Dr. Said M. El-Kurdi1 Bonding in polyatomic molecules Chapter 5.

Dr. Said M. El-Kurdi 1

Bonding in polyatomic molecules

Chapter 5

Dr. Said M. El-Kurdi 2

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.A polyatomic species contains three or more atoms.

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there is a problem in trying to derive a localized bonding scheme in terms of an atomic orbital basis set

Consider H2O

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5.2 Valence bond theory: hybridizationof 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.

Like all bonding theories, orbital hybridization is a model, and should not be taken to be a real phenomenon.

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Hybrid orbitals are generated by mixing the characters of atomic orbitals ( close in energy).

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.

if we begin with n atomic orbitals, we must end up with n orbitals after hybridization.

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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

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BeCl2

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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.

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The model of sp2 hybridization can be used to describe the -bonding in trigonal planar molecules such as BH3.

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sp3 Hybridization: a scheme for tetrahedraland 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.

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The directions of the orbitals that make up a set of four sp3 hybrid orbitals correspond to a tetrahedral array

CH4

The relationship between a tetrahedron and a cube; in CH4

NH3

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sp3d (dz2 ) trigonal bipyramidal

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Sp3d (dx2 y2) square-based pyramidal

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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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5.3 Valence bond theory: multiplebonding in polyatomic molecules

C2H4

121.3o

117.4o

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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This leaves a 2p atomic orbital on each C atom; overlap between them gives a CC -interaction.

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HCN

An sp hybridization scheme is appropriate for both C and N

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The -character in the CN bond arises from 2p–2p overlap.

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BF3

Boron trifluoride is trigonal planar

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BF3

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[NO3] D3h symmetry planar

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Of the 24 valence electrons, 18 are accommodated either in -bonds or as oxygen lone pairs.

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ligand group orbital (LGO) approach.

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

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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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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The number of ligand group orbitals formed = the number ofatomic orbitals used.

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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.Delocalized bonding is a general result within MO theory.

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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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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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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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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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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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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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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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The 2pz orbital

the 2pz orbital therefore has a1 symmetry.

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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?

what happens to each of the two H 1s orbitals when each symmetry operation is performed?

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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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(i) we can construct only two ligand group orbitals, (ii) the symmetry of each LGO must correspond to one of

the symmetry types in the character table.

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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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5.5 Molecular orbital theory applied tothe polyatomic molecules BH3, NH3 and CH4

BH3

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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 sethas 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

how many H 1s orbitals are left unchanged by each symmetry operation in the D3h point group

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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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The MO diagram for BH3 can now be constructed by allowing orbitals of the same symmetry to interact.

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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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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.

Building a MO diagram for NH3

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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 sethas e symmetry.

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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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CH4

the 2s orbital has a1 symmetry;the 2px, 2py and 2pz orbitals are degenerate and theorbital set has t2 symmetry.

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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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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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5.6 Molecular orbital theory: bondinganalyses soon become complicated

The BF3 molecule has D3h symmetry.

the atomic orbitals of the Batom 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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Ligand group orbitals involving the F 2s orbitals in BF3 and having a1’ and e’ symmetries

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5.7 Molecular orbital theory: learningto use the theory objectively

drawing a partial MO diagram for the molecule in questiondrawing a partial MO diagram for the molecule in question

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[NO3]