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dissertation entitled

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Date 4/43 M

MS U is an Affirmative Adieu/Equal Opportunity Institution 0-12771

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DATE DUE

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use chlRC/DateDuopfiS—p.“

ADVANCED ELECTRON PARAMAGNETIC RESONANCE STUDIES OF
BIOLOGICALLY RELEVANT RADICALS

By

Vladimir Bouchev

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment ofthe requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1999

ABSTRACT

ADVANCED ELECTRON PARAMAGNETIC RESONANCE STUDIES OF
BIOLOGIC&LY RELEVANT RADICALS

By

Vladimir Bouchev

Electron-Nuclear Double Resonance (ENDOR) and Electron Spin Echo Envelope
Modulation (ESEEM) spectroscopies have both established themselves as indispensable
methods for measuring small hyperfine couplings. Their application proved to be
especially appropriate to paramagnetic species in biologically important disordered
systems where the electron-nuclear hyperfine couplings are masked by inhomogeneous
broadening of the Electron Paramagnetic Resonance (EPR) lineshape.

This work presents an application of ENDOR and ESEEM methods in
combination with isotopic substitution and numerical simulations of experimental data to
the study of paramagnetic reaction intermediates emerging during the PyruvatezFerredoxin
Oxidoreductase (PFOR) catalyzed oxidative decarboxylation of pyruvate. A number of
hyperfine coupling parameters were determined and related to a substrate-derived
transient radical. The radical intermediate is found to be in close proximity to the thiamin
pyrophosphate (TPP) prosthetic group of the enzyme. Two models. the model of a o—type

radical and that of a n—type radical, were considered to account for the observed

couplings. The results ofthis study help understanding the mechanism ofthe PFOR
reaction.

A two-dimensional variant of ESEEM. the Hyperfine Sublevel Correlation
Spectroscopy (HYSCORE) has emerged as a powerful extension ofthe conventional.
one-dimensional ESEEM. In HYSCORE. frequencies that originate from the same
hyperfine coupling give rise to cross peaks in the spectra, thus summarizing the lineshape
information of many lD ESEEM data sets in cross-peak contours. This leads to
simplification ofthe assignment ofthe peaks. However. the HYSCORE of nuclei with spin
1 > l/2, for which ESEEM techniques demonstrate inherently high sensitivity has not been
fully explored. In this work, the HYSCORE echo modulation fimction for an S = 1/2, I =
1 spin system was derived using density matrix formalism. Its applicability to the
interpretation of the HYSCORE data for 2H-labeled tyrosyl radical has been demonstrated
through simulations. The simulations show that the 2D ESEEM function adequately
describes the experimental correlation patterns and reproduces. to a good approximation,

the t-suppression-effect modulated lineshapes ofthe observed HYSCORE cross peaks.

Acknowledgment

I am deeply indebted to my advisor, John McCracken, for teaching me EPR. I
would like to thank him for his guidance, help and support during my years at MSU.

I would like to express my thanks to Dr. Andrew lchimura for his valuable help
and collaboration in performing numerous ENDOR experiments. I have benefited greatly
from the enlightening discussions with Dr. Marilena DiValentini on pulsed EPR.

I wish to thank the members ofthe Dr. McCracken and Dr. Babcock groups who
more or less directly contributed to this work. Special thanks to Dr. Gydrgy Filep for
being a great friend and colleague.

I am grateful to my wife, Hristina, for her love, care and understanding.

TABLE OF CONTENTS

LIST OF TABLES .................................................................. . ............... vii
LIST OF FIGURES ................................................................................ viii
LIST OF ABBREVIATIONS ......................................... . ........................... xxi
INTRODUCTION .................................................................................... ]
Chapter 1:

Basic Principles of the Electron Magnetic Resonance

Spectroscopy .......................................................................................... 3

Illntroductlon3

1.2. Continuous-Wave Electron Paramagnetic Resonance ........................ 5
1.2. l. The Zeeman interaction .................................................... 5
1.2.2. The hyperfine interaction ................................................... 9
1.2.3. The nuclear quadrupole interaction ...................................... 24

1.3. Principles of Electron Nuclear Double Resonance (ENDOR)

Spectroscopy ........................................................................... 28
1.3.]. Energy levels and resonance conditions ................................. 28
1.3.2. Level populations and ENDOR effect ................................... 34
1.3.3. Factors influencing ENDOR signal intensity ........................... 39
1.3.4. ENDOR lineshapes ......................................................... 41
1.4. Principles of the Electron Spin Echo Envelope Modulation
(ESEEM) Spectroscopy ............................................................. 47
1.4.1. Pulses of microwave radiation and their effects ........................ 49
1.4.2. Two-pulse electron spin echo ............................................. 54
1.4.3. Three-pulse electron spin echo (stimulated echo) ..................... 56
1.4.4. Four-pulse electron spin echo ................... . ......................... 61
1.4.5. Origin ofESEEM .......................................................... 63
1.4.6. Density matrix description ofESEEM .................................. 73
References .................................................................................. 93
Chapter I]:
CW-EPR, ENDOR and ESEEM Studies of Pyruvate:Ferredoxin
Oxidoreductase (PFOR) Reaction Intermediates ........................................... 9e

11.1. Introduction ..............................................................
11.1.1. 2-Keto oxidoreductases .......................................

11.1.2. Mechanism ofthe oxidative decarboxylation of

pyruvate by PFOR .............................................

11.2. Application of Advanced EPR Methods to the Study
of CIostridium thermoaceticum PFOR Reaction

Intermediates ............................................................

11.2.1.Experimental..................

11.2.2. Results ..........................................................
11.2.3.Discussion ......................................................
11.2.4. Conclusmn

References ......................................................................

Chapter 111:
Hyperfine Sublevel Correlation Spectroscopy (HYSCORE)

of S = 1/2, 1 = 1 Spin Systems .........................................................

II1.l. Introduction .............................................................

............ 9o
............ 97

.......... 103

........... 111
..111

112
151
180

181

184

184

111.2. Principles of HYSCORE ........................... . ................. 189
111.3. HYSCORE Modulation Function for an
S = 1/2, 1 = 1 Spin System ........................................................ 207
111.4. Application of HYSCORE to the Study of a Tyrosyl
Radical Model System .......................................................... 217
111.4.]. Introduction .................................................... 217
111.4.2. EPR spectroscopic studies of tyrosyl radicals ...................... 218

111.43. HYSCORE of3, 5 ZH-labeled tyrosyl radical

model system ................................................
111.4.4. t-suppression effect in HYSCORE ........................

111.4.5. Simulations of the HYSCORE experimental

data for 3, 5 2I-I-Iabeled tyrosyl radical... .. . ... ..

111.5. Conclusion ...............................................................

References

vi

......................................................................

........... 222

228

....23e

253

254

 

LIST OF TABLES
Table 11-1 Hyperfine coupling constants from lH ENDOR of Closrridz'mn

'lhermoaceticum PFOR reaction intermediates .............................. 122

Table III-l Hyperfine tensors oftyrosyl radicals. . ........................................ 221

vii

Figure 1-1

Figure 1-2

Figure 1-3

Figure 1-4

Figure 1-5

Figure 1-6

Figure 1-7

LIST OF FIGURES

Energy levels ofa spin system consisting of one unpaired electron
(S = 1/2) and one magnetic nucleus with l = 1/2 as a function of an

externally imposed magnetic field .............................................

Interaction of magnetic dipoles “e and “n arising from an electron

spin and a nuclear spin, respectively. The dipoles are aligned with
the external magnetic field and are separated by a distance r. Angle

9 is between the inter-dipole vector r and the applied field B0 ...........

Valence bond structures for the cor“ fragment. The two possible

electron spin configurations in the s bonding orbital are shown for a
spin in the 2p,[ orbital of the carbon atom. (a) Spins parallel in the s

bonding orbital and the 2p7t orbital of carbon. (b) Corresponding

spins antiparallel .................................................................

Model used for calculation of the dipole-dipole magnetic coupling
or unpaired p,t electron density on Ca carbon atom with the nucleus

of a hydrogen atom. The spin density is concentrated equally at
effective centers of the pn orbital lobes on either side of Ca. rp is the

distance from the effective coupling centers to Ca nucleus. TCH is the

internuclear distance of C and H ...............................................

(a) Hyperconjugation in ethyl radical. The admixture of the two
exemplary valence bond structures can account for the significant
isotropic hyperfine coupling for B hydrogens in aliphatic radicals.

..8

..13

.17

.19

(b) Coordinate system for [3 coupling of hydrogens .......................... 20

Quadrupolar nuclei (3) oblate, (b) prolate. An oblate quadrupolar

nucleus in (c) a uniform electric field, ((1) an effective field gradient. . . ..

Energy-level diagram in a high magnetic field for the interaction of
one unpaired electron (S = 1/2) with an 1 = 1/2 nucleus (e. g. a
proton), detailing the electron Zeeman, nuclear Zeeman, and
hyperfine splittings. The case ofgn > O, Aiso > O. iAiso/Zi < vn is

viii

.25

no - hwfi-w

Figure 1-8

Figure 1-9

Figure 1-10

Figure 1—11

Figure 1-12

Figure 1-13

Figure 1-14

represented. The four energy levels on the right (1 to 4) are labeled
by IMS, MP. The heavy arrows indicate the induced EPR and NMR

transitions; the broken arrows the various relaxation rates ................

ENDOR spectra for (a) lAiSO/Zl < vn and (b) iAiso/21 > V“. The solid

lines represent the spectrum observed when the high field EPR
transition is monitored and the dashed lines give the spectrum

observed when the low field EPR line is monitored ........................

Energy-level diagram ofa hyperfine-coupled spin system in a high
magnetic field, consisting of one unpaired electron (S = 1/2) and

three equivalent nuclei (1 = 1/2) ...............................................

Population diagram for transient ENDOR with S = 1/2, 1 = 1/2,
gn > 0, Aiso > 0. (a) unsaturated EPR transition, (b) saturated EPR

transition, (c) transient ENDOR effect, ((1) final steady state .............

