INTRAMOLECULAR MOTION IN MUONIUM-

SUBSTITUTED FREE RADICALS

Feng Ji

B. Sc., East China University of Chemical Technology, Shanghai, China, 1985

M. Sc., East China University of Chemical Technology, Shanghai, China, 1988

THESIS SUBMITTED IN PARTIAL EULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

in the Department

Chemistry

Q Feng Ji 1994

SIMON FRASER UNIVERSITY

May 1994

All rights reserved. This work may not be reproduced in whole or in part, by photocopy

or other means, without permission of the author.

APPROVAL

Name: Feng Ji

Degree: Master of Science

Title of thesis: INTRAMOLECULAR MOTION IN MUONIUM-SUBSTITUTED FREE RADICALS

Examining Committee:

Chairperson: Dr. Ross H. Hill, Assistant Professor

Dr. Paul W. Percival, Professor Senior Supervisor

Dr. Saul Wolfe, University Professor

,. .-

Dr. S teve@nldcmft. ~ d i s t a n t Professor

Dr. T O ~ N . ~ e h : Professor Internal Examiner

Date Approved: J& k3 l q 9 4.

PARTIAL COPYRIGHT LICENSE

I hereby grant to Simon Fraser University the right to lend my

thesis, project or extended essay (the title of which is shown below) to

users of the Simon Fraser University Library, and to make partial or

single copies only for such users or in response to a request from the

library of any other university, or other educational institution, on its own

behalf or for one of its users. I further agree that permission for multiple

copying of this work for scholarly purposes may be granted by me or the

Dean of Graduate Studies. It is understood that copying or publication

of this work for financial gain shall not be allowed without my written

permission.

Title of ThesislProjectlExtendec 1 Essay:

Author: -

(signature)

FEnIG JI (name)

ABSTRACT

Muonium (p+e-), the light isotope of hydrogen, can add to unsaturated bonds to

form a P-muonium-substituted free radical. Muon Spin Rotation (pSR) and Muon Level

Crossing Resonance (WCR) techniques have proven valuable in the study of

conformations of Mu-substituted free radicals. Muon and other magnetic nuclear hmne

coupling constants for these radical species have been determined from pSR and pLCR

spectra. Measurements of the temperature variation of the hyperfine coupling constants

provided information on intramolecular motion and preferred conformations of Mu-

substituted free radicals.

Using pSR and/or pLCR techniques, several Mu-substituted free radicals have

been studied, namely, 1 -chloro-3-Mu-isopropyl (I), 1 -chloro-2-Mu-n-propyl (II), 1 -

chloro-2-methyl-3-Mu-isopropyl (111), 1,3-dithiolane-2-Mu-2-thiyl (IV) and 1,3-

dithiolane-2-Mu-2-selenenyl (V) radicals. Radicals I and I1 were formed from the same

precursor and pLCR resonances due to the 35Cl and 37Cl nuclei were observed in I. All

five radicals were identified from their hyperfine coupling constants. The hypedine

coupling constants of these radicals were measured over a wide temperature range.

By fitting a theoretical model to experimental data for radicals I and 11, it was

deduced that both Mu and chlorine eclipse the unpaired electron 2p, orbital in the

minimum energy conformation. The theoretical fits indicate V2 torsional barriers of 1.9 kJ

mol-l for CH~MU-~HCH,CI, 12 kJ mot1 for C H ~ M U C H - C H ~ C ~ in I and 2.1 kJ mol-I

for CH2-CHMUCH,Cl in 11. The unusually high barriers are rationalized as a

hyperconjugation effect between the unpaired electron and the C-Mu bond which

delocalizes the spin density at the radical center. The theoretical fit of the available data

for radical I11 shows Mu eclipses the axis of the unpaired electron 2p, orbital and a V,

torsional barrier of 1.5 id mol-' for CH,MU-6 (CH,)CH,Q was obtained. The difference

between the average hyperfine coupling constant (62 MHz) for the MU- group in the

1-chloro-2-methyl-3-Mu-isopropyl radical and the average value (68 MHz) for the

MU- group in the Mu-substituted tert-butyl radical implies that the chlorine

substituted group also affects the interaction between Mu and the unpaired electron.

A negative temperature dependence of hyperfine coupling constants measured

from pSR spectra for the 1,3-dithiolane-2-Mu-2-thiyl radical (IV) in solution, pure liquid

and pure solid 1,3-dithiolane-2-thione, and the 1,3-dithiolane-2-Mu-2-selenenyl radical

(V) in pure solid 1,3-dithiolane-2-selenone suggests that hyperconjugation between the

unpaired electron and the C-Mu bond is greater than for the C-S bond. A zero

temperature dependence of hyperfine coupling constants for radical V in solution is

consistent with the longer C-Se bond than the C-S bond. In the temperature range

investigated there is free rotation about the C-Se bond in solution.

In memory of my father

ACKNOWLEDGMENTS

I wish to thank my senior supervisor, Dr. Paul W. Percival, for all his steady

support, supervision and encouragement in carrying out this study.

I wish to express my gratitude to Dr. Jean-Claude Brodovitch for his helpful

suggestions and stimulating discussion, and to Dr. Dake Yu of the University of Calgary

for his assistance with the MINUIT fimng programs and valuable discussion.

Special thanks go to Mrs. Brenda Addison-Jones for her tireless efforts in teaching

me English and for reading the draft of my thesis.

I would like to express my thanks to Dr. Stanislaw Wlodek for his helpful ideas at

SFU, and to Mr. Curtis Ballard and Mr. Keith Hoyle for technical assistance at TRTUMF.

I would also like to thank the other members of my supervisory committee, Drs.

Saul Wolfe and Steven Holdcroft for the time and attention they devoted to me.

The financial support from the Department of Chemistry at Simon Fraser

University and Dr. Paul Percival is gratefully acknowledged.

TABLE OF CONTENTS

APPROVAL ............................................................................................................... n

... ABSTRACT ............................................................................................................... IU DEDICATION ........................................................................................................... v

ACKNOWLEDGMENTS .......................................................................................... vi

..................................................................................................... LIST OF TABLES x

. . .................................................................................................... LIST OF FIGURES xu

CHAPTER 1 . INTRODUCTION ......................................................................... 1

1.1. Muon and Muonium Chemistry .................................................................. 1

1.2. Basics of Muon Spin Rotation Spectroscopy (pSR) ....................................... 3

1.2.1. Transverse Field pSR ........................................................................... 5

............................................................. 1.2.2. Muonium in pSR Spectroscopy 6

............................. 1.2.3. Muonium Substituted Radicals in pSR Spectroscopy 9

1.3. Basics of Muon Level Crossing Resonance Spectroscopy (pLCR) .................. 11

. .............. CHAPTER 2 EXPERIMENTAL METHOD AND INSTRUMENTATION 16

2.1. Introduction to TRIUMF ............................................................................... 16

............................................................................................. 2.3. Signal Detectors 21

............................................................................................... 2.4. Magnetic Field 22

2.5. Temperature Controls .................................................................................... 22

2.6. Sample Cells ................................................................................................. -23

............................................................................................ 2.7. Data Acquisition 23

............................................................... 2.7.1. Electronics Setup for TF-pSR 23

................................................................ 2.7.2. Electronics System for pLCR 26

2.7.3. Data Analysis ........................................................................................ 26

CHAPTER 3 . INTRAMOLECULAR MOTION OF MU-SUBSTITUTED

.......................................................... CHLOROALKYL RADICALS 2 9

.................................................................................................. 3.1. Introduction 2 9

3.2. Chloroalkyl Radicals Formed from 3-Chloropropene ...................................... 31

........................................................................................ 3.2.1. Experimental -31

.................................................................................................. 3.2.2. Results 32

3.2.3. Theoretical Model and Data Fitting ................................................... 35

3.2.3.1. Temperature Dependence of the Hypefine Coupling Constants

for the CH,M u- Group in 1-Chloro-3-Mu-Isopropyl .................... 41

3.2.3.2. Temperature Dependence of the Hyperfine Coupling Constants

for the -CH2C1 Group in 1 .Chloro.3-Mu.Isopropy1.. .................... 42

3.2.3.3. Temperature Dependence of the Muon Hyperfine Coupling

Constant in 1 -Chloro-2.Mu.n.Propyl ........................................... -47

3.2.4. Discussion: Intramolecular Motion and Isotope Effects ......................... 47

...... 3.2.4.1. The CH2Mu- Group in the 1-Chloro-3-Mu-Isopropyl Radical 47

3.2.4.2. The -CH, Cl Group in the 1-Chloro-3-Mu-Isopropyl Radical ........ 51

3.2.4.3. -CH2Mu-CH2Cl in the 1-Chloro-2-Mu-n-Propyl Radical ............. 52

3.3. Chloroalkyl Radical Formed from 2-Methyl-3-Chloropropene ........................ 53

3.3.1. Experimental and Results ...................................................................... 53

3.3.2. Discussion ............................................................................................ 5 9

CHAPTER 4 . CONFORMATION OF MU-SUBSTITUTED THIYL AND

.......................................................... SELENENYL RADICALS 6 1

.................................................................................................. 4.1. Introduction 6 1

4.2. Experimental Data .................................................................................... 63

................................................................................... 4.3. Results and Discussion 63

................................................................ 4.3.1. Mu-Substituted Thiyl Radical 63

4.3.2. Mu-Substituted Selenenyl Radical ........................................................ 69

CHAPTER 5 . SUMMARY ........................................................................................ -73

REFERENCES ......................................................................................................... -75

LIST OF TABLES

. . ......................................................................... Properties of the positwe muon 2

Properties of muonium ................................................................................. 3 Muon hyperfine constants for CH,MU-~H-CH,C~ and

~H~<HMU-CH,CI in the liquid phase determined from transverse field

pSR spectra ...................................................................................................... 33 Level crossing resonance fields and hypefine coupling constants for

CH,Mu-CH-CH,Cl in the liquid phase ............................................................ 36

Level crossing resonance fields and hyperfine coupling constants for

C H2-CHMu-CH2C1 in the liquid phase .......................................................... 3 7

Representative fit to the temperature dependence of hyperfine coupling

constants of the CH,Mu- group in CH,Mu-CH<H2C1 in the liquid state ........ 43 Comparison of hyperhe coupling constant data for the CH,Mu- group in . CH,Mu-CH-CH,Cl and calculated values from the best fit .............................. 43

