Frontier Molecular Orbitals

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Third Year Organic Chemistry Course CHM3A2
Frontier Molecular Orbitals and Pericyclic
Reactions
- Prof Jon A Preece - School of
Chemistry University of Birmingham
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Prof Preeces Powerpoint Lecture Presentations
and answers to questions can be found at
Queries on course after reading around the
subject to j.a.preece_at_bham.ac.uk. Be Specific
with the problem(s) in your email. Give me three
times when you are free to see me. I will email
you back with a time to see me.
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Course Synopsis
Part Contents 1 Pericyclic Reactions These
lectures will begin with a definition of
Pericyclic reactions, and will be exemplified by
considering examples of cycloaddation,
sigmatropic, and electrocyclic reactions. It
will be highlighted how it is possible to use FMO
theory (and other theories) to predict the
constitution and stereochemical outcome of the
products. Attention will be drawn to the cyclic
transition state and the number of electrons
involved (Huckel or Mobius), highlighting that
when 4n2 electrons are involved the reaction
proceeds readily under thermal conditions, and
the reversibility of such reactions. The
concept of Linear Combination of Atomic Orbitals
to form a bond(s) (and antibond(s)) will be
revised, and extended to the linear combination
of frontier molecular orbitals. The p-molecular
orbitals of ethene, butadiene and
1,3,5-hexatriene will be considered and the
identities of the HOMO and LUMO will be
established, as well as the FMOs of a CH bond.
2i Electrocyclic Reactions This lecture will
extend the predicative nature of FMO theory
regarding the stereochemical outcomes to
electrocyclic reactions for 4 and 6 ?-electron
transition states (by defining the disrotatory or
conrotatory movement of the termini of the HOMO
in the Transition State). 2ii Cycloaddition
Reactions These lectures will introduce
cycloaddition reactions and the concepts of (i)
phase relationships of the FMOs, (ii) geometry of
approach of the FMOs (suprafacial and
antarafacial will be defined), and (iii) minimum
energy differences between the HOMO and LUMO.
These concepts will be exemplified by several
Diels-Alder and related reactions. Attention
will be drawn to the nature (chemical and
stereochemistry) of substituents and their
stereochemistry in the product. 3 Photochemically
Induced Pericyclic reactions These lecture will
extend the predicative nature of FMO theory
regarding the outcomes of electrocyclic reactions
and cycloaddition reactions by considering how
they can be induced photochemically, to give
alternative stereochemical outcomes and allow
reactions that did not go thermally.
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Part 1. Frontier Molecular Orbitals
Constructing molecular orbitals and
identifying the frontier molecular orbitals Part
2. Thermal Pericyclic Reactions (i)
Electrocyclic Reactions using FMO Theory (ii)
Cycloaddition Reactions using FMO Theory Part
3. Photochemical Pericyclic Reactions (i)
Electrocyclic Reactions using FMO Theory (ii)
Cycloaddition Reactions using FMO Theory
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Second Year Organic Chemistry Course CHM3A2 Recom
mended Reading I Fleming Frontier Orbitals and
Organic Chemical Reactions, John Wiley and Sons,
1996. Part 1 Ch 1 and Ch 2 Part 2 and
3 Ch 4
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Second Year Organic Chemistry Course CHM3A2 Fronti
er Molecular Orbitals and Pericyclic Reactions
Part 1(i) The Questions FMO Analysis Can Answer
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Ionic And Radical Reactions
To date you have seen two broad categories of
reaction
(i) Ionic reactions Here pairs of electrons
move in one direction e.g. SN2, SN1, E2 and
E1 mechnisms
(ii) Radical reactions Here single electrons
move in a correlated manner e.g. chlorination
of alkanes
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Pericyclic Reactions
Pericyclic reactions are the third distinct
class. They involve cyclic transition states In
which all bond breaking and bond making steps
take place in commensurate manner And there is
no sense of the flow of electrons.
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Pericyclic Reactions Electrocyclic Reactions
Stereospecific Reaction
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0
Clockwise
There is no real senses of flow for the electrons
in pericyclic reactions
Anti-Clockwise
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Pericyclic Reactions Cycloaddition Reactions
Kinetic Product
Thermodynamic Product
Stereospecific Reaction
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0
Regiospecific Reaction
0
100
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Revision 1,3Syndiaxial Interactions
1,3-syndiaxial interactions
1
3
2
axial
equitorial
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Thermodynamic and Kinetic Control
Thermodynamic Product Not Formed in
Cycloaddition Reaction
Kinetic Product Formed in Cycloaddition Reaction
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Pericyclic Reactions Sigmatropic Reactions
Stereospecific Reaction
Regiospecific Reaction
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0
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Pericyclic Reactions Why are they so specific?
