radical cage effects - macmillan group

Radical Cage Effects

Patrick SarverMacMillan Group Meeting

22 April 2020

Duncan, D. C.; Fox, M. A. J. Phys. Chem. A 1998, 102, 4559–4567.Dondi, D.; Fagnoni, M.; Albini, A. Chem. Eur. J. 2006, 12, 4153–4163.

A problem that has bugged me for a while…

*[W10O32]4–

HAT DC–H ≈ 100 kcal/molW

O

OO

O

O

OW

O

OO

O

O

OH

H

[HW10O32]4–

[W10O32]4–

WO

OO

O

O

O H

hvΦ ≈ 0.5

krbackHAT

DO–H ≈ 30 kcal/mol(Bordwell equation)

kd

WO

OO

O

O

OH

[HW10O32]4–

free radicals

krʹ

backHAT

Φlim = 0.46

From transient absorption spectroscopy:

kr/(kr + kd) = 0.930

almost every generated radical pair separates

From competition with electrophilic alkenes:

krʹ = 8 • 109

but recombination is diffusion limited!!

Duncan, D. C.; Fox, M. A. J. Phys. Chem. A 1998, 102, 4559–4567.Dondi, D.; Fagnoni, M.; Albini, A. Chem. Eur. J. 2006, 12, 4153–4163.

A problem that has bugged me for a while…

*[W10O32]4–

HAT DC–H ≈ 100 kcal/molW

O

OO

O

O

OW

O

OO

O

O

OH

H

[HW10O32]4–

[W10O32]4–

WO

OO

O

O

O H

hvΦ ≈ 0.5

krbackHAT

DO–H ≈ 30 kcal/mol(Bordwell equation)

kd

WO

OO

O

O

OH

[HW10O32]4–

free radicals

krʹ

backHAT

Φlim = 0.46

Why is back HAT such a minor pathway?

Outline

��Introduction to cage effects

• General definition, theoretical predictions

��Experimental support for the existence of cage effects

• Quantum yields, product ratios as a function of reaction medium

��Parameters determining the magnitude of cage effects

• Viscosity, reaction energetics, spin state, radical size, initial separation

��Recent case studies

• Presence in biorelevant systems, transient absorption studies

Lorand, J. P. The Cage Effect. In Progress in Inorganic Chemistry; Edwards, J. O., Ed.; Wiley: New York, 1972; Vol. 17.Koenig, T.; Fischer, H. “Cage” Effects. In Free Radicals; Kochi, J., Ed.; Wiley: New York, 1973; Vol. 1.

Definition of radical cage effects

radicals are (almost) always generated in pairs

if generated close together, they can react before diffusing apart

radical cage effect:

increased likelihood that diffusive separation will be slower than radical pair recombination in solution

Introduction to “cage” effects

A

��Pairs of radicals generated in the gas phase rapidly separate

B A• B•hν

kr

kd

low barrier to diffusion kd >> krradicals behave

“normally”

A•

B•

A Bhν

kr

kd

A•

B•

B•A•

high barrier to diffusion kr ≈ kdradicals can

recombine beforediffusing apart

gas phase

solution phase

��Pairs of radicals generated in solution must break through surrounding solvent to diffuse apart

Introduction to “cage” effects

��Radicals that have broken free of the initial cage can diffuse back together

A Bhν

kr

kd

A•

B•

B•A•kd

“primary cage”

kd

A• B•+

“secondary cage”

in most cases, no distinction is made between primary and secondary cage effects

free radicalsFcP =kr

kr + kd

fraction of radicalsthat react in-cage

rate of recombinationof radical pair

kr =

rate of diffusion ofresulting radicals

kd =

Franck, J.; Rabinowitsch, E. Trans. Faraday Soc. 1934, 30, 120–130

First report of “primary recombination effect”

��First prediction of differences between gas-phase and solution-phase radical recombination

17 April 1933 – becomes first German academic to resign in protest of laws

excluding Germans of Jewish descent from government positions, published

resignation in national press

November 1933 – moves to Johns Hopkins

recognized that molecular dissociation in solution would not result in a random distribution of radicals

Franck, J.; Rabinowitsch, E. Trans. Faraday Soc. 1934, 30, 120–130

Prediction of parameters that determine magnitufe of cage effects

��Franck and Rabinowitsch predict many of the effects that determine “cage efficiency”

different observed quantum yield in solution vs. gas phase

viscosity dependence ofcage effect magnitude

wavelength dependence due torole of excess energy infacilitating cage escape

all of these predictions were later experimentally validated

Rabinowitsch, E.; Wood, W. C. Trans. Faraday Soc. 1936, 32, 1381–1387.