Energy-level diagram for S = 1/2, 1 = 1/2 spin system showing EPR
and ENDOR transitions in the absence (3) and presence (b) of

quadrupole coupling ............................................................

ENDOR lineshapes (absorption: top, first derivative: bottom)
resulting from an axially symmetric hyperfine tensor with (a) zero
trace (purely dipolar hyperfine interaction) and (b) Aiso at 0. The

bottom parts illustrate the procedure for determining A“ and A_L- .. ..

Inhomogeneously broadened EPR lineshape (total linewidth 10 to
10000 Gauss). (a) BQan is the mean value of the resonant magnetic

field. Bo is the linewidth of the portion of the spectrum excited by a
microwave pulse. (b) The individual spin packets (linewidth of the

order of 10’3 Gauss) have magnetization components precessing
independently of each other at frequencies mi, (:30, co]: .. . . .

(a) A microwave pulse is a burst of monochromatic microwave
radiation of duration tp. (b) The frequency spectrum of a pulse gives

the spectral density of the field at the sample ...............................

..30

...32

..33

..36

...44

..45

....48

..50

 

Figure 1-15

Figure 1-16

Figure 1-17

Figure 1-18

Figure 1-19

Figure 1-20

Decomposition of a linearly polarized oscillating magnetic field,
Bx(t), into two counter-rotating circularly-polarized components, Br

and B] ............................................................................... 51

Two-pulse electron spin echo sequence and an exemplary two-pulse
ESEEM time-domain data set collected for the Ni(IIl)(CN)4(H20)2'
complex in a 50 % v/v water/ethylene glycol glass...........................55

Vector diagram illustrating the formation of the two-pulse electron
spin echo. (a) two-pulse electron spin echo sequence; (b) at thermal
equilibrium the magnetization M is aligned with the external
magnetic field B0; (c) the first (TE/2) pulse has torqued M onto the

XY plane of the rotating frame; (d) M is a superposition of spin

packets that dephase due to the differences in their precession

frequencies; (e) the second pulse rotates the spin packets about the

X axis through angle it. The direction of precession of each spin

packet is conserved. (t) the individual spin packets refocus along

Y to reform M, thus generating an echo ....................................... 57

Vector diagram illustrating the formation of the three-pulse electron

spin echo. (a) three-pulse electron spin echo sequence; (b), (c) same
events as in Figure 1-17; ((1) the second 1r/2 pulse converts the

transversal magnetization into a longitudinal one; (e) the

magnetization components precess about Z; (t), (g) the third 1t/2

pulse rotates the surviving magnetization components (directed

along Z) onto the XY plane; (h) the spin packets refocus along Y to
reform M, thus generating a stimulated echo ................................. 59

Vector diagram illustrating the formation of the four-pulse electron
spin echo. (a) after the second 7t/2 pulse the magnetization 6MZ

associated with a particular spin packet is brought along the Z axis;
(b) the it pulse inverts 5M2; (c) the fourth (it/2) pulse rotates 5M2

onto the XY plane; (d) spin packets start precess about Z; (e) during a
time period t after the last pulse various spin packets attain the
position shown, which creates the echo along the -Y axis .................. 62

Energy-level diagram for an S = l/2, 1 = 1/2 spin system described by
the Hamiltonian of Equation [1-54] ............................................. 64

 

Figure 1—21

Figure 1-22

Figure 1-23

Figure 1-24

Figure 1]-1

Figure 11-2

Figure 11-3

Figure 11-4

Vector model showing the interference between electron spin
packets that result from transition "branching" in a two-pulse
ESEEM experiment. The upper lefi insert represents the energy-
level diagram of Figure 1-20, while the upper right insert shows the
spin packets across the inhomogeneous line. (a) after the first pulse
spin packet A precesses in the XY plane at frequency a) A < (00

acquiring phase (wA - w0)t during time t; (b) the second pulse flips
spin packet A about X and induces its branching into two portions
that precess at frequencies (DA < mg and (”C > (no ; (c) spin packet A
is refocused along Y contributing fully to the spin echo, while spin
packet C is refocused at an angle 0 = (a) A - (DC)! with respect to Y,

giving a contribution to the echo weighted by cos(0) ........................ 66

Energy levels of a spin system and transitions involved in the
generation of electron spin echo signals. The resonance field at
frequency w is able to induce transitions in all intervals may - (DB j ...... 77

Various electron spin echo pulse sequences. Each sequence consists of
successive periods of nutation and free precession. (a) two—pulse
sequence, 1t/2 — I - 1r - t; (b) three-pulse sequence, n/2 - ‘t - ’K/Z - T —

1t/2 - t; (c) four-pulse sequence, 1t/2 - ‘l.’ - n/2 - t] - 1t - t2 - 1t/2 - t ......... 78

Simulations of (a) powder ENDOR spectrum and (b) a three-pulse
ESEEM spectrum for an S = 1/2, 1 = 1/2 spin system. Parameters:

g = 2004. en = 2.261 (311)), A” = 7.0 MHz, Al = 2.4 IVII-lz,

BO = 3200 G; t = 200 ns; dead-time, 240 ns .................................. 91

First derivative EPR spectra of PFOR from Hm. Halobium ................. 99
Four subunit catalytic model of 2-keto acid oxidoreductases .............. 101
Thiamin pyrophosphate prostetic group of PFOR ........................... 104

Mechanism ofthe PFOR catalyzed reaction. Steps: (1) pyruvate

xi

~—--- w-“wzp

Figure 11-5

Figure 11-6

Figure "-7

Figure “-8

Figure 11-9

binding; (2) formation of hydroxyethylidene-TPP intermediate;

(3) formation of HE-TPP radical and reduction of cluster A; (4) CoA
binding and reduction of cluster B; (5) formation of acetyl-CoA and
regeneration of TPP anion; (6) reduction of external electron
acceptors 106

First derivative EPR spectra of Clostridium Thermoaceticum PFOR
incubated with (a) sodium dithionite, (b) pyruvate and CoA, (c) CoA.

or (d) pyruvate. EPR parameters: spectral width, 2000 G; field center,
3400 G; modulation frequency, 100 kHz; modulation amplitude,

10 G; temperature, 10 K; microwave power, 2 mW; microwave
frequency, 9.447 GHz ........................................................... 107

First derivative EPR spectra of Clostridium Thermoaceticum PFOR
incubated with (a) pyruvate, and (b) CD3-labeled pyruvate. EPR

parameters: spectral width, 100 G; field center, 3360 G; modulation
frequency, 100 kHz; modulation amplitude, 0.5 G; temperature,

10 K; microwave power, 2 mW; microwave frequency, 9.446

GHz ................................................................................ 109

First derivative EPR spectra of PFOR with pyruvate, (a), 2H3C-

pyruvate, (b), 3-methyl-2-oxobutyrate, (c), and 2-oxobutyrate, ((1).
Experimental parameters: field center, 3376 G; field sweep width,

1000 G; modulation frequency, 100 kHz; modulation amplitude,

5.0 G; time constant, 10 ms; microwave power, 0.1 mW; microwave
frequency, 9.468 GHz; temperature, 4 K ..................................... 1 13

First derivative EPR spectra of PFOR reacted with pyruvate.

Experimental parameters: field center , 3377.2 G; field sweep width,

100 G; modulation frequency, 100 kHz; modulation amplitude, 1.0 G;
time constant, 10 ms; microwave power, 0.05 mW; microwave

frequency, 9.482 GHz; temperature: 9.1 K, (a), and 60 K, (b) ............. 1 15

First derivative EPR spectra of PFOR reacted with pyruvate, (a),

l3C-2 labeled pyruvate, (b), and 13C-3 labeled pyruvate, (c).
Experimental parameters: field center, 3377 G; field sweep width,

1000 G; modulation frequency, 100 kHz; modulation amplitude,

10.0 G; time constant, 10 ms; microwave power, 0.05 mW;

microwave frequency, 9.481 GHz; temperature, 9.0 K ..................... l 16

xii

 

Figure 11-10 First derivative EPR spectra of PFOR reacted with pyruvate, (a),

13C-2 labeled pyruvate, (b), and 13C-3 labeled pyruvate, (c).
Experimental parameters: field center, 3377.2 G; field sweep width,

100 G; modulation frequency, 100 kHz; modulation amplitude,

1.0 G; time constant, 10 ms; microwave power, 0.05 mW;

2.0 microwave frequency, 9.481 GHz; temperature, 60.0 K ............... l 19

Figure 11-11 ENDOR spectrum of PFOR/pyruvate. Experimental parameters:
static magnetic field, 3349 G; microwave frequency, 9.400 GHz;
microwave power, 10 mW; rf sweep width, 5.5 MHz; rf fm
modulation depth, 100 kHz; rf power, 220 W; time constant, 10 ms;
temperature, 60 K ................................................................ 121

Figure 11-12 ENDOR spectrum of PFOWpyruvate. Experimental parameters:
static magnetic field, 3349 G; microwave frequency, 9.400 GHz;
microwave power, 10 mW; rf sweep width, 5 MHz; rf fm
modulation depth, 100 kHz; rf power, 220 W; time constant, 10 ms;
temperature, 60 K. 300 scans were averaged ................................. 123

--—= _ “mm mi!