A model fit to the temperature dependence of the hyperfine coupling

constants of the -CH,Cl group in CH,Mu-CH-CH,Cl in the liquid state .......... 45

Comparison of hyperfine coupling constant data for the -CH,Cl group in . CH,Mu-CH-CH,Cl and calculated values from a model fit .............................. 45 Fitted parameters of a V, potential model for the analysis of the temperature

dependence of muon hyperfine coupling constants in C H,-CHMu-CH,Cl.. ...... 48

Comparison of muon hyperfine coupling constant data in

CH,-CHMu-CH,Cl and calculated values from a V, potential model fit .......... 48 . Muon hyperfine constants for CH,Mu-C (CH,)-CH2C1 in the liquid phase

determined from transverse field pSR spectra .................................................. 55 Level crossing resonance fields and hypefine coupling constants for

CH,Mu-C (CH,)-CH,Cl in the liquid phase .................................................... 56

3.12. A model fit to the temperature dependence of the hyperfine coupling . constants of the CH2Mu- group in CH2Mu-C(CH3)-CH2Cl in the liquid

phase ................................................................................................................ 57

3.13. Comparison of hyperfine coupling constant data for the CH2Mu- group in . CH,Mu-C (CH3)-CH2C1 and calculated values from a model fit ....................... 57

4.1. Muon hyperfine coupling constants for the 1,3-dithiolane-2-Mu-2-thiyl

radical in solution .......................................................................................... 64

4.2. Muon hyperfine coupling constants for the 1,3-dithiolane-2-Mu-2-thiyl

............................................................... radical in pure 1,3-dithiolane-2-thione 65

4.3. Muon hyperfine coupling constants for the 1,3-dithiolane-2-Mu-2-selenenyl

radical in solution and pure 1,3-dithiolane-2-selenone ....................................... 7 1

LIST OF FIGURES

1 Breit-Rabi diagram for a two spin- system ..................................................... 8

Fourier transform pSR spectrum obtained with 0.5 M 1,3dithiolane. 2.

thione in tetrahydrofuran ................................................................................... 11

High field energy level diagram for a three spin system of an electron. muon

........................................................................................ and magnetic nucleus 14

Cut-away drawing of the high field experimental setup for time differential

pSR and integral KLCR .................................................................................... 15

Layout of the TRIUMF cyclotron and experimental areas ................................. 17

A plan view of the M20 channel at TRIUMF ................................................ 19

Block diagram of plastic scintillator arrangement .............................................. 22

Schematic diagram of the pSR time differential electronics .............................. 24

Schematic diagram of the electronics setup used for pLCR experiments ........... -27

Fourier transform pSR spectrum of the products of the

Mu + CH2=CH-CH2C1 reaction at 298 K ........................................................ 33

pLCR spectrum of C H ~ M U . ~ H H ~ ~l and ~H2-CHMu--C H ~ C ~ at 269 K ..... 34

Schematic diagram showing the 2pz orbital at the a-carbon and the

definition of the dihedral angle for alkyl radicals ............................................... 37

Muon and proton hyperfine coupling constants for the CH2Mu- group in

Proton and chlorine hyperfine coupling constants for the -CH2C1 group in

........................................................................................ CH,Mu-CH-CH,Cl 4 6

3.6. Temperature dependence of the muon hyperfine coupling constants in . ........................................................................................ C H2-CHMu-CH2Cl 4 9

3.7. Qualitative energy level diagram for the effect of overlap between the 2p,

............................ orbital of the radical and the C-Mu bond. and the C-H bond 51

3.8. Qualitative energy level diagram showing change of the hyperconjugative

interaction between a radical and a C 4 bond due to a Mu-substituted

methyl group attached to the radical center.. ..................................................... 53 . 3.9. Fourier transform pSR spectrum of CH,Mu-C (CH,)-CH2C1 in the liquid

phase at 193 K ................................................................................................ 55

3.10. Temperature dependence of the muon and proton hyperfine coupling

............................................................... constants in CH2Mu-C (CH,)-CH2CI 58

4.1. Newrnan projection along the C-X bond (X=S or Se) of the radical showing

the possible orientations of the unpaired electron p,-orbit al............................... 62

4.2. Muon hyperfine coupling constants for C&~,S~CMU-S as a function of

temperature ...................................................................................................... 66

4.3. Qualitative energy level diagram showing the relative energies of the orbitals

...................................................... involved in the hyperconjugative interaction 67

4.4. Stacked Fourier transform pSR spectra of GH,S,CMU-s obtained in

10 kG applied transverse field at different temperatures .................................... 67

4.5. TF-pSR spectrum of GH,S~CMU-S in powder at 298 K ................................. 69

4.6. Muon hyperfine coupling constants for GH,S~CMU-& as a function of

temperature .................................................................................................. 72

CHAPTER 1. INTRODUCTION

1.1. Muon and Muonium Chemistry

The muon was the first unstable elementary particle observed. It was discovered in

1937 by Neddermeyer and Anderson [I] by its trace in photographic emulsions exposed to

cosmic rays. It occurs in two charge states, as p+ and p-, and has a rest mass equal to one-

ninth the mass of a proton. A negative muon can replace an electron in an atom, but its

huge mass (207 times the mass of an electron) leads to very low lying orbitals and

therefore to an atom with quite different chemical properties. In this case, a negative muon

is regarded as a "heavy electron" [2]. As chemists, we are interested in the positive muon.

In a weak interaction, the spins and angular momenta of the particles must be

conserved. Because the muon neutrino has negative helicity, the spin of the positive muon

must be anti-parallel to its momentum in the pion's center-of-mass co-ordinate system [3].

Hence, a 100% polarized beam of the muon can be produced by judiciously selecting the

momenta of the muons in the in-flight decay of the pions. Muon beams are produced at

several different places in the world; TRIUMF in Canada, PSI in Switzerland, KEK in

Japan and RAL in England. Some of the properties of the positive muon are summarized

in table 1.1.

In 1957, scientists realized that a positive muon could form a bound state with a

negative electron [4]. This one electron atom was named muonium (chemical symbol,

Mu). In muoniurn, the electron orbits the muon as its nucleus. Although the mass of the

muon is only one ninth that of the proton, it is still so much more massive than the

Table 1.1. Properties of the positive muon [5]

Positive muon

Charge

Mass

Spin

Magnetic moment

g-factor

Mean lifetime

Gyromagnetic ratio y,

P+

+e

206.8me

105.7 MeV c-2

1 - 2

4.49048 x 1030 J G-1

3.1833b

2.00233 1848

1.000006ge

2.197 14 ps

13.5544 kHz G-1

electron that the reduced mass of muonium is virtually the same as that of hydrogen.

Chemically, muonium can be regarded as a radioactive isotope of hydrogen. Muonium has

almost the same electronic structure, ionization energy, electron affinity and Bohr radius

as hydrogen. Some of the properties of muonium are shown in table 1.2.

Because of its properties, muonium is regarded as an isotope of H. Its collisions

with other atoms and molecules, especially chemical reactions, can be studied to examine

with improved sensitivity (relative to deuterium and tritium) such aspects as kinetic

isotope effects and quantum mechanical tunneling by comparing reactions of Mu with

those of H. In 1963, Brodskii [6] suggested that Mu-substituted free radicals could be

formed by addition of Mu to unsaturated molecules. The first direct observation of the

Mu-substituted free radical in high magnetic field was achieved by Roduner and Percival

Table 1.2. Properties of muonium [5,9]

Mass 207.8%

Bohr radius 0.5317i

l.Oo'%,(H)

Spin 1 for triplet

0 for singlet

Ionization potential 13.539 eV

Gyromagnetic ratio 1.394 MHz G-1

Hyperfine frequency 4463 MHz

Mean lifetime Limited by that of p+

[7]. Since then, a large number of this kind of free radicals have been studied using the

positive muon as probe. However this method only gives the values of muon hyperfine

coupling constants. After the Level Crossing Resonance (pLCR) technique was

developed, the measurements of the other nuclear hyperfine coupling constants in Mu-

substituted free radicals were realized [8].

1.2. Basics of Muon Spin Rotation Spectroscopy (pSR)

Muons are unstable particles and they are the products of pions. At TRIUMF, the

pions are generated by attacking a 9Be target with high energy protons from the cyclotron.

There are nuclear reactions which are described by:

Then the pions decay with a lifetime of 26 ns to give a muon and neutrino [lo]:

Finally, the muon will decay to a detectable positive electron, a neutrino and a

muon anti-neutrino [ 1 11.

This decay is induced by the weak interaction and as the result of parity non-

conservation. The electron neutrino has negative helicity while the positron and the muon

antineutrino have positive helicities. As a consequence of the conservation of energy,

momentum and angular momentum, this three body decay of the muon is spatially

anisotropic with positron emission. As a result, the positron is emitted preferentially in the

muon spin direction. In experiments, the positrons are detected with an efficiency 5 ( 0 ) which will not be constant over the entire energy range due to absorption and scattering in

the target and the counter as well as the effect of an external magnetic field on the

positron trajectories. The observed probability distribution is expressed by [12]:

where E is an average positron detection efficiency. The probability R of positron

emission at an angle 8 with respect to the spin direction is given by:

where KO is the spin asymmetry. If all the positrons were detected with the same

efficiency, the value of KO would be 113 [13]. In most muon experiments, the effective

asymmetry is less than 113. The time differential measurement of the asymmetric decay of

spin-polarized positive muons precessing in a transverse magnetic field forms the basis of

the pSR technique.

1.2.1. Transverse Field pSR

When a positive muon is stopped in the sample in a magnetic field perpendicular to

the initial muon spin direction, its spin precesses at its Larmor frequency o = y,B, where

y, = 13.5544 kHz G-l. The muon spin state is monitored by detecting the decay positron

that is preferentially emitted in the direction of the muon spin. To observe this transverse

field precession phenomenon, one can simply place a counter in the plane of the p+

precession at an angle @ with respect to the initial muon direction. In the experiment, a

spin polarized muon passes through a plastic scintillator counter and generates the signal.

