Upload
pedro-ribeiro
View
217
Download
0
Embed Size (px)
Citation preview
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 1/11
1-44
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)
1-45
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)
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 2/11
1-46
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
1-47
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 ”
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 3/11
1-48
Diatomic Molecules
1-49
energy
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 4/11
1-50
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
1-51
Bonding Analysis in CH3+
ψ 1
ψ 2 ψ 3
ψ 4
ψ 7
ψ 5 ψ 6
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 5/11
1-52
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
1-53
Problem 1-6: Based on QMOT determine whether BH3 is expected to adopt a
planar or pyramidal geometry.
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 6/11
1-54
Using Group Orbitals to Construct Ethane MO’s
1-55
Using Group Orbitals to Construct Ethene MO’s
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 7/11
1-56
Formaldehyde
1-57
Problem 1-7: Use QMOT to rationalize the electrophilic nature of CH3Cl.
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 8/11
1-58
Conjugated Systems: Butadiene
1-59
Conjugated Systems: Allyl Fragment
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 9/11
1-60
Conjugated Systems: Benzene
1-61
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
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 10/11
1-62
Hyperconjugation
1-63
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:
8/6/2019 E250Ed01
http://slidepdf.com/reader/full/e250ed01 11/11
1-64
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:
1-65
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