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µSR of Free Radicals

Iain McKenzie | CMMS | TRIUMF

What is a Radical?

August 16, 2011 µSR of Free Radicals 2

•  Radicals are atoms or molecules with one or more unpaired electrons.

What is a Radical?


7 valence electrons

(2 from each bond and

1 unpaired electron) C CH3CH3C

Mu

H H

•  Radicals are often highly reactive as it is usually energetically favorable for them to attain “closed shell configuration”

reactants! intermediates[ ]! products

•  Through a better understanding of the properties of the intermediates, we can better control chemical reactions

Why Study Radicals?


radicals carbenes

carbocations carbanions

•  Production of radicals often requires nasty mix of chemicals (e.g. Fenton’s reagent) and/or irradiation.

•  Reactive radicals are difficult to study with traditional spectroscopic techniques (EPR, UV-Vis, IR)

Difficulties in Studying Radicals


Signal ~ [R!]

R! + R! R!R Termination reaction

R! R!

Matrix Isolation Spin Trapping

R! R

•  Radicals produced by addition of Mu to an unsaturated bond

Muoniated Radicals


•  Extremely dilute (no self termination reactions) •  Distribution of radicals depends on relative addition rates

–  Mu adds preferentially to less substituted end of C=C bond –  Addition to isolated C=C bond faster than addition to phenyl ring –  Addition to C=C ~100x faster than to C=O

C CH2

H3C

H3C

C CH3CH3C

Mu

H H

Mu

•  Electron has a spin of 1/2

Hfccs and Spin Density


!

" :ms = +1 2

# :ms = $1 2

!

"! r ( ) = "#

! r ( ) + "$ ! r ( )

!

"SPIN ! r ( ) = "#! r ( ) $ "% ! r ( )

Electron density Spin density

•  The hfcc is directly proportional to the unpaired spin density at the nucleus

!

AX =2µ03h

geµB gXµX"

# $ %

& ' (SPIN ! r = 0( )

Electron and Spin Density in C6H6Mu


Blue: "# > "$ Positive spin density

Green: "# < "$ Negative spin density

Electron density Spin density

•  AX is the strength of the interaction between the spin of the electron and the magnetic dipole of the nucleus X

•  Muon and nuclear hfccs provide information about the structure, configuration and conformation of the radical

Hyperfine Coupling Constants


C CH

H

H

HMu + C C

Mu

HHH

H

Aµ Ap

(1)

Ap (2)

!-protons

"-protons

AX= AX(isotropic) + AX

(dipole)

"-muon

Transverse Field Muon Spin Rotation


µ+#

Sample

Positron Detector

Spin-polarized

muon beam

B

e+

Muon Detector

Electronic Clock



$12

Diamagnetic frequency $D

$43

Aµ

CD2Mu

!

"D = #µB

!

Aµ(MHz) = "43 # "12



!

"R = "µ ± 12 Aµ

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

!R1

Energy

B/Aµ

!R2

e--µ+-p+

•  Requires high concentration (~1 M) of precursor to prevent loss of polarization.

Limitations of TF-µSR


P12R ! 1

2 hM! 2

! 2 +""122

#

$%

&

'(

1/2

•  hM is the initial fraction of muon polarization in Mu

•  ! is the first-order reaction rate •  %&12 is the change in

precession frequency between Mu and the radical

•  You can’t tell the muon where to go i.e. multiple muoniated radicals are formed, often ones you don’t want

-0.004

-0.003

-0.002

-0.001

0.000

0.001

0.002

1700 1750 1800 1850 1900 1950

Magnetic Field / Gauss

RF A

sym

metr

y

Radio Frequency Muon Spin Resonance


Bres

!

"RF = #µBres $12 Aµ

•  Measure Aµ for slowly formed radicals (slow Mu addition or dilute solutions)

$RF = 10 MHz H3C

C

H3C

OMu

Level Crossing Resonance


µ+#Sample

Forward Positron Detector

Backward Positron Detector

Spin-polarized muon beam

e+

B

Time integrated asymmetry

A = NF ! NB

NF + NB

Level Crossing Resonance


!1 Resonance !

0 Resonance

!