Pericyclic reactions show high degrees of (i)
Stereoselectivity (ii) Regioselectivity,
and (iii) Diastereoselectivity
Thus, an obvious question to ask ourselves at
this point is why are pericyclic reactions so
selective?
To help begin to answer this question we shall
briefly need to revise the SN2 reaction mechanism
where YOU WILL remember that this reaction type
was highly stereoselective leading to inversion
of chiral centres.
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Revision SN2 Reaction Mechanism
Nucleophile attacks from behind the C-Cl
s-bond. This is where the s-antibonding orbital
of the C-Cl bond is situated.
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The concerted flow of both pairs of electrons in
the SN2 reaction mechanism leads to the
transition state which allows the stereochemical
information to be retained, i.e. a
stereoselective reaction.
This SN2 reaction mechanism should be contrasted
to the SN1 reaction mechanism where the
arrow-pushing is the same but the two pairs
electrons do not flow in a concerted fashion.
Instead, the haloalkane C-Cl bond heterolytically
cleaves to give the planar sp2 hybridised
carbocation reactive intermediate. Now the
nucleophile can attack from either side of the
carbocation leading to racemisation, i.e. a
non-stereoselective reaction.
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Revision Transition States
Discussion of reaction mechanisms frequently
include discussions of the nature of the
transition state for each step in a reaction
sequence  or at least for the slowest or rate
limiting step. A transition state is the point
of highest energy in a reaction or in each step
of a reaction involving more than one step. The
nature of the transition state will determine
whether the reaction is a difficult one,
requiring a high activation enthalpy (DG), or an
easy one. Transition states are always energy
maxima, I.e. at the top of the energy hill, and
therefore, can never be isolated there are no
barriers to prevent them from immediately
rolling downhill to form the reaction products
or intermediates (or even reform the starting
materials). A transition states structure is
difficult to identify accurately. It involves
partial bond cleavage and partial bond formation.
However, it is nigh on impossible to estimate
whether the transition state is an early one
(looks more like the starting materials) or a
late one (looks more like the products)
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Revision Transition States
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Pericyclic Reactions Transition States
Thus, now we can start to understand why
pericyclic reactions are so highly stereo-,
regio-, and diasteroselective.
Pericyclic reactions involve concerted flow of
pairs of electrons going through transition
states which retains stereochemical information
that was present in the starting material.
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Pericyclic Reactions Involve Cyclic Transition
States
Cyclic Transition State
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Pericyclic reactions involve ene and polyene
units. Thus, the transition states involve the
overlap of p-molecular orbitals in the case of
electrocyclic and cycloaddition reactions, and a
p-molecular orbital and s-molecular orbital in
the case of sigmatropic reactions.
How do the orbitals overlap?
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Frontier Molecular Orbitals
In order to understand the selectivity of
pericyclic reactions, we need to understand these
molecular orbitals and how they overlap.
In particular, we need to know how the Frontier
Molecular Orbitals (FMOs) interact in the
starting material(s) which lead to the cyclic
transition states.
We will first revise some simple molecular
orbitals of a C-H s-bond and a CC p-bond and
then extend this analysis to highly conjugated
linear polyenes and related structures/
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Learning Objectives Part 1 Frontier
Molecular Orbitals
CHM2C3B Introduction to FMOs

• After completing PART 1 of this course you should
  have an understanding of, and be able to
  demonstrate, the following terms, ideas and
  methods.
• Given a set of n p-orbitals you should be able to
  construct a molecular orbital energy level
  diagram which results from their combination.
• (ii) In this diagram you should be able to
  identify for each MO
• ?nodes
• ?the symmetric (S) or antisymmetric (A) nature
  of the MO towards a C2 axis or mirror plane
• ?the bonding, nonbonding or antibonding nature
  of it
• (iii) For a set of n molecular orbitals you
  should be able to identify the frontier molecular
  orbitals.
• ?the highest occupied molecular orbital (HOMO )
• ?the lowest unoccupied molecular orbital (LUMO)
• (iv) The HOMO (thermal reaction) interactions are
  important when evaluating the probability of an
  unimolecular reaction occurring and the
  stereochemical outcome see electrocyclic
  reactions.