Figure 11-13 ENDOR spectrum of PFOR/pyruvate. Experimental parameters:
static magnetic field, 3349 G; microwave frequency, 9.400 GHz;
microwave power, 20 mW; rf sweep width, 27 MHz; rf fm
modulation depth, 280 kHz; rf power, 220 W; time constant, 10 ms;
temperature: 4K, (a), 77K, (b), 200K, (c) .................................... 125

Figure 11-14 ENDOR spectrum of PFOR/pyruvate. Experimental parameters:
static magnetic field, 3322 G;microwave frequency, 9.400 GHz;
microwave power, 1 mW; rf sweep width, 27 MHz; rf fm
modulation depth, 280 kHz; rfpower, 220 W; time constant, 10 ms;
temperature: 4K .................................................................. 127

Figure 11—15 ENDOR spectrum of PFOR/2H3C-pyruvate. Experimental

parameters: static magnetic field, 3349 G; microwave frequency,

9.400 GHz; microwave power, 5 mW; rf sweep width, 27 MHz; rf fm
modulation depth, 100 kHz; rf power, 220 W; time constant, 10 ms;
temperature, 60 K ................................................................ 128

Figure 11-16 Solid line: ENDOR spectrum of PFOR/2H3C-pyruvate.
Experimental parameters: static magnetic field, 3349 G; microwave

xiii

 

 

Figure 11-17

Figure 11-18

Figure 11-19

Figure 11-20

Figure 11-21

frequency, 9.400 GHz; microwave power, 5 mW; rf sweep width,
6 MHz; rf fm modulation depth, 100 kHz; rfpower, 220 W; time
constant, 10 ms; temperature, 60 K ........................................... 129

ENDOR spectrum of PFOR reacted with 13C-3 labeled pyruvate,

(a), and 13C-2 labeled pyruvate, (b). Experimental parameters:

static magnetic field, 3348.5 G; microwave frequency, 9.396 GHz;
microwave power, 1 mW; rf sweep width, 35 MHz; rf fm

modulation depth, 158.5 kHz; rfpower, 220 W; time constant,

41 ms; temperature, 60 K ....................................................... 130

ENDOR spectrum of PFOR/3-methyl-2-oxobutyrate, (a).

Experimental parameters: static magnetic field, 3349 G; microwave
frequency, 9.410 GHz; microwave power, 2 mW; rf sweep width,

27 MHz; rf frn modulation depth, 100 kHz; rfpower, 220 W; time
constant, 10 ms; temperature, 60 K. ENDOR spectrum of PFOR/2-
oxobutyrate, (b). Experimental parameters: static magnetic field,

3349 G; microwave frequency, 9.410 GHz; microwave power,

2 mW; rf sweep width, 27 MHz; rf fm modulation depth, 100 kHz;

rf power, 220 W; time constant, 10 ms; temperature, 60 K ................ 134

ESE-EPR spectra of PFOR/pyruvate. Experimental parameters:
magnetic field sweep width, 900 G; microwave frequency, 9.600
GHz; pulse duration, 17 ns; I value, 205 ns; T value, 600 ns;

temperature, 4.2 K; pulse sequence repetition rate: 1 Hz, (a), and

Stimulated time domain ESEEM data for PFOR/pyruvate, (a).
Experimental parameters: magnetic field strength, 3429 G;

microwave frequency, 9.600 GHz; pulse duration, 17 ns; pulse

sequence repetition rate, 10 Hz; I value, 205 ns; initial T value, 100

ns; sample temperature, 4.2 K; number of data points, 1024; number

of events averaged for each data point, 14; number of scans, 2.
Corresponding frequency domain spectrum obtained by Fourier
transformation of the time domain data, (b) ................................. 138

Stimulated ESEEM spectra of PFOR/pyruvate. Experimental
parameters: magnetic field strength, 3429 G; microwave frequency.
9.600 GHz; pulse duration, 17 ns; pulse sequence repetition rate,

40 Hz; initial T value, 100 ns; sample temperature, 4.2 K; number of
data points, 1024; number of events averaged for each data point, 34;

xiv

Figure 11-22

Figure 11-23

Figure 11-24

Figure 1145

Figure 11-26

number of scans, 2; I value: 205 ns, (a); 240 ns, (b); 275 ns, (c); 340
ns, ((1); 480 ns, (e) ............................................................... 142

Stimulated ESEEM spectra of PFOR/pyruvate. Experimental

parameters: magnetic field strength, 3553 G; microwave frequency,

9.600 GHz; pulse duration, 17 ns; pulse sequence repetition rate, 40

Hz; initial T value, 100 ns; sample temperature, 4.2 K; number of

data points, 1024; number of events averaged for each data point,

12; number of scans, 2; I value: 203 ns, (a); 240 ns, (b); 340 ns, (c);

480 ns, (d) .............. . ......................................................... 144

Stimulated ESEEM spectra of PFOR/pyruvate. Experimental

parameters: magnetic field strength, 3429 G; microwave frequency.

9.600 GHz; pulse duration, 17 ns; initial T value, 100 ns; I value,

203 ns; sample temperature, 4.2 K; number of data points, 1024;

number of events averaged for each data point, 12; pulse sequence
repetition rate: 1 Hz, (a), and 40 Hz, (b) ..................................... 146

Stimulated ESEEM data for PFOR/2H3C-pyruvate. (a) Time-domain

data; (b) The corresponding frequency-domain data obtained by

Fourier transformation of trace (a). Experimental parameters:

magnetic field strength, 3429 G; microwave frequency, 9.600 GHz;

pulse duration, 17 ns; initial T value, 100 ns; pulse sequence

repetition rate, 10 Hz; sample temperature, 4.2 K; number of data

points, 1024; number of events averaged for each data point, 14;

number of scans averaged, 2; I value, 203 ns, (b), and 444 ns, (c) ....... 148

Fourier transform ofthe time-domain ratio ofthe two data sets
shown in Figure 1-20 and Figure 1-24 (a) .................................... 152

Stimulated ESEEM spectrum of PFOR/3-methyl-2-oxobutyrate, (a).
Experimental parameters: magnetic field strength, 3429 G;
microwave frequency, 9.600 GHz; pulse duration, 17 ns; initial T
value, 100 ns; I value, 205 ns; pulse sequence repetition rate, 40

Hz; sample temperature, 4.2 K; number of data points, 1024; number
of events averaged for each data point, 34; number of scans averaged,
4. Stimulated ESEEM spectrum of PFOR/2-oxobutyrate, (b).
Experimental parameters: magnetic field strength, 3435 G;
microwave frequency, 9.600 GHz; pulse duration, 17 ns; initial T
value, 100 ns; I value, 205 ns; pulse sequence repetition rate, 10

XV

‘ ._ A- ‘a‘_‘m.m

Figure “-27

Figure “-28

Figure 11-29

Hz; sample temperature, 4.2 K; number of data points, 1024;
number of events averaged for each data point, 34; number of
scans averaged, 4 ................................................................ 153

Simulated 1H ENDOR spectra for PFOR paramagnetic reaction
intermediate. Each simulation data set is plotted using dotted lines
and shown in comparison with the experimental spectrum (solid line).

Simulation parameters: g = 5.5856012, B = 3349 G; (a) AXXU) =
AyyU) = 11.95 MHz, A220) = 16.90 MHz, AXXQ) = Ayy(2) =
14.66 MHz, A229) = 19.10 MHz, number of0 increments in the
range 0° - 90°, 80, Gaussian linewidth, 0.40 MHz; (b) AXXU) =
AyyU) = 11.95 MHz,AZZ(1)=19.1O M}12,Axx(2)= Ayy(7-) =
14.66 MHz, Azz(2) = 16.90 MHz, number of0 increments in the
range 0° - 90°, 80, Gaussian linewidth, 0.40 MHz; (c) Axx = 11.65
MHz, Ayy = 15.50 MHz, Azz = 19.10 MHz, number of0 increments

in the range 0° - 90°, 40, number of (p increments in the range 0° -
90°, 40, Gaussian linewidth, 0.30 MHz ....................................... 157

Simulated 2H ENDOR spectra for PFOR paramagnetic reaction
intermediate. Each simulation data set is plotted using dotted lines
and shown in comparison with the experimental spectrum (solid line).

Simulation parameters: g = 085739, B = 3349 G; (a) Axx“) =
Aw“) = 1.80 MHz, A2211) = 2.60 MHZ, e2qQ(l) = 0.05 MHz,
AXXQ) = AW12) = 2.2 MHZ, A220) = 2.965 MHz, e2qo(2) = 0.04

MHz, 11(1) = 11(2) = 0.1, number of0 increments in the range 0° - 90°,
40, number of (1) increments in the range 0° - 90°, 40, Gaussian
linewidth, 0.092 MHz; (b) Am“) = AW“) = 1.83 MHz, A22“) =
2.93 MHz, AXXO) = AWQ) = 2.25 MHz, A2212) = 2.47 MHz,
eZqQ“) = equQ) = 0.05 MHz, 11(1) = 11(2) = 0.1, number of0
increments in the range 0° - 90°, 40, number of (0 increments in the
range 0° - 90°, 40, Gaussian linewidth, 0.0925 MHz; (c) Axx = 1.74

MHz, AW = 2.30 MHz, AZZ = 2.934 MHz, e2qQ = 005.11: 01,

number of 0 increments in the range 0° - 90°, 40, number of (1)

increments in the range 0° - 90°, 40, Gaussian linewidth,
0.085 MHz ........................................................................ 162

Hydroxyethyl thiamin pyrophosphate radical (HE-TPP) .................. 168

xvi

111

Figure 11-30

Figure 11-3]

Figure 11-32

Figure 11-33

Figure Ill-l

Figure 111-2

Resonance structures for HE-TPP radical .................................... 169

Simulated l4N ESEEM frequency domain spectrum. Simulation
parameters: nuclear Larmor frequency, v] = 1.05 MHz; A1 = 1.36

MHZ, A“ = 2.36 MHz; eZqQ = 1.9 MHz, 1] = 0.74; number ofO

increments in the range 0-90°, 60, number of (1) increments in the
range 0-90°, 40; I = 205 ns ..................................................... 173

Simulated 31P ENDOR spectra for PFOR paramagnetic reaction
intermediate. Each simulation data set is plotted using dotted lines
and shown in comparison with the experimental spectrum (solid
line). Simulation parameters: g = 2.2633, B = 3345 G; (a) Aiso =
0.53 MHz, T = 0 MHz, number of0 increments in the range 0° — 90°,
80, Gaussian linewidth, 0.09 MHz; (b) Aiso = 0 MHz, T = 0.59
MHz, number of 0 increments in the range 0° - 90°, 80, Gaussian
linewidth, 0.08 MHz; (c) Aiso = 6.15 MHz, T = 5.725 MHz, number

of 0 increments in the range 0° - 90°, 160, Gaussian linewidth, 0.09
MHz; (d) Aiso = 0.53 MHz, T = 0.12 MHz, number of0 increments

in the range 0° — 90°, 80, Gaussian linewidth, 0.07 MHz .................. 176

A constrained conformation of the HE—TPP radical. All valence bond
lengths and valence angles are set to their equilibrium values in the

optimal conformation. P2 - 0 distance is fixed at 2.5 A. Optimization

of the molecular geometry has been performed by adjusting dihedral
angles .............................................................................. 179