Bres"0 =

12

Aµ # Ak$µ # $k( )

#Aµ + Ak$e

%

& ' '

(

) * *

!

Bres"1 =

Aµ

2#µ

$Aµ

2#e

Pol

ariz

atio

n E

nerg

y

Magnetic Field

muon-proton spin flip-flip !M = 2

muon-proton spin flip-flop !M = 0

muon spin flip !M = 1

!

"e"µ"p

!

"e"µ#p

!

"e#µ"p

!

"e#µ#p

ALC-µSR of Mu13C60


Percival et al. Chem. Phys. Lett. 1995, 245, 90

Identification of Muoniated Radicals


TF-µSR Precession frequencies

RF-µSR Resonance field

ALC-µSR Resonance fields

Hyperfine Coupling Constants

Temperature Dependence of HFCs

Muon hfc (Aµ)

Distribution of unpaired electron

Nuclear hfcs (H, D, 13C, 14N'.)

Configuration and conformation Intramolecular motion

Solid

•  # carbon: nucleus with significant unpaired electron spin density

•  # proton: attached to an # carbon

•  $ carbon: one removed from # carbon

•  $ proton: attached to an $ carbon

•  ( carbon: one removed from $ carbon

•  ''''.

Nomenclature


More probable

Hyperfine Coupling of !-Nuclei


(a)! (b)!

C H H H C H H

H

•  #-nuclei lie in nodal plane but have negative spin density due to spin polarization of the bond

!

AX =QX"#

•  ") is the )-electron population at the adjacent carbon atom

•  Qp ~ -75 MHz

McConnell equation

for #-nuclei

Muoniated Cyclohexadienyl Radical


H

H H

H H

Mu

H

Para (1H #) Ap = -36.8 MHz " ~ +0.49

Meta (2H #) Ap = +7.5 MHz " ~ -0.10

Ortho (2H #) Ap = -25.5 MHz " ~ +0.35

Methylene (1H $) Ap = 125 MHz

Muon ($) Aµ = 514.6 MHz

Spin density around ring 2(0.35)+2(-0.10)+1(0.49)

~1

Out-of-plane Vibrations of !-Protons


•  Out-of-plane vibrations cause the magnitude of # proton hfccs to decrease

•  Direct overlap of nuclei with SOMO gives positive spin density contribution than partially counteracts negative spin density due to spin polarization

AX T( ) !AX!e"E! /kBT

!=0

#

$e"E! /kBT

!=0

#

$

Hyperfine Coupling of "-Nuclei


•  L: orientation independent mechanisms (~0 – 10 MHz)

•  M: spin density arising from hyperconjugation (~140 MHz)

•  * is the angle between C-X bond and SOMO

•  ") is the spin density on adjacent carbon

RC

HH

H

R

!"

More overlap with

SOMO

Less overlap with

SOMO

!

Ap" = L +M cos2 #[ ]$%

•  The preferred configuration of the radical can be determined from measuring the magnitude and temperature dependence of the hfcc.

Pseudo-Methyl Groups


R RC

R1

R2R3R RC

R1

R2

R3

AR1= L +M( )!"

AR2 (3)= L + 1

4M( )!"

AR1(2 )= L + 3

4M( )!"

AR3= L!"

dAR1

dT< 0

dAR2 (3)

dT> 0

dAR1(2 )

dT< 0

dAR3

dT> 0

Freely rotating: AR = L + 12M( )!"

Temperature Dependence of " Hfccs


!

" A µ

!

ApCH2!

A CH2Mu = 13 " A µ + 2

3 ApCH2

•  C-Mu bond preferentially aligns with SOMO

Methylene Groups in C6H6Mu


•  Hfccs depend on spin density on both adjacent carbons •  Methylene (CHMu) group not free to rotate •  Reduction of $ hfccs due to scissor motion of CHMu

group (slightly increases *)

Ap! = L +M cos2"!" #$ #C1

$ + #C5$( )

2

•  Asymmetric bond stretching potential results in C-Mu bond being longer than C-H bond.

•  Hfcc becomes increasingly positive with increasing bond length (although |Aµ| decreases if Aµ is negative).