Early “experimental” support for cage effects in dense media

��Physical model suggests increased density favors multiple consecutive collisions

shaker

plate ensures“chaotic agitation”

conductive pole

conductive ball (1)insulating ball (N)

when the conductive ball contacts theconductive pole, a signal is measured

25 balls (gas-like?)

[…]

50 balls (solution-like?)1 encounter

8 collisions

1 collision/encounter

1 encounter

7 collisions

total number of collisions isindependent of the number of balls

Rabinowitsch, E.; Wood, W. C. Trans. Faraday Soc. 1936, 32, 1381–1387.

Early “experimental” support for cage effects in dense media

��Physical model suggests increased density favors multiple consecutive collisions

shaker

plate ensures“chaotic agitation”

conductive pole

conductive ball (1)insulating ball (N)

when the conductive ball contacts theconductive pole, a signal is measured

= collisions/encounter

N = number of balls

Nnumber of collisions remains constantcollisions per encounter increasesnumber of encounters decreases

Noyes, R. M. J. Am. Chem. Soc. 1955, 77, 2042–2045.Koenig, T.; Fischer, H. “Cage” Effects. In Free Radicals; Kochi, J., Ed.; Wiley: New York, 1973; Vol. 1; pp 164–170.

Theoretical model of radical cage effects

��Noyes model predicts dependence on viscosity, initial separation, translational energy, mass, and radius

F =R0 – 2b

2b +R02b

AT + αAEα

1η

AT • AEα

+1η

2

“Having absolutely no imagination,I majored in chemistry”

“The only chemical reactions thatare well understood are those that

have not been investigated in detail”

A–Bkr

hν[A• •B]

primary cagekd

kd[A• | •B]

secondary cage

A• + B•kd

free radicals

α = probability of reaction per encounterβ = probability of reencounterβʹ = probability that a pair of molecules separating from an encounter will eventually react

βʹ = αβ + α(1 – α)β2 + α(1 – α)2β3 + … = αβ/(1 – β + αβ)

substitute for β; accountfor initial displacement

rearrange to solve for F = kd/kr

R0 = initial separation

b = diffusion radius

η = viscosity

AE = [m(hv – E)]1/2

6πb2= translation energy of the separating fragments

AT = [(3/2)mkBT]1/2

6πb2= kinetic energy term

Khudyakov, I.; Zharikov, A. A.; Burshtein, A. I. J. Chem. Phys. 2010, 132, 04104.

Theoretical model of radical cage effects

��More accurate models for cage reactions remain an active field of research

A–Bkr

hν[A• •B]

primary cagekd

kd[A• | •B]

secondary cage

A• + B•kd

free radicals

best described as asingle exponential (EM)

best described by a “contact model” (CM),accounting for the likelihood that separated

radicals could recombine

= EM + CMgeneralizedmodel

CM only

EM only

combined model accuratelyfits experimental data

Outline









Lampe, F. W.; Noyes, R. M. J. Am. Chem. Soc. 1954, 76, 2140–2144.Noyes, R. M. Z. Electrochem. 1960, 69, 153–156

Quantum yield of halide photodissociation

��Solution data shows much lower quantum yield

Br Brhν

2 Br•ɸ ≈ 1

I Ihν

2 I•ɸ ≈ 1

��Gas-phase data shows near perfect photodissociation efficiency

Br Brhν

[Br• •Br]

kr

kd2 Br•

I Ihν

[I• •I]

kr

kd2 I•

solvent ɸ

hexanes

USP 335

0.66

0.140.04

Strong, R. L. J. Am. Chem. Soc. 1965, 87, 3563–3567.

