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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
*RFI
(*I or *P)P
hν
F = funnel from excited to ground state surfaceI = ground state reactive intermediate*I = excited state of a reactive intermediate*P = excited state of product
R
Global paradigm for R + hν P:
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6.1 Introduction to a Theory of Organic Photoreactions
*RFI
(*I or *P)P
hν
F = funnel from excited to ground state surfaceI = ground state reactive intermediate*I = excited state of a reactive intermediate*P = excited state of product
R
Global paradigm for R + hν 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
Diatomic molecule
Nuclear geometry described by internuclear separation
From Prof. Robb’swebsite
Polyatomic molecule
Nuclear geometry representedby the center of mass
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6.3 Movement of a Classical Representative Point on a Surface
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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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Near r.t, collisions between molecules in solution provide a reservoir of continuous energy
(~0.6 kcal mol-1 per impact)
6.4 The Influence of Collisions and Vibrations on the Motion of the Rep. Point
on an Energy Surface
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6.4 The Influence of Collisions and Vibrations on the Motion of the Rep. Point
on an Energy Surface
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Near r.t, collisions between molecules in solution provide a reservoir of continuous energy
(~0.6 kcal mol-1 per impact)
Energy exchange with environmentmoves point along the energy surface
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6.5 Radiationless Transitions on P.E. Surfaces
a) Extended surface touching
b) Extended surfacematching
c) Surface crossing
d) Excited stateminimum over a g.s. maximum
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6.5 Radiationless Transitions on P.E. Surfaces
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Reactions of n, * statesStretching a bond
Exciplex, excimerformation
Pericyclicreactions
Twist about a C=C bond
a) Extended surface touching
b) Extended surfacematching
c) Surface crossing
d) Excited stateminimum over a g.s. maximum
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The Non-Crossing Rule
Diagrams from http://www.chemsoc.org/exemplarchem/entries/2002/grant/non-crossing.html#fig112
Surface Crossing Avoided crossing
• 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
Diagram from http://www.chemsoc.org/exemplarchem/entries/2002/grant/conical.html
n-2 dimensional Intersection space
2D branchingspace “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
The trajectory of the point as it approaches the apex of the CI is determined by:1) The gradient of the energy change as a function of nuclear motion2) The direction of nuclear motions which best mix the adiabatic wavefunctions that
determine its motion
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6.6 Diradicaloid Geometries
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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
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• 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 there’s a shallow minimum for a very stretched bond
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Bond Twisting and Breaking of Ethylene
C C
H
H
H
H
twist
C C
H
H
H
H
Diradicaloidgeometry at 90o
(6.4)
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• 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 orbitaldetermined by:
1) The energy gap between the 2 orbitals2) The degree of positive orbital overlap between the 2 orbitals
Principle of maximum positive overlap: reactions rates are proportional to thedegree of positive (bonding) overlap of orbitals
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Commonly Encountered Orbital Interactions
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When all other factors are equal, the reactions which is downhill thermodynamicallyis 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 thesymmetries of the reactant MOs are the same symmetries as the product Mos
Concerted photochemical reactions can only take place from S1(, *) since aspin change is required if we start in T1(, *)
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Favoured by the rule ofmaximum 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:
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Interactions define the orbital requirements which must be satisfiedfor an n, * reaction to be considered plausible
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6.9 Orbital and State Correlation Diagrams
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• 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 symmetryi j ij = ---ij
a a Sa s As a As s S
s symmetry: wavefunction does not change sign within the molecular plane
a symmetry: wavefunction changes sign above and below the molecular plane
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6.10 Typical State Correlation Diagrams for Concerted Photochemical Pericyclic Reactions
H
HH
H
H
H
Conrotatory Disrotatory
C2 xy
(6.8)
1 4
32
1
4
3
2C2 C2 C2-axes
(6.9)
1 4
32
1
4
2 3Reflection planexy
(6.10)
There are 2 main symmetry elements for the cyclobutene 1,3-butadiene reaction:
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S0(cyclobutene) = 22
S0(butadiene) = (1)2(2)2 CONS0(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:
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g.s. allowed pericyclic reactions g.s. forbidden pericyclic reactions
Smooth transformation Possible avoided
crossing
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Simplified schematic of the 2 lowest singlet surfaces for a concerted pericyclic reaction:
4N e- concerted pericyclic reactionsare generally photochemicallyallowed
4N + 2 e- concerted photoreactionsare generally photochemicallyforbidden
Concerted pericyclic reactionswhich are g.s. forbidden are generally e.s. allowed in S1 due toa miminum which corresponds to adiradicaloid
Pericyclic reactions which are g.s. allowed are generally e.s. forbiddenin S1 because of a barrier toconversion to product structure andthe lack of suitable surface crossingfrom S1 to S0
4N or 4N + 2 = # of e-s involved in bond making or bond breaking