December 5, 2002
Larisa Mikelsons

Global paradigm for R + h   P:
R h

*R
F
I
(*I or *P)
F = funnel from excited to ground state surface
I = ground state reactive intermediate
*I = excited state of a reactive intermediate
*P = excited state of product
P

Global paradigm for R + h   P:
Photochemical processes
R h

*R
F
I
(*I or *P)
F = funnel from excited to ground state surface
I = ground state reactive intermediate
*I = excited state of a reactive intermediate
*P = excited state of product
P
Molecular geometries of products differ from molecular geometries of reactants

Diatomic molecule

Nuclear geometry described by internuclear separation

Diatomic molecule

Nuclear geometry described by internuclear separation
From Prof.
Robb’s website
Polyatomic molecule

Nuclear geometry represented by the center of mass

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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 on particle at r
F = - dPE / dr (6.1)

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)
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Energy exchange with environment moves point along the energy surface

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

a) Extended surface touching b) Extended surface matching c) Surface crossing d) Excited state minimum over a g.s. maximum
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Reactions of n,

* states
Stretching a
 bond
Exciplex, excimer formation
Pericyclic reactions
Twist about a C=C bond

Surface Crossing Avoided crossing
Diagrams from http://www.chemsoc.org/exemplarchem/entries/2002/grant/non-crossing.html#fig112
• 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

2D branching space
n-2 dimensional
Intersection 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:
1) The gradient of the energy change as a function of nuclear motion
2) The direction of nuclear motions which best mix the adiabatic wavefunctions that determine its motion

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Diradicaloid geometry
Radical pairs, diradicals, zwitterions
Often correspond to touchings, CI, or avoided crossing minima

An exemplar for diradicaloid geometries produced by
 bond stretching and breaking:
H-H

H--------H

H + H
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• Along S
0 the bond is stable except at large separations, and a large E needed to stretch and break the
 bond a is
• The bond is always unstable along T
• Along S
1 and S
2
1 and little or no E a is needed for cleavage the bond is unstable and there’s a shallow minimum for a very stretched bond


H
H
C C
H
H twist
H
C C
H
H
H
Diradicaloid geometry at 90 o
(6.4)
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• There is an avoided crossing between S
0
(

) and S
2
(

*)
• S
0
(

) and T
1
(

,

*) touch (but it is not extended) at the diradicaloid geometry.
The same thing occurs with S
1 and S
2

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:
1) The energy gap between the 2 orbitals
2) 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

Commonly Encountered Orbital
Interactions
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When all other factors are equal, the reactions which is downhill thermodynamically is favoured over a reaction that is uphill thermodynamically

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 S
1 spin change is required if we start in T
1
(

,

*)
(

,

*) since a
Favoured by the rule of maximum positive overlap
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Photochemically allowed

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 satisfied for an n,

* reaction to be considered plausible

s symmetry: wavefunction does not change sign within the molecular plane
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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: s s
Orbital symmetry
 i a a a s
 j a s
State symmetry
 ij
= -- i
 j
S
A
A
S

6.10 Typical State Correlation Diagrams for
Concerted Photochemical Pericyclic Reactions
H
H
H
Conrotatory Disrotatory
(6.8)
H H
H
C
2
 xy
There are 2 main symmetry elements for the cyclobutene

1,3-butadiene reaction:
3
2 3
2
(6.9)
C
2
C
2
C
2
-axes
1 4 1
4
2 3 2 3 Reflection plane
 xy
(6.10)
1 4
1
4

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S
0
(cyclobutene) =

2

2
S
0
(butadiene) = (

S
0
(butadiene) = (

1
1
)
) 2 (

2
2 (

3
) 2 CON
*) 2 DIS

Assuming that the shape of the T
1 energy surface parallels the S
1 energy surface, we can create the following working adiabatic state correlation diagram:
Smooth transformation g.s. allowed pericyclic reactions
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Possible avoided crossing g.s. forbidden pericyclic reactions

Simplified schematic of the 2 lowest singlet surfaces for a concerted pericyclic reaction:
4N e- concerted pericyclic reactions are generally photochemically allowed
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4N + 2 e- concerted photoreactions are generally photochemically forbidden
Concerted pericyclic reactions which are g.s. forbidden are generally e.s. allowed in S
1 due to a miminum which corresponds to a diradicaloid
Pericyclic reactions which are g.s. allowed are generally e.s. forbidden in S
1 because of a barrier to conversion to product structure and the lack of suitable surface crossing from S
1 to S
0
4N or 4N + 2 = # of e-s involved in bond making or bond breaking