CCl4

solvent ɸ

0.22CCl4

quantum yield ≈ 1(gas phase)

Effect of solvent on quantum yield supports cage effects

I

��Effect of solvent on quantum yield rationalized based on cage effect

I I• I•hν

kr

kd

low barrier to diffusion kd >> kr ɸ ≈ 1

I•

I•

I Ihν

kr

kd

I•

I•

I•I•

high barrier to diffusion kr ≈ kd ɸ < 1

gas phase

solution phase

Noyes, R. M. Z. Electrochem. 1960, 69, 153–156Porter, N. A.; Landis, M. E.; Marnett, L. J. J. Am. Chem. Soc. 1971, 93, 795–796.

Quantum yield of halide photodissociation

��Iodine, azo photodissociation quantum yields show significant solvent viscosity effects

I Ihν

[I• •I]

kr

kd2 I•

solvent η (cP)hexane 0.29

1.7Bayol D

quantum yield decreases withincreasing solvent viscosity

ɸ

0.66

0.18

NF 65 54 0.086

NF 95 80 0.048

USP 180 180 0.038

hν

kr

solventoctane

decane

ɸ

0.044

0.039

dodecane 0.035

hexadecane 0.029

visc

osity

quan

tum

yie

ld

NN

PhMe

PhEt N

NPh

Me

PhEt

kd

NN

PhMe

PhEt

–N2Me

PhEt Ph•

visc

osity

quan

tum

yie

ld

Porter, N. A.; Landis, M. E.; Marnett, L. J. J. Am. Chem. Soc. 1971, 93, 795–796.

Effect of viscosity on product ratios

��Product ratios in hyponitrite decomposition support presence of cage effects

hνO

NN

Ot-But-Bu

–N2O

t-Bu Ot-Bu

krO

t-Bu Ot-Bu

in-cage productkd

Ot-Bu2 O

t-Bu2 H

cage escape product

FcP =(t-BuO)2

(t-BuO)2 + t-BuOH/2

HAT


% Nujol inoctadecane η (cP)

20% 0.6

1.140%

60% 2.8

70% 4.7

80% 8.7

visco

sity

t-BuO

H/(t-

BuO

) 2

FcP

0.16

0.21

0.30

0.36

0.46

90% 22 0.56

>95% of t-BuO• undergoesHAT under reaction conditions

Kodama, S. Bull. Chem. Soc. Jpn. 1962, 35, 824–827.

Formation of ethane from azomethane

��Quantum yield of ethane formation dramatically increases in condensed phases

hνMe

NN

Me–N2

kr

in-cage productkd

cage escape product

HAT

MeMe[Me• •Me]

2 Me• 2 MeH

gas phase

ΦN2 ≈ 1 ΦEtH ≈ 0.04

Lyon, R. K. J. Am. Chem. Soc. 1964, 86, 1907–1911.

~ ΦEtH

~ ΦMeH

kdtemp.

(T)in-cageproduct

visc. (η)

for reactions in solution:

in cyclohexane

ΦN2 ≈ 0.8 ΦEtH ≈ 0.6

further increase in ΦEtH observed in frozen solution


Photolysis of azomethane in the presence of styrene

��Presence of potential quencher does not affect the rate of formation of ethane in solution

hνMe

NN

Me–N2

kr

in-cage productkd

cage escape product

HAT

MeMe[Me• •Me]

2 Me• 2 MeH


Ph

(105 M–1 s–1)Ph

Me

results suggest allethane is formedin solvent cage

~ ΦEtH

~ ΦMeH

~ ΦEtH

~ ΦMeH

reactions run in styrene!

styrene adduct

Bevington, J. C. Trans. Faraday. Soc. 1955, 51, 1392–1397.

Cage effects in polymerization

��Under thermal conditions, a significant proportion of consumed AIBN does not initiate polymerization

60 ºCNN –N2

kr

PhPh

NC

Me MeCN

Me MeNC

Me Me CN

Me MeNC

Me MeCN

Me Me

kdin-cage product

2NC

Me MeNC

Me MeCN

Me Me

free radical dimerization

NC

Me Me

initated monomer

~40% yield

~60% yield

0.2 g/L AIBN

0.5 g/L AIBN

1.0 g/L AIBN

concentration dependent at low [styrene]

free radical dimerizationcompetitive with initiation

concentration independent at high [styrene]

~40% of dimerization occurs in solvent cage

Greene, F. D.; Berwick, M. A.; Stowell, J. C. J. Am. Chem. Soc. 1970, 92, 867–874.

