Molecular Orbitals - Conservation of Orbital Symmetry in Concerted Processes. Quantum mechanics : application of mathematics and physics to describe phenomena that exhibit quantized functions.
Molecular Orbitals - Conservation of Orbital Symmetry in Concerted Processes
Quantum mechanics Concerted Processes: 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.
vibrating strings or waves Concerted Processes
wave function: Eψ = h2d2ψ/2mdx2 + v(x)ψ
n = 3 nodes = 2
n = 2 nodes = 1
n = 1 nodes = 0
Electrons and Concerted Processesatomic 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 Concerted Processes 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: Concerted Processes
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 • •
π – molecular orbitals Concerted Processes
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 Concerted Processes - molecular orbitals for ethylene
π – molecular orbitals for 1,3-butadiene? Concerted Processes
How many AO’s in the π system? four
How many MO’s result? four
How many electrons in the π system? 4
1,3-butadiene Concerted Processes
+ Concerted Processes
allyl cation CH2=CH—CH2 3 AO’s 3 MO’s 2 π e-
Electrocyclic reactions: Concerted Processes
Δ or hv
conjugated polyene cyclic compound
The mechanism is concerted!
Electrocyclic reactions are both Concerted Processesstereoselectiveand 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 conserved for bonding to take place.photochemical electrocyclic reaction, the important orbital is HOMO* ( the first excited state ):
HOMO* = ψ3
Woodward – Hofmann Rules for Electrocyclic Reactions: conserved for bonding to take place.
4n + 2
Cycloadditions conserved for bonding to take place.
diene + dienophile cyclohexene
[ 4 + 2 ] cycloaddition
1. diene must be sigma-cis
2. syn- addition
The Diels-Alder cycloaddition is a concerted reaction: conserved for bonding to take place.
Molecular orbital symmetry must be conserved.
CH conserved for bonding to take place.2=CH2
Which orbitals? conserved for bonding to take place.thermal = HOMO + LUMO
HOMO = highest occupied molecular orbital
LUMO = lowest unoccupied molecular orbital
[ 2 + 2 ] cycloadditions do not occur readily under thermal conditions, but occur easily photochemically.
thermal: LUMO + HOMO conditions, but occur easily photochemically.
Woodward – Hofmann Rules for Cycloadditions: conditions, but occur easily photochemically.
[ i + j ]
4n + 2
Sigmatropic rearrangements conditions, but occur easily photochemically.
“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