Molecular Orbitals - Conservation of Orbital Symmetry in Concerted Processes
Dec 22, 2015
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.
n = 3 nodes = 2
n = 2 nodes = 1
n = 1 nodes = 0
vibrating strings or waves
wave function: Eψ = h2d2ψ/2mdx2 + v(x)ψ
PHASE!
Electrons and atomic wave functions.
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
Molecular Orbitals (MOs)
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
Bonding when:
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 antibonding σ* • •
one node
ψ1 = φA + φB bonding σ • •
no nodes
•
π – molecular orbitals
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
π – molecular orbitals for 1,3-butadiene?
CH2=CH—CH=CH2
How many AO’s in the π system? four
How many MO’s result? four
How many electrons in the π system? 4
cis -3,4-dimethyl-cyclobutene
heat
cis,trans -2,4-hexadiene
trans -3,4-dimethyl-cyclobutene
heat
trans,trans -2,4-hexadiene
Electrocyclic reactions are both stereoselective and stereospecific
In the concerted electrocyclic reactions, symmetry must be conserved for bonding to take place.
The molecular orbital involved = highest occupied molecular orbital in the polyene. HOMO
C C C C
C C C C
C C C C
C C C C
LCAOs MOs
E
3
1
2
4
HOMO
cis -3,4-dimethyl-cyclobutene
heat
cis,trans -2,4-hexadiene
trans -3,4-dimethyl-cyclobutene
heat
trans,trans -2,4-hexadiene
CH3
H
CH3
H
CH3
H
H
CH3
In a photochemical electrocyclic reaction, the important orbital is HOMO* ( the first excited state ):
C C C C
C C C C
C C C C
C C C C
LCAOs MOs
E
3
1
2
4
HOMO* = ψ3
Woodward – Hofmann Rules for Electrocyclic Reactions:
conrotatory disrotatory
disrotatory conrotatory
thermal photochemical
4n
4n + 2
Cycloadditions
Diels-Alderdiene + dienophile cyclohexene
[ 4 + 2 ] cycloaddition
1. diene must be sigma-cis
2. syn- addition
+[ 4 + 2 ]
The Diels-Alder cycloaddition is a concerted reaction:
Molecular orbital symmetry must be conserved.
C C C C
C C C C
C C C C
C C C C
LCAOs MOs
E
3
1
2
4
C C
C C
LCAOs MOs
E
1
2 LUMO
HOMO
LUMO
HOMO
CH2=CH2
CH2=CHCH=CH2
Which orbitals? thermal = HOMO + LUMO
HOMO = highest occupied molecular orbital
LUMO = lowest unoccupied molecular orbital
HOMO
LUMO
symmetryallowedsupra-supra
LUMO
HOMO
[ 2 + 2 ] cycloadditions do not occur readily under thermal conditions, but occur easily photochemically.
+hv
+heat
NR
Woodward – Hofmann Rules for Cycloadditions:
supra-supra
forbidden
supra-supra
allowed
supra-supra
allowed
supra-supra
forbidden
4n
4n + 2
Thermal Photochemical[ i + j ]
Sigmatropic rearrangements“no mechanism, no reaction – reaction.”
Migration of an atom or group with its sigma bond within a conjugated π framework.
G G | |
C—(C=C)n (C=C)n—C
[ 1,3 ]
[ 1,5 ]
[ 1,7 ]
Suprafacial migration of R
allowed with inversionof configuration
allowed with retentionof configuration
allowed with inversionof configuration
H
D
OAc
H* H
H
OAc
D*
[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*
Sigmatropic rearrangements
suprafacial allowed or forbidden HOMO (π + 1)
retention or inversion of configuration