Stereospecificity in in-cage recombination

��Stereorentention in radical-radical recombination product supports in-cage reaction

105 ºCNN –N2

krPh

Me HPh

Me HPh

Me HPh

Me H

krot(R,R) product

(retention)

Ph

HMe Ph

Me H

Ph

H MePh

Me H

meso product

Ph

H MePh

H Me

(S,S) product(inversion)

Ph

MeH Ph

Me H kr

krot

Ph

MeH Ph

H Me kr

Ph

HMe

NPh

HMe

t-Bu

O

t-BuNO

scavenger preventsdimerization

outside of cage

withouttBuNO

withtBuNO

31%

21%

48%

27%

23%

50%

recombination in cage is competitive with molecular rotation

(88% yield) (28% yield)

Lyon, R. K.; Levy, D. H. J. Am. Chem. Soc. 1961, 83, 4290.

Isotopic labeling in azomethane photolysis

��Statistical mixture of products observed in gas phase, exclusively homoproducts observed in solution

hνH3C

NN

CH3–N2

kr

in-cage productkd

cage escape products

H3CCH3

Rebbert, R. E.; Ausloos, P. J. Phys. Chem. 1962, 66, 2253–2258.

[H3C• •CH3]

hνD3C

NN

CD3–N2

kr

in-cage product

kd

D3CCD3[D3C• •CD3]

•CH3 •CD3 D3CCD3H3C

CH3 H3CCD3

1 2 1: :

free radicals formstatistical mixture of

combination products+

CH3CH3 CH3CD3 CD3CD3

gas phase 25 50 25

isooctane ~50 <2 ~50

recombination outcompetescage escape in solution

Taylor, J. W.; Martin, J. C. J. Am. Chem. Soc. 1966, 88, 3650–3651.

Isotope labeling experiments

��Perester decompositon shows oxygen scrambling competitive with free radical generation

hν

kr kd2 Me•

Me O

18OO Me

O

Me O

18OO Me

O

hν

kr

Me 18O

OO Me

O

“scrambled” perester

–2 CO2

labeled perester

rate of peresterscrambling

rate of peresterdisappearance

in cage recombination iscompetetive with cage escape

kr ≈ kd

free radicals

37% isolated yield

Pryor, W. A.; Smith, K. J. Am. Chem. Soc. 1970, 92, 5403–5412.

Perester decomposition: viscosity effects

��The importance of cage effects to efficiency of methyl radical formation is supported by rate-viscosity relationship

hν

kr kd2 Me•

Me O

18OO Me

O

Me O

18OO Me

O

hν

kr

Me 18O

OO Me

O


–2 CO2

labeled perester

d(AcO)2/dt is a function ofsolvent viscosity

free radicals

solvent

heptane

octane

kobs/105

7.7

7.3

decane 6.9

dodecane

tetradecane

6.3

6.0

hexadecane 5.4supports in-cage recombination

visco

sity

reac

tion

rate

Outline









Barry, J. T.; Berg, D. J.; Tyler, D. R. J. Am. Chem. Soc. 2017, 139, 14399–14405.

Effect of viscosity on cage efficiency

��Bulk viscosity provides predicts cage efficency for a single solvent system, but not between systems

hν

kr


MoOC

OC CO

Me MoCO

COOC

Me MoOC

OC CO

Me MoCO

COOC

Mekd

FcP =kr

kr + kd


MoOC

OC CO

Me2

MoOC

OC CO

Me2Cl

CCl4

all free radicals quenched

at a given bulk viscosity, different solventsgive different cage efficiencies


Microviscosity as a better predictor of cage effects

��Bulk viscosity does not necessarily predict rate of diffusion at a molecular scale

hν

kr


MoOC

OC CO

Me MoCO

COOC

Me MoOC

OC CO

Me MoCO

COOC

Mekd

MoOC

OC CO

Me2

MoOC

OC CO

Me

How can we measure the rate ofdiffusion of a transient radical?