The high precision clock in the computer is started subject to a pile-up gate. When the

decay positron is detected in the counter, the clock is stopped, otherwise the clock will be

reset at the end of the data gate. At time t, the angle between the incident muon spin and

positron detector will be w,t + $. As a result, the positron detection probability N(t) will

be proportional to 1 + A,cos(o,t + $). The probability also depends on detector

dimension, target geometry and beam polarization. In general, the number of positron

counts in a particular direction is collected in a histogram. The forrn of a pSR histogram is

P I :

where N(t) is the number of counts in a histogram time bin, No is a normalization factor

determined by the solid angle of the positron detector and the total number of stopped

muons, B is a time-independent background parameter which accounts for random

accidental events, o, is the muon precession frequency and AD is the asymmetry of the

sample. For a general case in which there are several different p+ containing species, each

evolving and undergoing spin relaxation at different rates, the time histogram of detected

positrons is formulated as follows:

where A,,, and Gi(t) are the initial asymmetry and the relaxation function of the i-th

component respectively.

1.2.2. Muonium in pSR Spectroscopy

Muonium is a typical two spin-+ system and it is characterized by the spin

Hamiltonian [I 11:

where A, is the hyperfine coupling constant between the muon and electron, ve and v, are

the Zeeman frequencies of the electron and muon, 9, and i, are the z-axis components of

the electron and muon spin operators. There are four spin states which divide into one

triplet state and one singlet state at zero magnetic field. If a magnetic field is applied to

muonium, the degeneracy of the triplet states is lifted. The variation of the energy levels of

the four spin states as a function of the strength of the applied field can best be illustrated

by use of the Breit-Rabi Diagram in figure 1.1. The eigenstates are labeled according to

their quantum numbers [13]:

1

where c = - [I+ ]i JI J i z

B is the applied magnetic field and B, is the internal magnetic field of muoniurn (1585 G).

There are four allowed transition frequencies in a transverse field experiment. Due to the

limitation of the timing resolution for conventional apparatus, only two transitions

(1 1) + 12). 12) + 13)) are observed in pSR spectroscopy at low magnetic field. At high

magnetic field, the muon and electron spin interactions are decoupled, the eigenstates are

shown as follows:

There are only two transitions (1 1) + I2), 13) + 14)), denoted by R, which are allowed at

high field.

Eney

T (4 1

Figure 1.1. Breit-Rabi diagram for a two spin-3- system. The energy levels of the muonium spin

states as a function of the magnetic field. The arrows indicate the allowed transitions

which correspond to pSR. In low fields, only two transitions denoted by solid lines are

resolvable. In high field, the two transitions indicated by R are observable in pSR

experiments.

1.2.3. Muonium Substituted Free Radicals in pSR Spectroscopy

A free radical is a paramagnetic species which contains an unpaired electron. When

a muonium stops in the sample which contains molecules with unsaturated bonds, radicals

will be formed. In most cases, the muonium is located at the P position except for some

molecules [14]. The first observation of Mu-substituted free radicals was made at high

transverse magnetic fields in 1978 [7]. In Mu-substituted free radicals, the electron spin is

coupled to the magnetic nuclei and muon. The corresponding spin Harniltonian in isotropic

samples can be written as [15]:

where v,, v, and v, are the Zeeman frequencies of the electron, muon and the k-th nuclear

spin, A, and A, are the isotropic Ferrni contact hyperfine constants. A basis of product

spin functions is given as follows:

N

For N nuclei with quantum numbers L, the Harniltonian leads to 4n(21, + 1) eigenstates. n

Through theoretical calculation [15] for transverse field, the transition selection rule is

AM = f 1 with M = m, +me + mk (mp . . are magnetic quantum numbers). Usually, k

there are a large number of transitions between these eigenstates. Consequently the

spectroscopy is too complicated to get any information on the Mu-substituted free

radicals. However in the high field limit (v, >> Ak, A&, the spectroscopy is considerably

simplified and the transitions degenerate to only two lines. The spin states for this

Hamiltonian can be approximately represented by individual eigenstates of equation 1.18

and the selection rule is % = f 1 and Am, = Am, = 0. The two observable frequencies

are:

where

1 V, =-{[A: +(v, +v,)~]'-v, +v,)

2

is the muon Larmor frequency v, shifted by

(1.21)

a small amount dependent on the relative

magnitudes of the electron Larrnor frequency and the muon hyperfine constant. In

experiments, the pSR signals of Mu-substituted radicals are analyzed in frequency space

rather than in time space. At TRIUMF, a Fast Fourier Transform (FFT) program is used.

Fourier transformation provides a mean of extracting the precession frequencies of various

species. Figure 1.2 is a typical TF-pSR spectrum of the Mu-substituted l,3-dithiolane-2-

Mu-2-thiyl radical. By use of the high field pSR technique, many Mu-substituted radicals

have been studied and many muon hypedine coupling constants have been measured 1161.

However, there are some problems limiting the applications of TF-pSR spectroscopy. The

first one is that conventional pSR spectroscopy can only detect radicals for which

formation rates are much larger than the precession frequency of their precursors.

Secondly, TF-pSR technique can only give us muon hyperfine coupling constants.

Measurement of nuclear hyperfine coupling constants in Mu-substituted free radicals was

not possible until development of the pLCR technique in the mid-80's.

0 200 400 Frequency (MHz)

Figure 1.2. Fourier transform pSR obtained with 0.5 M 1,3-dithiolane-2-thione in

tetrahydrofuran. v,,, v,: radical precession frequencies. v,: diamagnetic signal,

due to sample cell and solvent.

1.3. Basics of Muon Level Crossing Resonance Spectroscopy (pLCR)

For many years, it has been known that the mixing effect of near degenerate levels

occurs in atomic spectroscopy and nuclear quadrupole resonance [17]. In 1984, Abragam

suggested taking advantage of the depolarizing effect of avoided level crossing in high

longitudinal magnetic fields on muon spin polarization to detect nuclear hyperfine coupling

constants of paramagnetic ions [18]. The nuclear hyperfine coupling constants would

provide important infomation on the electron spin density distribution at the neighboring

nuclei. The phenomenon of pLCR in Mu-substituted radicals began to be investigated

experimentally in 1986 [8].

In the liquid phase, dipolar contributions to the hyperfine interaction are averaged

to zero owing to rapid isotropic reorientational tumbling of the radicals. The remaining

isotropic interaction leads to level crossings of energy levels via coupling to a third, distant

state. The spin Hamiltonian of a Mu-substituted free radical with N magnetic nuclei is

given by equation 1.17. In high magnetic fields, Zeernan states are eigenstates except in

the range near a pLCR resonance where the eigenstates are the mixtures of two Zeeman

states. A theoretical treatment was developed by Kiefl et al. [8] and independently by

Heming et al.[19], by solving the spin Hamiltonian equation. At high field muon-nuclear

spin flip-flop transitions leading to particle depolarization are expected to exist at:

where ye and y, are the muon, electron and nuclear gyromagnetic ratios, A, and A, are

the muon and nuclear isotropic coupling constants, and M, is the quantum number for the

z-component of the total angular momentum of equivalent nuclei. By measuring the pLCR

resonance field Bo, the nuclear hyperfine coupling constant A, would be determined.

The expression for the muon polarization in a multi-spin system at the high field

limit is given by:

which is a sum of Loaentzian lines with full width at half maximum:

4 1 2 = "'0 (1 + -$I2 h2

W , Y Y ~ @O

and amplitude:

where N is the dimension of the energy matrix, and h is the radioactive muon decay rate.

The selection rule of pLCR for isotropic spin systems is A(m, + m,) = 0. In solids, the

anisotropic interaction gives rise to an additional resonance with the selection rule

A(m, + m, ) = 1. Figure 1.3 is a basic schematic diagram of pLCR energy levels.

Using the pLCR technique, both the magnitude and sign of the hypefme coupling

constants of the muon and other nuclei are determined. By analyzing the temperature

dependence of the hyperfine coupling constants of the muon and nuclei in Mu-substituted

free radicals, information on preferred conformations of Mu-substituted free radicals and

their torsional barriers can be derived.

Due to the longitudinal field applied, there is no problem with dephasing caused by

slow reactions. Radicals will be observed even when a Mu-precursor has a lifetime of a

microsecond, as long as the transition frequency coo is high enough to produce a significant

@CR signal in the remaining lifetime of the muon. The loss of polarization during the

precursor stage is negligible in high longitudinal field. In experiments, the time-integrating

method can make full use of the muon beam since it does not require that only one muon

is in the sample at a time.

Muon Nucleus Spin Flip-Flop

(AM=O)

Flip (AM=I)

Muon Nudeus Spin Flip--Flip

(AM=2) B >

Figure 1.3. High field energy level diagram for a three spin system of an electron, muon and

magnetic nucleus. pLCR resonances occur when the states with opposite muon spins

become near degenerate in energy, allowing the system to oscillate between them.

The pLCR spectrum is the time-integrated positron rate recorded as a function of

magnetic field. Resonances are observed as changes in decay positron count rates in

detectors placed in the "forward" and "backward" directions relative to the initial spin

polarization. The muon polarization is proportional to experimental asymmetry A. A is

defined as:

where XNf and XNb are the total number of positrons detected in the forward and

backward directions. A diagram of the experimental setup is shown in figure 1.4.

Superconducting UP

solenoid , I

\ counters

Muon

counter

Backward Forward

counters counters

TF-pSR experinent: Down

heed spin rotator) sL- counters

B

pLCR experiment: 4

Figure 1.4. Cut-away drawing of the high field experimental setup for time differential pSR and

integral pLCR. In the diagram, the spin direction is perpendicular to the magnetic field

in TF-ySR experiments and is parallel to the magnetic field in pLCR experiments.

CHAPTER 2. EXPERIMENTAL METHOD AND INSTRUMENTATION

2.1. Introduction to TRIUMF

TRIUMF is Canada's national meson facility. It provides world leading facilities for

experiments in subatomic research with beams of pions, muons, protons and neutrons.

TRIUMF is managed as a joint venture by four universities, which are University of

British Columbia, University of Alberta, Simon Fraser University, and University of

Victoria. TRIUMF is operated under a contribution from the National Research Council

of Canada.

TRIUMF is a cyclotron that accelerates negatively charged hydrogen ions over a

wide energy range from 60 MeV to 520 MeV. TRIUMF is known as a meson factory

because it has the capability of generating a high intensity of pi-mesons. The current of the

proton beam can reach 150 PA. The TRIUMF cyclotron and experimental areas are

shown in figure 2.1.

