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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 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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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
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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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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 a)Extended surface touching b) Extended surface matching c)Surface crossing d)Excited state minimum over a g.s. maximum
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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
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The Non-Crossing Rule Diagrams from http://www.chemsoc.org/exemplarchem/entries/2002/grant/non-crossing.html#fig112 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
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Conical Intersections Diagram from http://www.chemsoc.org/exemplarchem/entries/2002/grant/conical.html 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
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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 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
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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
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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: 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
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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 S 1 ( , *) since a spin change is required if we start in T 1 ( , *) 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 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
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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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S 0 (cyclobutene) = 2 2 S 0 (butadiene) = ( 1 ) 2 ( 2 ) 2 CON S 0 (butadiene) = ( 1 ) 2 ( 3 *) 2 DIS
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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
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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 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
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