Isotope Effects on Bond Length


rC-Mu + 1.049 rC-H

13C Hfccs


Ci H C Ci Cj Ci Cj

!," spin polarization

Karplus Fraenkel equation for planar

radicals

!

aCi= SCi + QCX

X

j=1

3

"#

$ % %

&

' ( ( )Ci

+ QXCC )C j

j=1

3

"

!

SCi = -12.7 G

= +19.5 G

!

QCHC

!

QCiC j

C = +14.4 G

!

QC jCi

C = -13.9 G

•  µSR spectra do not give direct access to the radical structure. This must be inferred.

•  Magnetic properties of a radical often depend on the subtle interplay of several different effects.(e.g. vibrational averaging, solvent effects, substituent effects'.)

•  Quantum calculations are used to –  support and compliment the experimental results to determine

the electronic and geometric structure of the radical starting from its spectral properties

–  evaluate the role of different effects on determining the magnetic properties of a radical

Quantum Calculations


•  Use unrestricted method (treats # and $ electrons separately) to correctly account for spin polarization.

•  Density functional methods (such as B3LYP) give isotropic hfcc that are in good agreement with experimental values and are practical for larger radicals.

•  The larger the basis set, the more accurate the wavefunction but the computational time is much longer

•  Benchmark your calculations against closely related known systems

Ab Initio Calculations


•  How do stable carbenes react with a simple free radical?

Mu Adducts of Carbenes


Aµ 278.8 MHz

AC(C2) 136.0 MHz

AN(N1) 8.3 MHz

AN(N3) 8.3 MHz

Ap(CH3C5) -

Aµ 401.0 MHz

AC(C2) 7.4 MHz

AN(N1) 0.5 MHz

AN(N3) 4.0 MHz

Ap(CH3C5) 53.1 MHz

B3LYP/6-311G**//B3LYP/EPR-III

Mu Adducts of Carbenes


•  Structure assigned by comparing hfccs with DFT calculations of possible radicals.

0 100 200 300 400

Frequency / MHz

Fourier

Pow

er

D

R

R

Aµ = 246.4 MHz

8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1

Magnetic Field / kG

A+ -

A–

AN = 13.7 MHz

3.1 3.5 3.9 4.3 4.7 5.1 5.5

Magnetic Field / kG

A+ -

A–

AC = 139.6 MHz

Delocalized electron

Dipolar Coupling


B || z

*

B || z

*

r

•  Judge whether the unpaired electron is mostly in the positive or the negative sector of a double cone with opening angle * = 54.7°

Point dipole

3cos2! !1r3

3cos2! !1r3

Dipolar Coupling of !-Nuclei


Dipolar Coupling of "-Nuclei


•  Hyperfine tensor can be represented as an ellipsoid

•  Dipolar coupling is traceless

Motional Averaging


!

Bxx + Byy + Bzz = 0

ALC Lineshapes


!

P z B,"( ) = 1#0.5q2Pz

0

$ 2%( )2 + q2 + &µ2 B # Bres

'1( )2

!

P z B( ) = P z B,"( )0

#

$ f "( )2# sin"d"

q = ! 34Dµ|| sin! cos!

Dµ: magnitude of dipolar hfcc *: angle between unique axis and magnetic field.

Powder %1 shape obtained by integrating over all * and weighting by probability f(*).

Bres!1 =

12!µ

"12!e

#

$%%

&

'(( Aµ

iso + 12 Dµ

|| 3cos2" "1( ))*

+,

Motional Averaging of C6H6Mu


Byy + 0 Bxx = 8.6 MHz Bzz = - 8.6 MHz

Bzz Bxx

Byy

!

Dµ"

!

Dµ"

!

Dµ||

!

Dµ"

!

Dµ"

!

Dµ||

Dµ|| = -6.8 MHz

Dµ|| = +5.8 MHz

ALC Lineshapes


17000 18000 19000 20000 21000 22000

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

Polarization

Magnetic Field / G17000 18000 19000 20000 21000 22000

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

Polarization

Magnetic Field / G

Dynamics of Muoniated Norbornyl Radical


• Asymmetric shape indicates Dµ

|| < 0 • Preferred rotation around indicated axis. • Decreasing |Dµ

||| with increasing temperature due to wobbling of rotation axis.

