CHEM 101/105 BONDING (continued) Lect-16

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CHEM 101/105 BONDING (continued) Lect-16 A Second covalent bonding theory, MOLECULAR ORBITAL THEORY accounts for covalent bonding by... before looking at MO, return for a moment to the individual unbonded atom case. Be reminded that electrons of such an atom are held in energy levels that are represented by its electron configuration.

The Molecular Orbital method uses linear combinations of symmetry-related orbitals of bonded atoms, to form molecular orbitals that will contain all the electrons present in a molecule. The molecular orbitals should be considered as energy levels of the molecule. A corresponding energy level diagram is constructed. Electrons are introduced into the diagram and a net bond order is determined. The magnitude of the bond order

depends on the number of electrons in the molecule and the type of molecular orbitals they occupy.

Consider the MO analysis of bonding in hydrogen molecule as formed from two separated hydrogen atoms: Each separated hydrogen atom has one electron in its vs and it is in a 1s atomic orbital. Both electrons have the same energy, and this feature is represented by placing them at the same vertical level in the diagram. Next consider the shapes and trigonometric signs of

s

atomic orbitals. They are spherical in shape and have a positive trigonometric sign. Orbitals can overlap if they have the same symmetry and trigonometric sign.

ONE linear combination is the SUM of their functions

[

ψ

1s H atom a( )

+

ψ

1s H atom b( )] which can be diagrammed as shown to the right. The result INCREASES electron density directly between the two nuclei, and is a SIGNA BOND

(

σ

)

The OTHER is the DIFFERENCE of their functions

ψ

1

s

(H atom a)

ψ

1

s

(H atom b)

This result decreases electron density directly between the two nuclei and is called a

SIGMA ANTIBOND

(

σ

* )

The sigma bonding MO

(

σ

)

is MORE stable than the separated atoms and is represented on a LOWER level in the energy diagram, relative to the two separated hydrogen atoms.

The sigma antibonding MO

(

σ

* )

is LESS stable than the separated atoms and is represented on a HIGHER level in the energy diagram, relative

to the two separated hydrogen atoms. The resulting molecular orbital energy diagram has three sections.

The CENTER section displays energy levels for the molecule.

Left and right sections display energies of separated atoms

+

+

plus

SUM Combination of two 1s atomic orbitals The signs are trignometric, NOT CHARGES.

+

+

-DIFFERENCE Combination of two 1s atomic orbitals The signs are trignometric, NOT CHARGES.

MINUS

+

σ *

1s

1s

H a H b

σ

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It remains to introduce two electrons into the center part of the diagram. They are entered in lower levels first, then into higher levels. As before, pairing of electrons is avoided until necessary. In this case both electrons are placed in the lower SIGMA BONDING MO, and paired. This happens because the energy difference between

σ

bonding and

σ *

is greater (in this case) than the repulsion between two paired electrons occupying the same molecular orbital.

In MOLECULAR ORBITAL ENERGY LEVEL DIAGRAMS the BOND ORDER is determined by the following expression:

(

)

Bond Order

=

bonding electrons

antibonding electrons

2

There are TWO electrons in the SIGMA BONDING MO, and NONE in the SIGMA STAR ANTIBONDING MO, so Bond Order =

2

0

2

1



 =

This analysis informs that the two atoms in hydrogen molecule are joined by a

single bond

, and that all electrons are paired so the molecule will be

diamagnetic

. Using this same MOLECULAR ORBITAL approach, analyze the bonding, and resulting properties, for each of the following:

ex.

H

2 1-

H

2 1+

He

2

Include hydrogen molecule in this series and decide which has the longest bond length? diamagnetic? least likely to be stable? smallest bond dissociation energy?

The

2s

atomic orbitals can also combine to form

σ

and

σ *

molecular orbitals . So expand this approach to include larger atoms and analyze the bonding in each of the following cases:

ex.

Li

2

Be

2

LiBe

Be

21+

In this series which has the shortest bond length? diamagnetic? least likely to be stable? largest bond dissociation energy?

Consider next how

2 p

atomic orbitals are combined to form molecular orbitals. Recall the shape of the

p

atomic orbitals and also make note of their trigonometric signs as shown below:

σ *

1s

1s

H a H b

↑ ↓

σ

pz

+

-+

-px

+

-py

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Orbitals can combine when (1) they are of the same symmetry, i.e.,

pz

of atom A can overlap with

pz

of atom B, but not with the

py

or

px

of atom B, and (2) when their lobes are of same trigonometric sign.