When negatively charged hydrogen ions accelerated inside the TRIUMF cyclotron

reach a particular velocity, they are passed through a metal foil which captures the

electrons and transmits only protons. At TRIUMF, there are three stripping foils which

extract three proton beams simultaneously. Beam Line 1 (BL1) delivers beam to the

Meson Hall, Beam Line 2 (BL2) guides beam to the cyclotron vault's east wall and Beam

Line 4 (BL4) provides beam to the Proton Hall.

ME

SO

N

HA

LL

ER

VIC

E A

NN

EX

H- I

ON

SO

UR

CE

Figu

re 2

.1.

Layo

ut o

f the

TR

IUM

F cy

clot

ron

and

expe

rim

enta

l are

as [2

0].

In the meson hall, a proton beam passes through two production targets to provide

sources of muons and pions to a number of secondary beam channels before being stopped

in the thermal neutron facility. The frst production target lATl is very thin and it can

provide muon/pion beams to three different channels, which are M13, a low energy pion

and surface muon channel; M11, a high energy and good resolution pion channel; M15, a

high quality surface muon channel. The second target 1 A n is thick and it can generate

high intensity muon/pion beams to several channels which are M9, a low energy pion and

cloud muon channel; M8, a high flux pion channel for cancer therapy research; M20, a

general purpose muon channel for both backward decay and surface muons.

The most attractive feature of the TRIUMF cyclotron is its 100% macroscopic

duty cycle. On a macroscopic time scale, the proton beam looks like a continuous current.

The microscopic duty cycle is a 5 nanosecond burst of protons every 43 nanoseconds.

Almost all experiments of our group (SFUMU) are canied out at M15 and M20.

The rest of them are operated at M13. The experimental data in this thesis were collected

at M20B.

2.2. Beamline M20

The M20 channel, which is capable of producing moderately high fluxes of

backward and surface muon beams, has two legs (M20A and M20B). Leg A is used for

backward muon decay. The backward muons of momenta up to 86 MeV c-I are delivered

to the experimental area. Leg B is used to deliver surface muons to the experimental

apparatus. Figure 2.2 shows layouts of the M20 channels.

At TRIUMF, the meson factory creates three different types of muon, namely,

forward, backward and surface muon. The forward muon has the highest energy of the

three but poor quality. It is contaminated seriously by pions, positrons and protons. It has

a high stopping range (35 g ~ m - ~ ) so that it is rarely used for experiments.

The backward beam is produced from pions decaying in flight and has polarization

of 60% - 80%. The momentum range of the backward muon is from 60 - 120 MeV c-l.

The stopping range is about 5 g cm-2. At present, the backward muon beam is not used in

our group because it is too energetic to be stopped properly in the sample cell.

The surface muon beam forms from pions decaying at rest within a few pm of the

surface of a production target. It has 100% muon polarization. It is nearly monoenergetic

(4.1 MeV) with a nominal momentum of 28.6 MeV c-l. Its stopping range is very small,

only 0.15 + 0.01 g cm-2. Small quantities of sample in thin window cells are used in the

experiment. Almost all the surface muons can be stopped within the volume of the sample

cell. Because of the low energy and momentum of the surface muons, they are readily

affected by the external magnetic field. The radius of curvature is less than 1 m kG-I [21],

so it is difficult to inject the surface muons into a strong transverse magnetic field

Besides, surface muon beams are contaminated by positrons. In order to solve those

problems, DC separators are installed to remove the positrons from the muon beam and to

rotate the muon spin so that it is transverse to the momentum. The spin rotator consists of

a horizontal magnetic field and a vertical electric field. Magnetic field affects both the spin

and momentum of the muon while electric field affects the momentum only. When

optimized magnetic field and electric field are applied, the muon spin will be rotated

without any change of its momentum. This kind of beam is easily injected into a strong

magnetic field oriented longitudinally to the momentum but transversely to the muon spin.

In addition, using this technique, a single experimental apparatus which is used for both

longitudinal field (muon spin parallel to the magnetic field) and transverse field (muon spin

perpendicular to the magnetic field) experiments is available.

2.3. Signal Detectors

Scintillation detectors are used to detect high energy particles. Scintillators are

made of fluorescent compound dissolved in a transparent plastic matrix. The whole

detector consists of plastic scintillator, plexiglas light guide and photomultiplier tube.

Figure 2.3 shows a diagram of a plastic scintillator detector used at TRIUMF.

When a particle passes through the detector, the fluorescent compound captures

energy from the charged particle and reernits energy as a tiny flash which is conducted to

the photomultiplier then amplified and converted to an electrical signal pulse. In order to

reduce the background noise, the plastic scintillators and light guides are wrapped in black

tape. Since the high magnetic field affects the photomultiplier tube, the light guides are

over 1 meter long. This limits the time resolution of the pSR spectrum to about 1

nanosecond.

2.4. Magnetic Field

The experiments of this thesis were carried out at high magnetic field. Both

transverse field and longitudinal field are provided by HELIOS (a custom-built solenoid).

The magnet was designed to have a magnetic field as high as 70 kG. The high field can be

controlled by the use of the remote computer. The field dependence of spectra (e.g.

W R ) were collected automatically.

Figure 2.3. Block diagram of plastic scintillator arrangement.

2.5. Temperature Controls

There were two types of temperature control apparatus used in our group for

different temperature ranges. One was a circulator and the other was a cryostat. For the

circulator there was a constant temperature bath. The temperature of the sample was kept

constant by circulating fluid through insulated tubes between a bath and a copper plate to

which the sample cell was attached. Because of an unavoidable temperature gradient

between the constant temperature bath and the sample cell, the real sample temperature

was measured by a silicon diode which was embedded between the cell and copper plate.

It was found that the variation of temperature over the sample volume is less than 1 OC.

In low temperature experiments, a cold helium cryostat was used. The cryostat

consisted of a compressor unit and a cold head. The temperature was controlled by a

cryogenic digital thermometer. There were three different kinds of temperature sensor

attached on a copper plate which were silicon diode, platinum, and carbon glass resistance

thermometer. The silicon diode sensor was the only one which was recognized by the

cryogenic temperature controller. However its reading varied with magnetic field in high

field experiments. The latter two sensors were field independent but the platinum

thermometer only can measure temperatures higher than 70 K. Another thermometer,

carbon glass resistance, was installed because it had excellent performance under the

conditions of low temperature (< 70 K). The sample temperature was measured with the

platinum resistance thermometer or the carbon glass resistance thermometer at different

temperature ranges. The uncertainty of the low temperature setup was less than 0.5 K.

2.6. Sample Cells

The sample cells used in my research were made of stainless steel. The window of

the sample cell was made from one thousandth inch thin stainless steel foil so that surface

muons can pass through the window and stop in the cell. Samples were prepared on the

vacuum line in our laboratory and the freeze-pump-thaw method was applied for each

sample preparation. The cell was sealed after freeze-pump-thaw three times to ensure an

oxygen free sample.

2.7. Data Acquisition

2.7.1. Electronics Setup for TF-pSR

A simplified TF-pSR time-differential electronics schematic diagram is shown in

figure 2.4.

Figure 2.4. Schematic diagram of the pSR time differential elecmnics. CFD is the constant fraction

discriminator in the electronics. TDC is the time to digital converter.

Time differential pSR maps the time evolution of the muon spin polarization. The

muon beam rate should be reduced until less than one muon on average enters the target

during the time window at over which one wishes to examine the muon behavior. The time

window is generally chosen to be between two and five muon lifetimes. Since the number

of events falls off exponentially with the time, longer gates are impractical. In pSR

experiments, the signal from the photomultiplier is first transformed to a standard nuclear

instrument and measurement (NIM) pulse of tens of ns width and then sent to electronics

units. A muon passes through a muon counter which generates a start pulse for a high

precision clock, subject to a pile-up gate. The muon thermalizes as muonium in the sample

and precesses in the local transverse field. At some later time, the muon decays and emits

a positron preferentially along its spin direction at the moment of decay. When the decay

positron is detected in one of the positron counters (Left Up, Left Down, Right Up, Right

Down, see figure 1.4), the clock is stopped and the event is added to the appropriate time

bin in the histogram corresponding to that muon counter. A good decay positron is

identified by a coincidence of the positron signal with the data gate. If more than one

event occurs within a data gate, they are all rejected. It is important to reject so-called

second muon events. Otherwise, there are two muons in the target and a subsequently

emerging positron cannot be assigned unambiguously to the right parent. If such ill-

defined events are not excluded, spectral distortion will result because the observation of

long lived muons will be increasingly suppressed by second muons. It is necessary to reject

both events of the sequence 1st p+-2nd p+-positron and 1st p+-positron-2nd p+ within the

data gate (time windows). In addition, ill-defined events in which a p+ stop is followed by

two positrons should be rejected too. If no second muon and second positron signal are

detected, the event is good and can be stored in the computer.

2.7.2. Electronics System for pLCR

Figure 2.5 is a diagram of the pLCR electronics setup. As described previously,

pLCR is a time-integrated spectroscopy. Unlike TF-pSR, it can make full use of the muon

beam. In our experiments, the positrons are detected by eight different positron counters

at different positions, which are Forward Top Left, Forward Bottom Left, Forward Top

Right, Forward Bottom Right, Backward Top Left, Backward Bottom Left, Backward

Top Right, Backward Bottom Right. Positron events detected from the four forward

counters are defined as F. The signals from the four backward counters are defined as B.

F' - B* The muon decay asymmetry A* is defined as F' + B' ' where f: corresponds to the

direction of the small modulation field (50 G). At each field point, the modulation field is

toggled up to 20 times. The total muon counts are sent to a preset scaler while the

positron counts are fed into the computer and visual scalers. When the preset value is

reached, the data acquisition is stopped, the scalers are read and saved in the computer.

Then the preset scaler is cleared and the phase of the modulation field is reversed. After

the same number of flip-flops of the modulation field is reached, the main field (HELIOS)

is incremented. The entire data of pLCR spectroscopy are collected by computer

automatically.

2.7.3. Data Analysis

All data collected from pSR and pLCR are fitted with theoretical lineshapes using

the MINUIT program on the TRIUMF computer. The MINUIT program, written by F.

James et al. [22], is conceived as a tool to find the minimum value of a multi-parameter

function and analyze the shape of the function around its minimum.

