1. Bonding in polyatomic molecules
Chapter 5
Bonding in polyatomic molecules
Dr. Said M. El-Kurdi

2. A polyatomic species contains three or more atoms.
5.1 Introduction
In Chapter 2, we considered three approaches to the bonding in diatomic molecules:
Lewis structures;
valence bond (VB) theory;
molecular orbital (MO) theory.
A polyatomic species contains three or more atoms.
Dr. Said M. El-Kurdi

3. Consider H2O
there is a problem in trying to derive a localized bonding scheme in terms of an atomic orbital basis set
Dr. Said M. El-Kurdi

4. 5.2 Valence bond theory: hybridization of atomic orbitals
The word ‘hybridization’ means ‘mixing’ and when used in the context of atomic orbitals, it describes a way of deriving spatially directed orbitals which may be used within VB theory.
Like all bonding theories, orbital hybridization is a model, and should not be taken to be a real phenomenon.
Dr. Said M. El-Kurdi

5. sp Hybridization: a scheme for linear species
Hybrid orbitals are generated by mixing the characters of atomic orbitals ( close in energy).
A set of hybrid orbitals provides a bonding picture for a molecule in terms of localized -bonds.
sp Hybridization: a scheme for linear species
if we begin with n atomic orbitals, we must end up with n orbitals after hybridization.
Dr. Said M. El-Kurdi

6. Dr. Said M. El-Kurdi

7. sp hybrid orbital which possesses 50% s and 50% p character.
represent two wavefunctions which are equivalent in every respect except for their directionalities with respect to the x axis.
The model of sp hybridization can be used to describe the -bonding in a linear molecule such as BeCl2
Dr. Said M. El-Kurdi

8. BeCl2
Dr. Said M. El-Kurdi

9. 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.
Dr. Said M. El-Kurdi

10. The model of sp2 hybridization can be used to describe the -bonding in trigonal planar molecules such as BH3.
Dr. Said M. El-Kurdi

11. Dr. Said M. El-Kurdi

12. 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.
Dr. Said M. El-Kurdi

13. The directions of the orbitals that make up a set of four sp3 hybrid orbitals correspond to a tetrahedral array
Dr. Said M. El-Kurdi

