12
Chapter 2 Pauling “3-Electron Bonds”, 4-Electron 3-Centre Bonding, and the Need …
located in atomic orbitals centred on the A and Β nuclei. This modification
enables emphasis to be put on Pauling’s earlier conclusion that the strength of a
“3-electron bond” is approximately equal to that of a 1-electron bond, and that
some unpaired-electron charge is associated with each of the two atoms. This unpaired-electron charge is available for (fractional or partial) sharing with unpaired
electron charges on other atoms, and it provides the basis for the development of
an “increased-valence” theory.
In Chapters 3–9, we shall examine the electronic structures of numerous paramagnetic molecules, for which Pauling’s “3-electron bonds” may be utilized in
their valence-bond structures. Lewis-type valence-bond descriptions for the
dimers of some of these molecules will also be considered. In Chapters 10–25, the
incorporation of Pauling’s “3-electron bonds” into the valence-bond structures for
diamagnetic molecules will be described. The resulting valence-bond structures
for diamagnetic systems are designated as “increased-valence” structures, to stress
the point that they involve more electrons in nearest-neighbour and non-neighbour
bonding than do Lewis-type valence-bond structures, which have electron-pair
bonds and lone-pairs of electrons.
The remainder of this chapter provides a discussion of the need for an “increased-valence” theory. A reading of it is not required in order to follow the
Pauling “3-electron bond” and Lewis theory of Chapters 3–9.
2-2 Electron Deficient and Electron Excess Bonding Units
Nearly all molecules that involve atoms of main-group elements and an even
number of electrons have diamagnetic ground-states. (Molecular O 2 is one important exception, to which we have referred in Section 2-1.) For these molecules, the
familiar Lewis valence-bond structures, with electron-pair bonds and lone-pairs of
electrons, are mostly used to provide qualitative valence-bond descriptions of their
electronic structures. Sometimes, as is the case for 2
H , 2
N , 2
H O , 2 6
C H , 2 4
C H
and butadiene of Figure 2-2, one Lewis structure alone can give a fairly adequate
description of the bonding. If necessary, bond polarity can be indicated in these
structures, either by arrowheads or by fractional net charges
and
, as is
shown for 2
H O . The bond line represents a pair of shared electrons with opposite
spins, the sharing (in orbital theory) arising from atomic orbital overlap. Each
lone-pair of electrons also involves two electrons with opposite spins, as is shown
for 2
N and 2
H O . (The crosses and circles (x and ) represent electrons with z
s
spin quantum numbers of +½ and -½, respectively). For each of the molecules of
Figure 2-2, the Lewis structure has the maximum number of electron-pair bonds
linking pairs of adjacent atoms. Any other Lewis structure for these molecules,
such as the “long-bond” and ionic or polar structures displayed for 2
H O and butadiene, have fewer covalent bonds between adjacent atoms, but of course they can
participate in resonance with the primary valence-bond structure.
Chapter 2 Pauling “3-Electron Bonds”, 4-Electron 3-Centre Bonding, and the Need …
located in atomic orbitals centred on the A and Β nuclei. This modification
enables emphasis to be put on Pauling’s earlier conclusion that the strength of a
“3-electron bond” is approximately equal to that of a 1-electron bond, and that
some unpaired-electron charge is associated with each of the two atoms. This unpaired-electron charge is available for (fractional or partial) sharing with unpaired
electron charges on other atoms, and it provides the basis for the development of
an “increased-valence” theory.
In Chapters 3–9, we shall examine the electronic structures of numerous paramagnetic molecules, for which Pauling’s “3-electron bonds” may be utilized in
their valence-bond structures. Lewis-type valence-bond descriptions for the
dimers of some of these molecules will also be considered. In Chapters 10–25, the
incorporation of Pauling’s “3-electron bonds” into the valence-bond structures for
diamagnetic molecules will be described. The resulting valence-bond structures
for diamagnetic systems are designated as “increased-valence” structures, to stress
the point that they involve more electrons in nearest-neighbour and non-neighbour
bonding than do Lewis-type valence-bond structures, which have electron-pair
bonds and lone-pairs of electrons.
The remainder of this chapter provides a discussion of the need for an “increased-valence” theory. A reading of it is not required in order to follow the
Pauling “3-electron bond” and Lewis theory of Chapters 3–9.
2-2 Electron Deficient and Electron Excess Bonding Units
Nearly all molecules that involve atoms of main-group elements and an even
number of electrons have diamagnetic ground-states. (Molecular O 2 is one important exception, to which we have referred in Section 2-1.) For these molecules, the
familiar Lewis valence-bond structures, with electron-pair bonds and lone-pairs of
electrons, are mostly used to provide qualitative valence-bond descriptions of their
electronic structures. Sometimes, as is the case for 2
H , 2
N , 2
H O , 2 6
C H , 2 4
C H
and butadiene of Figure 2-2, one Lewis structure alone can give a fairly adequate
description of the bonding. If necessary, bond polarity can be indicated in these
structures, either by arrowheads or by fractional net charges
and
, as is
shown for 2
H O . The bond line represents a pair of shared electrons with opposite
spins, the sharing (in orbital theory) arising from atomic orbital overlap. Each
lone-pair of electrons also involves two electrons with opposite spins, as is shown
for 2
N and 2
H O . (The crosses and circles (x and ) represent electrons with z
s
spin quantum numbers of +½ and -½, respectively). For each of the molecules of
Figure 2-2, the Lewis structure has the maximum number of electron-pair bonds
linking pairs of adjacent atoms. Any other Lewis structure for these molecules,
such as the “long-bond” and ionic or polar structures displayed for 2
H O and butadiene, have fewer covalent bonds between adjacent atoms, but of course they can
participate in resonance with the primary valence-bond structure.