Figure 2.5. Schematic diagram of the electronics setup used for pLCR experiments.

In TF-pSR spectroscopy, the time differential data are transformed to frequency

space and the peaks are fitted with Lorentzian shapes [23] to determine the radical

frequencies precisely.

In pLCR spectroscopy, the time integrated data are fitted by two Lorentzian

functions corresponding to the opposite directions of the modulation field. The resonance

field B is assigned definitely.

CHAPTER 3. INTRAMOLECULAR MOTION OF MU-SUBSTITUTED CHLOROALKYL RADICALS

3.1. Introduction

As described in section 1.2.3, Mu-substituted free radical can be formed by the

addition of muonium to one end of the unsaturated bond in the molecule and the unpaired

electron is left on the other side of the bond. In general, the site of the unpaired electron is

named a, and the point of Mu attachment is labeled P. Addition of Mu to an unsaturated

bond system can form a P-radical or P-muonium-substituted radical. It is well known that

the hyperfine coupling constants of P-position protons in aUcy1 radicals follow the

McConnell relation [24].

where L and M are constants (M >> L) and 0 + 8, represents the dihedral angle between

the axis of the unpaired electron p, orbital at the a center atom and the Cp-H axis. 8, is

the lowest energy dihedral angle. Krusic et a1 [25] suggested that the empirical constant L

has contributions from spin polarization while M is related to the delocalisation of the

unpaired electron by hyperconjugation. It is assumed that the transitions between the

torsional levels are very rapid on the experimental time scale and the observed hyperfie

coupling constant (hfc) is a Boltzrnann-weighted average over the various torsional states.

As muonium is a light isotope of hydrogen, it is widely accepted that the hyperfme

coupling constants of P-muonium-substituted radicals follow the McConnell relation too

[16]. In the high temperature limit, where the torsional eigenstates are a continuum, the

term cos2 (0 + 0,) in equation 3.1 averages to and A, = L++ M . In the low

temperature limit, if €lo = 00, the term cos2 (0 + 0,) averages to 1 and 4 will approach the

value of L + M and thus show an overall negative temperature dependence; applying the

same principle, a positive temperature dependence of A, results from $ = 900, where A, =

L in the low temperature limit. So a study of the temperature dependence of the hyperfine

coupling constants can provide unambiguous information on the preferred conformation of

the Mu-substituted free radical. By fitting the temperature dependence of the P hyperfine

coupling constants under the theoretical model, information on the intramolecular motion

can be obtained. Many Mu-substituted ethyl radicals formed from different kinds of

deuterated molecules have been studied by Ramos et al. [26,27] by analyzing the

temperature dependence of the muon hyperfine coupling constants. The rotation barriers

of these radicals were estimated. It was found that the torsional banier of the Mu-

substituted radical is higher than the equivalent non-Mu radical. The torsional barrier for . . W,H-CD2 is 0.376 W mol-1 while the barrier for CD2Mu-CD, is 3.452 W mol-1. For

the empirical constants L and M in the McConnell relation, the absolute values for

CD2Mu-CD, are larger than CD2H-CD,. The torsional banier for CH2Mu-CH2 is

2.845 kJ mol-1 while the barrier for CH,CH, is only 0.107 kJ mol-l [28]. It implies that

there is an incredibly strong isotope effect for muonium on the torsional barrier in

comparison with the proton. From studies of muon hypexfine coupling constants of Mu-

substituted free radicals formed from various unsaturated organic compounds, Cox et al.

[29] suggested that the hyperconjugation between the C-Mu bond and the unpaired

electron determines the isotope effects of hyperfine coupling constants and preferred

conformation of these radicals.

In the mid-1980's the pLCR technique was developed. It is used to determine

proton and other magnetic nuclear hypefine coupling constants. Using the pLCR

technique, Percival et al. [30,31] have measured proton hyperfine coupling constants for

the Mu-substituted tert-butyl radical and various isotopically substituted ethyl radicals. By

fitting the temperature dependences of muon and proton hyperfine coupling constants in

the %Mu- group for ten-butyl radical simultaneously, a more reliable torsional barrier

was obtained. Since the 1990's, Mu-substituted chloroalkyl radicals formed from 3-

chloropropene [32] and 2-methyl-3-chloropropene have been investigated in our group.

pSR signals due to radicals and pLCR resonances due to proton and chlorine were

detected. All the radical structures were assigned from the muon, proton and chlorine

hyperfine coupling constants. The details are in the following sections.

3.2. Chloroalkyl Radicals Formed from 3-Chloropropene

3.2.1. Experimental

Measurements of muon and nuclear hfcs for Mu-substituted free radicals formed

from 3-chloropropene were made over a temperature range of 100 K to 300 K. The

melting point of 3-chloropropene is - 134.5 OC (1 38.7 K). The target consisted of a sample

of pure, oxygen free 3-chloropropene sealed in a stainless steel cell. The liquid samples

were degassed by the method of freeze-pump-thaw. The volume of the sample cell is 4 rnl

and thin stainless steel foil (1 x inch) is used as the cell's window. The experimental

temperatures were controlled by a helium-cooled cryostat at low temperatures or by a

circulator at high temperatures.

To compare the muon hfcs with proton hfcs, the muon hfcs are scaled to their

proton equivalents by multiplying by the appropriate ratio of magnetic moments (y& =

0.31413, A,' = 0.31413AP).

As explained in chapter 1 (equation 1.22), the pLCR resonance field BR depends

on the muon and nuclear hfcs, and their gyromagnetic ratios. With the knowledge of the

muon hfcs and the help of ESR hfcs for the different nuclei in the radical C H ~ ~ H - C H ~ C ~

[33], resonance fields in the pLCR spectrum can be predicted. Then it is possible to search

efficiently for the pLCR signals concerned with each set of magnetically equivalent nuclei

in the Mu-substituted radicals. In order to suppress systematic errors arising from beam

fluctuations, a modulation field (ca. 40 G ) was applied. This resulted in the differential-like

shape of the signals.

3.2.2. Results

With the expectation that Mu could add to the double bond, the following reaction

scheme for the formation of Mu-substituted free radicals was assumed.

where radical I could be the major and I1 could be the minor product because for Mu-

substituted radicals secondary species are formed more predominantly than primary

species [16]. The Fourier Transform pSR spectrum of the products of the Mu addition to

3-chloropropene at 298 K is shown in figure 3.1. There are two pairs of signals in the TF-

pSR spectrum and the muon hfcs for both pairs were measured at different temperatures

from spectra. However, for the weaker pair of signals, the data could only be obtained in

the range of 200 K to 300 K. Below 200 K, the weaker pair were broadened. A summary

of muon hfcs is listed in table 3.1. For both species, the muon hfc decreases when the

temperature increases. The pLCR spectrum collected at 269 K is shown in figure 3.2.

. Table3.1. Muon hypefine coupling constants for CH2Mu-CH<H,Cl and

CH~-CHMU-CH~CI in the liquid phase determined from transverse field pSR spectra.

297.6 296.56(7) 315.3(1)

297.4 296.57(9) 316.1(2)

273.7 301.61(5) 327.4(4)

246.6 308.72(5) 330.0(2)

220.0 317.16(3) -

196.7 325.94(5) 354.7(9)

17 1 .O 339.4(1) -

157.5 345.5(2) -

109.5' 385.3(6) -

data in the solid phase.

0 200 400 Frequency (MHz)

Figure 3.1. Fourier transform pSR spectrum of the products of the Mu + CH,=CHXH,Cl

reaction at 298 K.

temperature was lowered, the intensity of the two resonances labeled I1 in figure 3.2

became weaker so that they could not be detected below 200 K. There are three groups of

resonances in the pLCR spectrum, two at low field (below 10 kG), three medium field (ca.

14 kG) and two high field (ca. 20 kG). At medium range, two of the proton hfcs are

typical of P-hydrogen (60 to 70 MHz) [30,31] and the third hfc (ca. 25 MHz) could be

from a khydrogen located on a fragment containing a chlorine atom [33]. It is widely

accepted that the hfcs of a magnetic nuclei are negative. Thus the two high field

resonances could be assigned to a-proton hfcs since the hfcs calculated from these two

fields are close to -60 MHz. One of the advantages of the pLCR technique is that the

pLCR spectrum can provide the sign of the hfc. In these assignments, the two resonances

which disappear at 200 K can be associated with the minor radical product (11), which

showed a similar behavior during the transverse field experiments. Finally, the two lowest

fields (below 10 kG) can be unambiguously assigned to 35Cl and 37C1. The ratio of the hfics

(l.2O5f O.OO4 averaged over all temperatures) is in good agreement with that predicted

from the gyromagnetic ratios, y(35Cl)ly(37C1) = 1.201. All the pLCR data relevant to these

two radical species (I and 11) are summarized in table 3.2 and table 3.3. For the minor

radical (11), the chlorine atom is in the y position so that the hfc is too small to give a

measurable pLCR signal.

3.2.3. Theoretical Model and Data Fitting

In order to obtain information on intramolecular motion in Mu-substituted radicals,

the temperature dependence of muon and nuclear hfcs was analyzed by the method of

Ramos et al. [26] and Percival et al. [31]. For a single alkyl radical the main part of the

unpaired electron spin density derives from the 2p, orbital of the a-carbon. Assuming

Tab

le 3

.2.

Lev

el c

ross

ing

reso

nanc

e fi

elds

and

hyp

erfi

ne c

oupl

ing

cons

tant

s fo

r th

e m

ain

radi

cal C

H2M

u-C

H-C

H2C

1 in

the

liqui

d

phas

e.

Tem

pera

ture

C

H,M

u CH

C

H2C

1 C

H2C

l C

H2C

I

* E

SR re

sults

obt

aine

d fr

om th

e C

H,-

~H

-CH

~C

I radi

cal a

t 14

6 K

[33

].

Table 3.3. Level crossing resonance fields and hyperfine coupling constants for the

minor radical CH2-CHMu-CH2~l in the liquid phase.

