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Molecular Orbital Theory

• In principle, the electronic structure of molecules can be worked out in the

same way as for atoms:

 –> solve the Schrödinger equation!

• This gives molecular orbitals rather than atomic orbitals –> compared to valence bond theory, electrons are not confined to the 

bonding region between two atoms but highly delocalized

• Challenge: It is difficult to solve the Schrödinger equation for molecular

species (only through approximation!)

But: Approximate MO’s can be also constructed through linear combination

of AO’s or group orbitals 

=> qualitative molecular orbital theory (QMOT)

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Rules for the Use of MOs

• When two AOs to give MOs, two MOs will be produced

• For mixing, AOs must have similar energies

• Each orbital can have a total of two electrons (Pauli principle)

• Lowest energy orbitals are filled first (Aufbau principle)

• Unpaired electrons have parallel spin (Hund’s rule)

Bond order = 1/2 (bonding electrons – antibonding electrons)

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LCAO approximation

• LCAO = “Linear Combination of Atomic Orbitals”

• The wavefunctions of molecular orbitals (MO) can be approximated by taking linearcombinations of atomic orbitals

Note: the number of MOs must be equal the number of atomic orbitals of the constituent atoms! 

Ψσ  =

1

2Ψ1s

( H a) +Ψ1s

( H b)[ ]

linear combination (addition) of the wavefunction from two 1s orbitals

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LCAO approximation

• A second MO (molecular orbital) can be obtained via subtraction of twoAOs

Ψσ  *=

1

2Ψ1s

( H a) −Ψ1s

( H b)[ ]

linear combination (subtraction) of the wavefunction from two 1s orbitals

nodal plane

 –> the resulting wavefunction has a nodal plane perpendicular tothe H–H bond axis (electron density = zero); the energy of anelectron in this orbital is higher compared to the additive linearcombination = “antibonding orbital ”

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Diatomic Molecules

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energy

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Molecular Orbitals of Polyatomic Molecules

• Concept of linear combination can be also applied to polyatomic molecules

 –> the resulting MOs are delocalized over the entire molecule

• Symmetry analysis by group theory predicts those linear combinations, which

lead to bonding, anti-bonding or non-bonding MOs

• The energy of the resulting MOs is measured via photoelectron spectroscopy or

estimated with quantum chemical calculations

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Bonding Analysis in CH3+

ψ 1

ψ 2 ψ 3

ψ 4

ψ 7

ψ 5 ψ 6

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Pyramidal Methyl Radical: Walsh Diagrams

Geometric distortion of CH3+ (planar) to •CH3 (pyramidal) alters the shape and energy of

the MO’s:

=> Walsh Diagram : depicts the orbital energies as a function of angular distortions

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Problem 1-6:  Based on QMOT determine whether BH3 is expected to adopt a

planar or pyramidal geometry.

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Using Group Orbitals to Construct Ethane MO’s

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Using Group Orbitals to Construct Ethene MO’s

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Formaldehyde

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Problem 1-7:  Use QMOT to rationalize the electrophilic nature of CH3Cl.

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Conjugated Systems: Butadiene

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Conjugated Systems: Allyl Fragment

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Conjugated Systems: Benzene

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Reactive Intermediates: Carbocations

Nomenclature: carbenium ions R3C+, “protonated carbene”

carbonium ions R5C+, “protonated quartenary carbon”

Carbenium ions are trigonal planar ; stabilized through neighboring CH3 groups

=> “hyperconjugation

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Hyperconjugation

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Reactive Intermediates: Carbocations

Carbonium ions are typically unstable in solution, detected by mass spectrometry

CH5+ can be generated with very strong

acids such as FSO3H

“Non-classical carbocations” can be

considered carbonium ions:

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Reactive Intermediates: Carbanions

CH3 – has a total of 8 valence electrons –> pyramidal geometry is preferred

Inversion barrier strongly dependent on hybridization:

Barriers: NH3 ~5kcal/mol

NF3 ~50 kcal/mol

Note: Substituents that stabilize a carbanion by π

delocalization will favor planar structure:

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Reactive Intermediates: Radicals and Carbenes

Methyl radical: CH3 7 valence electrons; geometry trigonal planar, low barrier

Carbenes: neutral species, CR2; two spin state possible:

=> with smaller HCH bond angles, the singlet state becomes preferred! Also, substitution withπ donors leads to stabilization of the singlet state