CrOC CO

CO

Δ mass = –40.9 DaΔ vol. = –6.81 Å3

Δ dipole = –1.37 D

diffusion measured via DOSY

n-hexane/parrafin

toluene/polystyrene

methanol/tetraglyme

solvent bulk viscosity(cP)

microviscosity(s/m2) × 109

0.36–20.61

0.61–30.22

0.66–2.86

0.29–6.28

0.60–0.83

0.59–2.22


Microviscosity as a better predictor of cage effects

��Microviscosity enables successful prediction across solvent systems

hν

kr


MoOC

OC CO

Me MoCO

COOC

Me MoOC

OC CO

Me MoCO

COOC

Mekd

MoOC

OC CO

Me2

Li, X.; Ogihara, T.; Abe, M.; Nakamura, Y.; Yamago, S. Chem. Eur. J. 2019, 25, 9846–9850.

Application of microviscosity to organic radicals

��Microviscosity also applied to organic systems

hνNN –N2

krMeO2C

Me MeCO2Me

Me MeMeO2C

Me Me CO2Me

Me Me

MeO2C

Me MeCO2Me

Me Me

kd

2MeO2C

Me Me

MeO2C

Me Me

H MeO2C

Me

and

+

PhSD MeO2C

Me Me

DMeO2C

Me Me

Hmodel for diffusionrate determination

Meadows, L. F.; Noyes, R. M. J. Am. Chem. Soc. 1960, 82, 1872–1876Clark, K. B.; Griller, D. Chem. Phys. Lett. 1990, 168, 477–481.

Effect of irradiation wavelength on cage efficiency

��Iodine, chlorine photodissociation show significant wave length effects

X Xhν

[X• •X]kr

kd2 X•

λ (nm) hν–EI–I

(kcal/mol)

405 35.0

30.0436

ɸ

0.83

0.66

546 16.6 0.46

579 13.9 0.44

643 8.9 0.40

wav

elen

gth

exce

ss e

nerg

y

735 3.3 0.31

quan

tum

yie

ld

I2 in hexane

Cl2 in CCl4

λ (nm) hν–ECl–Cl

(kcal/mol)

308 35

27337

ɸ

0.16

0.22

higher excess photonic energy

higher excess kinetic energy of products

more efficient cage escape

higher quantum yield of radical generation

Madsen, D. et al. J. Phys. Chem. A 2003, 107, 3606–3611.Thøegensen, J.; Thomsen, C. L.; Poilson, J. A.; Keiding, S. R. J. Phys. Chem. A 1998, 102, 4186–4191.

Are these effects present in polyatomic radicals?

��Small polyatomics show similar effects of irradiation wavelength on cage escape

HO Clhν

[HO• •Cl]kr

kd HO•Cl•

highest energymost cage escape

slowest recombination

lowest energyleast cage escape

fastest recombination

OClOhν

[OCl O]kr

kd OClO

in CCl4 in H2O

higher energy light

more efficient cage escape

Harris, J. D.; Oelkers, A. B.; Tyler, D. R. J. Organomet. Chem. 2007, 692, 3261–3266.

Wavelength effects in photodissociation of organometallic complexes

��Decrease in cage escape obeserved when irradiating Mo–Mo complexes with shorter-wavelength light

hν

kr

MoOC

OC CO

Me MoCO

COOC

Me MoOC

OC CO

Me MoCO

COOC

Mekd

MoOC

OC CO

Me2

λ (nm)

546

436

transition

π → σ*

σ → σ*

404 σ → σ*

366 σ → σ*

FcP

0.27 ± 0.02

0.42 ± 0.03

0.45 ± 0.05

0.40 ± 0.05

FcP =kr

kr + kd


does the excited transition, and not excess energy, determine FcP in this case?

Tadamitsu, S.; Hidenori, S.; Hiroyasu, I. Bull. Chem. Soc. Jpn. 1985, 58, 2875–2881.

Does radical spin state affect cage efficiency?

