Physical Chemistry Third Edition

874 21 The Electronic Structure of Polyatomic Molecules

Figure 21.5a shows a cube centered at the nucleus with faces perpendicular to the

coordinate axes. The 2pz,2px, and 2pyorbitals have the largest positive values along

the respective positive axes. The three 2porbitals contribute to the 2sp^3 (1) hybrid

orbital such that its largest positive value lies between the positive axes, toward the

upper right front corner of the cube, as shown in the figure with an arrow. This direction

is an axis of cylindrical symmetry of this hybrid orbital. The symmetry axes of the

other three hybrid orbitals are shown in the figure, pointing toward alternate corners of

the cube.

Exercise 21.4

Pick one of the 2sp^3 hybrid orbitals other than 2sp^3 (1) and argue that its orbital region is directed

as shown in Figure 21.5a.

Since connecting the four alternate corners of a cube with line segments constructs

a regular tetrahedron, the angle between any two of the axes shown in Figure 21.5a is

called thetetrahedral angleand is equal to 109 degrees, 28 minutes, 16. 39 ...seconds

(≈109.5◦).

(b)

(a)

xy plane

(between axes)

2 sp^3 (1)

zzz

2 s 2 pz





y

x

z

2 sp^3 (1) direction

2 sp^3 (4) direction

2 sp^3 (2) direction 2 sp^3 (3) direction

Figure 21.5 Thesp^3 Hybrid Orbitals.(a) The addition ofsandpatomic orbitals to

formsp^3 hybrid orbitals (represented by vectors in the directions of positive contributions).

(b) The orbital regions of 2s,2p, and 2sp^3 orbitals.