Temperature 6 H2 CHMu

* data obtained from the CH~-CH~-CH~CI radical [33].

there is rotational motion about the Ca-Cp bond and making the approximation that the

internal rotation of the CXRR' group about the C a q p internuclear axis is independent

from other motions such as vibrational motion, molecular rotation and solvent interaction,

and the bonds in Mu-substituted radicals are taken as rigid, the torsional Harniltonian is:

where I =- ''I2 is the reduced moment of inertia for the two groups (CaR'R"' and 4 +I2

CpXRR') and V(8) is the rotation potential which influences the rotational motion about

the Ca-Cp bond.

As shown in figure 3.3, $ is the dihedral angle between the axis of the unpaired

electron 2p, orbital and the Cp-X bond and is defined as:

where 8, is the value of @ at the potential minimum. If the correlation times for transitions

between torsional states are much shorter than the time scale of the pSR experiment, and

the torsional energy levels have a Boltzmann distribution, the observed P-hfc is the

Boltzmann weighted average of the quantum mechanical expectation values of the

torsional states. It follows that:

where (A(@)). is the expectation value of the bhfc for the radical in the i-th torsional

state. By fitting the temperature dependence of the P-hfcs, information on radical

conformations and intramolecular motion can be obtained. V(8) has the form of a

sinusoidal function and can be presented as a Fourier series:

For a methyl group, with local qv symmetry, a three-fold potential and a six-fold

potential could be applied. However, in a Mu-substituted methyl group, the Gv symmetry

is broken and a two-fold potential is retained. The barrier can be described by a truncated

Fourier series, and the two-fold potential which is expected can be defined as:

R R" R"'

Figure 3.3. Schematic diagram showing the 2pz orbital at the a-carbon and the definition of the

dihedral angle $I for alkyl radicals.

The Hamiltonian (equation 3.3) together with the potential function (equation 3.6)

can be used to calculate the torsional energy levels and the corresponding eigenfunctions.

Finally, the P-hfc can be calculated by equation 3.5. In the treatment of the torsional

eigenstates, the wavefunction is constructed as a linear combination of free rotor

functions:

Usually 21 free rotor wavefunctions were selected as a basis set (n- = 10);

further increases did not change the free rotor energy level significantly [31]. For

occupancy of the j-th torsional level, the expectation value A&@) can be evaluated from:

the expectation term (j 1 cos2 (0 + 0, )I j) can be expressed as [27]:

++c;-, (cos 20, +sin 2eo)]

where the coefficients cJ, are obtained by solution of the secular problem using the

Hamiltonian given by equation 3.3 and equation 3.7. The elements in the secular

determinant are as follows:

where 6,, = 1 for n=m

4,=0 for n z m

A FORTRAN subroutine, which was called by MINUIT, was written for the chi-

square minimization fit of equation 3.5 to the experimental data. The chi-square value is

given by:

m 2 FCN = (A; (exP) - (theor))

i=l ~:(enor)

where A'Jexp) and kj(exp) are the experimental hfcs for muon and nucleus. In these fits

the geometries optimized from PC-Model were used to calculate reduced moments of

inertia for different C,-Cp bonds in various chloroallcyl radicals. For radical I the reduced

moment of inertia for CH~MU-~HCH~CI is 3 . 8 3 6 ~ 1V47 kg rn2 while the value for

C H , M U ~ H ~ H ~ C I is 3 . 5 5 9 ~ 1V4 kg m2. For radical I1 the reduced moment of inertia

for ~H~-CHMUCH,CI is 2 . 9 6 5 ~ 10" kg m2. The data fits are not sensitive to the

reduced moments of inertia [26].

3.2.3.1. Temperature Dependence of the Hyperfine Coupling Constants

for the CH2Mu- Group in 1-Chloro-3-Mu-Isopropyl

With the data available it is possible to use the theoretical model described in

section 3.2.3 to fit the temperature dependence of hfcs. A simultaneous fit was made to

the two sets of data on Afl) in table 3.1 and P$(CH2Mu-) in table 3.2. The muon hfcs for

the CH2Mu- group show a negative temperature dependence. From the McComell

relation this implies that the C-Mu bond eclipses the axis of the unpaired electron 2p,

orbital in the minimum energy conformation. The dihedral angle for the Mu in the

preferred conformation was assumed to be zero, 8,(Mu)=0•‹. Since the CH,Mu- group no

longer has the G, symmetry of an unsubstituted methyl group, it was suitable to postulate

a two-fold potential for the rotation of the Mu-substituted group as a main contribution to

the rotation barrier. Due to the inherent symmetries for a methyl group, a three-fold

potential is still considered together with a two fold sinusoidal function when fitting. The

quality of the fits is judged by the reduced chi-square, x:, and reasonable values for the

parameters. Using the MINUIT program, the representative fit parameters listed in table

3.4 were obtained for the temperature dependence of the hfcs of the Mu-substituted

methyl group in I in liquid phase. Fit I11 in table 3.4 is the best set of parameters. The

comparison of experimental data and calculated values for fit I11 is shown in table 3.5.

Figure 3.4 displays the best fit curves for the experimental data.

3.2.3.2. Temperature Dependence of the Hyperfine Coupling Constants

of the -CH2CI Group in l-Chloro-3-Mu-Isopropyl

The -CH,Cl group could be considered as a chlorine substituted methyl group.

Due to a negative temperature dependence of the chlorine hfcs as shown in table 3.2, it

was suggested that the minimum energy conformation corresponds to chlorine eclipsing

the axis of the unpaired electron 2p, orbital at the radical center. The dihedral angle for C1

was fixed to be zero all the time when fitting. Given the small set of experimental data

only a two-fold potential was considered in this fit since one benefits to increase the

degrees of freedom. The fit parameters and the calculated hfcs for proton and chlorine are

displayed in table 3.6 and table 3.7. The fitted curves resulting from a two-fold potential

model are shown in figure 3.5.

Table 3.4. Representative fit to the temperature dependence of hyperfine coupling . constants for the CH,Mu- group in CH2Mu-CH-CH2Cl in the liquid phase.

-39

223

1.9

0.4

17

102

118 fixed

1.18

-37 -36

220 217

1.9 1.9 - -

-69 10

273 117

122 115 fixed

1.11 1

Table 3.5. Comparison of hyperfine coupling constant data for the CH,Mu- group in

C H 2 ~ u - k ~ - ~ ~ , c 1 and calculated values from the best fit.

Temperature /K A',(exp.) /MHz A',(calc.) /MHz

Figure 3.4. Muon and proton hyperfine coupling constants for the CH,Mu- group in

MU-CH-CH,CI. Solid lines are best fit curves. The cross represents the

data measured in the solid state which was excluded from fit.

Table 3.6. A model fit to the temperature dependence of the hyperfine coupling

constants of the -CH2C1 group in CH,MU-~H-CH~CI in the liquid state.

Table 3.7. Comparison of hyperfine coupling constant data for the -CH2C1 group in

CH~MU-~H-CH~C~ and calculated values from a model fit.

Temperature /K q e x p . ) /PVWz AJcalc.) /MHz

Figure 3.5. Proton and chlorine hyperfine coupling constants for the group -CH,Cl in

CH,MU-CH-CH~CI. Solid lines are fitted curves. The cross and solid triangle are the

data points corresponding to the radical CH,-c H-CH~C~ [33].

3.2.3.3. Temperature Dependence of the Muon Hyperfine Coupling

Constant in 1-Chloro-2-Mu-n-Propyl

As shown in table 3.3, although only a few values of the muon and protons hfcs

were obtained, the value of the muon hfc increases on cooling. The dihedral angle for Mu

can be considered as zero at the potential minimum. The same steps as described in

section 3.2.3.2 were performed. A V2 torsional potential model fit of the muon hfcs was

obtained. The parameters of the fit and calculated hfcs are listed in table 3.8 and table 3.9,

respectively. A fitted curve is shown in figure 3.6.

3.2.4. Discussion: Intramolecular Motion and Isotope Effects

3.2.4.1. The CH2Mu- Group in the 1-Chloro-3-Mu-Isopropyl Radical

An average hyperfine coupling constant for the CH2Mu- group is defined as:

From table 3.5, the average value for the CH2Mu- group at 298 K was determined

as 71.1 MHz, which is larger than the value (67.3 MHz) [33] for the unsubstituted

chloroalkyl radical. It seems that there is an isotope effect. Besides, at the high

temperature limit, free rotation of the CH2Mu- group, where the eigenstates are

effectively a continuum, the (cos2 $) term in equation 3.9 averages to t , the hfc at the

high temperature limit goes to L+tM. Extrapolating the fitted curves in figure 3.4, it is

known that A;(CH,Mu-) is equal to 75.7 MHz and A&CH2Mu-) is equal to 67.8 MHz.

Table 3.8. Fitted parameters of a V, potential model for the analysis of the 0

temperature dependence of muon hyperfine coupling constants in CH2-CHMu-CH2Cl.

Table 3.9. Comparison of muon hyperfine coupling constant data in 0

CH2-CHMu-CH,CI and calculated values from a V2 potential model fit.

Temperature /K A',(exp.) /MHz A'Jcalc.) /MHz

Figure 3.6. Temperature dependence of the muon hyperfine coupling constants in the

CH&HMu-CH,CI radical. The solid line represents the fit of the model to the

experimental values.

There is an apparent difference between these limiting values which implies a residual

isotope effect. The residual isotope effect represents the hfc difference between

isotopically substituted groups caused by other than the preferred confoxmation. From the

above comparisons, it was concluded that there is a strong interaction between the C-Mu

bond and the unpaired electron at the radical center. It is consistent with the

hyperconjugation effect. Roduner et al. [34] calculated that the C-Mu bond is longer than

the C-H bond by 4.9% in the anharmonic potential. The zero point energy level of the

C-Mu bond is higher than the level of the C-H bond because of a marked difference

between their reduced masses. The increased C-Mu bond length enhances the

hyperconjugation between the C-Mu bond and the unpaired electron orbital (SOMO). The

higher zero point energy of the C-Mu bond makes the C-Mu bond weaker. Electron

release is more facile from the C-Mu bond than from the C-H bond. The

hyperconjugation increases the muon hfcs for all conformations even at the high

temperature limit. This is why the values of L(Mu) and M(Mu) are different from the

values of L(H) and M(H). In addition, it is noted that the proton hfc (66.7 MHz) of the

Mu-substituted radical at the high temperature limit is close to the one (67.3 MHz) from

the ESR experiment [33]. It suggests that the C-H bond length is not much affected by

the neighboring Mu.

