1. Bonding in polyatomic molecules
Chapter 5
Bonding in polyatomic molecules
TOPICS
Hybridization of atomic orbitals
Molecular orbital theory: ligand group orbitals
Delocalized bonding
Partial molecular orbital treatments

2. 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

3. 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.

4. 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.

5. 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.

6. The probability of finding the electron somewhere in space is taken to be 1.

7. 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.

8. 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.

9. 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.

10. 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

12. 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.

13. 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.

14. BF3
B [He]2s22p1 F [He]2s22p5
Fig. 5.10
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.

15. Worked example 5.2 Valence bond treatment of the bonding in [NO3] 
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]  .

16. (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.

17. 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.

18. In constructing an MO diagram for XH2 (Figure 5
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.

20. A bent triatomic: H2O

21. 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).

22. 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.

23. 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.

26. BH3

28. NH3

30. CH4

32. Molecular orbital theory: BF3

34. 5.7 Molecular orbital theory: learning to use the theory objectively
p-Bonding in CO2

35. p-Bonding in[NO3]

36. 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.

37. 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).

39. 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.

40. 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.

42. 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.

44. Bonding pictures for B2H6 which assume either sp3 or sp2 hybridized B centres are frequently adopted, but this approach is not entirely satisfactory.