molecular orbital theory mot...nov 12, 2015  · atomic orbitals are truly wave functions and we can...

Molecular Orbital Theory (MOT)

Thursday 11/12/2015

Friday, November 13, 15

Agenda

Molecular Orbital Theory - bonding and antibonding

Hybridization

Friday, November 13, 15

RecapAtomic orbitals are truly wave functions and we can represent each orbital having a + or - wave function that can either overlap constructively or destructivelyThe probability density is highest when r = 0 - closest to the nucleusGreater concentration of electrons between the two positive nuclei > creates the bond!

Friday, November 13, 15

RecapGraphing the probability density gave us a visual representation of electron density for our H2 moleculeProbability density is lower when we just examine the two individual H atoms wave functions

Friday, November 13, 15

Destructive InterferenceStarting with our 1sa and 1sb wave functions:

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Probability Density Anti Bonding Orbitals

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Now let’s PLOT the probability density to get a visual of what the electron density really looks like for an anti bonding orbital:

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Energy LevelsNow let’s examine the energy associated with anti bonding wave functions:

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When would we use σ1s*? If there was an excited state of a Hydrogen molecule:

Hydrogen doesn’t stay in these excited states because it would fall apart or dissociate

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Significance of Energy Difference13

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Diatomic Helium, He2

Let’s look at the energy level diagram for He2 molecule:

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Lithium Dimer, Li2

Let’s look at the energy level diagram for Li2 molecule:

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E

1s

2s

1s

2s

1s

*1s

2s

*2s B.O. = 1/2 (4-2) = 1

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Lithium Dimer, Li2

Bond order follows then:

0 = No bond

1 = Single bond

2 = Double bond

3 = Triple bond

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Hybridization

Molecular orbital theory (MOT)

•For molecular orbitals to be formed two conditions must be met:

1.The atomic orbitals must be relatively close in energy for effective overlap

2.The symmetry of the atomic orbitals (sign of the wavefunction, Ψ) must be identical. (i)i.e. both Ψ+ could be positive and sum to form the σ bonding

molecular orbital. in contrast the subtractive combination would have one Ψ+ positive and one Ψ- negative resulting in σ* anti-bonding orbital

Friday, November 13, 15

Combination of atomic orbitals Molecular orbitals formed Type

s + s

σ bonding

s + sσ*

anti-bonding

s + px

σ bonding

s + pxσ*

anti-bonding

s + py non-bonding

s + pz non-bonding

px + px

σ bonding

px + pxσ*

anti-bonding

+

-

+

-

+ NB

+ NB

+

-Friday, November 13, 15

Combination of atomic orbitals Molecular orbitals formed Type

py + py

π bonding

py + py

π* anti-bonding

pz + pz

πbonding

pz + pz

π* anti-bonding

px + py non-bonding

px + pz non-bonding

py + pz non-bonding

+

+

+

+

+ NB

+ NB

+ NB

Friday, November 13, 15

Hybridization

Molecular orbital theory (MOT)

• In MOT x atomic orbitals combine to form x new molecular orbitals• i.e. two 1s1 atomic orbitals

combine to form two new molecular orbitals, σ and σ*.

Friday, November 13, 15

Hybridization

Hybridization

• Hybridization is a term used to describe the mixing of atomic orbitals to generate a set of new hybrid orbitals that are equivalent.• A hybrid orbital results from the mixing of different types of

atomic orbital on the same atom• VBT uses hybridization to provide an electronic description of

polyatomic molecules such as CH4 and NH3 but it can also account for geometries of molecules.• Three different types of hybridization:

• sp3 as seen in methane• sp2 as seen in ethene• sp as seen in ethyne

Friday, November 13, 15