Sequence of events during a four-pulse ESEEM experiment. The
amplitude of the four-pulse echo is measured as a function of t1

and 12 .............................................................................. 185

(a) An exemplary 2D time-domain data matrix, with only 33 of all
the 128 tl—slices shown. (b) 3D representation ofthe HYSCORE

frequency-domain magnitude spectrum obtained by 2D Fast Fourier
Transformation of the time-domain data matrix and taking the

absolute value of the resulting complex matrix. (c) Contour plot of

the above spectrum .............................................................. 186

xvi i

11:1

1151

1131

i121”

F12111

1
"Still

Figure III-3 Schematic HYSCORE 2D spectrum for an S = 1/2, 1 = 1/2 spin
system. Solid squares: peaks observed for ideal pulses. Open
squares: diagonal peaks that are observed only for non-ideal pulses
that cause partial excitation ..................................................... 191

Figure Ill-4 HYSCORE absolute value spectrum of irradiated (a) succinic acid
and (b) malonic acid after Fourier transformation with respect to t]

and t2 .............................................................................. 198

Figure Ill—5 Schematic HYSCORE contour plots of cross peaks arising from an
S = 1/2, 1 = 1/2 spin system considered at the level of first-order
perturbation theory. (a) (01 > All/2; (b) 0)] < Ai/Z ........................... 201

Figure III-6 Simulated HYSCORE contour plots arising from an S = 1/2, 1 = 1/2
spin system with an axially symmetric hyperfine tensor. Parameters:
v1: 3 MHz; (a) All = 3.6 MHz, A1: 1.2 MHz; (b) A“ = 5.2 MHz,
A1 = 0.4 MHZ .................................................................... 204

Figure III-7 Simulated HYSCORE contour plots arising from an S = 1/2, 1 = 1/2
spin system with a rhombic hyperfine tensor. Parameters: v1 = 3

MHz, Axx = - 0.04 MHz, Ayy = 1.64 MHz, AZZ = 4.40 MHz ............ 206

Figure III-8 Spin-density distribution in the tyrosine neutral radical .................... 219

Figure III-9 (a) Time-domain HYSCORE data (128x128 data points) from

3,5 2H-tyrosyl, with r = 200 ns; (b) the corresponding HYSCORE
frequency-domain contour plot. BO = 3129 G, v = 8.910 GHz ............ 223

Figure Ill-10 Definition of the position of the external magnetic field vector, BO,

in the principal axis system of a hyperfine tensor with rhombic
symmetry ......................................................................... 224

Figure III-ll (a) HYSCORE contour plot of 3,5 2H—tyrosyl (same as Figure

.wiii

111-9b); (b) the corresponding frequency-domain simulation using

the following parameters: nuclear Larmor frequency, v] = 2.1

1V11-12;Axx = - 3.82 MHZ, AyV = - 2.98 MHz, AZZ = -1.0 MHz;

tau-value, I = 200 ns ............................................................ 226

Figure III-12 Calculated suppression effect as a function of A22 (0 < AZZ < 6001)
and (.011 assuming (0 = 10.11 i All/2|. Dark (light) shading corresponds

to weak (strong) suppression effect. The sum of the suppression
function over (01I results in an amplitude function with only two

suppression holes at 00 = 0 and 0) = 2(1)] (top) ............................... 230

Figure Ill-13 HYSCORE contour plot of 3,5 2H-tyrosyl radical taken at various
values of I: (a) 200 ns; (b) 300 ns; (c) 400 ns; (d) 500 ns; (e) 600 ns. ..232

Figure 111-14 Simulated HYSCORE spectra of3,5 2H-tyrosyl radical. (a) A 3D
plot of the time-domain simulated data (128x128 points). (b) The
corresponding 3D frequency-domain magnitude spectrum obtained
by 2D Fourier transformation of the time-domain data in (a). (c)
Contour plot of the frequency spectrum. Parameters: nuclear
Larmor frequency, v1 = 2.1 MHz; Axx = - 2.3 MHz, Ayy = - 3.1

MHz, AZZ = -09 MHz; n = 0.1; e2qo = 0.22 MHz; 71 = 0.7 usec‘l;

tau-value, I = 200 ns; number of 0 increments over the interval

0-90°, 30; maximum number qu) increments over the interval
0-90°, 30 .......................................................................... 238

Figure III-15 Frequency-domain contour plots for the 3,5 2H-tyrosyl radical
HYSCORE time-domain simulations performed with the C
program "mims4" using the following parameters: nuclear Larmor
frequency, v] = 2.1 MHz; Axx = - 2.3 MHz, Ayy = - 3.1 MHz,

AZZ = -09 MHz; n = 0.1; eZqQ = 0.22 MHz; 1 = 0.7 usec’];
number oftime-domain data points, 128x128; number of0

increments over the interval 0-90°, 30; maximum number of (1)

increments over the interval 0-90°, 30; tau-value, I = 150 ns (a),
200 ns (b), 300 ns (c), 400 ns ((1), 500 ns (e), 600 ns (t) .................... 243

Figure III-16 Frequency-domain contour plots for the 3,5 2H-tyrosyl radical
HYSCORE time-domain simulations performed with the C program

xix

“r

o a- t“---

"mims4" using the following parameters: nuclear Larmor frequency,
v]: 2.1MHZ;Axx = - 2.3 MHZ, Ayy = - 3.1 MHZ, AZZ = -0.9 MHz;

number oftime-domain data points, 128x128; number of0
increments over the interval 0-90°, 30; maximum number of (1)
increments over the interval 0-90°, 30; 71 = 0.7 usec'l; tau-value.

r = 200 ns; n = 0.1; e2qQ = 0, (a), equ = 0.3 MHZ, (b) .................. 250

XX

Ac

C

CoA
CODH/ACS
CW

1D

2D

3D
ENDOR
EPR

ESE
ESEEM
ESR

Fd

fm
FORTRAN
FT

GO
I-IE-TPP
HF 1
HYSCORE
MATLAB

MW
NAD
NMR
NQI
PDC
PDH
PFOR
PGHS
PS 11
rf
RNR
TPP

LIST OF ABBREVIATIONS

Acetyl

The C programming language

Coenzyme A

CO dehydrogenase/acetyl-coenzyme A synthase
Continuous-wave

One-dimensional

Two-dimensional

Three-dimensional

Electron-nuclear double resonance

Electron paramagnetic resonance

Electron spin echo

Electron spin-echo envelope modulation
Electron spin resonance

Ferredoxin

Frequency modulation

Formula translator (programming language)
Fourier transform

Galactose oxidase

Hydroxyethyl-thiamin pyrophosphate
Hyperfine interaction

Hyperfine sublevel correlation spectroscopy
Matrix laboratory (programming and visualization software
package)

Microwave

Nicotinamide adenine dinucleotide

Nuclear magnetic resonance

Nuclear quadrupole interaction

Pyruvate decarboxylase

Pyruvate dehydrogenase
PyruvatetFerredoxin Oxidoreductase
Prostaglandine H synthase

Photosystem 11

Radio frequency

Ribonucleotide reductase

Thiamin pyrophosphate

xxi

INTRODUCTION

Electron paramagnetic resonance spectroscopy (EPR) has established itself as the
most informative method for the investigation of molecules with unpaired electrons.
However, for paramagnetic species stabilized in disordered solid matrices such as
polycrystals, glasses, frozen solutions, biological and polymeric matrices, the resolution
of the traditional, continuous-wave (CW) EPR is reduced due to inhomogeneous
broadening of the EPR lineshape, which can mask the details of the EPR spectra. Both
electron-nuclear double resonance spectroscopy (ENDOR) and electron spin echo
envelope modulation spectroscopy (ESEEM) have proven especially suitable for
resolving small electron-nuclear hyperfine interactions in samples of randomly oriented
paramagnetic species.

Chapter 1 of this Dissertation covers the basic principles of EPR spectroscopy. It
emphasizes the main characteristics, advantages and drawbacks of the continuous-wave,
double resonance, and time-domain EPR methods. In principle, ENDOR and ESEEM
offer identical information on hyperfine interactions. However, the two techniques are
considered complementary to each other since they show different degree of applicability
towards various systems. Thus, ESEEM is more useful for measuring weaker hyperfine
couplings of nuclei with small magnetic moments, whereas ENDOR experiments on such
systems are typically difficult to perform.

Chapter 11 presents a CW-EPR, ENDOR, and ESEEM study of pyruvate:
ferredoxin oxidoreductase (PFOR) paramagnetic reaction intermediates. These EPR

techniques are used in combination with isotopic substitutions to characterize the

magnetic and structural properties of the trapped transient intermediates. Determination
of the electronic and nuclear structures of paramagnetic reaction intermediates provides
insight into the molecular mechanisms of the enzyme catalyzed reaction.

Chapter 111 first gives an introduction to a relatively recent two-dimensional

(2D) version of ESEEM, the hyperfine sublevel correlation spectroscopy (HYSCORE).
In HYSCORE frequencies that originate from the same hyperfine coupling give rise to
cross peaks in the spectra, simplifying peak assignments and summarizing the lineshape
information of many 1D ESEEM data sets in cross-peak contours. The HYSCORE
mOdulation function for a spin system consisting of an unpaired electron (spin S = 1/2)
COupled to a nucleus of spin 1 = 1 is derived using the density matrix formalism. The
funCtion is applied to interpret through simulations experimental HYSCORE data for a

deuterium-labeled tyrosyl radical model system.