303 K

234 K

183 K

173 K

Calculated Aμ Exp. Aμ

1 618 235.4

2 764 154.9

Organosilicon Radicals


1

2

Difference between calculated and experimental Aµ values means these are not the radicals are formed.

•  Observation of secondary radical formed by radical addition to silylene

•  Confirmed by observing products of equimolar 1 and 2

Organosilicon Radicals


Organometallic Radicals


•  How does H/Mu react with ferrocene?

Fe Fe FeMuH

Mu

FeMu

H

Mu

endo exo

Cp Adducts 17 electrons

Ferrocene Fe Adduct 19 electrons

•  What are the structures of the resulting radicals?

ALC-µSR of Ferrocene

0.5 1.0 1.5 2.0

-6

-4

-2

0

10 K 25 K 37 K 50 K 62 K 75 K

Cor

rect

ed In

tegr

al A

sym

met

ry /

%

Magnetic Field / T


%1 Resonance 2

3

4

5

6

7

8

0 20 40 60 80 100

230

235

240

245

250

0 20 40 60 80 1000.2

0.3

0.4

Am

plitu

de /

a.u.

|Aµ| /

MH

zTemperature / K

FWH

M /

T

Temperature / K

Aµ0 = 250.5±0.6 MHz

Aµ1 = 126±13 MHz

%E = 1.4±0.1 kJ mol-1

ALC-µSR of Ferrocene


0 2 4 6 88

9

10

11

12

13

14

15

16

17

18

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Asy

mm

etry

/ %

Time / µs

10 K 37 K 50 K 75 K 100 K

(a) (b)

! µ / µs-1

Temperature / K

2

3

4

5

6

7

8

0 20 40 60 80 100

230

235

240

245

250

0 20 40 60 80 1000.2

0.3

0.4

Am

plitu

de /

a.u.

|Aµ| /

MH

z

Temperature / K

FWH

M /

T

Temperature / K

,e and ,µ increasing with temperature

Chemical reaction?

DFT Calculations of Mu Adducts of Ferrocene


UB3LYP/6-311+G(d,p)

more stable by 79.8 kJ mol-1

R. M. Macrae, Physica B 374-375, 307 (2006)

Aµexo

21 MHz

Aµendo

-3 MHz AµFe

-304 MHz

Reaction of Mu with Aromatic Compounds


No addition at tertiary carbons*

CH3

CH3

CH3

CH3

Mu

H

CH3

CH3

Mu

Mu

Mu

HMu

H

Mu

H

Mu

HMu H

Brodovitch et al. Can. J. Chem. 81, 1 (2003)

Strained Aromatic Compounds


H2C CH2

H2C CH2

H2C CH2

H2C CH2

H2C CH2

H2C CH2

Mu

Mu

H

H2C CH2

H2C CH2

H

Mu

Mu

[2.2]paracyclophane

exo endo bridge

H2C CH2

H2C CH2

H2C CH2

H2C CH2

H2C CH2

H2C CH2

Mu

Mu

H

H2C CH2

H2C CH2

H

Mu

Mu

12.6o

ALC-µSR of [2.2]Paracyclophane


0.6 0.8 1.4 1.6 1.8 2.0 2.2

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Cor

rect

ed A

sym

met

ry /

%

Magnetic Field / T

%1 Endo

%1 Bridge

%1 Exo

Exo Aµ = 530.9 MHz %1 = 1.95 T 67±1 % Endo Aµ = 169.9 MHz %1 = 0.62 T 22±1 % Bridge Aµ = 469.0 MHz %1 = 1.72 T 11±1 %

UB3LYP/6-311G(d,p)//UPBE0/EPR-II

•  µSR is a powerful technique for characterizing free radicals in the solid, liquid or gas phases

References •  E. Roduner, Chem. Soc. Rev. 22, 337 (1993) •  C. J. Rhodes, J. Chem. Soc. Perkin Trans. 2, 1379

(2002) •  I. McKenzie and E. Roduner, Naturwissenschaften 96,

873 (2009)

Conclusions and References


µsr of free radicals - triumf.info · un accélérateur de la démarche scientifique canadienne...

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