Chapter 6: A Qualitative Theory of Molecular Organic Photochemistry

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Chapter 6 A Qualitative Theory of Molecular
Organic Photochemistry
December 5, 2002 Larisa Mikelsons
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6.1 Introduction to a Theory of Organic
Photoreactions
Global paradigm for R h? ? P
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6.1 Introduction to a Theory of Organic
Photoreactions
Global paradigm for R h? ? P
Photochemical processes
Molecular geometries of products differ from
molecular geometries of reactants
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6.2 Potential Energy Curves and Potential Energy
Surfaces
Diatomic molecule ? Nuclear geometry described
by internuclear separation
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6.2 Potential Energy Curves and Potential Energy
Surfaces
From Prof. Robbs website
Diatomic molecule ? Nuclear geometry described
by internuclear separation
Polyatomic molecule ? Nuclear geometry
represented by the center of mass
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6.3 Movement of a Classical Representative Point
on a Surface
Point (representing a specific instantaneous
nuclear configuration) moving along a potential
energy curve possesses potential energy and
kinetic energy Point attracted to the PE curve
by the Coulombic attractive force of the
positive nuclei for the negative
electrons Force acting F - dPE / dr (6.1) on
particle at r
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6.4 The Influence of Collisions and Vibrations on
the Motion of the Rep. Point on an Energy Surface
Near r.t, collisions between molecules in
solution provide a reservoir of continuous
energy (0.6 kcal mol-1 per impact)
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6.4 The Influence of Collisions and Vibrations on
the Motion of the Rep. Point on an Energy Surface
Near r.t, collisions between molecules in
solution provide a reservoir of continuous
energy (0.6 kcal mol-1 per impact) Energy
exchange with environment moves point along the
energy surface
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6.5 Radiationless Transitions on P.E. Surfaces

• Extended surface
• touching
• b) Extended surface
• matching
• Surface crossing
• Excited state
• minimum over a
• g.s. maximum

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6.5 Radiationless Transitions on P.E. Surfaces

• Extended surface
• touching
• b) Extended surface
• matching
• Surface crossing
• Excited state
• minimum over a
• g.s. maximum

Twist about a CC bond
Reactions of n, ? states Stretching a ? bond
Exciplex, excimer formation
Pericyclic reactions
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The Non-Crossing Rule
Surface Crossing Avoided crossing
Diagrams from http//www.chemsoc.org/exemplarchem/
entries/2002/grant/non-crossing.htmlfig112
Valid for Zero order approx.s Valid for
higher approx.s (with distortions Two curves
may cross of a molecule and loss of
idealized symmetry) Applies to polyatomic
molecules 2 states with the same energy and
same geometry mix to produce 2 adiabatic
surfaces which avoid each other
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Conical Intersections
n-2 dimensional Intersection space
2D branching space
Ultrafast motion, Born-Oppenheimer approx.
breaks down ? no time for mixing so surface
crossings are maintained Concerted reaction
path where stereochemical info may be conserved
Since ?E 0, rate of transition limited only
by the time scale of vibrational relaxation
Diagram from http//www.chemsoc.org/exemplarchem/
entries/2002/grant/conical.html

• The trajectory of the point as it approaches the
  apex of the CI is determined by
• The gradient of the energy change as a function
  of nuclear motion
• The direction of nuclear motions which best mix
  the adiabatic wavefunctions that
• determine its motion

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6.6 Diradicaloid Geometries
Diradicaloid geometry Radical pairs,
diradicals, zwitterions Often correspond to
touchings, CI, or avoided crossing minima
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The Dissociation of the Hydrogen Molecule
An exemplar for diradicaloid geometries produced
by ? bond stretching and breaking H-H ??
H--------H ?? H H
Along S0 the bond is stable except at large
separations, and a large Ea is needed to
stretch and break the ? bond The bond is always
unstable along T1 and little or no Ea is needed
for cleavage Along S1 and S2 the bond is
unstable and theres a shallow minimum for a
very stretched bond
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? Bond Twisting and Breaking of Ethylene
There is an avoided crossing between S0(?) and
S2(?) S0(?) and T1(?,?) touch (but it is
not extended) at the diradicaloid geometry.
The same thing occurs with S1 and S2
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6.7 Orbital Interactions

• Theory of frontier orbital interactions
  reactivity of organic molecules is
• determined by the very initial CT interactions
  which result from the e-s in an
• occupied orbital moving to an unoccupied (or half
  occupied) orbital
• Extent of favourable CT interaction from the e-s
  in the HO to the LU orbital
• determined by
• The energy gap between the 2 orbitals
• The degree of positive orbital overlap between
  the 2 orbitals
• Principle of maximum positive overlap reactions
  rates are proportional to the
• degree of positive (bonding) overlap of orbitals

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Commonly Encountered Orbital Interactions
When all other factors are equal, the reactions
which is downhill thermodynamically is favoured
over a reaction that is uphill thermodynamically
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An Exemplar for Photochemical Concerted
Pericyclic Reactions
Woodward-Hoffmann rules pericyclic reactions can
only take place if the symmetries of the reactant
MOs are the same symmetries as the product
Mos Concerted photochemical reactions can only
take place from S1(?, ?) since a spin change is
required if we start in T1(?, ?)
Favoured by the rule of maximum positive
overlap Photochemically allowed
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An Exemplar for Photochemical Reactions Which
Produce Diradical Intermediates
Orbital interactions of the n, ? state with
substrates
Interactions define the orbital requirements
which must be satisfied for an n, ? reaction to
be considered plausible
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6.9 Orbital and State Correlation Diagrams
s symmetry wavefunction does not change sign
within the molecular plane a symmetry
wavefunction changes sign above and below the
molecular plane

• If there are only doubly occupied orbitals,
  the state symmetry is automatically S
• If two (and only two) half-occupied orbitals ?i
  and ?j occur in a configuration,
• the state symmetry is given by the following
  rules
• Orbital symmetry State symmetry
• ?i ?j ?ij ---?i?j
• a a S
• a s A
• s a A
• s s S

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6.10 Typical State Correlation Diagrams for
Concerted Photochemical Pericyclic Reactions
There are 2 main symmetry elements for the
cyclobutene ? 1,3-butadiene reaction
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S0(cyclobutene) ?2?2
S0(butadiene) (?1)2(?2)2 CON S0(butadiene)
(?1)2(?3)2 DIS
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Assuming that the shape of the T1 energy surface
parallels the S1 energy surface, we can create
the following working adiabatic state correlation
diagram
Smooth transformation
Possible avoided crossing
g.s. allowed pericyclic reactions g.s.
forbidden pericyclic reactions
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Simplified schematic of the 2 lowest singlet
surfaces for a concerted pericyclic reaction
4N e- concerted pericyclic reactions are
generally photochemically allowed 4N 2 e-
concerted photoreactions are generally
photochemically forbidden Concerted pericyclic
reactions which are g.s. forbidden are generally
e.s. allowed in S1 due to a miminum which
corresponds to a diradicaloid Pericyclic
reactions which are g.s. allowed are generally
e.s. forbidden in S1 because of a barrier
to conversion to product structure and the lack
of suitable surface crossing from S1 to S0
4N or 4N 2 of e-s involved in bond making
or bond breaking