• The HOMO/LUMO (thermal reaction) interactions of
  the reacting species are important when
  evaluating the probability of (i) a
  bimolecular reaction occurring and the
  stereochemical outcome see cycloaddition
  reactions, and (ii) a unimolecular reaction
  occurring and the stereochemical outcome see
  sigmatropic reactions.
• The geometry, phase relationship and energy of
  interacting HOMOs and LUMOS is important for
  evaluating the probability of a reaction
  occurring and the stereochemical outcome.

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s-Bond Two s Atomic Orbitals
Molecular Orbitals
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s-Bond One s Atomic Orbital and One sp3 Atomic
Orbital
Molecular Orbitals
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p-Bond Two p Atomic Orbitals
Molecular Orbitals
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The linear combination of n atomic
orbitals leads to the formation of n
molecular orbitals
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A SIMPLE Mathematical Description of a MO
The combination of two (or more) p-atomic
orbitals (or any orbitals) to afford 2
p-molecular orbitals can be described by the
following simple mathematical relationship
p ccf1 cdf2
p caf1 cbf2
fm Electronic distribution in the atomic
orbitals
Cn Coeffecient a measure of the contribution
which the atomic orbital is making to the
molecular orbital
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The probability of finding an electron in an
occupied molecular orbital is 1.
The probability of finding an electron in an
occupied molecular orbital is the Sc2
Thus, for the ethene p-molecular orbitals
p ccf1 cdf2
Sc2 cc2 cd2 1
1
2
Cc 1/v2
Cd -1/v2
Negative
p caf1 cbf2
Sc2 ca2 cb2 1
1
2
Ca 1/v2
Cb 1/v2
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So what about the combination of 3 or 4 or 5 or 6
p-atomic orbitals. That is to consider
conjugated systems
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The Allyl Cation, Radical and Anion 3p AOs to
give 3p MOs
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Allyl Cation
Allyl Radical
Allyl Anion
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Thus, allyl systems result from the combination
of 3 conjugated p-orbitals. Therefore, this will
result in 3 p-molecular orbitals.
When we constructed the p-molecular orbitals of
ethene, each contributing AO was the same size,
i.e. the coeffecient c were 1/v2 or -1/v2.
When there are three or more p-atomic orbitals
combining the size of each contributing p-atomic
orbital will not be equal (but they will be
symmetrical about the centre).
Finally, we refer to the p-MOs and p-MOs as y1,
y2, y3 (yn)
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The Allyl p-Molecular Orbitals
We can consider the molecular orbital (the
electron density) being described by a SINE WAVE
starting and finishing one bond length beyond the
molecule
y3 2 Nodes
y3
Nodal position 4/3 1.33
1.33
Nodes
Nodal position 4/2 2
y2 1 Nodes
y2
2
y1 0 Nodes
Nodal position 4/1 4
y1
1
2
3
4
4
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For our analysis of molecular orbitals we do not
have to concern ourselves with the
coefficients. We can draw the p-AOs that make up
the p-MOs all the same size. However, we have to
always remember they are not the same size.
But it is of the utmost importance that we know
how to calculate where the nodes are placed
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Bonding, Non-Bonding, and Anti-bonding Levels
Anti-bonding
Non-bonding
Bonding
We can consider the molecular orbital (the
electron density) being described by a sine wave
starting and finishing one bond length beyond the
molecule
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LUMOs and HOMOs
LUMO Lowest Unoccupied Molecular Orbital
HOMO Highest Occupied Molecular Orbital
Allyl Radical (3e)
Allyl Anion (4e)
Allyl Cation (2e)
LUMO
LUMO
LUMO
HOMO
HOMO
HOMO
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Question 1 4 p-Molecular Orbital System
Butadiene
Construct the p-molecular orbitals of
butadiene. Identify the number of nodes, nodal
positions, HOMO and LUMO.
yn
Nodal Position
Number of Nodes
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Answer 1 4 p-Molecular Orbital System Butadiene
Construct the p-molecular orbitals of
butadiene. Identify the number of nodes, nodal
positions, HOMO and LUMO.
yn
Nodal Position
Number of Nodes
y4
3
5/4 1.25
y3
2
LUMO
5/3 1.66
y2
1
HOMO
5/2 2.5
y1
0
5/1 5
1
2
3
4
5
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A Reminder Sinusodal Wave Function
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Coefficients, cn
Each molecular orbital is described by an
equation
?n caf1 cbf2 ccf3 cnfn
Where c is referred to as the coefficient
Such that the
Sc2 1
That is to say the probability of finding an
electron in a molecular orbital is 1
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?3 caf1 cbf2 ccf3 cdf4
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We Keep FMO Analysis Simple!!
