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Molecular Orbitals - Conservation of Orbital Symmetry in Concerted Processes. Quantum mechanics : application of mathematics and physics to describe phenomena that exhibit quantized functions.
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Molecular Orbitals - Conservation of Orbital Symmetry in Concerted Processes
Quantum mechanics: application of mathematics and physics to describe phenomena that exhibit quantized functions.
eg. Electrons in atoms behave like waves. Wave mechanics can be used to solve for energies and orbitals.
The math is very complicated and time consuming. By making assumptions and approximations, it is possible to get solutions that are useful, if not exact.
In fact, we do not need to do any math if we understand the results on a qualitative level.
wave function: Eψ = h2d2ψ/2mdx2 + v(x)ψ
n = 3 nodes = 2
n = 2 nodes = 1
n = 1 nodes = 0
Three dimensional in a spherical potential energies and probabilities of finding an electron with given energy, orbitals.
s, p, d, f Atomic Orbitals (AOs)
phase is important!
n = 1, no nodes, lowest energy, s orbital
n = 2, one node, higher energy, p orbital
Covalent bonds result from the overlap (combinations) of atomic orbitals to produce molecular orbitals.
Molecular orbitals result from Linear Combinations of Atomic Orbitals.
LCAO wave mechanics of MO’s
φ = atomic wave function
ψ = molecular wave function
For molecule A—B
ψ = φA φB
a) appreciable overlap of atomic orbitals
b) energies of atomic orbitals are ~ equal
c) same symmetry
Hydrogen H2 H:H
LCAO of two AO’s two MO’s
ψ2 = φA- φB antibondingσ* • •
ψ1 = φA+ φB bondingσ • •
ethylene CH2=CH2 look only at π orbitals
How many AO’s in the π system? p + p two
How many MO’s result? also two
How many electrons in the π system? 2
ψ = pz pz
How many AO’s in the π system? four
How many MO’s result? four
How many electrons in the π system? 4
allyl cation CH2=CH—CH2 3 AO’s 3 MO’s 2 π e-
Δ or hv
conjugated polyene cyclic compound
The mechanism is concerted!
Electrocyclic reactions are both stereoselectiveand stereospecific
In the concerted electrocyclic reactions, symmetry must be conserved for bonding to take place.
The molecular orbital involved = highest occupied molecular orbital in thepolyene. HOMO
In a photochemical electrocyclic reaction, the important orbital is HOMO* ( the first excited state ):
HOMO* = ψ3
4n + 2
diene + dienophile cyclohexene
[ 4 + 2 ] cycloaddition
1. diene must be sigma-cis
2. syn- addition
Molecular orbital symmetry must be conserved.
HOMO = highest occupied molecular orbital
LUMO = lowest unoccupied molecular orbital
[ 2 + 2 ] cycloadditions do not occur readily under thermal conditions, but occur easily photochemically.
[ i + j ]
4n + 2
“no mechanism, no reaction – reaction.”
Migration of an atom or group with its sigma bond within a conjugated π framework.
[1,3] sigmatropic rearrangement of carbon requires inversion of configuration about a chiral center:
Conservation of molecular orbital symmetry is useful in concerted reactions.
Electrocyclic reactions: stereochemistry, conrotatory or disrotatory
thermal HOMO (polyene)
photochemical HOMO* (polyene)
Cycloadditions: supra-supra allowed or forbidden
thermal LUMO & HOMO
photochemical LUMO & HOMO*
suprafacial allowed or forbidden HOMO (π + 1)
retention or inversion of configuration