Chapter5 Bonding in Polyatomic Molecules

Chapter 5 Bonding in polyatomic molecules 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

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Orbital hybridization - sp

ψ sp _ hybrid =

ψ sp _ hybrid = Hybrid orbitals – generated by mixing the characters of atomic orbitals

1 (ψ 2 s + ψ 2 px ) 2

1 (ψ 2 s − ψ 2 px ) 2

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Orbital hybridization – sp2

ψ sp 2 _ hybrid =

1 2 ψ 2 s + ψ 2 px 3 3

ψ sp 2 _ hybrid =

1 1 1 ψ 2 s − ψ 2 px + ψ 2 p y 3 6 2

ψ sp 2 _ hybrid =

1 1 1 ψ 2 s − ψ 2 px − ψ 2 p y 3 6 2

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sp3 hybrid orbitals – one s and three p atomic orbitals mix to form a set of four orbitals with different directional properties

(

)

(

)

(

)

ψ sp 3 _ hybrid =

1 ψ 2 s −ψ 2 p x + ψ 2 p y −ψ 2 p z 2

(

)

ψ sp 3 _ hybrid =

1 ψ 2 s −ψ 2 p x − ψ 2 p y −ψ 2 p z 2

ψ sp 3 _ hybrid =

1 ψ 2 s +ψ 2 px +ψ 2 p y +ψ 2 p z 2

ψ sp 3 _ hybrid =

1 ψ 2 s + ψ 2 p x −ψ 2 p y −ψ 2 p z 2

sp3d hybrid orbitals – one s, three p, and one d atomic orbitals mix to form a set of five orbitals with different directional properties

[Ni(CN)5]3-

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Valence bond theory – multiple bonding in polyatomic molecules

Valence bond theory – multiple bonding in polyatomic molecules

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Valence bond theory – multiple bonding in polyatomic molecules

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Molecular orbital theory: ligand group orbital approach in triatomic molecules

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Molecular orbital theory: BF3

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Consider the S3 operation (=C3·σh) on the pz orbitals in the F3 fragment.

C3 2 ψ2

ψ1 S3

ψ3

ψ2

ψ1

Unique, ‘S3’

S3

ψ1

ψ3

S3

ψ1

ψ3

ψ2

S3

S3 ψ2

ψ2

ψ2

σh

C3

ψ1

ψ3

S3

ψ3

ψ3

ψ1

Unique, ‘S32’ The resulting wavefunction contributions from the S3 and S32 operations are –ψ3 and –ψ2, respectively.

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BF33 Resonance Structures

The presence of the resonance contributions account for the partial double bond character in BF3

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SF6

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5

Find number of unchanged radial 2p orbitals that are unchanged under each Oh symmetry operation.

2

3

C2 Note the C2 axis bisect the planes containing 4 p orbitals. The C2 axis contains no 2p orbitals.

1

4

C2 6

E

C3

C2

C4

6

0

0

2

C2 i S4 (C42) 2 0 0

S6

σh

σd

0

4

2

Use the reduction formula to find the resulting symmetries: a1g, t1u, eg Could derive the equations for the LGOs for the F6 fragment.

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1 (ψ 1 +ψ 2 +ψ 3 +ψ 4 +ψ 5 +ψ 6 ) 6 1 ψ (t1u )1 = (ψ 1 −ψ 6 ) 2 1 ψ (t1u ) 2 = (ψ 2 −ψ 4 ) 2 1 ψ (t1u )3 = (ψ 3 −ψ 5 ) 12 ψ (eg )1 = (2ψ 1 −ψ 2 −ψ 3 −ψ 4 −ψ 5 + 2ψ 6 ) 12 1 ψ (eg ) 2 = (ψ 2 −ψ 3 + ψ 4 −ψ 5 ) 2

ψ (a1g ) =

Three-center twoelectron interactions

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