For the purpose of this course and the third year
course (Applied Frontier Molecular Orbitals and
Stereoelectronic Effects) you are expected
(i) to be able to place the nodal planes in
the correct place (ii) but not to be able to
assign the coefficients to the molecular
orbitals. That is to say you can draw the
p-orbitals that make up each molecular orbital
as the same size, whilst remembering that in
reality they are not and for high level FMO
analysis this needs to be taken into account.
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Question 2 5 p-Molecular Orbital System
Pentadienyl
Construct the p-molecular orbitals of the
cyclopentenyl system. Identify the number of
nodes and nodal positions.
yn
Molecular Orbitals
Nodal Position
Number of Nodes
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Answer 2 5 p-Molecular Orbital System
Pentadienyl
Construct the p-molecular orbitals of the
cyclopentenyl system. Identify the number of
nodes and nodal positions.
Molecular Orbitals
yn
Nodal Position
Number of Nodes
y5
6/5 1.2
4
y4
3
6/4 1.5
y3
2
6/3 2
y2
1
6/2 3
y1
0
6/1 6
6
5
1
2
3
4
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Question 3 Pentadienyl Cation, Radical Anion
Introduce the electrons and identify the HOMOs
and LUMOs
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Answer 3 Pentadienyl Cation, Radical Anion
Introduce the electrons and identify the HOMOs
and LUMOs
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Question 4 Pentadienyl Cation Anion
Generate the cation and anion and draw the
resonance structures of the above species
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Answer 4 Pentadienyl Cation, Radical Anion
Generate the cation and anion and draw the
resonance structures of the above species
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6 p-Molecular Orbital System 1, 3, 5-Hexatriene
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7 p-Molecular Orbital System
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Question 5 6p MO System
By shading the p atomic orbitals, generate the
molecular orbitals for hexa-1,3,5-triene
. Identify the number of nodes characterising
each molecular orbital. With reference to both
a mirror plane (m) and a two-fold axis, designate
the orbitals as symmetric (S) or antisymmetric
(A). Using arrows to represent electrons,
associate the six p-electrons with the
appropriate molecular orbitals of
hexa-1,3,5-triene in its ground state.
Finally, identify the HOMO and LUMO.
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Answer 5 6p MO System
By shading the p atomic orbitals, generate the
molecular orbitals for hexa-1,3,5-triene
. Identify the number of nodes characterising
each molecular orbital. With reference to both
a mirror plane (m) and a two-fold axis, designate
the orbitals as symmetric (S) or antisymmetric
(A). Using arrows to represent electrons,
associate the six p-electrons with the
appropriate molecular orbitals of
hexa-1,3,5-triene in its ground state.
Finally, identify the HOMO and LUMO.
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Question 6 MO System
Protonation of A affords B. Draw the three
resonance structures of B in which the positive
charge has formally been shifted from the oxygen
atom onto three of the five carbon atoms .
Considering only these three resonance
structures, how many (i) carbon atoms
are involved in the hybrid structure, (ii)
carbon p-orbitals are there, (iii)
p-electrons are associated with the carbon atoms,
and (iv) molecular orbitals are
associated with the combination of these carbon
p-orbitals
In an analogous fashion to how question 1 was set
out, draw out the molecular orbitals resulting
from the p-orbital combination on this carbon
framework, making sure you identify all of the
items listed in question 1.
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Answer 6 5p MO System
Protonation of A affords B. Draw the three
resonance structures of B in which the positive
charge has formally been shifted from the oxygen
atom onto three of the five carbon atoms .
Considering only these three resonance
structures, how many (i) carbon atoms
are involved in the hybrid structure, (ii)
carbon p-orbitals are there, (iii)
p-electrons are associated with the carbon atoms,
and (iv) molecular orbitals are
associated with the combination of these carbon
p-orbitals
In an anologous fashion to how question 5 was set
out, draw out the molecular orbitals resulting
from the p-orbital combination on this carbon
framework, making sure you identify all of the
items listed in question 5.
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What is the Driving Force for Controlling
Pericyclic Reactions?
