A Driver’s Guide to Photochemistry: Roads (ie. Surfaces), Crossings and Intersections

1. A Driver’s Guide to Photochemistry: Roads (ie. Surfaces), Crossings and Intersections (A Discussion of MMP+ 6.1-6.6) Tracy Morkin November 26, 2002.

2. Our Road Map Where have we been? Where are we going next? • photochemical reactions • (ie. R ≠P) • - state correlation diagrams • the consequences of different • nuclear geometries • Born-Oppenheimer Approximation • may break down • photophysical properties • (ie. R = P) • - state energy diagrams • Franck-Condon Principle - similar • nuclear geometries • Born-Oppenheimer Approximation

3. How do we know with path R will take? We use exemplars of chromophores: Then, we address the theory: 1. Conical intersections and Frontier MO Theory (start today) 2. Stereochemical consequences of orbital symmetrey (Tues. Dec. 3) 3. Conservation of Energy and Spin (Wednesday Dec. 4) 4. Prof. Robb’s visit (Thursday Dec. 5)

4. Potential Energy Curves vs. Potential Energy Surfaces taken from Ch. 3 from Prof. Robb’s website r centre of mass similar nuclear geometry between ground and excited state significantly different nuclear geometries between R, I and P.

5. Potential Energy and Force Force acting on the particle at r: r = potential energy curve at a given geometry

6. Single Point on an Energy Surface Importance of geometry on 1. energy barriers on excited and ground state surfaces 2. energy minima on excited and ground state surfaces 3. touching and intersecting points of surfaces 4. avoided crossings that create minima 5. barrier-free and adiabatic reactions

7. Influence of Collisons and Vibrations on an Energy Surface • Collisions are a reservoir of continuous • energy (~0.6 kcal/mol per impact) • Collisons can add or remove energy from • a system • Example: solution-phase vs. gas phase • lifetimes - few collisions in the • gas phase

8. Ground State vs. Photochemical Reactions Photochemical Reactions Ground State (Thermal) Reactions Single Surface Multiple Surfaces How does a particle on the excited surface return to the ground state? FUNNELS!

9. 4 Topologies for Funnels: 2-D R* R* I* I I R R Extended surface touching Extended surface matching P* R* R* P* R P R P Surface Crossing Equilibrated Surface Minimum

10. 4 Topologies of Funnels: 3-D Extended surface touching Extended surface matching Conical Intersection Avoided Crossing

11. R* P* R* P* P R P Non-Crossing Rule and Avoided Crossings R Surface Crossing Avoided Crossing Two energy curves with a common geometry, energy and nuclear positions. When the two states are the same, there will be a mixing to produce 2 adiabatic surfaces. Born-Oppenheimer Approx. applies

12. Conical Intersections Born-Oppenheimer Approx. breaks down! • associated with FAST motions - there is no TIME • for Y* to respond to nuclear motion and mixing does • NOT occur. • the surface crossing is maintained! • Consequences of Conical Intersections: • energy gap is 0, so the probability of the transition is 100% • limited only by vibrational relaxation, so the timescale is on the order of femto- • or picoseconds • no “jump” between surfaces, the reaction can appear concerted and stereochem. • can be conserved

13. Avoided Crossings vs. Conical Intersections AC CI Conical Intersection Avoided Crossings - point enters cone with initial geometry and is affected by: a) gradient of energy change as a function of nuclear motion b) direction of nuclear motion that is best mix of Y* and Y∞ - the excited state equivalent of a concerted reaction • point can wander in • energy minimum • finds a trajectory that • depends on nuclear • motion

14. Diradicaloid Geometries Diradicaloids - correspond surface touchings, conical intersections or avoided crossings - serve as funnels - possibility of zwitterionic structures s Bond Stretch: p Bond Twist:

15. Energy Diagram • Note point of intersection - • Could be: • Touching surfaces • Avoided crossing • Conical intersection • diradicaloids are short-lived due to their (nearly) degenerate orbitals and • the rate-determining step is often the primary photochemical reaction (ex. bond cleavage).

16. s-Bond Stretching: Dissociation of H2 • Stretching the s bond produces a diradaloid geometry • On the g.s. surface, S0, all geometries are stable except at large nuclear distances • which produce 1D • Along the T1 surface, all geometries are unstable and minimum activation is needed to • Produce 3D • 4. Along S1 and S2 the bond is unstable and have shallow minima; cleavage produces Z states

17. p Bond Twisting: Ethylene twist 1,2-diradical

18. Consequences of Twisting • twisting about the C-C bond of an electronically excited ethylene relieves e-e • repulsion form the p* e. • ***twisting lowers the energy of all the excited states • energies of S2, S1 and T1decrease as a function of twisting: electronic excitation • has effectively broken the p bond and the bonding is more like a single C-C bond • S0increases because the p bond is being broken • Minima (funnels) in S2, S1 and T1 surfaces at 90∞ geometry • Avoided crossing at Z2 and D1 • S0 and T1 touch at 90∞, but not extended as in H2 example • In S2 and S1, get zwitterionic behavior once twist starts • In T1, get diradical behavior at all geometries