The number of hybrid orbitals equals the number of atomic orbitals that mix together.

Hybridization is the mechanism that is implicit in VSEPR, in which the electron pairs involved in bonding are distributed to minimize their Coulomb repulsion. When a given atom interacts with other atoms and forms chemical bonds, the electrons on that atom may adjust in order to accommodate the electron pairs associated with chemical bonds in a structure of minimum energy.

1 135 Hybridization The orbitals that we use for electron configurations are characteristic of an isolated atom. When a given atom interacts with other atoms and forms chemical bonds, the electrons on that atom may adjust, that is, they hybridize, in order to accommodate the electron pairs associated with chemical bonds in a structure of minimum energy. Hybridization is the mechanism that is implicit in VSEPR, in which the electron pairs involved in bonding are distributed to minimize their Coulomb repulsion. Hybrid orbitals also result in the optimum overlap of the orbitals that form chemical bonds. Tetrahedral Hybrids Hybridization can occur with many atoms in the Periodic Table, but carbon provides one of the most common examples. The diagram below shows that when a carbon atom interacts with four bonding atoms (like hydrogen in methane), the 2s and 2p orbitals mix together to form four equivalent hybrid orbitals. The number of hybrid orbitals equals the number of atomic orbitals that mix together. When one 2s and three 2p orbitals mix together, or hybridize, they form four sp 3 hybrid orbitals that point toward the corners of a tetrahedron.

2 136 Remember that in VESPR theory, the polygon whose vertices minimize the Coulomb repulsion of four electron pairs is a tetrahedron. Consistent with VSEPR, hybrid sp 3 orbitals are used to describe the structure of NH 3 and H 2 O. The lone pairs occupy hybrid orbitals. Trigonal Planar Hybrids Bonding in ethylene provides another interesting example of hybrid orbitals. Here, one 2s orbital mixes with two 2p orbitals to form three sp 2 hybrids. The third 2p orbital (the 2p z ) remains unchanged, as indicated in the diagram below. In this case, three electron pairs are involved in bonding, and maximum overlap (in bonding language) and minimum electrostatic repulsion (in VSEPR language) occurs for a trigonal planar geometry. The diagram below indicates that the three sp 2 hybrids are coplanar, and point toward the corners of an equilaterial triangle. The hybrid orbitals make an angle of 120 with respect to one another.

3 137 Looking at ethylene from the top (shown in the diagram below), you can see the trigonal geometry about the individual carbon atoms. One of the sp 2 hybrids on each carbon is used to provide overlap between the atoms. Two of the sp 2 hybrids on each carbon are used to make bonds to hydrogen. These bonds are called σ bonds. They are cylindrically symmetric about the bond axis. But now, there is one final issue, and that is what happens with the unhybridized 2p orbital. The diagram at the left shows that the unhybridized orbital is perpendicular to the plane in which the trigonal sp 2 hybrids lie. So, now let s look at the orientations of the unhybridized orbitals on both carbons in ethylene

4 138 The diagram on the previous page shows that these unhybridized 2p orbitals can overlap. The electron density is no longer cylindrically symmetric. Such a bond is called a π- bond. This bond can accommodate a pair of electrons. Note that the carbon-carbon bond in ethylene is comprised of one σ -bond and one π- bond. We can get an idea of the contributions of each kind of electron to the bonding from a consideration of bond strengths and bond lengths. C-C single bond: 347 kj/mol 1.54 Å C=C double bond: 614 kj/mol 1.34 Å The double bond is 0.20 Å shorter than the single bond, and is 267 kj/mol stronger. Note: In BF 3, the 2s and 2p orbitals on boron can produce three sp 2 hybrids, consistent with trigonal planar geometry. In this case, there are no electrons to go into the unhybridized 2p orbital. Linear Hybrids Finally, the 2s orbital on carbon can hybridize with one 2p orbital to produce two sp hybrids. Maximum overlap with the electrons in atoms bound to this atom will occur in a linear configuration. Note that two unhybridized 2p orbitals are left. The total number of orbitals after hybridization must equal the number of unhybridized orbitals. The diagram below shows the shapes of the sp hybrids.

5 139 The diagram below shows the appearance of the two sp hybrids on carbon along with the unhybridized 2p orbitals. In acetylene, C 2 H 2, one sp hybrid on each carbon atom participates in a σ -bond between the carbons, and the other sp hybrid binds hydrogen atoms. The molecule is linear. Now, the unhybridized 2p orbitals can overlap to form two different π-bonds. We say the carbon-carbon bond in aceetylene is a triple bond, consisting of one σ-bond and two π-bonds. The effect of the additional π-bond is indicated below: C C triple bond: 839 kj/mol 1.20 Å The effect of the second π-bond is to strengthen the carbon-carbon bond by an additional 225 kj/mol (beyond the double bond), and shorten it by 0.14 Å Comment: bonding in N 2 also involves sp hybridization on the nitrogen. One sp hybrid on each nitrogen atom is used to form a σ- bond between the atoms, and the unhybridized orbitals form two π-bonds. The remaining sp hybrids (one on each atom) accommodate lone electron pairs. Summary of structures for 2, 3, and 4 electron pairs

6 140 Hybrids containing d-orbitals In the fourth row of the Periodic Table, the 3d orbitals become energetically accessible, and they can play a role in the formation of hybrid orbitals. This is the same region of the Periodic table where octet expansion occurs. The Trigonal Bipyramid: The combination of one d-orbital, one s-orbital, and three p-orbitals results in a set of five hybrids that describe a trigonal bipyramid. These hybrids are called dsp 3 hybrids, and are associated with structures with five electron pairs around the central atom. PCl 5 and I 3 - are classic examples. The equilaterial and axial positions of the trigonal bipyramid are chemically inequivalent. Axially bonded atoms are more weakly bonded and the bond lengths are longer. Octahedral: Finally, the hybrid orbitals formed with two d-orbitals, one s-orbital, and three p-orbitals results in a set of six hybrids that describe an octahedron. These hybrids are called d 2 sp 3 hybrids, and are associated with structures with six electron pairs around the central atom. All positions on an octahedron are chemically equivalent. Hybrid orbitals for 5 and 6 electron pairs