Chapter 1

Basic Principles of the Electron Magnetic Resonance Spectroscopy

1.1. Introduction

Since its discovery by Zavoisky in 1945, 1) Electron Paramagnetic Resonance
(EPR) spectroscopy has undergone rapid development. It has established itself as the
most versatile method for the investigation of molecules with unpaired electrons. Apart
from the highly sensitive detection of paramagnetic species, information on the electron
spin state, electronic and spatial structure, and internal dynamics can be obtained from
the EPR studies. A great diversity of systems, which range from single crystals
containing unpaired electrons to complex biological and polymeric matrices, has proven
amenable to study by EPR spectroscopy. However, as the field of application of the
conventional EPR spectroscopy has broadened, the limitations of the spectral
interpretations have become increasingly apparent. For instance, EPR linewidth changes
may occur over the range of rotational correlation times from approximately 1 us to 1 us.
I‘Ience, EPR is less applicable at regions of much slower or faster molecular motions.
Another limitation is associated with significantly overlapped EPR spectra due to the
preSence of multiple radical species. For paramagnetic species stabilized in disordered
Solid matrices (polycrystals, glasses, frozen solutions) the resolution of EPR is strongly
redu(led, owing to inhomogeneous EPR line broadening. However, obtaining information

n Weak magnetic interaction is necessary to solve structural problems, espec1ally 1n the

studies of biologically relevant paramagnetic species that are effectively immobilized in
proteins. To overcome these limitations various modifications of the method have been
developed. Multiple resonance methods, in which the sample is irradiated simultaneously
with more than one resonant field, offer the possibility of improving the spectral
resolution by introducing additional selection rules. In the electron-nuclear double
resonance (ENDOR) technique nuclear magnetic resonance (NMR) quanta are detected
in the microwave range (quantum transformation) resulting in a sensitivity enhanced by
several orders of magnitude over conventional NMR spectroscopy of radicals. An
alternative approach to the traditional CW-EPR experiment is the pulsed EPR
spectroscopy, which is primarily based on the electron spin echo (ESE) phenomenon.
ESE is a time-domain method, in which the time evolution of the spin system is recorded
directly. The electron spin echo envelope modulation (ESEEM) technique of pulsed EPR
spectroscopy has emerged as a powerful method for the measurement of electron-nuclear
hyperfine couplings that are masked by inhomogeneous broadening of the EPR lineshape.
The numerous theoretical and experimental methods of EPR and their
applications are extensively covered in a number of books and reviewsz'm) In this
Chapter only a short overview ofthe basic principles of EPR will be given. The
diSCUSSion will be confined to organic radical states in accordance with the goal of this
Dissertation. Section 1.2 gives an overview on the fundamentals of EPR and the types of
rnagnetic interactions of a paramagnetic system. Section 1.3 outlines the ENDOR
ex13$Timent and the resulting ENDOR spectra. Section 1.4 describes briefly the electron
Spin ECho phenomenon and introduces the basic ESEEM experiment by means of a

Se ' . . . . . .
I“lClaSSical description as well as a denSity matrix formalism.

1.2. Continuous-Wave Electron Paramagnetic Resonance

The basic electron spin resonance experiment involves the application of a
microwave oscillating magnetic field to invert the electron magnetic moment, along with

its associated spin, in an imposed external magnetic field. Molecules or atoms that have
unpaired electrons possess electron spin angular momentum, which results in a
permanent magnetic dipole moment, tie, given by

ue=-geuBS [11]

where ge is the "g-factor", equal to 2.0023 for a completely free electron, ”B is the Bohr
magneton (113 = e h / (2 me c), where e is the electron electrical charge, me is the electron

mass, and c is the speed of light), and S is the spin angular momentum of the molecule or
atom due to its unpaired electrons. For a species with a single unpaired electron, S = 1/2.
According to the classical electrodynamics, a torque ue x B0 will be exerted on the spin
in the presence of an external magnetic field Bo. It causes the spin to have preferred
orientation in the field, precessing around the magnetic field axis at the classical Larmor

frequency 600 = ge “B mm. The energy ofthis interaction is E = - tie-BO.

we Zeeman interaction

The quantum mechanical approach to the electron motion is more relevant than

t . . . . .
he Classmal theory. For a quantum mechanical system the interaction energy With the

external magnetic field is quantized. There will be (2 S + 1) states associated with
different energies and spin orientations. For example, an S = 1/2 species placed in an
external magnetic field will have two possible energy configurations and two possible
orientations of the electron spin - antiparallel and parallel to the external magnetic field.

The quantization ofthe electron spin angular momentum in an external magnetic field is
described by the Zeeman Hamiltonian given by

He,Zeeman = ge 11B BO'S' [1‘2]

A number of other interactions between the unpaired electrons and their environment
may exist. These include the interaction of the unpaired electrons with magnetic nuclei,
the interaction among the unpaired electrons, and the coupling between the spin and
orbital motion of the unpaired electron. The spin-orbit coupling is described by the

Hamiltonian H“) = - 2» LS, where L is the orbital angular momentum and it is the spin-

orbit constant for a particular shell in a particular atom. Normally a vector coupling
approach is used to compound the spin and orbital angular momenta into a resultant
rnOment. This corresponds to combining Helecman and If“, and introducing an
eff6ctive spin. As a result, the effects of spin-orbit coupling are incorporated into a g-

tensor. The combined Hamiltonian is given by

HeZeeman = “B BO'g'S»

where g is, in general, anisotropic and different from g6 for a free electron. However, for
randomly oriented organic free radicals such as those that are subject of this study the g-
tensor is isotropic and the deviations from ge are small, usually by less than 1%. With a

scalar g and an external magnetic field along the Z axis (B0 = [0, 0, BOD the Zeeman
Hamiltonian reduces to Heleeman = g 11B B0 S2. The two eigenstates of this

Hamiltonian in the case of a S = 1/2 system are characterized by the magnetic quantum

number MS having values of-1/2 (state 10>) and +1/2 (state |a>). Physically, the two

states correspond to different alignment of the magnetic moment with respect to the
external magnetic field. The magnetization is parallel to the field direction in state |a>,

and antiparallel with respect to the field in state 10>. The two eigenvalues are given by

E0L = g 14B 130/2, [1-4a]

13,3 = - g 118 130/2, [I-4b]

the energy splitting between the two levels being AB = g “B BO, Figure 1-1. EPR

transitions between the two energy states are induced by applying a uniform, linearly
p01arized microwave radiation to the sample and the change in the power of the
microwave radiation returning from the sample to the detector is measured. At resonance,

the Splitting between the energy levels equals the energy of the incident microwave

radiation:

gHBBo=hw0

    

    

 

 

w
0
H
O

Ms = '1/2

 

 

 

 

Figure 1-1: Energy levels of a spin system consisting of one unpaired electron (S =
1 /2) and one magnetic nucleus with l = 1/2 as a function of an externally imposed
magnetic field. When hyperfine interaction (cf. Section 1.2.2.) is present

(Characterized by the isotropic hyperfine constant a), each of the two energy levels is

 

[30 two sublevels, which results in two EPR lines separated by a.

 

 

In an EPR experiment, the sample is irradiated at a fixed microwave frequency,
while the magnetic field is swept to adjust the energy level splitting to the energy of the
electromagnetic quantum. For paramagnetic species with g = 2.0 and with microwave
frequency 9. GHz, the resonance occurs at field strength

B0 = h (Do/(g LLB) = 3215 G. [1-6]

When the sample is in thermal equilibrium with its environment in the EPR

spectrometer, the number of the oz spins, Na, relative to the number of the B spins, NB’ is

given by the Boltzmann factor,

Na/NB = exp[- AE/(kB r)], [1-7]

Where RE is the Boltzmann's constant and T is the sample temperature. At 298 K this
ratio equals 09986; i. e., for every 10000 molecules in state |B> there will be 9986
rnOlecules in state IOL>. Because of this population difference net absorption of microwave

power will be detected. The ratio decreases with decreasing the temperature. For

example, it becomes 0.8976 at 4 K meaning that the resolution is expected to improve

Upon lowering the temperature from 298 K to 4 K.

12.2. The hyperfine interaction

An important feature of the EPR spectra is their hyperfine structure. It arises from

t . . . . . .
he magnetic interaction between the electron spin and the magnetic dipole moments of

 

 

surrounding nuclei. A nucleus with an uneven number of protons or an uneven number of
neutrons has spin 1, associated with a magnetic moment tin = y l, where y is the
magnetogyric ratio for the isotope. (By analogy with the electron magnetic moment, the
nuclear magnetic moment is expressed sometimes as tin = gn “Rn l, where gn is the
nuclear g factor and HB,n is the nuclear Bohr magneton.) Subsequently, a magnetic

nucleus located in the vicinity of the unpaired electron generates a local magnetic field,

Blocala that can add to or subtract from the applied external field. Thus, the total field the
electron experiences is B = B0 + Blocal~ and the EPR condition is

g ”B (B0 + Blocal) : h- “)0- [1'8]

It is evident that the value of the external field necessary to achieve resonance will

depend on Blocal- The nuclear spin is quantized in the total magnetic field composed of
the external field Bo and the field due to the electron, yielding (2 I + 1) distinct nuclear

Spin states. (Figure 1-1 shows the situation for I = 1/2). Each of the (21 + 1) nuclear spin

States will generate a different Blow] magnetic field. Consequently, there will be (21 + 1)
different B0 values which will satisfy the EPR condition resulting in (2 1 + 1) lines in the
EPR spectrum. These lines will have equal intensity as the nuclear spin states are almost

eClllally populated. For example, the hyperfine interaction of the electron with a single lH
nucleus (1 = 1/2) results in two EPR lines because half of the paramagnetic species will

have their proton spin aligned with the external field (magnetic quantum number M] = +

1 /2) While the other half will have spin antiparallel to the external magnetic field

10

(magnetic quantum number M1 = - 1/2). Therefore, half of the paramagnets in the sample

(M1 = + 1/2) will resonate at applied field strength

B0 = h (Do/(g uB) - a/2, [I-8a]

while the other half (M1 = - 1/2) will resonate when

B0 = h (Do/(g NB) + a/2. [I-8b]

In the above expressions a is the hyperfine coupling constant. It should be noted that

these resonance conditions are valid only when a << h (Do/(g uB), since they do not

account for the nuclear Zeeman interaction.

