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

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

MMP How do we know with path R will take? 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) We use exemplars of chromophores:

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

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

MMP Single Point on an Energy Surface Importance of geometry on1. 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

MMP 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

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

MMP Topologies for Funnels: 2-D Extended surface touchingExtended surface matching Surface CrossingEquilibrated Surface Minimum R R R* R R I I* I P* P P

MMP Topologies of Funnels: 3-D Extended surface touching Extended surface matching Conical Intersection Avoided Crossing

MMP Non-Crossing Rule and Avoided Crossings Surface Crossing R R* P* P Avoided Crossing R R* P* P 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

MMP Conical Intersections Born-Oppenheimer Approx. breaks down! associated with FAST motions - there is no TIME for  * 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

MMP Avoided Crossings vs. Conical Intersections ACCI Avoided Crossings Conical Intersection point can wander in energy minimum finds a trajectory that depends on nuclear motion - 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  * and  ∞ - the excited state equivalent of a concerted reaction

MMP Diradicaloid Geometries Diradicaloids - correspond surface touchings, conical intersections or avoided crossings - serve as funnels - possibility of zwitterionic structures  Bond Stretch:  Bond Twist:

MMP 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).

MMP  -Bond Stretching: Dissociation of H 2 Stretching the  bond produces a diradaloid geometry On the g.s. surface, S 0, all geometries are stable except at large nuclear distances which produce 1 D Along the T 1 surface, all geometries are unstable and minimum activation is needed to Produce 3 D 4. Along S 1 and S 2 the bond is unstable and have shallow minima; cleavage produces Z states

MMP  Bond Twisting: Ethylene twist 1,2-diradical

MMP Consequences of Twisting twisting about the C-C bond of an electronically excited ethylene relieves e-e repulsion form the  * e. ***twisting lowers the energy of all the excited states energies of S 2, S 1 and T 1 decrease as a function of twisting: electronic excitation has effectively broken the  bond and the bonding is more like a single C-C bond S 0 increases because the  bond is being broken Minima (funnels) in S 2, S 1 and T 1 surfaces at 90 ∞ geometry Avoided crossing at Z 2 and D 1 S 0 and T 1 touch at 90 ∞, but not extended as in H 2 example In S 2 and S 1, get zwitterionic behavior once twist starts In T 1, get diradical behavior at all geometries