chapter 6: a qualitative theory of molecular organic photochemistry december 5, 2002 larisa...

Chapter 6: A Qualitative Theory of Molecular Organic

Photochemistry

December 5, 2002

Larisa Mikelsons

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:

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

6.2 Potential Energy Curves and Potential Energy Surfaces

Diatomic molecule

Nuclear geometry described by internuclear separation

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

6.3 Movement of a Classical Representative Point on a Surface

QuickTime™ and aGIF decompressor

are needed to see this picture.

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



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

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 environmentmoves point along the energy surface

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

6.5 Radiationless Transitions on P.E. Surfaces

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QuickTime™ and aPhoto - JPEG decompressor


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

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

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

6.6 Diradicaloid Geometries



Diradicaloid geometry

Radical pairs, diradicals, zwitterions

Often correspond to touchings, CI, or avoided crossing minima

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 there’s a shallow minimum for a very stretched bond

Bond Twisting and Breaking of Ethylene

C C

H

H

H

H

twist

C C

H

H

H

H

Diradicaloidgeometry at 90o

(6.4)



• 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

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

Commonly Encountered Orbital Interactions



When all other factors are equal, the reactions which is downhill thermodynamicallyis favoured over a reaction that is uphill thermodynamically

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(, *)



Favoured by the rule ofmaximum positive overlap

Photochemically allowed

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 satisfiedfor an n, * reaction to be considered plausible

6.9 Orbital and State Correlation Diagrams



• 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

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:



S0(cyclobutene) = 22

S0(butadiene) = (1)2(2)2 CONS0(butadiene) = (1)2(3*)2 DIS

Assuming that the shape of the T1 energy surface parallels the S1 energy surface,we can create the following working adiabatic state correlation diagram:



g.s. allowed pericyclic reactions g.s. forbidden pericyclic reactions

Smooth transformation Possible avoided

crossing



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

chapter 6: a qualitative theory of molecular organic photochemistry december 5, 2002 larisa...

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