From the physical point of view the origin of the hyperfine interaction in the

hydrogen atom is the non-zero ls electron density at the nucleus. In general, the electrons

in s-orbitals have a non-zero probability density at the nucleus and can give rise to
hyperfine interaction. This hyperfine interaction is isotropic because of the spherical
Symmetry of s-orbitals. Fermi has shown that the energy of the isotropic hyperfine

l nteraction (also referred to as an instance of Fermi contact interaction) is given by

Hiso 7' " (2/3) ”0 l‘l/(O)l2 “6.2 lin.z~ [1'9]

«39‘

 

where 110 is the permeability of vacuum and l\l’(0)l2 is the electron probability distribution

over a spherical volume. Using the operator relations between the magnetic moment and

the spin angular momentum (cf. Equation I-I), one obtains the result

Hiso = Aiso Sz 12» [1‘10]

where Aiso is the isotropic hyperfine coupling constant given by

Aiso = (2/3) no g 1113 Y lu/(0)|2. [1-11]

In more general form (used with an arbitrary external field BO),

Hiso = Aiso 8'1 - [1'12]
Aiso is the hyperfine coupling constant expressed in frequency units (i. e., Aiso/h)- It is

related to the constant a, given in magnetic-field units, as a = AiSO/(g LLB).

Electron-nuclear magnetic interaction can also be due to magnetic interaction
between the magnetic dipoles ofthe electron and the nearby nucleus. This interaction

arises when the electron resides on a orbital with orbital quantum number L> 0, which

has non-spherical symmetry. Since the electron probability distribution is zero at the

Ucleus no Fermi contact interaction IS possrble. Hence, this hyperfine interaction IS

12

l 2 n Bo

 

 

ll

 

 

Figure 1-2: Interaction of magnetic dipoles lie and “n arising from an electron spin

and a nuclear spin, respectively. The dipoles are aligned with the external magnetic

field and are separated by a distance r. Angle 0 is between the inter-dipole vector r

 

and the applied field 30

 

 

anisotropic, Figure 1-2. According to the electromagnetic theory. the magnetic field at the

nucleus due to the electron dipole moment tie at distance r is

Be = - (HO/4 TC) V(ue-r) / r3 = (HO/4n) { - tie/r3 + 3 (ue'l‘) r/r5}. [1-13]

The energy ofthe nuclear magnetic dipole in this field is

13

Hanjso = ' un°Be : ' (HO / 4 7t) i " (He'un) / 1'3 + 3 (He'r)(l>1n'r)/r5 } [1'14]

By replacing the magnetic moments with the appropriate operators one can obtain the

 

followmg expressron for Haniso:

Haniso = - ( L10 / 4 n) g us v {<I-S) / r3 + 3 (S-r) (I'r) / r5}. [1-15]

After expanding the vectors and averaging over the electron spatial variables, the

above spin Hamiltonian can be rewritten in a matrix form:

Haniso =‘(li0/47‘)8HBYX
r<r2 -3x2/r5> <-3 x y/r5> <-3 x z/r5> ‘—
[Sx Sy Szi <-3xy/r5> <r2 ~3y2/r5> <-3yz/r5> Iy
<-3xz/r5> <~3yz/r5> <r2 -322/r5> _17_

 

 

L—

: st-T-i. [1-16]

(The angular brackets in the above expression imply that integration over the electron
Space distribution has been performed.) The matrix T is symmetric about its diagonal and
tfaceless. The isotropic and anisotropic hyperfine coupling can be combined to yield one
matrix, A,

A 2 Al801+ T, [1-17]

whose trace is Tr{A} = 3 Aiso In liquids oflow viscosity the anisotropic component of

the hyperfine interaction is time-averaged to zero. However, in more rigid systems such
as crystals, it may be the dominant component of the hyperfine interaction. When the
crystal is rotated (i. e., the unit vector n along BO is changed) the value of nt - A - n
changes. Since A is symmetrical it can always be cast into diagonal form by a suitable
choice of axes. Single crystal EPR measurements yield A which can then be separated
into its two components. The anisotropic portion of the hyperfine interaction provides
geometric information and is related to the symmetry of the paramagnetic species. The
isotropic part reports on the unpaired electron spin density and is related to the nature of
the molecular wavefunctions.

The observed isotropic nuclear magnetic couplings arise from unpaired spin
density in atomic orbitals centered on the coupling nucleus. If the isotropic hyperfine
coupling comes from a particular atomic orbital of the coupling atom in the radical, the
unpaired spin density of that atomic orbital can be obtained from the ratio of the
measured coupling parameter to that for the corresponding orbital for the free atom. This
is the case of hydrogen hyperfine coupling in o-type organic radicals, in which the

unpaired electron is primarily located in the o orbital that would normally form a
Chemical bond. The c orbitals have in principle a considerable s-atomic orbital
Component. The extensive s-unpaired spin density at the hydrogen gives rise to hyperfine
Coupling constants oflarge magnitudes (150 - 400 MHz) and positive sign. For instance,
the measured isotropic proton hyperfine constant in the formyl radical, H‘CO, is 384

man) which, together with the experimental value of 1420 MHz for the coupling in

t . . . . . .
he hYdTOgen atom, yields a unpaired electron spin population in the hydrogen ls orbital

15

equal to 0.27. This value implies that the resonance structure [H-+:CO] corresponding to
an excited state has a significant contribution to the overall electronic structure ofthe

radical. The participation ofthis structure produces a positive spin density on the Is
orbital of the hydrogen atom by direct transfer of the unpaired electron. It should be noted
that along with its large isotropic component the hyperfine interaction in o-type radicals
may also exhibit a large anisotropy.

There exist indirect coupling mechanisms that result in significant isotropic
hyperfine coupling of the unpaired electron located in particular molecular orbital with
nuclei situated in the node of the orbital, where the isotropic hyperfine coupling should
be identically zero. Isotropic hyperfine coupling can originate from the phenomenon of

spin polarization of covalent chemical bonds. For example, the proton coupling in a CaH
fragment of a 1: -type free organic radical, in which the unpaired electron occupies a it
molecular orbital (constructed as a linear combination of carbon 2pZ atomic orbitals), has

a large isotropic component. This evidences the presence of some induced unpaired
electron density on the proton. According to Hund's rule for an atom, the state of highest
spin multiplicity has the lowest energy. This is due to the favorable exchange interaction

between two electrons with parallel spins located in different orbitals ofthe same atom.

ThUS, because of the exchange interaction, an on spin unpaired electron located in the 2pZ

Orbital of Co will constrain the Ca electron participating in the 0 bond to an 0t spin state,

Figure 1-3. Consequently, the generated positive spin density at the carbon will induce
negative electron spin density (i. e., excess ofB spin over 0!. spin) at the proton (relative to

he Pit Spin densrty on Ca) smce the electrons partiCipating in a covalent bond must be of

131305113 Spin. The negative spin denSity induced on the proton gives rise to negative

16

 

 

 

Figure 1-3: Valence bond structures for the Ca'H fragment. The two possible
electron spin configurations in the s bonding orbital are shown for a spin in the 2p,I
orbital of the carbon atom. (a) Spins parallel in the s bonding orbital and the 2p7r

orbital of carbon. (b) Corresponding spins antiparallel.

 

 

 

hyperfine coupling constants for 0t protons. For planar conjugated organic radicals, there

exrsts a linear correspondence between the isotropic proton hyperfine parameter Aim”
and the unpaired 1t electron population pnca of the adjacent carbon 2pZ orbital that

cOntributes to the rt system. It is given by the well known McConnell relation: '8)

l7

AisoH = QaCH 01:01 ~ [1-18]

where QO‘CH , QQCH < 0, is an experimentally obtained proportionality constant. This
relation holds remarkably well for a wide range of neutral rt radicals and is applicable to

nuclei other than protons.

The anisotropic component of the proton hyperfine coupling for an CaH fragment
is of magnitude comparable to the isotropic component. It is due to the dipole-dipole
interaction of the proton magnetic moment with onC spin density on the CL carbon. The

principal elements of the hyperfine tensor A are commonly found to be along the axis of

a coordinate system defined, as shown in Figure 1—4, by the p,r orbital (i. .e. the 2pZ

orbital of Ca ) as the x axis, the CaH bond as the z axis, and the z x x cross product as
the y axis.

Another effective model for the hyperfine coupling mechanism is
hypercory'ugation. It can account for the EPR observed splittings from protons in the
alkyl groups of alkyl-substituted rt-type radicals. Hyperconjugation can occur when two
fragments of a molecule interact provided there is a compatibility in the symmetry
PFOperties and energies of their wavefunctions. For example, the admixture of valence
bond structures as those shown in Figure 1-5 (a) for the ethyl radical equalizes the
rnagnetic couplings of all five hydrogens. Both the molecular-orbital theory and the
Valence bond theory predict that the spin density on the B hydrogens is positive as
Opposed to that on the OL hydrogens. Similarly to or proton hyperfine coupling, the

SQUOPIC B proton coupling is proportional to the TI spin denSity on the or carbon to which

 

 

 

 

 

 

Figure I-4: Model used for calculation of the dipole-dipole magnetic coupling or

unpaired p7t electron density on C0L carbon atom with the nucleus of a hydrogen atom.
The spin density is concentrated equally at effective centers of the p.,[ orbital lobes on
either side of Ca. rp is the distance from the effective coupling centers to Ca nucleus.

“71-1 is the internuclear distance of C and H.

 

l9

 

~C— C
\\H
H H
1
H\ .H
C:C
\\H
H H
2
a

 

 

Figure 1-5: (a) Hyperconjugation in ethyl radical. The admixture of the two
exemplary valence bond structures can account for the significant isotropic hyperfine
coupling for B hydrogens in aliphatic radicals. (b) Coordinate system for B coupling

of hydrogens.