Linear combinations of two

pz

atomic orbitals. Note the orientation and resulting molecular orbitals formed:

ψ

2pz atom a( )

+

ψ

2pz atom b( )

ψ

2pz atom a( )

ψ

2pz atom b( )

There is a conservation at play here. Two atomic orbitals can only form two molecular orbitals. In this case TWO

pz

atomic orbitals combine to form TWO molecular orbitals a

σ ( )

p

and a

σ * ( )

p

.

Linear combinations of two

px

atomic orbitals. Note the orientation and resulting molecular orbitals formed.

ψ

2px atom a( )

+

ψ

2px atom b( )

ψ

2px atom a( )

ψ

2px atom b( )

Linear combinations of two

py

atomic orbitals result in a similar set of bonding and anti-bonding molecular orbitals, except for the fact that they are normal to the MO sets from the

px

and

pz

. So six

p

-type atomic orbitals combine to form six MO's; one

σ

and two

Π

bonding, and one

σ

* and two

Π

* anti-bonding.

+

-

+

-+

-

-2pz atom a

2pz atom b

p "sigma" bonding MO

PLUS

-

+

+

-2pz atom b

2pz atom a

p "sigma" anti-bonding MO

-

+

-

+

MINUS

Relative Energy

2pz atom a

2px atom b

+

-+

-+

+

-

-A

A

bonding MO

PLUS

2pz atom a

2px atom b

+

-A

A*

anti-bonding MO

-+

+

+

-MINUS

RELATIVE ENERGY

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As noted before, SIGMA bonds overlap on a direct line between the two nuclei of the bonded atoms, and PI bonds do not.

The molecular orbital energy level diagram including

p

-type atomic orbitals becomes a little more involved in that some levels change relative energies as heavier FRO8 homonuclear diatomic molecules are encountered. For our purposes, two diagrams will be used: (1) one is for FRO8 diatomic up to, and including dinitrogen (

N

2 ), and (2) the other for heavier atoms. As noted before, each molecular orbital energy level can accommodate TWO electrons, and electrons won't pair until necessary.

Consider the first diagram (Figure A) and use it to analyze bonding in the following homonuclear diatomic molecules: ex.

B

2

C

2

N

2

Compare bond lengths, magnetic character, and bond dissociation energies for this series.

Figure A.

The second diagram (Figure B) is used for diatomic molecules/ions heavier than

N

2 . It differs in that relative energies of the PI BONDING MO's, and the SIGMA BONDING MO resulting from combining

2 pz

atomic orbitals, are SWITCHED. This diagram is shown below.

Use it to analyze bonding in the following homonuclear diatomic molecules: ex.

O

2

F

2

Compare bond lengths, magnetic character, and bond dissociation energies for this series.

Use both diagrams (as required) to analyze bonding and properties of the following substances:

ex.

BC

NO

1−

CO

OF

BF

CN

1−

O

21+

O

21−

O

22−

1s

2p

1s

2s

2p

2s

F

F*

F

F*

A

A

F

A

A*

F*

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Figure B.

A table showing bond orders and some properties of diatomic substances is on the next page.

1s

2p

1s

2s

2p

2s

F

F*

F

F*

A

A

F

A

A*

F*

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Main Group FRO8 Diatomic Molecules and Ions

Bond Orders and Magnetic Character - via Molecular Orbital Theory

Experimental Bond Dissociation Energies (kJ / mole) and Bond Lengths (Angstroms) BOND ORDER 1 1.5 2 2.5 3 2.5 2 1.5 1 Total VSE 6 7 8 9 10 11 12 13 14 Magnetic Char. para 2 para 1 diamag para 1 diamag para 1 para 2 para 1 diamag Figure A A A A A B B B B Specie B 2 C 2 N 2 O 2 F 2 BDE 274 602 941 493 139 Bond Length 1.589 1.243 1.098 1.207 1.417 Specie BN BO BF O 2 1+ O 2 1- O 2 2- BDE 385 799 548 393 Bond Length 1.281 1.204 1.262 1.123 1.26 1.49

Specie BeO BeF

BDE 444 568 Bond Length 1.331 1.361 Specie CN 1+ CN CN 1- Cl 2 1+ Cl 2 BDE 786 415 239 Bond Length 1.173 1.172 1.14 1.892 1.988 Specie CO 1+ CO CF Br 2 BDE 804 1069 443 190 Bond Length 1.115 1.128 1.272 2.281 Specie N 2 1+ NO 1+ NO I 2 BDE 841 677 149 Bond Length 1.116 1.062 1.151 2.667 BOND ORDER 1 1.5 2 2.5 3 2.5 2 1.5 1 Total VSE 6 7 8 9 10 11 12 13 14

Figure

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