Chapter 6: A Qualitative Theory of Molecular Organic Photochemistry December 5, 2002 Larisa Mikelsons

6.1 Introduction to a Theory of Organic Photoreactions Global paradigm for R + h  P:

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

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’s website Polyatomic molecule  Nuclear geometry represented by the center of mass

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 actingF = - 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

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

6.5 Radiationless Transitions on P.E. Surfaces a)Extended surface touching b) Extended surface matching c)Surface crossing d)Excited state minimum over a g.s. maximum

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

The Non-Crossing Rule Diagrams from Surface CrossingAvoided 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 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 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

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 S 0 the bond is stable except at large separations, and a large E a is needed to stretch and break the  bond The bond is always unstable along T 1 and little or no E a is needed for cleavage Along S 1 and S 2 the bond is unstable and there’s a shallow minimum for a very stretched bond

 Bond Twisting and Breaking of Ethylene 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

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: 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 When all other factors are equal, the reactions which is downhill thermodynamically is 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 the symmetries of the reactant MOs are the same symmetries as the product Mos Concerted photochemical reactions can only take place from S 1 ( ,  *) since a spin change is required if we start in T 1 ( ,  *) Favoured by the rule of maximum 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 satisfied for 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 symmetry  i  j  ij = ---  i  j aaS asA saA ssS 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 There are 2 main symmetry elements for the cyclobutene  1,3-butadiene reaction:

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