Chapter 6 A Qualitative Theory of Molecular Organic Photochemistry

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: F h R *R I (*I or *P) 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 6.1 Introduction to a Theory of Organic Photoreactions Global paradigm for R + h  P: Photochemical processes F h R *R I (*I or *P) 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 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 From Prof. Robb’s website Diatomic molecule  Nuclear geometry described by internuclear separation 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 instantaneo nuclear configuration) moving along a potential energy curve possesses potential energy and kinetic energy Qu ic kTime ™ and a GIF d eco mpres sor are n eed ed to se e th is pi cture. Point attracted to the PE curve by the Coulombic attractive force of the positive nuclei for the negative electrons Force acting F = - dPE / dr on particle at r (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) Qu ic kTime ™ and a GIF d eco mpres sor are n eed ed to se e thi s pi cture. 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) Qu ic kTime ™ and a GIF d eco mpres sor are n eed ed to se e thi s pi cture. Energy exchange with environment moves point along the energy surface 6.5 Radiationless Transitions on P.E. Surfaces a) Extended surface touching Extended surface matching Surface crossing Excited state minimum over a g.s. maximum b) c) d) 6.5 Radiationless Transitions on P.E. Surfaces a) Extended surface touching Extended surface matching Surface crossing Excited state minimum over a g.s. maximum Reactions of n, * states Stretching a  bond b) c) d) Qu ic kTime ™ a nd a Ph oto - J PEG d ec ompres so r are n eed ed to se e th is p i cture. Exciplex, excimer formation Pericyclic Twist about a C=C bond reactions The Non-Crossing Rule Surface Crossing Avoided crossing Diagrams from http://www.chemsoc.org/exemplarchem/entries/2002/grant/non-crossing.html#fig112 • Valid for Zero order approx.s • Two curves may cross • Applies to polyatomic molecules • Valid for higher approx.s (with distortions of a molecule and loss of idealized symmetry) • 2 states with the same energy and same geometry “mix” to produce 2 adiabatic surfaces which “avoid” each other Conical Intersections 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 6.6 Diradicaloid Geometries Diradicaloid geometry Radical pairs, diradicals, zwitterions Qu ic kTime ™ and a GIF d eco mpres sor are n eed ed to se e th is pi cture. 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 Qu ic kTime ™ a nd a GIF d eco mpres sor are n eed ed to se e th is p i cture. • 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 H C H C H H H twist H C C H (6 .4) H Dir adica loid o ge ome try at 90 Qu ic kTime ™ and a GIF d eco mpres sor are n eed ed to se e thi s pi cture. • 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 orbital determined by: 1) 2) The energy gap between the 2 orbitals 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 Qu ic kTime ™ a nd a GIF d eco mpres sor are n eed ed to se e th is p i cture. 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 S1(, *) since a spin change is required if we start in T1(, *) Favoured by the rule of maximum positive overlap Q ic kTime ™ and a u G d eco mpres sor IF are n eed ed to se e thi s pi cture. Photochemically allowed An Exemplar for Photochemical Reactions Which Produce Diradical Intermediates Orbital interactions of the n, * state with substrates: Q ic kTime ™ and a u G d eco mpres sor IF are n eed ed to se e thi s pi cture. Interactions define the orbital requirements which must be satisfied for an n, * reaction to be considered plausible 6.9 Orbital and State Correlation Diagrams s symmetry: wavefunction does not change sign within the molecular plane Qu ic kTime ™ a nd a GIF d eco mpres sor are n eed ed to se e th is p i cture. 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: Orbital symmetry i a a s s j a s a s State symmetry ij = ---ij S A A S 6.10 Typical State Correlation Diagrams for Concerted Photochemical Pericyclic Reactions H H Conrotatory H Disrotatory H H H C2 xy (6 .8) There are 2 main symmetry elements for the cyclobutene  1,3-butadiene reaction: 3 2 1 3 C2 4 1 4 Reflection plane xy 2 1 4 3 2 C2 C2-axes (6 .9) 2 1 4 3 (6 .10) S0(cyclobutene) = 22 Qu ic kTime ™ a nd a GIF d eco mpres sor are n eed ed to se e th is p i cture. S0(butadiene) = (1)2(2)2 CON S0(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: Smooth transformation Q ic kTime ™ and a u G d eco mpres sor IF are n eed ed to se e thi s pi cture. Possible avoided crossing g.s. allowed pericyclic reactions 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 4N + 2 e- concerted photoreactions are generally photochemically forbidden Concerted pericyclic reactions which are g.s. forbidden are generally e.s. allowed in S1 due to a miminum which corresponds to a diradicaloid Pericyclic reactions which are g.s. allowed are generally e.s. forbidden in S1 because of a barrier to conversion to product structure and the lack of suitable surface crossing from S1 to S0 4N or 4N + 2 = # of e-s involved in bond making or bond breaking Qu ic kTime ™ a nd a GIF d eco mpres sor are n eed ed to se e th is pi cture.