chemical structure: chemical bonding. molecular orbitals

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Chemical Bonding 2 MOLECULAR ORBITALS

University of Lincoln presentation

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http://chemistryfm.blogs.lincoln.ac.uk/


Molecular Orbitals

What you need to know…

• In a covalent bond, atomic orbitals overlap to produce MOLECULAR ORBITALS

• Drawing molecular orbital diagrams for the homonuclear diatomics: H2, Li2, Be2, B2, C2, N2, O2, F2

• Using molecular orbital diagrams to rationalise observed trends in the properties of molecules



The Covalent Bond – Recap

Non-bonded atoms – NO OVERLAP of

atomic orbitals

Bonded atoms – OVERLAP of

atomic orbitals

TWO ATOMS ONE MOLECULE



Which orbitals will overlap?

Rules:• Only orbitals with the same symmetry

(shape) will overlap– s-orbitals overlap with s-orbitals– p-orbitals overlap with p-orbitals

• The more similar their energy, the better the overlap (and hence, the better the bond)



Extent of Overlap, S

No overlap

No bond

Weak overlap

Weak bond

Good overlap

Good bond

S is negligible S is small S is large

Same symmetry

Different energy

Same symmetry

Some difference in energy

Same symmetry

Similar energy



Molecular Orbital Theory

Where are the electrons most likely to be found in a

molecule?

Link to “Molecular orbitals” video



Remember…

• Heisenberg’s Uncertainty Principle “Electrons are so small, it is impossible to be sure where they are at any given time”

• Schrödinger “It is possible to define volumes of space

where the electrons are most likely to be found”

– s p d and f atomic orbitals



Consider 2 Hydrogen atoms, A and B (1s1)

A B

Electron is most likely to be found within this volume



If 2 H atoms BOND to form the H2

molecule…

Because A and B are bonded together, the electrons are more likely to be found in the shared space BETWEEN the nuclei



• ATOMIC ORBITALS are volumes of space in which you are most likely to find an electron in an atom

• MOLECULAR ORBITALS are volumes of space in which you are most likely to find an electron in a molecule

• MOLECULAR ORBITAL THEORY states that in a molecule, all electrons are housed within molecular orbitals

Definitions



ATOMIC Orbitals

MOLECULAR Orbitals

H + H H2

Orbital summery



How many molecular orbitals are formed when two atoms

overlap?



TWO molecular orbitals are formed for every

two atomic orbitals that overlap:

1. A bonding orbital (low energy)2. An anti-bonding orbital (high

energy)



Remember

Only the occupied atomic orbitals are relevant

(i.e. those containing electrons)



EN

ER

GY

Bonding

Anti-bonding*

MOLECULAR ORBITALS

Atomic orbitals

of Atom A

Atomic orbitals of Atom

B



Molecular Orbitals from

s-orbital Overlap



When the overlap is directly in-line with the two nuclei the resulting bond

is called a SIGMA () bond

s-orbitals produce sigma bonds

Therefore, the two molecular orbitals are called:

bonding * anti-bonding



(1s) Bonding and *(1s) Anti-bonding orbitals for the

Hydrogen Molecule

Electrons in Electrons in an an

antibonding antibonding orbital try to orbital try to pull a bond pull a bond apart, and apart, and

result in bond result in bond weakeningweakening

or

or

ψ bonding

ψ antibonding

ψ bonding

ψ antibonding



Bonding and antibonding video

Link to “Bonding and antibonding” video


Molecular Orbital Diagram1s orbital overlap – H2

Energ

y

Ψ (antibonding)

Ψ (bonding)

Ψ (1s)A Ψ (1s)B

σ*(1s)

σ*(1s)



Molecular Orbital Diagram2s orbital overlap – Li2

Energ

y

2s 2s

σ*(2s)

σ*(2s)



Molecular Orbital Diagram2s orbital overlap – Be2

Energ

y

2s 2s

σ*(2s)

σ (2s)Be Be

Be2

Be Be

Be2



Molecular Orbitals from

p-orbital Overlap



-Bonds with p-Orbitals

z

By convention, the z-axis always runs along the main axis of the molecule

Pz-orbitals produce -bonds

End-on overlap produces a -bond

z

2pZ 2pZ σ(2pZ)



-Bonds with p-Orbitals

z

xx

Px- and Py-orbitals produce -bonds

Sideways overlap results in a bond called a Pi () bond

2px 2px π(2px)

z

x x



Molecular Orbitals from p-Orbital Overlap

• Pz-orbitals give -bonding and

*-antibonding molecular orbitals

• Px- and Py-orbitals give -bonding and *-antibonding orbitals Since -overlap is better than -overlap, the -bonding orbital is the lowest in energy (most stable) and conversely the *-antibonding is the highest in energy (least stable)



Molecular Orbital Diagram 2p-orbital overlap

Sometimes the (2pz) is higher in energy than the (2px) and (2py)

Energ

y

2p 2p

σ*(2pZ)

σ (2pZ)

π*(2py)π*(2px)

π(2py)π(2px)



2s- and 2p-orbital overlap

Energ

y

A Diagram representing the energy solutions for n=1, 2 and 3 for the Schrödinger equation of a multi-electron atom

1s

2s

3s

2p

3p

3d

N = 1

N = 2

N = 3

The 2s atomic orbital is lower in energy than the 2p atomic orbitals

Sometimes the (2pz) is higher in energy than the (2px) and (2py)

Link to “Energy level diagrams” video



2s and 2p overlap MO diagramEnerg

y

2p 2p

σ*(2pZ)

σ (2pZ)

π*(2py)π*(2px)

π(2py)π(2px)

2s 2s

σ*(2s)

σ (2s)

A molecular orbital diagram showing the approximate molecular orbitals when combining 2s and 2p orbitals. Suitable when forming homonuclear diatomic molecules involving O and F with the nuclai lying on the z-axis.