In table 3.4, the best fit was obtained when OO(Mu) was fixed to zero, which

supports the idea that the minimum energy conformation has the C-MU bond eclipsing the

axis of the unpaired electron 2p, orbital. This is in good agreement with the arguments

described. The qualitative energy level diagram of the interaction between the unpaired

electron and the C-Mu bond, the C-H bond is shown in figure 3.7.

Figure 3.7. Qualitative energy level diagram for the effect of overlap between the 2pz orbital of the

radical and the C-Mu bond (solid line), and the C-H bond (dashed line). It is raised in

energy relative to the C-H orbital because of the enhanced zero-point energy for C-Mu.

3.2.4.2. The -CH2CI Group in the 1-Chloro-3-Mu-Isopropyl Radical

From ESR experiments it is known that the chlorine of the P-chloroethyl radical is

eclipsed by the unpaired electron 2p, orbital [35]. The best fit parameters of our

experimental data listed in table 3.6 are consistent with the above argument about the

preferred conformation for the -CH2C1 group. It is also in good agreement with the results

of more sophisticated calculation performed on the P-chloroethyl radical [36]. In a simple

V, fit curve as shown in figure 3.5, there are two points (cross and triangle points) . corresponding to CH,-CH-CH2Cl [33]. It is clear from figure 3.5 that, although there is a

reasonable agreement between Pt, for the H and Mu-substituted radicals, & is

significantly higher for the Mu-substituted radicals. To accommodate the larger observed

4, values, our model fit gives a high value for V2 = 12 kJ rnol-1, compared with the value

of 8.4 kJ mol-I computed recently for the P-chloroethyl radical [37]. In reference 35, it is

shown in particular that the hyperconjugation of the SOMO into the o*,,, antibonding

orbital is the major contributing factor determining the lowest energy conformation. In the

Mu-substituted radical, due to the strong interaction between the C-MU bond and the

unpaired electron, comparing the C-H bond, the SOMO energy level goes up and the

energy gap between the SOMO and o*,,, reduces. It is more stabilized and there is a

strong interaction between those two orbitals when the C-Cl bond eclipses the unpaired

electron orbital. This mechanism makes the hyperfine coupling constant of the chlorine

significantly larger than the value from ESR measurement, while the proton hfc of the

-CH,Q group is not affected much. A qualitative energy level diagram is shown in figure

3.8.

3.2.4.3. -CHMu-CH2CI in the 1-Chloro-2-Mu-n-Propyl Radical

As listed in table 3.8, the reasonable parameters can be obtained only when the

dihedral angle between the C-Mu bond and the axis of the unpaired electron 2p, orbital is

set to be zero. Applying the same interpretation used before, there is a strong

hyperconjugation effect between the C-Mu bond and SOMO comparing the C-H bond

and C-C bond. Although in the minor radical different atoms and groups are attached to

the P-carbon, and the -CH2C1 group is very bulky, the hyperconjugation effect is still a

dominant interaction. In contrast, a steric effect sometimes controls the Mu-substituted

radical preference, i.e. (CH,),CX(CH,)~MU [29]. In this radical, the muon hfcs decrease

when temperature decreases, the dihedral angle of 8,(Mu) is 90". In our minor radical,

only one bulky group is not enough to result in a steric effect. A longer bond length of the

C-MU bond dramatically influences the preferred conformation of the Mu-substituted

radicals. It is consistent with the argument that the hyperconjugation effect is stronger

than the steric effect in many Mu-substituted radicals 1291 and this effect determines the

preferred conformation and rotation barrier around the Ca-Cp bond [26].

SOMO' SOMO

Figure 3.8. Qualitative energy level diagram showing change of the hyperconjugative interaction

between a radical and a C-CI bond due to a Mu-substituted methyl group attached to the

radical center. SOMO' is the orbital when a Mu substituted group is attached to a radical

carbon.

3.3. Chloroalkyl Radical Formed from 2-Methyl-3-Chloropropene

3.3.1. Experimental and Results

At the same time as radicals I and I1 were investigated, a related radical formed by

muon irradiation of 2-methyl-3-chloropropene was studied. It was expected that 1-chloro-

2-methyl-3-Mu-isopropyl (In) can be formed, as shown in equation 3.14.

Mu + CH2=C(CH3)-CH2Cl - CH,MU-c (cH,)-CH~CI

I11

This radical is an interesting case for the study of intramolecular motion, since

three different kmethyl groups -CH,, -CH,Mu and -CH2C1 are attached to the carbon

radical center. The temperature dependence of the hfcs provides information on

intramolecular motions of three different groups which can be compared with radical I and

tert-butyl radical. A 1M solution sample of 2-methyl-3-chloropropene was prepared since

the melting point of this pure compound is 261 K. The melting point of this solution can

be reduced to 120 K after it is dissolved in isopentane. Using the same type of stainless

steel sample cell and the same procedure as before in sample preparation, muon hfcs and

nuclear hfcs were measured by the use of TF-pSR and pLCR over the temperature range

of 130 K and 240 K. All the muon hfcs are listed in table 3.10. The hfcs of the nuclei are

assigned by the same steps used in section 3.2.2. The measurements of the nuclear hfcs are

summarized in table 3.1 1.

Although nuclear hfcs were determined at only a few temperatures, it is still

worthwhile to fit the temperature dependence of these data, especially for the CH,Mu-

group in III. For the Mu-substituted methyl group, a two-fold potential function which has

the form of equation 3.7 was adopted. There is a negative temperature dependence of the

muon hfcs and a positive temperature dependence of the proton hfcs in the CH,Mu-

group. The preferred dihedral angle between the C-Mu bond and the axis of the unpaired

electron 2p, orbital can set to be zero in the fit. The relevant parameters from the fit are

listed in table 3.12. Table 3.13 is the comparison of the experimental data and calculated

data fiom a model fit. The fit curves are shown in figure 3.10.

As shown in table 3.11, the proton hfc for the -CH, group is almost temperature

independent, which is in good agreement with the observation for the Mu-substituted tert-

butyl radical [31]. Since the hfcs for chlorine and protons in the -CH,Cl group were

obtained at one temperature, there was not too much information obtained.

Table 3.10. Muon hyperfine coupling constants in CH,Mu-C (CH+CH2C1 in the liquid phase determined from transverse field pSR spectra.

Temperature /K A, /MHz A', /MHz

* pure liquid sample.

0 200 400 Frequency (MHz)

Figure 3.9. Fourier transform pSR spectrum of CH,MU-C(CHJ-CH,CI in the liquid phase at

193 K.

Tabl

e 3.

1 1.

Lev

el c

ross

ing

reso

nanc

e fie

lds a

nd h

yper

fine

coup

ling

cons

tant

s for

CH

2Mu-

C (C

HJ-

C&

CI

in th

e liq

uid

phas

e.

* pu

re li

quid

sam

ple.

** E

SR r

esul

ts c

olle

cted

from

CH

,-t

(cH

,)-C

H~C

I rad

ical

[32]

.

Table 3.12. A model fit to the temperature dependence of the hyperfine coupling

constants of the CH,Mu- group in CH2Mu-C (CH3)-CH2C1 in the liquid phase.

Table 3.13. Comparison of hyperfine coupling constant data for the CH2Mu- group in

CH,MU-C (cH,)-CH,C~ and calculated values from a model fit.

Temperature /K A',(exp.) /MHz A'Jcalc.) /MHz

Figure 3.10.

A,, (CH ,MU-)

Temperature dependence of the muon and proton hyperfine coupling constants in the

CH,MU-c (CHJ-CH,Cl radical. Solid lines remesent the fitted curves.

3.3.2. Discussion

Considering the CH,Mu- group, T(CH,MU-) (62.6 MHz) is larger than % (59.5

MHz), the data obtained from ESR experiment for unsubstituted 1-chloro-2-methyl-

isopropyl radical. Obviously there is an isotope effect due to Mu substitution. Furthermore

extrapolation of the fit parameters in table 3.12 to high temperature limiting values gives

68.1 MHz and 55.2 MHz for A'JCH,Mu-) and A&CH,Mu-), respectively. There is a

residual isotope effect because of the difference between the C-MU bond and the C-H

bond. There is a strong interaction between the C-Mu bond and the unpaired electron

orbital, a similar situation as in I. The C-Mu bond aligned with the axis of the unpaired

electron 2p, orbital is the preferred conformation for the CH,Mu- group.

It is very significant to compare the X(CH,MU-) collected from radical 111 with

the value for the Mu-substituted tert-butyl radical. It is clear that X(CH,MU-) (62 MHz)

at 193 K for radical I11 is smaller than the value (68 MHz) for the Mu-substituted tert-

butyl radical 1311. The difference is due to the -CH,Cl group, which is attached to the

radical center. Because of the strong electronegativity of the chlorine, the electron of the

2p, orbital at the radical center is delocalized onto the -CH,Cl group. There is . hyperconjugation between the -CH,Cl group and the -CH- group [36], which means . there is delocalization of the electron around the -CH- group into the empty molecular

orbital of the -CH2C1 group. Thus, the -CH,Cl group decreases the spin density at the

radical center. The similar observation has been made in ESR experiments for the two

analogous hydrogen radicals. The average hfc of the -CH, group (63.7 MHz [381) in the

tert-butyl radical is higher than the value (59.5 MHz [33]) in the 1-chloro-2-methyl-

isopropyl radical.

Despite the fact that the temperature dependence of the hfcs listed in table 3.1 1

was collected from the solution sample, the solvent effect can be ruled out. As listed in

table 3.1 1, A(CH,Mu-) and A(CH,-) measured from the pure sample are 62.6 MHz and

58.6 MHz, respectively, while the hfcs from the solution sample are 62 MHz and 57 MHz.

There are no remarkable differences.

CHAPTER 4. CONFORMATION OF MUONIUM SUBSTITUTED THIYL AND SELENENYL RADICALS

4.1. Introduction

At the end of the 1970's, Nelson et al. [39] attempted to detect RS type radicals by

the ESR technique. They characterized the hfcs of this type of radical in the solid state but

failed in detecting the radicals in solution because of the rapid decay and line-broadening

effect. After the pSR technique was well-developed and the addition of the muonium to an

unsaturated bond to form a radical was well known, Rhodes et al. [40] used this technique

to identify various Mu-substituted thiyl radicals at two different temperatures; but, it was

only a brief study and few hfcs of these radicals were measured. Not too much information

on the conformations of these radicals was obtained except the position of adducts in

these radicals was characterized from their hfcs. The S and Se-centered radicals were

investigated in our group because our collaborator, Dr. Pinto, has a long term interest in

confornational effects of chalcogen atoms [41]. From reference 40 it is known that the S

and Se-centered radicals would be formed when muonium reacts with 1,3-dithiolane-2-

thione and 1,3-dithiolane-2-selenone (referred to as thione and selenone respectively):

There could be two possible conformations for the radical products which are depicted in

figure 4.1.

