Chapter 5
Bonding in polyatomic molecules
TOPICS
Hybridization of atomic orbitals
Molecular orbital theory: ligand group orbitals
Delocalized bonding
Partial molecular orbital treatments
5.1 Introduction
Polyatomic species: contains three or more atoms
Three approaches to bonding in diatomic molecules
1. Lewis structures
2. Valence bond theory
3. Molecular orbital theory
5.2 Valence bond theory: hybridization of atomic orbitals
Hybrid orbitals are generated by mixing the characters of
atomic orbitals.
A set of hybrid orbitals provides a bonding picture for a
molecule in terms of localized s - bonds.
sp Hybridization: a scheme for linear species.
The notation sp means that one s atomic orbital and one p atomic orbital mix to
form a set of two hybrid orbitals with different directional properties.
If we begin with n atomic orbitals, we must end up with n orbitals after
hybridization.
Effectively, we are
representing the valence
state of Be in a linear
molecule as consisting of
two degenerate sp hybrids,
each containing one
electron; this is represented
by the notation (sp)2.
sp2 Hybridization: a scheme for trigonal planar species
The notation sp2 means that one s and two p atomic orbitals mix to form a set
of three hybrid orbitals with different directional properties.
The probability of finding the electron somewhere in
space is taken to be 1.
Fig. 5.5 The bonding in trigonal planar BH3 can be conveniently described in terms of
the interactions between a set of sp2 hybrid orbitals centred on the B atom and three H
1s atomic orbitals. Three pairs of electrons are available (three electrons from B and one
from each H) to give three 2c-2e s -bonds.
sp3 Hybridization: a scheme for tetrahedral and related species
The notation sp3 means that one s and three p atomic orbitals mix to form a set
of four hybrid orbitals with different directional properties.
Fig. 5.6 (a) The directions of the orbitals that make up a set of four sp3 hybrid orbitals
correspond to a tetrahedral array.
(b) The relationship between a tetrahedron and a cube; in CH4, the four H atoms occupy
alternate corners of a cube, and the cube is easily related to a Cartesian axis set.
Worked example 5.1 Hybridization scheme for the nitrogen atom in NH3
Use VSEPR theory to account for the structure of NH3, and suggest an
appropriate hybridization scheme for the N atom.
Other hybridization schemes
sp3d hybrid orbitals: one s, three p, and one d atomic orbitals mix to form a set
of five orbitals with different directional properties
5.3 Valence bond theory: multiple bonding in polyatomic molecules
C2H4
C [He]2s22p2
H 1s1
The p-component of the overall carbon–carbon
bond is weaker than the s-component and hence a
C=C double bond, though stronger than a CC
single bond, is not twice as strong; the CC bond
enthalpy terms in C2H4 and C2H6 are 598 and 346
kJ mol1 respectively.
Fig. 5.8 (a) Ethene is a planar molecule with H  C H and C C H bond angles close
to 120o . (b) An sp2 hybridization scheme is appropriate to describe the s-bonding
framework. (c) This leaves a 2p atomic orbital on each C atom; overlap between them
gives a C C p-interaction.
HCN
C [He]2s22p2
N [He]2s22p3
H 1s1
Fig. 5.9 (a) The linear structure of HCN; colour code: C, grey; N, blue; H, white.
(b) An sp hybridization scheme for C and N can be used to describe
the s -bonding in HCN.
(c) The p-character in the C N bond arises from 2p–2p overlap.
BF3
B [He]2s22p1
F [He]2s22p5
Fig. 5.10
(a) BF3 possesses a trigonal planar
structure.
(b) 2p–2p overlap between B and F
leads to the formation of
a p -interaction.
(c) Boron–fluorine double bond
character is also deduced by
considering the resonance structures
for BF3; only those forms that
contribute significantly are shown.
Worked example 5.2 Valence bond treatment of the bonding in [NO3] 
(a) The [NO3]  ion has D3h symmetry. What does this tell you about its structure?
(b) Draw a set of resonance structures (focusing only on those that contribute
significantly) for the nitrate ion.
(c) Use an appropriate hybridization scheme to describe the bonding in [NO3]  .
(c) Using a hybridization
scheme, we should end
up with a bonding
picture that corresponds
to that depicted by the
resonance structures.
NO s–bonds is beween sp2 hybrid
Orbital of N and sp2 hybrid orbital of O.
The next step is to consider multiple
bonding character.
Each N and O atom has an unused 2p
atomic orbital lying perpendicular to the
plane of the molecule. Overlap between
the 2p atomic orbital on nitrogen with
one of those on an oxygen atom gives
rise to one localized p -bond.