Molecular Orbital Diagram F2

Energ

y

2p 2p

σ*(2pZ)

σ (2pZ)

π*(2py)π*(2px)

π(2py)π(2px)

2s 2s

σ*(2s)

σ (2s)F F

The formation of F2. The 1s atomic orbitals are emmited. The F nuclei lie on the z-axis



Molecular Orbital DiagramO2Energ

y

2p 2p

σ*(2pZ)

σ (2pZ)

π*(2py)π*(2px)

π(2py)π(2px)

2s 2s

σ*(2s)

σ (2s)O O

The formation of O2. The 1s atomic orbitals are emmited. The O nuclei lie on the z-axis



Using Molecular Orbital Diagrams to Rationalise

(explain) Observed Trends in the Properties of Molecules



Consider the homonuclear diatomics B2, C2 andN2

Experimental FACTS:

• The vapour phase of B2 contains PARAMAGNETIC B2 molecules

• The C2 molecule is a gas phase species and is DIAMAGNETIC

• The N2 molecule is DIAMAGNETIC and has a particularly high bond energy



Definitions…

• A PARAMAGNETIC molecule contains one or more unpaired electrons

• A DIAMAGNETIC molecule contains no unpaired electrons



Lets start with B2FACT: The vapour phase of BFACT: The vapour phase of B22 contains contains

PARAMAGNETICPARAMAGNETIC B B22 molecules molecules

B

B

B B

Group 13 (3 valence electrons)

B

The ATOM

2 possible molecular structures:

B≡B B–B Bond Order =3 Bond order = 1

NOTE: Neither of these structures have unpaired electrons. They are therefore DIAMAGNETIC (not correct)



Consider the MO Diagram of B2

Energ

y

2p 2p

σ*(2pZ)

σ (2pZ)

π*(2py)π*(2px)

π(2py)π(2px)

2s 2s

σ*(2s)

σ (2s)B B



What about the bonding?

MO diagrams can give us the BOND ORDER:

BOND ORDER =½[( Number of

bonding electrons

)-( Number of anti-bonding electrons

)]



Bond order in B2

No. bonding electrons = 4

No. anti-bonding electrons = 2

BOND ORDER = ½(4-2)= 1(single bond)



Molecular Structure of B2

B B

B–B

FACT: The vapour phase of B2

contains PARAMAGNETIC

B2 molecules



What is the Molecular Structure of C2?

FACT: The CFACT: The C22 molecule is a gas phase molecule is a gas phase species and species and is DIAMAGNETIC

C

C

C

Group 14 (4 valence electrons)The ATOM

Possible molecular structure:

C=C Bond Order =2

NOTE: This structure has no

unpaired electrons and is therefore DIAMAGNETIC

(correct)



MO Diagram of C2

No unpaired electrons – therefore DIAMAGNETIC. No. bonding electrons = 6 No. anti-bonding electrons = 2BOND ORDER = ½(6-2)= 2 (double bond)

Energ

y

2p 2p

σ*(2pZ)

σ (2pZ)

π*(2py)π*(2px)

π(2py)π(2px)

2s 2s

σ*(2s)

σ (2s)C C



FACT: The C2 molecule is a gas phase species and is DIAMAGNETIC

C C

C=C Bond Order =2

In this case, the MO diagram agrees with our initial structure

Molecular Structure of C2



What is the Molecular Structure of N2?

FACT: The N2 molecule is DIAMAGNETIC and has a particularly high bond energy

N

N

N

Group 15 (5 valence electrons)The ATOM

Possible molecular structure:

N≡N Bond Order =3

NOTE: This structure has no

unpaired electrons and is therefore DIAMAGNETIC

(correct)



MO Diagram of N2

No. bonding electrons = 8. No. anti-bonding electrons = 2 BOND ORDER = ½(8-2)= 3 (triple bond). No unpaired electrons – therefore DIAMAGNETIC

Energ

y

2p 2p

σ*(2pZ)

σ (2pZ)

π*(2py)π*(2px)

π(2py)π(2px)

2s 2s

σ*(2s)

σ (2s)N N



FACT: The N2 molecule is

DIAMAGNETIC and has a particularly high bond energy

N N

N≡N Bond Order =3

In this case, the MO diagram agrees with our initial structure

Molecular Structure of N2

Triple bond is very strong – hence would expect a high

bond energy



Summary



Definitions

• Molecular Orbital Theory• Molecular Orbitals • Paramagnetism• Diamagnetism


What should you know?

• In a covalent bond, atomic orbitals overlap to produce MOLECULAR ORBITALS

• How to draw MO diagrams:H2, Li2, Be2, B2, C2, N2, O2, F2

• How to use the MO diagram to determine molecular structure (including the bond order)

• How to use the MO diagram to rationalise magnetic behaviour (paramagnetism or diamagnetism)


Acknowledgements

• JISC• HEA• Centre for Educational Research and

Development• School of natural and applied sciences• School of Journalism• SirenFM• http://tango.freedesktop.org

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