Figure 4.1. Newman projection along the C-X bond (X=S or Se) of the radical showing the possible

orientations of the unpaired electron pprbital.

This family of radicals is potentially interesting because the resulting radical center

has no substituent groups and the lowest energy spatial orientation of the unpaired

electron p,-orbitals is then governed only by the extent of the interaction of this unpaired

electron with the neighboring orbitals. In the absence of other effects (like steric

hindrance), one finds that for alkyl radical, the lowest energy conformation corresponds in

general to the Cp-Mu bond aligned with the axis of the unpaired electron p,-orbital. This

preference has been interpreted as due to o-n; hyperconjugative overlap and in this context

muoniurn was found to be more susceptible to this effect than H in the same position

[27,42]. For the Mu-substituted radical centered on chalcogen atoms very little data are

available and it would be interesting to see to what extent hyperconjugation can be

invoked to interpret the results.

4.2. Experimental Data

The 1,3-dithiolane-2-thione is commercially available and was used as received

The 1,3-dithiolane-2-selenone was provided by Dr. Pinto's laboratory. This compound was

prepared from the 1,3-dithiolane-2-thione following the reaction, equation 4.2 [43].

The targets consisted of either 0.5M solution in re-distilled dry tetrahydrofuran

(THF) or the pure compounds, sealed oxygen-free in stainless steel cells. AU the

experiments were performed at M20B at TRIUMF. The experiment setup is the same as

described in Chapter 2 of this thesis.

43. Results and Discussion

4.3.1. Mu Substituted Thiyl Radical

TF-pSR spectra for both pure and dilute sample were measured. This showed that

a radical was formed in both samples. The experiments covered the temperature range

from 30 K to 320 K for the pure sample, 170 K to 312 K for the solution sample. The

hyperfine coupling constants (Ap) for thione are summarized in table 4.1 and the

corresponding temperature dependence of the hfcs is shown in figure 4.2.

Table 4.1. Muon hyperfine coupling constants for the 1,3-dithiolane-2-thiyl radical in

solution.

Temperature /K A,, I M H z

The values of A,, which are around 350 MHz in the liquid state at room

temperature are quite consistent with a S-centered radical, (otherwise a much smaller % value would be attained for a C-centered radical [40]). A negative temperature

dependence (ca -0.17 MHz K-l) observed from the thiyl radical in solution implies that the

lowest energy conformation corresponds to the picture shown in figure 4.l(a). The

observed low energy conformation of the thione can be rationalized by a larger

hyperconjugative interaction of the SOMO with the o*,,, than with the o*, orbitals

which is shown in figure 4.3. The stabilization is proportional to an orbital overlap integral

and to the inverse of the energy difference between the SOMO and the interacting orbital

[#I. To a first approximation, the primary overlap between the SOMO and the fragment

orbitals o*,, and o*,,, remains the same. In this case it follows that the o*,,, energy

level is lower than the o*, energy level.

Table 4.2. Muon hyperfine coupling constants for the 1,3-dithiolane-2-thiyl radical in

pure 1,3-dithiolane-2-rhione.

Temper a ture /~

Figure 4.2. Muon hyperfine coupling constants for C,H,S,CMU-s as a function of temperature in

solution and pure compound. Open triangle: 0 . 5 M m solution. Cross: pure compound.

Dashed line: melting point.

SOMO

Figure 4.3. Qualitative energy level diagram showing the relative energies of the orbitals involved

in the hyperconjugative interaction.

200 Frequency (MHz)

Figure 4.4. Stacked Fourier transform pSR spectra of C,H,S,CMU-s obtained in 10 kG applied

transverse field at: a) 293 K (solid phase), b) 325.5 K (near melting point), c) 311 K

(liquid phase). The radical frequencies are labeled v, and the diamagnetic frequency v,

A more complete set of data was obtained in pure 1,3-dithiolane-2-thione. As

shown in figure 4.2, there is a marked discontinuity of the variation of A, at the melting

point (306 K). As the temperature is lowered from the liquid state, where frequencies

associated with only one radical are observed, a shift of 65 MHz occurs at the melting

point, and two signals are detected in the solid state as shown in figure 4.4. TF-pSR

spectra for the powder thione were also measured. One of them is shown in figure 4.5.

There is a splitting of radical signals (v,) but not any orientation dependence from the

experiment observation. The splitting results from the anisotropic effect in the powder. In

principle the anisotropic hfcs can be determined from the powder spectrum as it has been

done at PSI [45]. In the solid phase, the anisotropic component of the hyperfine

interaction is no longer motionally averaged to zero and the value of the observed hfc is

expected to be dependent on crystal orientation. Although our thione sample is

plycrystalline, there could be a dominant crystal orientation which determined orientation

dependent hfcs of the thione in the solid state. In addition it was found that melting and

refreezing or skewing of the sample changed the amplitudes but not the frequencies of the

precession signals. This is most likely because of a new distribution of crystal orientations.

So in our solid thione sample there are some crystals which give orientation dependent

hfcs whereas powder gives the distribution of the hfcs over all orientations.

In figure 4.2, the variation of A, with temperature is practically parallel in the

thione solution and in the pure liquid, with a small offset attributable to solvent effect. But

the large shift in A, when going from the liquid to the solid state (ca. 70 MHz) could

result from the inhibition of an inversion mode which in the liquid phase may have been

coupled to the torsional mode involving the Mu-containing group. Similar results were

observed in Mu-substituted tert-butyl radical in pure isobutene [31]. For our system, no

substituent is attached to the S radical center, only torsional motion influences the

hyperfine interactions. The implication is that there must be very strong intermolecular

0 200 400 Frequency (MHz)

Figure 4.5. TF-pSR spectrum of C,H,S,CMU-s in powder at 298 K.

interactions in the crystal which effectively tend to lock into position the unpaired electron

p,-orbital.

4.3.2. Mu-Substituted Selenenyl Radical

The hfcs of 1,3-dithiolane-2-Mu-2-selenenyl radical (V) in both solution and pure

selenone were measured by the TF-pSR technique. In solution the signals broaden with

increasing temperature suggesting that the Mu-substituted radical is not stable. The hfcs of

radical V obtained from pSR spectra are listed in table 4.3 and the diagram of the

temperature dependence of the hfcs is shown in figure 4.6.

In solution the temperature dependence of the hfcs was found to be almost zero

indicating that the high temperature limit has been reached. A zero temperature

dependence is consistent with the longer C S e bond than the C S bond [46]. Moreover,

radical signals could not be detected in pure liquid selenone above the melting point (318

K) despite several trials. This is in agreement with the observation that the radical in

solution is very unstable. Although good measurements of muon hfcs were made in the

solid, there is scattering of the data points near the melting point which cannot be

explained by statistical fluctuation simply. The situation is similar to the case in pure solid

thione. This observation could be due to macro-crystallites with a different distribution of

orientation each time the sample was melted and then refrozen.

In the solid a negative temperature dependence of muon hfcs is clearly shown in

figure 4.6. It implies that the preferred conformation is where the axis of the unpaired

electron p,-orbital eclipses the C-Mu bond. It means that there is a strong interaction

between the unpaired electron and the C-Mu bond in the Mu-substituted selenenyl radical.

Table 4.3. Muon hyperfhe coupling constants for the 1,3-di thiolmo-2-SCkntnYl radical in solution and pure 1,3-dithiolane-2-selenone.

Temperature /K A, /MHz

Pure Compound: 279.1

288.7

298.2

298.2

298.2

304.4

311.0

311.2

31 1.2

31 1.7

311.9

312.7

Solution:

Figure 4.6. Muon hyperfine coupling constants for C,H,S,CMU-~e as a function of temperature.

Open triangle: O.5IWMF solution. Open square: pure compound.

CHAPTER 5. SUMMARY

The purpose of my thesis was to study the intramolecular motion and preferred

conformations of Mu-substituted free radicals. Mu-substituted free radicals can be formed

by the addition of muonium to an unsaturated bond of the molecule. Hyperfine coupling

constants of several radicals were measured using muon spin rotation and muon level

crossing resonance techniques. By analyzing the temperature dependences of the hfcs for

these radicals and fitting a theoretical model to experimental data, information was

obtained on preferred conformations and intramolecular motion of these radicals.

Analysis of the experimental data shows that the C-Mu bond aligns with the axis

of the unpaired electron 2p, orbital in 1-chloro-3-Mu-isopropyl (I), l-chloro-2-Mu-n-

propyl (11) and 1-chloro-2-methyl-3-Mu-isopropyl (111) in their minimum energy

conformations. The C-Cl bond of -CH2C1 also eclipses the unpaired electron 2p, orbital in

I. The torsional barriers for CH2Mu- group rotation and CH2C1- group rotation in I are

1.9 kJ mol-I and 12 kJ mol-1, respectively. The dramatically high barrier of -CH2C1 group

rotation in I indicates that the Mu in the p-position enhances hyperconjugation effects for

a Cl substituent in the eposition. For CH~--CHMUCH~CI in I1 the torsional barrier is 2.1

kJ mol-1, while for CH,MU-~ (CH,)CH~CI in 111 this barrier is 1.5 kJ mol-l.

In the study of 1,3-dithiolane-2-Mu-2-thiyl radical (IV) and 13-dithiolane-2-Mu-

2-selenenyl radical (V), the preferred conformation of the C-Mu bond eclipsing the

unpaired electron p, orbital for these two radicals indicates that the hyperconjugative

interactions between the unpaired electron and the C-Mu bond is greater than for the C-S

bond. A zero temperature dependence of hfcs for radical V in solution s ~ ~ & ~ ~ bat then

is free rotation about the C-Se bond.

pSR and pLCR are very powerful techniques in the study of the conformations

and intramolecular motion of Mu-substituted free radicals.

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