MMP+ 6.1-6.6

A Driver’s Guide to Photochemistry:

Roads (ie. Surfaces), Crossings and Intersections

(A Discussion of MMP+ 6.1-6.6)

Tracy MorkinNovember 26, 2002.

MMP+ 6.1-6.6

Our Road Map

Where have we been? Where are we going next?

R R* I Phν

- photophysical properties (ie. R = P)- state energy diagrams- Franck-Condon Principle - similar nuclear geometries- Born-Oppenheimer Approximation

R* I PhνR I* or P*I*

- photochemical reactions (ie. R ≠P)- state correlation diagrams- the consequences of different nuclear geometries- Born-Oppenheimer Approximation may break down

MMP+ 6.1-6.6

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:

RR'O OR2R4R3R1

MMP+ 6.1-6.6

Potential Energy Curves vs. Potential Energy Surfaces

similar nuclear geometry betweenground and excited state significantly different nuclear

geometries between R, I and P.

taken from Ch. 3

from Prof. Robb’swebsite

R R* I Phν R*I PhνRI* or P*I*r centre of mass

MMP+ 6.1-6.6

Potential Energy and Force

Force acting on theparticle at r:

r = potential energy curve at a given geometry

F =-dPEdr

MMP+ 6.1-6.6

Single Point on an Energy Surface

Importance of geometry on 1. energy barriers on excited and ground state surfaces2. energy minima on excited and ground state surfaces3. touching and intersecting points of surfaces4. avoided crossings that create minima5. barrier-free and adiabatic reactions

MMP+ 6.1-6.6

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+ 6.1-6.6

Ground State vs. Photochemical Reactions

Multiple Surfaces

Ground State (Thermal) Reactions Photochemical ReactionsI PR R* I PhνR

Single Surface

How does a particle on the excited surface return to the ground state? FUNNELS!

MMP+ 6.1-6.6

4 Topologies for Funnels: 2-D

Extended surface touching Extended surface matching

Surface Crossing Equilibrated Surface Minimum

RR

R* R*

R*

RR

R*

II*

I

P*P*

PP

MMP+ 6.1-6.6

4 Topologies of Funnels: 3-D

Extended surface touching

Extended surface matching

Conical Intersection

Avoided CrossingIR*ORH*OHR+ I* or P*R* *Nap*excimers

FR* P* FR* P+*

MMP+ 6.1-6.6

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+ 6.1-6.6

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+ 6.1-6.6

Avoided Crossings vs. Conical Intersections

I* or I R* I* or IproductsAC CI

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 motionb) direction of nuclear motion

that is best mix of * and ∞- the excited state equivalent of a concerted reaction

MMP+ 6.1-6.6

Diradicaloid Geometries

Diradicaloids - correspond surface touchings, conical intersections or avoided crossings - serve as funnels - possibility of zwitterionic structures

Bond Stretch:

Bond Twist:

MMP+ 6.1-6.6

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+ 6.1-6.6

-Bond Stretching: Dissociation of H2H-HHHHH

• Stretching the 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 3D4. Along S1 and S2 the bond is unstable and have shallow minima; cleavage produces Z states

MMP+ 6.1-6.6

Bond Twisting: EthyleneHHHH HHHHtwist1,2-diradical

MMP+ 6.1-6.6

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 S2, S1 and T1 decrease as a function of twisting: electronic excitation has effectively broken the bond and the bonding is more like a single C-C bond• S0 increases because the 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