136
Sizes and Shapes of Molecules
same principal quantum number to give three different kinds of molecular orbitals. A basic principle involved in all hybridization processes is that you will
always get the same number of molecular orbitals as the number of atomic
orbitals that were used. At the moment we shall hybridize atomic orbitals
without regard to the element involved or the number of electrons that are
available.
In each of the following hybridizations we shall deal with one . v and three p
atomic orbitals. When we don't hybridize all of them, we must consider how the
resulting molecular orbitals are related to the atomic orbitals we don't use.
1. Hybridize one s and three p atomic orbitals to get
(a) four identical sp
3 tetrahedral molecular orbitals
2. Hybridize one s and two p atomic orbitals to get
(a) three identical sp
2 trigonal (A-coplanar) molecular orbitals, and
(b) one atomic p orbital perpendicular to the A plane.
3. Hybridize one . s and one p atomic orbital to get
(a) two identical sp digonal (linear) molecular orbitals, and
(b) two mutually perpendicular atomic p orbitals that are perpendicular
to the line of molecular orbitals.
If you refer back to the earlier figures in this chapter, you can see that,
whenever P == 4 (corresponding to tetrahedral electron-pair geometry), you
were actually using sp
3 molecular orbitals of the central atom to hold lone pairs
and/or to end-overlap with ligand orbitals so as to make the molecular orbitals
needed to hold bond pairs. Similarly, A-coplanar electron-pair geometry uses
sp'
2 molecular orbitals, and linear electron-pair geometry uses sp molecular
orbitals. These orbitals often are described as sp''\ sp-, and sp without further
description because the symbolism itself implies hybridization (and the number
and kind of each atomic orbital used) as well as the geometry involved. These
are summarized in Table 9-2.
The other electron-pair geometries that are listed in Table 9-2 are also related
to specific hybrid molecular orbitals, but they are more complicated because
they involved orbitals as well asi and p. In every case, the . s and/? orbitals are
of the same principal quantum number. However, if the d symbol is listed first
(as in d'
2 .sp
3 ), the d orbitals used in hybridization are of principal quantum
number one less than that of . v and p. If the d symbol is listed at the end (as in
sp
3 d'
2 ), all orbitals are of the same principal quantum number.
A Molecular Orbital Description (Pi Bonds)
When the unhybridized p atomic orbitals that are associated with sp- and sp
molecular orbitals contain no electrons, we need not worry about them. But
every time you draw an electron-dot formula that involves a double or a triple
Sizes and Shapes of Molecules
same principal quantum number to give three different kinds of molecular orbitals. A basic principle involved in all hybridization processes is that you will
always get the same number of molecular orbitals as the number of atomic
orbitals that were used. At the moment we shall hybridize atomic orbitals
without regard to the element involved or the number of electrons that are
available.
In each of the following hybridizations we shall deal with one . v and three p
atomic orbitals. When we don't hybridize all of them, we must consider how the
resulting molecular orbitals are related to the atomic orbitals we don't use.
1. Hybridize one s and three p atomic orbitals to get
(a) four identical sp
3 tetrahedral molecular orbitals
2. Hybridize one s and two p atomic orbitals to get
(a) three identical sp
2 trigonal (A-coplanar) molecular orbitals, and
(b) one atomic p orbital perpendicular to the A plane.
3. Hybridize one . s and one p atomic orbital to get
(a) two identical sp digonal (linear) molecular orbitals, and
(b) two mutually perpendicular atomic p orbitals that are perpendicular
to the line of molecular orbitals.
If you refer back to the earlier figures in this chapter, you can see that,
whenever P == 4 (corresponding to tetrahedral electron-pair geometry), you
were actually using sp
3 molecular orbitals of the central atom to hold lone pairs
and/or to end-overlap with ligand orbitals so as to make the molecular orbitals
needed to hold bond pairs. Similarly, A-coplanar electron-pair geometry uses
sp'
2 molecular orbitals, and linear electron-pair geometry uses sp molecular
orbitals. These orbitals often are described as sp''\ sp-, and sp without further
description because the symbolism itself implies hybridization (and the number
and kind of each atomic orbital used) as well as the geometry involved. These
are summarized in Table 9-2.
The other electron-pair geometries that are listed in Table 9-2 are also related
to specific hybrid molecular orbitals, but they are more complicated because
they involved orbitals as well asi and p. In every case, the . s and/? orbitals are
of the same principal quantum number. However, if the d symbol is listed first
(as in d'
2 .sp
3 ), the d orbitals used in hybridization are of principal quantum
number one less than that of . v and p. If the d symbol is listed at the end (as in
sp
3 d'
2 ), all orbitals are of the same principal quantum number.
A Molecular Orbital Description (Pi Bonds)
When the unhybridized p atomic orbitals that are associated with sp- and sp
molecular orbitals contain no electrons, we need not worry about them. But
every time you draw an electron-dot formula that involves a double or a triple