8.2 Bond Lengths
211
Furthermore, there is a ring point (see definition in 2.18) with an electron density
ρ = 0.0099 au corresponding to a six-membered ring H 2 C 2 C 3 C 4 C 5 H 5 . This effect
contributes to the stabilization of the planar cis-structure.
8.3 Valence-Shell Electron-Pair Repulsion (VSEPR) Model
The orientation of the bonds originating from one atom may be predicted using
the VSEPR model developed by Gillespie and Nyholm (1957). The method is not
quantitative, but it furnishes useful information on the structure of molecules. Only a
summary is given here. The reader is referred to the book of Gillespie and Hargittai
(1991) for a detailed discussion.
At the beginning of the twentieth century, Lewis (1916) suggested that atoms are
held together in a covalent bond by sharing a pair of electrons. Indeed, two electrons
can be brought into the same region by the electrostatic attraction of nuclei provided
that they are of opposite spin. The pairs of electrons that are not forming bonds
are called non-bonding pairs or lone pairs. This concept of electron pairs is a very
convenient model but just an approximate one because, from the quantum mechanical
point of view, it is not possible to define the position of an electron.
One assumes that the electron pairs, bonding pairs (bp) as well as lone pairs (lp),
in the valence shell are at the same distance from the nucleus (i.e., on a sphere)
and repel each other as a consequence of the Pauli principle and, thus, are as far
apart as possible. The number of electron pairs determines the position of the bonds;
see Table 8.3. Two pairs of electrons in a valence shell have a linear arrangement,
three pairs have a triangular arrangement, four pairs have a tetrahedral arrangement
(because the angles at 109° 28
are larger than the square-planar angles of 90°),
five pairs have a trigonal bipyramidal arrangement, and six pairs have an octahedral
arrangement. See Fig. 8.2.
The method is quite simple. It is enough to know which atoms are bonded together.
Then, one determines the number of valence electrons on the central atom (called
A). The easiest demonstration is by examining an example.
Example. Ammonia, NH 3 . The central atom, nitrogen, has five valence electrons;
each hydrogen atom contributes one electron. The number of electrons is: 8 = (5 +
1×3). Dividing by two gives the number of electron pairs: 4. There are three bonding
pairs and one lone pair. The shape of ammonia is pyramidal, the lone pair occupying
one vertex of the tetrahedron of electron pairs.
A lone pair (lp) occupies more angular space than a bonding pair (bp) because it
is attracted by a single nucleus and, therefore, tends to spread out as far as possible.
On the other hand, a bonding pair is subject to the attraction of two nuclei and, for
this reason, takes up less angular space. The magnitude of electron-pair repulsion
decreases in the order:
211
Furthermore, there is a ring point (see definition in 2.18) with an electron density
ρ = 0.0099 au corresponding to a six-membered ring H 2 C 2 C 3 C 4 C 5 H 5 . This effect
contributes to the stabilization of the planar cis-structure.
8.3 Valence-Shell Electron-Pair Repulsion (VSEPR) Model
The orientation of the bonds originating from one atom may be predicted using
the VSEPR model developed by Gillespie and Nyholm (1957). The method is not
quantitative, but it furnishes useful information on the structure of molecules. Only a
summary is given here. The reader is referred to the book of Gillespie and Hargittai
(1991) for a detailed discussion.
At the beginning of the twentieth century, Lewis (1916) suggested that atoms are
held together in a covalent bond by sharing a pair of electrons. Indeed, two electrons
can be brought into the same region by the electrostatic attraction of nuclei provided
that they are of opposite spin. The pairs of electrons that are not forming bonds
are called non-bonding pairs or lone pairs. This concept of electron pairs is a very
convenient model but just an approximate one because, from the quantum mechanical
point of view, it is not possible to define the position of an electron.
One assumes that the electron pairs, bonding pairs (bp) as well as lone pairs (lp),
in the valence shell are at the same distance from the nucleus (i.e., on a sphere)
and repel each other as a consequence of the Pauli principle and, thus, are as far
apart as possible. The number of electron pairs determines the position of the bonds;
see Table 8.3. Two pairs of electrons in a valence shell have a linear arrangement,
three pairs have a triangular arrangement, four pairs have a tetrahedral arrangement
(because the angles at 109° 28
are larger than the square-planar angles of 90°),
five pairs have a trigonal bipyramidal arrangement, and six pairs have an octahedral
arrangement. See Fig. 8.2.
The method is quite simple. It is enough to know which atoms are bonded together.
Then, one determines the number of valence electrons on the central atom (called
A). The easiest demonstration is by examining an example.
Example. Ammonia, NH 3 . The central atom, nitrogen, has five valence electrons;
each hydrogen atom contributes one electron. The number of electrons is: 8 = (5 +
1×3). Dividing by two gives the number of electron pairs: 4. There are three bonding
pairs and one lone pair. The shape of ammonia is pyramidal, the lone pair occupying
one vertex of the tetrahedron of electron pairs.
A lone pair (lp) occupies more angular space than a bonding pair (bp) because it
is attracted by a single nucleus and, therefore, tends to spread out as far as possible.
On the other hand, a bonding pair is subject to the attraction of two nuclei and, for
this reason, takes up less angular space. The magnitude of electron-pair repulsion
decreases in the order: