278 Chapter Eight
configurations of the sand patomic orbitals important in bond formation. What are
drawn are boundary surfaces of constant ^2 R^2 that outline the regions within
which the probability of finding the electron has some definite value, say 90 or 95 per-
cent. The diagrams thus show ^2 in each case; Fig. 6.11 gives the corresponding
radial probabilities. The sign of the wave function is indicated in each lobe of the
orbitals.
In Fig. 8.9 the sand pzorbitals are the same as the hydrogen-atom wave functions
for sand p(ml0) states. The pxand pyorbitals are linear combinations of the
p(ml1) and p(ml1) orbitals, wherepx ( 1 1 ) py ( 1 1 ) (8.2)The 1 2 factors are needed to normalize the wave functions. Because the energies
of the ml1 and ml1 orbitals are the same, the superpositions of the wave
functions in Eq. (8.2) are also solutions of Schrödinger’s equation (see Sec. 5.4).
When two atoms come together, their orbitals overlap. If the result is an increased
^2 between them, the combined orbitals constitute a bonding molecular orbital. In
Sec. 8.4 we saw how the 1sorbitals of two hydrogen atoms could join to form the
bonding orbital S. Molecular bonds are classified by Greek letters according to their
angular momenta Labout the bond axis, which is taken to be the zaxis: (the Greek
equivalent of s) corresponds to L0, (the Greek equivalent of p) corresponds to
L, and so on in alphabetic order.
Figure 8.10 shows the formation of and bonding molecular orbitals from sand
patomic orbitals. Evidently Sfor H 2 is an ssbond. Since the lobes of pzorbitals are
on the bond axis, they form molecular orbitals; the pxand pyorbitals usually form
molecular orbitals.1
2 1
2 Figure 8.10The formation of ss, pp, and ppbonding molecular orbitals. Two pyatomic orbitals
can combine to form a ppmolecular orbital in the same way as shown for two pxatomic orbitals
but with a different orientation.ppπ+xyz+==pxpzpxpz ppσssσ+=s s+ ++–+–++++
- +–
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