1. “Cage” Reactions Involving Radical Pairs1
“Cage” Reactions Involving Radical Pairs
Model System
• •
• •
(R1-R2) homolytic cleavage 3(R1R2) ISC 1(R1R2)
recombinations
disproportionations

2. The States of a Spin Correlated Radical Pair2
The States of a Spin Correlated Radical Pair
vector model of electron spin
Alpha
Beta
T’s: aa, bb, ab
T0 = projection along Hz is 0; magnetic Q#=0
S is similar to T0, just different phasing of spins (180 out of phase)
Conversion of T0 --> S = rewinding of one spin
In the absence of external Hz, the relative orientation of the triplet states are well-defined, therefore, the net spin of triplet is always =1
The consequence of a the application of a strong Hz field is the splitting of T+ and T- from T0
T0=S therefore transition still probable
T+/T- --> S transition is quenched (slow interconversion)
• •
• •
3(R1R2)
1(R1R2)

3. ISC in Triplet Radical Pairs3
ISC in Triplet Radical Pairs
At 0 H-field, all 3 triplet levels may undergo electron-nuclear hyperfine-induced ISC to S (nearby nuclear spins make magnetic communications, e.g. H atom spin +/- 1/2)
Presence of H field, T+/- splits, hyperfine induced ISC not possible
Howeve, T0 is still degenerate with S, so hf induced ISC is still possible
H >> hf between the electron and nearby nuclear spin, ISC is determined by ext. H

4. Spin Rephasing Mechanism for ISC4
Spin Rephasing Mechanism for ISC
spin clock
(top-down view, projection in the xy-plane)
In the presence of magnetic fields
Pure T0 = 12 o’clock
Pure S = 6 o’clock
When electron exchange energy, J of the two unpaired e >>> electron-nuclear hf constant, a
Meaning that the radical pairs are in close proximity (solvent cage) then T0 and S do not mix (12/6)
Solvent-separated, e xchange E < e-n hf, then they mix
Diffusive separation --> primary geminate pair still spin correlated --> rotate
This occurs when: net H torque on the the e spin vectors are different = external H + nearby nuclear spins (hf coupling) + e orbital motion (spin-orbit coupling)
J < a T0 S

5. Timescales for ISC in Radical Pairs5
Timescales for ISC in Radical Pairs
T S
kTS ~ (3 X 106)(gH ±Ms a1 )
Spin-orbit coupling, g rate, kTS
Typical organic radical, g ~
Earth’s H ~ 1G X 103 Hz
Lab H ~ 100,000G X 108 Hz
Hyperfine coupling, a
Typical organic radical, a ~ G 3 X X 108 Hz
Spin-orbit = orbital motion of the e makes magnetic communcation w/ e spins
Suppose the primary geminate radical pairs R1 and R2 do not posses magnetic nuclei, but does have different g-factors (spin-orbit coupling)
2 mechanisms: Spin Rephasing (g) and Spin Flipping (a)

6. Power of Spin in Product Distribution6
Power of Spin in Product Distribution
T S
kTS ~ (3 X 106)(gH ±Ms a1 )
Ms = 0
Spin Rephasing
No nuclear spin flip involved
a >>>H
Spin Flipping
Sort magnetic nuclei from
nonmagnetic nuclei!
Ms = ± 1/2 , a1 is positive
Increase rate of T-->S rephasing by increasing the H-field
Ms = magnetic quantum number
Suppose the primary geminate radical pairs R1 and R2 do not posses magnetic nuclei, but does have different g-factors (spin-orbit coupling)
So caged products are enriched in +1/2 and the escaped products are enriched in -1/2
Mechanism not available to a nucleus with does not possess spin.
then kTS+1/2 > kTS-1/2
Sort nuclear spin states!
Polarized (non-Boltzmann)
product distribution!