��Different results observed via direct excitation and sensitization

hν

kr

kdN

OO

O

Me

N

O

Ar O Ar

O

N

O

Ar O Ar

O

NH

O

Ar

O Ar

O

cage products

NH

O

Ar HO Ar

O


kr ≈ 0

1

N

O

Ar O Ar

O

3

3sens.

NH

O

Ar HO Ar

O


ISCX

direct excitation

benzophenone sensitization

ɸcage

0.08

≈ 0

ɸdiff.

0.09

0.81

1radical pair large kr

3radical pair kr ≈ 0

HAT fromsolvent

Xspin forbidden

HAT fromsolvent

Levin, P. P.; Khudyakov, I. V.; Kuzmin, V. A. J. Phys. Chem. 1989, 93, 208–214.

Cage effects in benzophenone HAT

��Magnetic field effects reveal role of intersystem crossing in cage recombination


Ph Ph

OPh

HO

Ph Ph

O

PhO

T1

HAT* H3

Ph Ph

O

PhO

H+

ISC

Ph Ph

O

PhO

H1


Ph Ph

O

PhO

H+

Ph Ph

OPh

HO

S0

hν,then ISC

FcP =kr

kr + kd


B (T)

0.34

0

FcP

0.34

0.47

HAT

X

B = 0.34 T

B = 0 T

Harris, J. D.; Oelkers, A. B.; Tyler, D. R. J. Am. Chem. Soc. 2007, 129, 6255–6262.

Spin barriers in recombination of transition metal radicals

��Lack of heavy atom effects suggest that there is no spin barrier to transition metal radical recombination

hν

kr

MoOC

OC CO

Me MoCO

COOC

Me MoOC

OC CO

Me MoCO

COOC

Mekd

MoOC

OC CO

Me2

Mo

Fe

Ti

shaded: PhCl (control)

empty: PhI (ISC promoter)

1

MoOC

OC CO

Me MoCO

COOC

Me

3

ISC

kdMo

OCOC CO

Me2

heavy atoms have no effect on radical cage efficiency

there is no significant spin barrier to recombination

reactions run in the presenceand absence of heavy atoms to probe for ISC rate effects

cage-escaped radicals

Sheldon, R. A.; Kochi, J. J. Am. Chem. Soc. 1970, 92, 4395–4404.

Effect of radical size on cage effects

��Propionyl peroxide shows much higher cage efficiency than acetyl peroxide

65 ºCR O

O

kd

R O

OO R

O

RO

O

–2 CO2 [R• •R]

R O

O

2

kr

kd2 R•

R R

kr

–CO2

R O

O

•RR O

OR

yield R–R

6%

35–40%

Me

Et

yield R–CO2R

19%

nd

in-cageproduct

��Similar trend not observed under photochemical conditions

Herk, L.; Feld, M.; Swarc, M. J. Am. Chem. Soc. 1961, 83, 2998–3005.

R O

OO R

O

hν R R

in-cage productsR H R(–H)

%cage reaction

Et Pr Bu i-Pr i-Bu

cage escape

55 57 51 54 57

no effect of R on cage efficiency

Male, J. L.; Lindfors, B. E.; Covert, K. J.; Tyler, D. R. J. Am. Chem. Soc. 1998, 120, 13176–13186.

Systematic study of radical size in organometallic radicals

��Clear dependence observed between silyl substituent and cage efficiency

hν

kr

MoOC

OC CO

MoCO

COOC

MoOC

OC CO

MoCO

COOC

MoOC

OC CO

2

all free radicals quenchedby CCl4

R3SiO OSiR3 R3SiO OSiR3

kd

R3SiO

n-Hexn-Pri-PrMe

FcP =kr

kr + kd


for a given viscosity,FcP is a function of

radical size



��Observed linear plot of m1/2/r2 consistent with Noyes original model

hν

kr

MoOC

OC CO

MoCO

COOC

MoOC

OC CO

MoCO

COOC

MoOC

OC CO

2


R3SiO OSiR3 R3SiO OSiR3

kd

R3SiO

(1/FcP) – 1 =kd

kr

ratio of diffusionto recombination

for a given viscosity,FcP is a function of

radical size

m1/2/r2 dependencepredicted by Noyes

lowest viscosity

highest viscosity



��Results with M = W show significant variation from predicted m1/2/r2 relationship

hν

kr

MOC

OC CO

R MCO

COOC

Me MOC

OC CO

R MCO

COOC

Rkd

MOC

OC CO

R2


M = Mo, R = Me

M = Mo, R = Me3SiOCH2CH2–

M = W, R = Me

r(kcal/mol)

