Chemistry - A Molecular Science

changed) to produce -Q and then the two waves are added to produce S. The ends of P and -Q have different phases, so they add dest

ructively to nearly annihilate one another,

while the regions in the middle have the same phase and add constructively to produce an amplified region in S.

Mixing atomic orbitals is done in a manne

r very similar to that described above:

adding two atomic orbitals in a region wher

e they have the same phase is constructive,

while adding them in a region where they ha

ve opposite phase is destructive and often

results in annihilation. In addition we will use the following rule when mixing orbitals:

The number of orbitals produced must equal the

number of atomic orbitals that are mixed.

Thus, mixing two atomic orbitals A and B must produce two new orbitals. One new orbital is obtained by adding the two atomic orbitals, A + B. The second orbital is produced when one atomic orbital is subtracted from the other atomic orbital, A - B. To subtract orbital B, we change its phase to produce -B

and then add -B to orbital A.

The orbitals that adopt the geometries fo

r two, three, and four electron groups

predicted by VSEPR (Figure 6.1) can all be constructed from combinations of the atom's s and p orbitals. These combinations are called

hybrid orbitals

, and the process by which

they are formed is called

hybridization

. Hybrid orbitals are constructed to have the

geometry of the electron groups, so we conclude that

Hybrid orbitals are occupied by lone pairs and

σ bonds. The p orbitals that are not used in

the construction of the hybrid orbitals are used to form

π bonds.

The orbitals constructed from the addition a

nd subtraction of one s and one p orbital

are called

sp hybrid orbitals

. The sp hybrid orbitals are formed from s + p and s - p. In

Figure 6.14a, the s and p orbitals are added to produce s + p, one sp hybrid orbital. Both atomic orbitals are positive (blue) to the right, but they have opposite phases to the left. Thus, they add constructively to the right to produce a large lobe, but they add destructively to the left to produce a small

negative lobe. The other hybrid is produced by

taking the difference between the atomic orbitals (Figure 6.14b). To obtain s - p, we change the phase of the p orbital and then add it

to the s orbital. Now, the regions to the

left have the same phase and add constructively and those on the right add destructively. The two sp hybrid orbitals are centered on th

e same atom, so they would look like Figure

6.14c. However, the small negative lobes are

not used in bonding a

nd are usually omitted.

Thus, the two sp hybrid orbitals are normally represented as in Figure 6.14d. Note that forming the two sp hybrid orbitals required the use of only one p orbital, so an sp hybridized atom would have two p orbitals available to form

π bonds.

= =

s+p

(a) (b)

(c)

(d)

net result

same phasesconstructive

opposite phases

destructive

s-p

2 neworbitals

Figure 6.14 Mixing s and p orbitals (a) The blue regions combine constructively to produce a large region to the right, but the blue and red regions combine destructively to produce a small red region to the left. (b) The phase of the p orbital is reversed, so this combination produces s - p. (c) The two new orbitals are shown centered on the same atom. (d) The common represent

ation of the two orbitals that

does not show the smaller lobes.

Chapter 6 Molecular Structure & Bonding

© by

North

Carolina

State

University