Molecular orbital diagrams:
ligand group orbital approach in triatomic molecules
In order to overcome the difficulty of drawing MO diagram for four sets of orbitals or
more, it is common to resolve the MO description of a poly atomic molecule into a three component problem , a method known as the ligand group orbital (LGO) approach .
Consider the two 1s a tomic
orbitals of the two H atoms .
Each 1s atomic orbital has
two possible phases and,
when the two 1s orbitals
are taken as a group , there
are two possible phase
combinations .
The number of ligand group
orbitals formed = the number of
atomic orbitals used.
In constructing an MO diagram for XH2 (Figure 5.11), we consider the interactions
of the valence atomic orbitals of X with the ligand group orbitals of the H ----- H
fragment. Ligand group orbital LGO(1) has the correct symmetry to interact with the
2s atomic orbital of X, giving an MO with H- X- H s-bonding character. The
symmetry of LGO(2) is matched to that of the 2pz atomic orbital of X.
An important result of the MO treatment of the bonding in XH2 is that the s -bonding
character in orbitals 1 and 2 is spread over all three atoms, indicating that the bonding
character is delocalized over the H-X -H framework. Delocalized bonding is a general
result within MO theory.
A bent triatomic: H2O
Mulliken Symbol Notation
1)- A or B: 1-dimensional representations
E : 2-dimensional representations
T : 3-dimensional representations
2)- A = symmetric with respect to rotation by the Cn axis
B = anti-symmetric w/respect to rotation by Cn axis
Symmetric = + (positive) character
Anti-symmetric =  (negative) character
Subscripts 1 and 2 associated with A and B symbols indicate whether a C2
axis  to the principle axis produces a symmetric (1) or anti-symmetric (2)
result.
Although the symmetry labels in the character tables are upper case (e.g. A1, E,
T2g) The corresponding symmetry labels for orbitals are lower case (e.g. a1, e, t2g).
To illustrate its use, let us consider the 2s atomic orbital of the O atom in water :
Apply each symmetry operation of the C2v point group in turn.
Applying the E operator leaves the 2s atomic orbital unchanged.
Rotation about the C2 axis leaves the atomic orbital unchanged.
Reflections through the sv and sv ’ planes leave the 2s atomic orbital
unchanged. These results correspond to the following row of characters:
and this matches those for the symmetry type A1 in the C2v character table.
We therefore label the 2s atomic orbital on the oxygen atom in water as an a1
orbital.
The oxygen 2 px orbital
This matches the row of characters for symmetry type B1 in the C2v character
table, and the 2px orbital therefore possesses b1 symmetry.
The oxygen 2 py orbital
This corresponds to symmetry type B2 in the C2v character table, and the 2py
orbital is labelled b2.
The oxygen 2 pz orbital
Like the 2s orbital, the 2pz orbital there-fore has a1 symmetry.
BH3
NH3
CH4
Molecular orbital theory: BF3
5.7 Molecular orbital theory: learning to use the theory objectively
p-Bonding in CO2
p-Bonding in[NO3]
SF6
The valence orbitals of the S atom in
SF6 can be classified as follows:
. the 3s orbital has a1g symmetry;
. the 3px, 3py and 3pz orbitals are
degenerate and the orbital set has t1u
symmetry.
octahedron.
Separate sets of LGOs can therefore
be formed from the F 2s orbitals and
from the F 2p orbitals. Furthermore,
the 2p orbitals fall into two classes:
those that point towards the S atom
(radial orbitals, diagram 5.7) and
those that are tangential to the
octahedron (diagram5.8).
Three-centre two-electron interactions
In a 3c-2e bonding interaction , two electrons occupy a bonding
MO which is delocalized over three atomic centres.
Consider [HF2]
The bonding in [HF2] can be described in terms of the
interactions of the H1s orbital (sg symmetry) with the LGOs of an
F--- F fragment. If we assume a relatively large sp separation for
fluorine, then sets of LGOs can be constructed as follows:
. LGOs formed by combinations of the F 2s orbitals;
. LGOs formed by combinations of the F 2pz orbitals;
. LGOs formed by combinations of the F 2px and 2py orbitals.
Although the H 1s orbital is of the
correct symmetry to interact with
either of the F---F sg LGOs, there
is a poor energy match between
the H 1s orbital and F---F 2s2s
combination.
A more advanced problem: B2H6
The structure of B2H6( D2h symmetry) is shown in Figure 5.31.
Features of particular interest are that:
. despite having only one valence electron, each bridging H atom is
attached to two B atoms;
. despite having only three valence electrons, each B atom is attached
to four H atoms;
. the B  H bond distances are not all the same and suggest two types
of B  H bonding interaction.
Bonding pictures for B2H6 which assume either sp3 or sp2 hybridized B
centres are frequently adopted, but this approach is not entirely
satisfactory.