259.1 2.95

3.53361.3

1.85

1.53

347.0 2.95 2.14

M(g/mol) m1/2/r2

higher m1/2/r2 predicts more cage escape, lower FcP,but W compound shows high FcP

M = W

M = Mo

DW–W ≈ 56 kcal/mol; DMo–Mo ≈ 32 kcal/mol

reduced exothermicity prevents cage escape?

OO

Braden, D. A.; Parrack, E. E.; Tyler, D. R. Coord. Chem. Rev. 2001, 211, 279–294.

Effects of spacer length on cage recombination

��Different spacers generate radicals at different initial distances

��Diffusion of spacer occurs on the order of diffusion of generated radicals

AB

hν

OOA

B

NNO

OAB

NNO

OAB

hνF =

R0 – 2b

R0 R0

2b +R02b

AT + αAEα

1η

AT • AEα

+1η

2

initial separation of radicals

Noyes equation predicts probability of cage escapeis a function of initial distance between radicals

Koenig, T.; Fischer, H. “Cage” Effects. In Free Radicals; Kochi, J., Ed.; Wiley: New York, 1973; Vol. 1; pp 171–174.

F = [1/(fraction of radicals that react in-cage)] – 1

CO2 N2 CyH PhMe

D•109 (m2/s), in H2O

D•109 (m2/s), in CCl4

1.99

3.20

2.19

3.60

0.84

1.22

0.85

1.50

complicates interpretation of experiments based on

extrusion of gaseous spacers

Koenig, T.; Deinzer, M. J. Am. Chem. Soc. 1968, 90, 7014–7019.

Generation of same radical pair via two different precursors

��Significant differences in cage effects concluded

0 ºC

ON

NO

t-Bu –N2O

t-BuMe

O

generated in situ

Me O

O kr

kd

Ot-BuMe O

O

+

Me O

OO

t-Bu

in-cage product

Me O

18OO

labeled perester

kr

t-Bu Me 18O

OO

t-Bu


100 ºC

Fc =kr

kr + kd


generated via hyponitrite

radical pair generation Fc (100 ºC)

0.05

0.40generated via perester

calculation method

extrapolation based on viscosity

comparison of scrambling to consumption of perester

25% at 0 ºC

kr

Outline









Groves, J. T.; Nemo, T. E. J. Am. Chem. Soc. 1983, 105, 6243–6248.

Cage effects in iron porphyrin oxidation

��Reaction in the presence of scavenger suggests both cage and non-cage processes

Fe(TTP)Cl (10 mol%)PhIO (1 equiv.)

OH O Br

without BrCCl3

with BrCCl3(20 equiv.)

31% 6% na

24% 3.6% 18%

(solvent)

Groves, J. T.; Huang, X. J. Biol. Inorg. Chem. 2017, 22, 185–207.

yield in the presence of scavenger supports

in-cage recombination

Fe

X

OH

Fe

X

OH

kr

kd

Fe3+

XO

H

Fe

X

OH

free radicals

BrCCl3kdBr

Austin, R. N. et al. Angew. Chem. Int. Ed. 2008, 47, 5232–5234.

Cage effect confounds radical clock studies of AlkB

��A range of cyclopropane radical clocks give vastly different lifetimes for the alkyl radical


H OH

AlkB

nn

HO OH

nn

AlkB

unrearrangedproduct (U)

rearrangedproducts (R)

HO

R/U krearr (s–1) τ (ns)

1.6

4.7

1.6

2.0 × 109

2.8 × 107

2.0 × 108

0.78

7.8

170

why do different radical clocks give different lifetimes?

Austin, R. N. et al. Angew. Chem. Int. Ed. 2008, 47, 5232–5234.

