hydrocarbons and s-character of C hybrid orbitals defined by the maximum overlap criterion (see also ref. 156).

The hybridization parameter < >, arbitrary so far, is best chosen so as the bond hybrids bi and b2 point in the direction of the two O—H bonds, giving in this way strongest bonding with His orbitals and satisfying the principle of maximum overlap. According to Equation (2.214), 26 = 105° gives o)Ki 40°, and we obtain the set (Figure 2.21) ... 

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