The driving force which controls the product
outcome in pericyclic reactions is the in phase
combination of the FMOs (the HOMO and LUMO) of
the reacting species in the transition
state. FMO Theory is Extremely Powerful.
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Pericyclic Reactions Involve Conjugated Polyene
Systems
Pericyclic reactions involve conjugated polyene
systems. Enes and Polyenes are made by the
linear combination of p-AOs. Thus, we first need
to construct the molecular orbitals of
polyenes. Then we need to identify the Frontier
Molecular Orbitals. Finally, we will need to
construct the correct geometry for orbital
overlap of the FMOs in the transition states of
the reactions.
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HOMOs and LUMOs Highest Occupied Molecular
Orbitals Lowest Unoccupied Molecular Orbitals
In bimolecular reactions (like the SN2 and the
Diels-Alder reaction), interaction between the
two molecular components is represented by
interaction between suitable molecular orbitals
of each. The extent of the interaction depends
upon the geometry of approach of the components
since the relative geometry affects the amount of
possible overlap. It also depends on the phase
relationship of the orbitals and also upon
their energy of separation, a small energy
favouring a greater interaction. Generally,
the two reactants will interact, via the highest
occupied molecular orbital (HOMO) of one
component and the lowest unoccupied molecular
orbital (LUMO) of the other component, the
so-called frontier molecular orbitals (FMOs).
Consider the next five frames to appreciate this
paragraph of text. Consider an SN2 Reaction
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Revision Transition State Geometries of
Nucleophiles Attacking sp3 Tetrahedral Centres

Inversion of Configuration Supports this Attack
Angle
LUMO
LUMO
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The orbital containing the lone pair of electrons
on the Nu is the HOMO (Highest Occupied
Molecular Orbital) The s orbital of the C-X
bond is the LUMO (Lowest Unoccupied Molecular
Orbital) Any bimolecular reaction can be
analysed in this fashion
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Frontier Molecular Orbital Theory (FMOs)
This analysis of FMOs (HOMOs and LUMOs) for such
a simple reactions may seem pointless for a
simple SN2 reaction. It is not! Understand
it. Appreciate that for a bimolecular reaction
the HOMO of one component interacts with the LUMO
of the second component. (Additionally, for
unimolecular reaction the HOMO of the molecular
component dictates the reaction course). In this
course we will examine the use of FMOs to explain
and predict the outcomes of a class of reactions
referred to as pericyclic. The use of FMOs is
an extremely powerful tool to the synthetic
organic chemist when analysing and predicting the
outcome of pericyclic reactions.
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Summary Sheet Part 1 Frontier Molecular
Orbitals
CHM3A2 Introduction to FMOs
Molecular orbital theory is a powerful and
versatile asset to the practice of organic
chemistry. As a theory of bonding it has almost
superseded the valence bond theory. Molecular
orbital theory has proven amenable to pictorial
non-mathematical expression, given the right
answers to some decisive questions in organic
chemistry, proven the theory of most theoretical
chemists, given insight into not only to the
theory of bonding, but also to the theory of
making and breaking chemical bonds, and proven a
theory which has been able to explain the pattern
of reactivity in a class of reactions, known as
pericyclic reactions. In this course we will
concentrate solely on the use of MO theory in
predicting the outcome of pericyclic reactions.
But it should not be forgotten that MO theory is
applicable to other types of chemical
reraction To understand the importance of MO
theory, we shall consider three types of
pericyclic reactions and show how frontier
molecular orbitals of the reactants can be used
in a predicative nature to work out whether the
reaction will proceed and what the
stereo/regiochemical outcome will be. The three
types of pericyclic reactions we will consider
are electrcyclic reactions cycloaddition
reactions sigmatropic reactions We will see how
it is possible to predict the stereoselectivity,
diastereoselectivity, and regioselectivity of
pericyclic reactions by the analysis of the FMOs
of the transition states
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The precise construction of the p-molecular
orbitals by the linear combination of p-atomic
orbitals is extremely important if FMO theory is
to yield the correct stereochemical product
outcomes, Key points to note when constructing
p-molecular orbitals from the combination of
p-AOs are (i) the combination of n Aos always
affords n MOs (ii) The lowest p-MOs (?1) has no
nodal planes (iii) The next highest (?2) has one
nodal plane, and so on (iv) The nodal planes
need to be placed exactly in the Mos as described
in the lecture notes (v) Electrons fill from the
lowest MO first with no more than two electrons
in each MO.