 

2(1

 

 

 

 

 

li‘<

 

Figure I-5 (b)

21

 

-i

the magnetically coupled proton is attached: '9)

AisoHB = QBCH(9) pnCa - [1'19]

In this case, however, the magnitude ofthe coupling will depend on the orientation of the

CB“ bond with respect to the 2p,[ orbital of the C0L carbon atom where the unpaired

electron is located. This orientation is given by the dihedral angle 0 between the plane

defined by atoms Ca, CB, and H, and the plane containing the both the 2pZ orbital ofthe

Ca carbon and the CaCB bond, Figure I-S (b). The function 0501(0) has the form

QBCH(9) = QBO + QB2 c052(9) , [1-20]

where Q50 << Q52. The typical values reported in the literature are 8-9 MHz for (Q50

pnC0L ) and 122-125 MHz for (Q92 pnCO‘).5) The orientationally independent term in the

above expression has been viewed as arising either from torsional oscillations around the

CaCB bond or from direct or consecutive spin polarization involving both CaCB and
CBH bonds. The second term is associated with hyperconjugation.
Ifthere is free internal rotation about the CaCB bond then the isotropic hyperfine

coupling is orientationally averaged. Since <c0520> = 1/2, QBCHrot = Q30 + 1/2 Q92,

and

AisoHB = QBCI—Lrot 91:01 5 “2 QZBpnca [1'21]

The last equation is used to derive experimental values for QBCH by measuring the B

methyl proton couplings from spectra of radicals in solutions. For alkyl radicals QBCHJO!
= 164 MHz.5)

Superimposed on the isotropic [3 proton coupling in n-type radicals is a much
smaller (ca. 10% ofthe value ofthe isotropic component) anisotropic component arising
primarily from the direct magnetic dipole-dipole interaction of the B protons with the 1'!
spin density of Ca atom. To a great extent, the anisotropic coupling tensor for B protons
has axial symmetry. From the principal values of the dipolar hyperfine tensor, the dipolar
field generated by the unpaired electron spin density on Ca can be obtained and the Ca-H

distance can be calculated in the dipolar approximation:

(AH - A1) / 3 = T = p1.“ g m gn pan/r3 . [1-22]

The hyperconjugation model of hyperfine coupling of [3 protons can be extended
to y protons. Unlike the [3 proton splittings that are generally about the same magnitude

(or even larger) as the splittings for an or proton replacing the substituent to Ca, the

hyperfine couplings arising from y protons are up to two orders of magnitude smaller. For

example, the y proton isotropic hyperfine coupling constant in the acetoxyl radical

(CH3COO-) equals 4.8 MHzZO)

23

1.2.3. The nucleagguadmpole interaction

Nuclei with nuclear spin I 2 1 can have a non-spherical charge distribution
resulting in a quadrupole moment that is collinear with the magnetic moment, Figure 1-6.
The quadrupole moment can interact with an inhomogeneous electric field adopting a
preferred orientation in the field. The electric field gradient is determined by the
electronic structure of the paramagnetic species, reflecting non-uniformities in the
surrounding electron density. Hence, measuring the quadrupole parameters can yield
structural information. The nuclear spin (through its associated magnetic moment) is
quantized along the axis of the effective magnetic field generated by the spectrometer and
the nearby unpaired electrons. The effect of this magnetic interaction is modified by the
quadrupole interaction since the quadrupole moment acts to orient the nucleus in the
direction of the largest electric field gradient. Consequently, the competition between the
effects of the magnetic moment and the quadrupole moment can manifest itself in the
result of the EPR experiments. Due to the collinearity of the axes of the nuclear
quadrupole moment and the nuclear spin angular momentum, the Hamiltonian for the

quadrupole interaction can be expressed in terms of the nuclear spin,

HNQI = K [3 122 -12 + n (it2 - 1.2)]. [1-231

Where K is the quadrupole coupling constant, K = eZqQ/[4 h 1 (21-1)], r] is the asymmetry

Parameter defined through the principal values Vii of the electric field gradient tensor, 1]

= lex - V3,), l/VZZ . The eigenvalues ofthis Hamiltonian are Ei = - K (1 i n), E0 = 2K,

24

which yields the frequencies v+ = K (3 + n), v_ = K (3 - 1]), v0 = 2 K n. HNQ] is
frequently written as HNQI = I-Q-l, in terms of the traceless tensor Q whose elements are

Qij = Vij eQ / [21 (21 - 1)], where eQ is the quadrupole moment.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure I-6: Quadrupolar nuclei (a) oblate, (b) prolate. An oblate quadrupolar nucleus

in (c) a uniform electric field, (d) an effective field gradient.

 

 

25

The nuclear quadrupole frequencies can be directly observed in ESEEM (or
ENDOR) under conditions of "exact cancellation". In the case of an S = 1/2, I = 1 system,
if the isotropic hyperfine constant equals twice the nuclear Larmor frequency the energy
levels in one spin manifold collapse, which results in appearance of pure quadrupole

frequencies, v+, v, , and v0.

The general spin hamiltonian which describes the EPR spectra (as well as other
magnetic resonance spectra, e. g., ENDOR or ESEEM) is composed of electron Zeeman,
nuclear Zeeman, nuclear hyperfine and quadrupolar effects, as well as other interactions

not considered above, e. g, electron-electron dipolar and exchange interactions:

H = Heleeman + Hn_.Zeeman + HHFC + HNQI + [1'24]

In principle, these interactions can all occur simultaneously for a given paramagnetic
species. The observed positions and relative intensities of the lines can, in general, be
obtained from this Hamiltonian by numerical diagonalization and spectral simulations
rather than by finding analytic solutions for energies and transition probabilities.
However, analyses for many systems can be obtained using analytical results derived for
various limiting cases. These limiting cases are determined by the relative magnitudes of
the different interactions and their anisotropies. Thus, for the majority of organic radicals
the anisotropy ofg is not important. Since the nuclear Zeeman energy is always weak
compared to the electron Zeeman interaction and typically weaker than the hyperfine

term, the nuclear Zeeman term can often be omitted. In many cases, it is possible to treat

20

the hyperfine interaction as perturbation, provided the magnitude of the electron Zeeman
interaction is predominant.

Analysis of the EPR spectra allow extracting the tensor elements for the various
interactions, the most precise information being obtained from measurements on single
crystals. However, such measurements are only possible for a limited number of
substances. The materials of biological interest are normally not found in a single-crystal
form and, in most cases, the preparation of single crystals containing biologically
important radicals is difficult. The EPR of samples in the form of polycrystals, glasses,
powders, or frozen solutions yields "powder" type spectra. These spectra are the sums of
the EPR spectra of the individual, randomly oriented paramagnetic species for all
possible orientations. Hence, the analysis of the powder spectra is more complex.
Moreover, for paramagnetic species stabilized in disordered solid matrices, the resolution
of EPR is reduced to a few gauss, owing to inhomogeneous spectral broadening caused
by the presence of multiple, small hyperfine couplings. In these cases no hyperfine
information is obtainable, if the splittings are narrower than the inhomogeneous spectral
width (usually tens to hundreds of gauss).

Various modifications of the EPR spectroscopy have been developed, which
allow resolving weak hyperfine couplings in disordered systems of the order ofa few
Hertz. Two of the most widely used methods are the Electron Nuclear Double Resonance
(ENDOR) and the Electron Spin Echo Envelope Modulation (ESEEM) spectroscopy.
These techniques not only yield the weak couplings but have the advantage of reducing

the number of peaks and decreasing the linewidths associated with the various transitions.

27

In the following two Sections, the principles of these methods will be introduced and

their applicability, advantages and limitations will be briefly discussed.
1.3. Principles of Electron Nuclear Double Resonance (ENDOR) Spectroscopy

Electron Nuclear Double Resonance (ENDOR) spectroscopy is the most widely

used technique for measuring weak nuclear hyperfine and quadrupole couplings in

disordered systems of paramagnetic species. 10'1st 1) ENDOR yields the NMR spectrum
of the paramagnetic system by detecting the change in the amplitude of the saturated EPR
signal upon sweeping the frequency of an additional radiofrequency field. Because
hyperfine couplings on the order of a few kiloHertz can be resolved, ENDOR inherently
provides much higher resolution than the conventional EPR spectroscopy. This section

presents a phenomenological introduction to ENDOR spectroscopy.

1.3.]. Energy levels and resonance conditions
The spin Hamiltonian describing the interaction of one electron (spin quantum

number. S = 1/2) with a number of nuclei each of spin 1i in an external magnetic field Bo

is composed of electron Zeeman, nuclear Zeeman, hyperfine, and quadrupole interactions

(if nuclei of spin I > 1/2 are present):

H =HBBo 'g-S-Zgn.iu8.n30 'li +hZS'Ai '11 ”1211 '01 '11 [1-25]

I l l

28

where g, Ai and Qi denote the electronic g, hyperfine, and nuclear quadrupole coupling
tensors, respectively, LLB and “B,n are the electronic and nuclear Bohr magnetons,
respectively, gn i is the nuclear g factor for nucleus i, and h is Planck's constant. The

eigenfrequencies ofthis Hamiltonian can be easily obtained in the simple case ofa single
nucleus of spin I = 1/2 (e. g, a proton) interacting with the electron. In the high-field

approximation, in which S and I are quantized along the external field BO, and with the

assumption of all interactions being isotropic these are given by

E(MS, M])/h = veMS - vnM] + Aiso MS M] , [1-26]
where

Ve = g MB Bo/h, [1-27]

Vn = gn UB,n Bo/IL [1-28]

are the free electron and free nuclear frequencies (related to the Zeeman energies) and

MS and M] are the electron spin and nuclear spin projections. The corresponding
eigenvectors are simple product functions IMS, M1>. This leads to the energy level

diagram shown in Figure I-7. Two EPR transitions, 1<->2 and 3<->4, are obtained by

applying the selection rules for electron spin transitions,

AMS = i], AM] = 0. [1-29]

The corresponding resonance frequencies are

29

 

 

 

 

 

 

 

 

 

 

 

 

-1 /2.:,.— _ ............... +_>
ll gA iso/4 1 I ‘I
s” l ' ,
+1/2,.-———~.:“§ vn + j Va 2 x l 1‘ Wm
ll NMR] : ‘. v.1{x |++>
:' + l /2‘.JL. j \I ,' i
PRII v. 5W " 5
EU/h E EPR] : el 1",sz :
i .i' :
Ve EPR] : ~ :
Y ' E
-1/2,»-.——-—“" ll 3
-1 /2 41—— V13 i
NMRII 5
+1 /2————- I l
a b

 

 

Figure 1-7: Energy-level diagram in a high magnetic field for the interaction of one
unpaired electron (S = 1/2) with an I = 1/2 nucleus (e. g. a proton), detailing the

electron Zeeman, nuclear Zeeman, and hyperfine splittings. The case of gn > 0, Aiso >
0, lAiso/zl < vn is represented. The four energy levels on the right (1 to 4) are labeled
by [M5, M1>. The heavy arrows indicate the induced EPR and NMR transitions; the

broken arrows the various relaxation rates. (After Ref. 12)

 

3 0

 

VEPR = v6 1- Aim/2 [1-30]
The application of the NIVIR selection rules

AM] = i1, AMS = 0, [I-31]
yields two NMR transitions, I<->3 and 2<->4, at the frequencies:

VNMR = M: i Aiso/Zl- [1-32]

These NMR transitions are detected in ENDOR via intensity change of a simultaneously

irradiated EPR transition.

