Page 61 - Arrow Pushing in Inorganic Chemistry A Logical Approach to the Chemistry of the Main Group Elements

1.25 ELEMENTS OF BONDING IN HYPERVALENT COMPOUNDS 41
is still tetravalent in both compounds but its OS is 0. In the same manner, CN often equals
valence. While these equalities can be understood on a case-by-case basis, it’s probably
best to view them as coincidental.
Another very important concept in this connection is that of FC. FC is the charge remain-
ing on an atom when all the ligands have been removed homolytically. FCs are the charges
that are commonly shown in structural formulas and reaction mechanisms. Thus the FC on
nitrogen in NH + is +1 and that on boron in BH − is −1.
4 4
The valence of atoms bearing a nonzero FC can be a bit of a tricky affair. Let’s consider
the ions NH 4 + and NH 2 − and compare them with NH . The nitrogen in ammonia is clearly
3
−
trivalent. In NH 4 + and NH , nitrogen uses four and two electrons, respectively, to form
2
bonds with hydrogen atoms. In addition, the nitrogen has lost one of its original valence
+ −
electrons in NH ;inNH , the nitrogen has gained an extra electron relative to its free
2
4
atomic state. To account for these excess charges, it is helpful to recognize that valence is
the number of electrons an atom uses in forming bonds plus the net number of electrons it
has lost in forming the molecule/ion in question. This is not a new definition of valence;
it’s perfectly equivalent to the “more accurate” definition that we have presented above.
Thus, nitrogen in NH 4 + is pentavalent: four valence electrons used in bonding plus one
lost. Similarly, nitrogen in NH − is monovalent: two valence electrons used in bonding and
2
one electron gained relative the free, neutral atom, that is, 2 + (−1) = 1. Thus, a very useful
relation is the following:
valence = no. of bonds + formal charge

Some of the consequences of this definition can seem a bit mind-bending, until you get
−
used to them. Thus, applying this definition, we get an oxygen valence of 0 for OH and 4
+
for H O ! After a while, these results won’t seem quite as bizarre as they might do now.
3
1.25 ELEMENTS OF BONDING IN HYPERVALENT COMPOUNDS

A hypervalent molecule is characterized by a main-group element atom with more than
eight electrons in its valence shell, according to the molecule’s Lewis structure. Figure 1.6
presents the Lewis structures of a selection of hypervalent molecules and ions, with dif-
ferent central atoms but all with fluoride as the terminal ligands. To assist with electron
bookkeeping, we have indicated the valence electrons of the central atoms as dark blue
dots, those of fluorine as crosses, and those corresponding to any excess negative charge as
red crosses.
The main question we will try to address in this section concerns how the central atom
in a hypervalent molecule accommodates more than eight valence electrons. For a long
time, such “expanded octets” were thought to reflect participation by the d orbitals of the
central atom. That explanation is now believed to be incorrect. Instead, a perfectly straight-
forward explanation is available from standard molecular orbital theory, which we will
discuss below using the trigonal bipyramidal molecule PF as an example.
5
2
We may view the equatorial atoms of PF as a planar PF unit with an sp -hybridized
3
5
P atom. The lone pair on the P then might be thought of as occupying an unhybridized
p orbital, which we will call the p orbital. This lone pair interacts with the p orbitals of
z
z
two F atoms, each of which is assumed to have an unpaired electron, forming two apical
P–F bonds. As shown in Figure 1.7, the three p orbitals form bonding, nonbonding, and
z