Similar rates of cage escape and recombination alter rearranged vs. unrearranged

��Similar rates of recombination and diffusion complicate interpretation of radical clocks


OFeIV

OFeIV

H OFeIV

OFeIII

HHAT kr

(>>krearr)O

H

OFeIII

FeIII

kd

OFeIV

OFeIII

Hkrearr

OFeIV

OFeIII

H

unrearrangedproduct (U)

kd

OFeIII

FeIII O H

rearrangedproducts (R)

kr ≈ kd >> krearr

R:U is a function of cage efficiency

for kr ≈ kd = 5 × 109

for kr ≈ kd = 5 × 109, model predicts R/U ≈ 1 for 107 < krearr < 1010

Garr, C. D.; Finke, R. G. J. Am. Chem. Soc. 1992, 114, 10440–10445.

Cage effects in the chemistry of coenzyme B12

��“Base off” analogue of B12 shows significant in-cage recombination in ethylene glycol

CoIIIO Ad

OH OH

110 ºC

kr CoIIO Ad

OH OHβ-hydride

elimination

CoIIO Ad

OH OH

H

in-cage productskd

CoIIO Ad

OH OH

free radicals

OMe Ad

OH OHO

OH OH

N

NN

N

H2Ncage escape products

TEMPO

O Ad

OH OH

TEMPO

trapped product

1

2 34

[TEMPO] β–hydride (1) HAT (2) Minisci (3) TEMPO (4)

00.12 M0.75 M0.85 M

33%24%9%7%

45%1%0%0%

15%0%0%0%

073%89%91%

?

inhibition of β-hydrideby TEMPO supports stepwise mechanism

Garr, C. D.; Finke, R. G. J. Am. Chem. Soc. 1992, 114, 10440–10445.

Cage effects in the chemistry of coenzyme B12

��Kinetic dependence of starting material disappearance on TEMPO supports in-cage trapping

CoIIIO Ad

OH OH

110 ºC

kr CoIIO Ad

OH OHβ-hydride

elimination

CoIIO Ad

OH OH

H

in-cage productskd

CoIIO Ad

OH OH

free radicals

TEMPO

O Ad

OH OH

TEMPO

trapped product

1

4

Is TEMPO trapping the primary or secondary radical pair?

for Fc = 0.96

Noyes, R. M. J. Am. Chem. Soc. 1955, 77, 2042–2045.

Experimental support for secondary cage effects

��Early theoretical studies predict significant kinetic importance of primary and secondary cage effects

A–Bkr

hν[A• •B]

primary cagekd

kd[A• | •B]

secondary cage

A• + B•kd

free radicals

only free radicals quenched

free radicals + secondary cage quenched

some primary cage quenching observed

Φ vs. [radical scavenger]

experimental techniques generally only provide the total cage effect

Oelkers, A. B.; Tyler, D. R. Photochem. Photobiol. Sci. 2008, 7, 1389–1390.

Combined approach enables separation of primary and secondary effects

��Mathematical treatment enables determination of secondary cage effect from primary and total cage effects

primary cage (~5 ps) secondary cage

free radicals

hν

kr

MoOC

OC CO

R MoCO

COOC

Me MoOC

OC CO

R MoCO

COOC

Mekd

MoOC

OC CO

R2

kd

MoOC

OC CO

R MoCO

COOC

R

kdtotal cage effect = f(primary cage effect, secondary cage effect)

determined by transientabsorption spectroscopy

determined by quantum yieldof reaction with scavenger

total cage effect primary secondary

n = 3n = 8

n = 13n = 18

0.42 ± 0.030.48 ± 0.030.59 ± 0.040.70 ± 0.04

0.42 ± 0.020.42 ± 0.030.44 ± 0.010.43 ± 0.02

00.220.450.68

ligand

R = –CH2CH2N(Me)C(O)(CH2)nMe

FcP =Fc1

1 – Fc2(1 – Fc1)

secondary cage effectsaccount for difference in

cage efficiency as a function of molecular size

Outline









Radical cage effect

broadly observed in synthetically relevant radical reactions, but often ignored

radical cage effect:

increased likelihood that diffusive separation will be slower than radical pair recombination in solution

likely plays a significant role in the success or failure of important single-electron transformations

radical cage effects - macmillan group

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