14. CH4
The relationship between a tetrahedron and a cube; in CH4

15. NH3

16. sp3d (dz2 ) trigonal bipyramidal
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17. Sp3d (dx2 y2) square-based pyramidal
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18. Hybridization of s, px, py, pz, dz2 and dx2 y2 atomic orbitals gives six sp3d2 hybrid orbitals corresponding to an octahedral arrangement.
hybridize only the s, px, py and dx2 y2 atomic orbitals, the resultant set of four sp2d hybrid orbitals corresponds to a square planar arrangement
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20. 5.3 Valence bond theory: multiple bonding in polyatomic molecules
C2H4
117.4o
121.3o
each C centre is approximately trigonal planar and the -bonding framework within C2H4 can be described in terms of an sp2 hybridization scheme
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21. This leaves a 2p atomic orbital on each C atom; overlap between them gives a CC -interaction.
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22. An sp hybridization scheme is appropriate for both C and N
HCN
An sp hybridization scheme is appropriate for both C and N
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23. The -character in the CN bond arises from 2p–2p overlap.
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24. Boron trifluoride is trigonal planar
BF3
Boron trifluoride is trigonal planar
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25. BF3
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26. [NO3]
D3h symmetry
planar
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27. Of the 24 valence electrons, 18 are accommodated either in -bonds or as oxygen lone pairs.
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29. MO approach to bonding in linear XH2: symmetry matching by inspection
5.4 Molecular orbital theory: the ligand group orbital approach and application to triatomic molecules
MO approach to bonding in linear XH2:
symmetry matching by inspection
ligand group orbital (LGO) approach.
consider the bonding in a linear triatomic XH2 in which the valence orbitals of X are the 2s and 2p atomic orbitals.
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30. These are called ligand group orbitals (LGOs)
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.
These are called ligand group orbitals (LGOs)
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33. The number of ligand group orbitals formed = the number of
atomic orbitals used.
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34. Delocalized bonding is a general result within MO theory.
The -bonding character in orbitals 1 and 2 is spread over all three atoms, indicating that the bonding character is delocalized over the HXH framework.
Delocalized bonding is a general result within MO theory.
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35. Character tables: an introduction
5.4 Molecular orbital theory: the ligand group orbital approach and application to triatomic molecules
Character tables: an introduction
The H2O molecule
Each point group has an associated character table
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36. Symmetry labels give us information about degeneracies as follows:
The left-hand column in a character table gives a list of symmetry labels.
Symmetry labels give us information about degeneracies as follows:
. A and B (or a and b) indicate non-degenerate;
. E (or e) refers to doubly degenerate;
. T (or t) means triply degenerate.
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37. A bent triatomic: H2O
The labels in the first column (under the point group symbol) tell us the symmetry types of orbitals that are permitted within the specified point group.
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38. 1 means that the orbital is unchanged by the operation,
The numbers in the column headed E (the identity operator) indicate the degeneracy of each type of orbital; in the C2v point group, all orbitals have a degeneracy of 1, i.e. they are non-degenerate.
Each row of numbers following a given symmetry label indicates how a particular orbital behaves when operated upon by each symmetry operation.
1 means that the orbital is unchanged by the operation,
1 means the orbital changes sign,
0 means that the orbital changes in some other way.
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39. Apply each symmetry operation of the C2v point group in turn.
Applying the E operator leaves the 2s atomic orbital unchanged.
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.
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40. The same test is now carried out on each atomic orbital of the O atom.
The oxygen 2px orbital
This matches the row of characters for symmetry type B1 in the C2v character table, and the 2px orbital therefore possesses b1 symmetry.
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41. The oxygen 2py orbital
This corresponds to symmetry type B2 in the C2v character table, and the 2py orbital is labelled b2.
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42. the 2pz orbital therefore has a1 symmetry.
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43. The next step is to work out the nature of the H-----H ligand group orbitals that are allowed within the C2v point group.
Since we start with two H 1s orbitals, only two LGOs can be constructed.
what happens to each of the two H 1s orbitals when each symmetry operation is performed?
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44. and a ‘0’ means that ‘no orbitals are unchanged by the operation’
in which a ‘2’ shows that ‘two orbitals are unchanged by the operation’,
and a ‘0’ means that ‘no orbitals are unchanged by the operation’
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45. we can construct only two ligand group orbitals,
the symmetry of each LGO must correspond to one of the symmetry types in the character table.
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46. We now compare the row of characters above with the sums of two rows of characters in the C2v character table.
A match is found with the sum of the characters for the A1 and B2 representations. As a result, we can deduce that the two LGOs must possess a1 and b2 symmetries, respectively.
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48. 5.5 Molecular orbital theory applied to
the polyatomic molecules BH3, NH3 and CH4
BH3
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49. the 2s orbital has a1’ symmetry; the 2pz orbital has a2’’ symmetry;
By using the same approach as we did for the orbitals of the O atom in H2O, we can assign symmetry labels to the orbitals of the B atom in BH3:
the 2s orbital has a1’ symmetry;
the 2pz orbital has a2’’ symmetry;
the 2px and 2py orbitals are degenerate and the orbital set
has e’ symmetry.
We now consider the nature of the three ligand group orbitals that are formed from linear combinations of the three H 1s orbitals.
how many H 1s orbitals are left unchanged by each symmetry operation in the D3h point group
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50. This same row of characters can be obtained by summing the rows of characters for the A1’ and E’ representations in the D3h character table. Thus, the three LGOs have a1’ and e’ symmetries
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51. The MO diagram for BH3 can now be constructed by allowing orbitals of the same symmetry to interact.
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53. The e’ orbitals also exhibit delocalized character, and the
The MO approach describes the bonding in BH3 in terms of three MOs of a1’ and e’ symmetries.
The a1’ orbital possesses -bonding character which is delocalized over all four atoms.
The e’ orbitals also exhibit delocalized character, and the
bonding in BH3 is described by considering a combination of all three bonding MOs.
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54. Building a MO diagram for NH3
1. The point group is C3v.
2. XN  3 and XH  2.2 so the energy levels of the AO’s on N will be lower than those on the H atoms.
3. From the C3v character table, the symmetry of the AO’s on N are: A1(2s), A1(2pz), and E(2px,2py). Each of these orbitals can interact with the LGOs from the H3 framework.
4. Fill the MO’s with the 8 valence electrons.
In NH3, the HOMO is a mostly nitrogen-based orbital that corresponds to the lone pair of electrons from VBT. This is why ammonia acts as a Lewis base at the N atom. The LUMO is the 2e level that has more H character - this shows why NH3 can also act as a Lewis acid through the H atoms.
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55. each of the 2s and 2pz orbitals has a1 symmetry;
Building a MO diagram for NH3
By seeing how each symmetry operation affects each orbital of the N atom in NH3, the orbital symmetries are assigned as follows:
each of the 2s and 2pz orbitals has a1 symmetry;
the 2px and 2py orbitals are degenerate and the orbital set
has e symmetry.
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56. To determine the nature of the ligand group orbitals, we consider how many H 1s orbitals are left unchanged by each symmetry operation in the C3v point group
It follows that the three ligand group orbitals have a1 and e symmetries.
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58. the 2s orbital has a1 symmetry;
CH4
the 2s orbital has a1 symmetry;
the 2px, 2py and 2pz orbitals are degenerate and the
orbital set has t2 symmetry.
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59. In order to construct the LGOs of the H4 fragment in CH4, we begin by working out the number of H 1s orbitals left unchanged by each symmetry operation of the Td point group.
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60. This same row of characters results by summing the rows of characters for the A1 and T2 representations in the Td character table
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61. 5.6 Molecular orbital theory: bonding analyses soon become complicated
The BF3 molecule has D3h symmetry.
the atomic orbitals of the B
atom in BF3 are assigned the following symmetries:
the 2s orbital has a1’ symmetry;
the 2pz orbital has a2’’ symmetry;
the 2px and 2py orbitals are degenerate and the orbital set has e’ symmetry.
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62. Ligand group orbitals involving the F 2s orbitals in BF3 and having a1’ and e’ symmetries
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65. 5.7 Molecular orbital theory: learning to use the theory objectively
drawing a partial MO diagram for the molecule in question
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66. [NO3]
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