If vn > [Aim/21, Figure I-8, the two ENDOR lines are equally spaced about the
free nuclear frequency VH and separated by the hyperfine constant lAiso I. If vn < |AiSO/2|,
the lines are centered around lAiso /2| and their separation is 2v". For the hypothetical
case vn = lAiso/Zl only one signal would be detected.

From Equation 1-32 it follows that both the hyperfine constants and the free
nuclear frequencies are obtainable from an ENDOR experiment. Nuclei can be identified

from vn using tabulated nuclear g factors. The ENDOR data can be used to assign a

certain hyperfine constant to a specific nucleus. The hyperfine constants can also be
measured from the EPR spectra. However, the EPR spectra involving contributions from

different sets of equivalent protons coupled to the unpaired electron can become too

31

IA

isol

ll
v

 

: v v (MHz)

 

 

 

II
a
l?
2vn
l
|AiSO|/2 v (MHZ) |
b

 

Figure I-8: ENDOR spectra for (a) lAiso/Zl < vr1 and (b) lAiso/Zl > Vn- The solid lines

represent the spectrum observed when the high field EPR transition is monitored and
the dashed lines give the spectrum observed when the low field EPR line is monitored.

(After Ref. 2)

 

 

 

complex for an ambiguous interpretation. The resolution enhancement and reduced
complexity of the ENDOR spectra is demonstrated in Figure 1-9, which represents the
energy level diagram for a hyperfine-coupled system consisting of one unpaired electron

(S = 1/2) and three equivalent nuclei each of spin Ii = 1/2, e. g, a group of methyl
protons. The four nuclear spin sublevels for each MS = +l/2 and MS = -l/2 correspond to

the possible values ofthe total nuclear spin angular momentum, I = 3/2, 1/2, with

degeneracies d(I = 3/2) = l and d(l = 1/2) = 3. Owing to the transition-frequency

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. 11 ll '30
.———— .......... .. l /2
+1/2 _.-———{ " ll “
5 ............ 11 ll +1/2
A +3/2
130/11 EPR
- -3/2
ll
, : ..___.. A -1/2
-1/2 ——-2,
__ A +1/2
+3/2
Aiso
Aiso
I' ’1
1’ t VNMR —>
B0
EPR ENDOR

 

 

 

Figure I-9: Energy-level diagram of a hyperfine-coupled spin system in a high
magnetic field, consisting of one unpaired electron (S = 1/2) and three equivalent

nuclei (1 = 1/2).

 

 

33

degeneracies, four EPR transitions are obtained with binomial intensity distribution
(1:3:3:1). On the other hand, the ENDOR spectrum exhibits only two signals because of

the degeneracy of all NMLR transitions within the same MS state. Addition of

nonequivalent nuclei to the system multiplicatively increases the number of signals in the
EPR spectrum, whereas the number of ENDOR signals increases additively. Thus, while

the spectral density in EPR is given quantitatively by

 

 

k
1‘] (211111 + 1)
i=1
k . [I-33]
22 Mi lnili
i=1
the ENDOR spectral density is generally much smaller and represented by
2k [1-34]
Amax

where k stands for the total number of sets i of equivalent nuclei, “1 is the number of

equivalent nuclei in each group i, each of spin Ii, and Amax denotes the largest hyperfine

constant.

1.3.2. Level populations and ENDOR effect
To explain how an ENDOR response is generated various relaxation pathways

and consequent energy level populations have to be considered. The theory of the

34

 

ENDOR mechanisms incorporates the relaxation theory and is rather complex. Here only
a qualitative description from an elementary mechanistic point of view will be given.
Suppose the four energy levels in Figure I-7 are initially in thermal equilibrium with each
other so that their relative populations are given by Boltzmann's law. The population
difference between the nuclear spin sublevels (I<—>3, 2<—>4) is much smaller (ca. 10'6 )
than that between the electron spin levels ( l<—>2 and 3<—>4) (on the order of 10'3 at room
temperature and BO ~ 3000 G), thus the former can be neglected. Since the population

difference between electron spin levels is small compared with kBT at a temperature

.____ J‘v—x‘ .
~1— .__.. _ .4..-

above a few Kelvin, the electronic Boltzmann factor can be expanded,

N(Ms = 1/2)/N(Ms = - H2) = exp< - g #13 BO «mo 1 =

l - g “B Bo /(kBT) = 1 - 8, [1-35]

where e = g 1,113 BO/(kBT). Initially, the upper electron spin level will be I - e as less

populated as the lower electron spin level, Figure l-10 (a). In conventional EPR
experiments EPR transitions between these electron levels are induced with sufficiently
low microwave power to avoid saturation. With no saturation the thermal equilibrium
populations are maintained by the electron spin-lattice relaxation interactions. In this case

the electron spin-lattice relaxation (characteristic time Tle ) will cause the hot spins to

return from the upper electron spin level at a higher rate than the rate of induced
absorption. However, ifa strong microwave field is applied to drive an EPR transition

between the electron spin levels, e. g, between levels 3 and 4, so that the induced

35

M3 M1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 +1/2 -I/2-—A 1-8 -—ll__]’8 71—15mm
T1e hvC T1c hve T16 hve
2 -1/2-1/2 ‘ 1 1 1
4 -1/2+1/2 1 1 1-2/2 ‘ ’ 1-3/2
a b c

i—a

 

j

hvc

 

 

 

 

 

\ k

 

1-38/4
1-33/4

‘hva

l +e/4

1-38/4

 

ENDOR effect, ((1) final steady state. (After Ref. 1 1)

 

Figure 1-10: Population diagram for transient ENDOR with S = 1/2, I = 1/2, gn > 0,

Aiso > O. (a) unsaturated EPR transition, (b) saturated EPR transition, (c) transient

 

 

transition rate competes successfully with the electron spin-lattice relaxation, these levels

will become equally populated as shown in Figure 1-10 (b). The EPR signal will fade

away as the population difference goes to zero. The population difference between the

electron spin levels can be restored and the EPR line desaturated by additionally pumping

either 1<——>3 or 294 NMR transition using a strong saturating radiofrequency field,

Figure 1-10 (c). Both absorption (4<—->2) and emission (193), which equalize the

populations of the corresponding NMR levels, can be induced by the coherent external

radiation field with equal probability. From Figure 1-10, it is clear that the maximum

36

ENDOR effect amounts to 1/4 of the unsaturated EPR intensity. It should be noted that
the ENDOR signal is always an absorption signal since it is the increase in the intensity
of the saturated EPR transition that is monitored. This detection scheme leads to a
ENDOR signal that is about 105 times as intense as the signal in a conventional NMR

experiment on paramagnetic systems.

 

The above simplified description ofthe ENDOR experiment is used in the Fl
explanation of the first ENDOR experiment performed by Feherzz) and is relevant to a
transient ENDOR effect. It ignores the existence of relaxation processes other than the i
electron spin—lattice relaxation. In fact, in the presence of saturating microwave and

radiofrequency fields the three energy levels involved would eventually become equally
populated after a short time and the EPR signal would disappear, Figure I-10 (d). To

obtain a steady-state change of the EPR signal intensity the effective relaxation time

T leeff must be changed - by providing a parallel relaxation path for the electron spins.

Along with the radiationless electron spin-lattice (characteristic rate We = (2Te)‘l)
relaxation, the existence of nuclear spin—lattice (characteristic rate Wu) and cross-
relaxation processes due to simultaneous electron and nuclear spin relaxation transitions
(characteristic rates le and sz ) have to be taken into account. When the EPR
transition 192 is partially saturated, Figure 1-7 (b), the subsequent change in the EPR
signal intensity will depend on the microwave induced transition rate in competition with
all other processes that contribute to the effective electron spin relaxation between the
two EPR levels. The effective relaxation rate comprises the electron spin-lattice

relaxation We] as well as the bypass process 1—>3—>4—~>2 involving nuclear spin

37

 

 

relaxation Wnl (I—>3), electron spin relaxation Wez (3—->4), and nuclear spin relaxation
W112 (4—>2). Other bypass processes include the cross—relaxation rates le or Wx2
together with Wn rate(s). The effective relaxation rate between levels I and 2 can be

enhanced by applying an external radiofrequency field, in resonance with the nuclear

transitions, which competes with Wn] or W112. This causes a higher efficiency of the

relaxation bypass and leads to desaturation of the EPR transition with a concomitant

 

increase of the EPR signal intensity.
It is evident that the magnitude of the ENDOR effect will depend upon the i

relative magnitudes of the various relaxation rates, We, Wn, le, and sz. If cross
relaxation does not play a significant role (1. e., WX < We, Wn) then the relaxation rates
We and WD have to be of comparable magnitudes in order to avoid a relaxation

bottleneck along the bypass route for the electron spin. The above condition is usually
satisfied for radicals in solutions as well as for radicals in solids that are not strongly

coupled to the vibrational modes of the matrix. Since the rate We is inversely
proportional to the rotational correlation time IR (the time constant for Brownian
rotational motion of molecules in solution), whereas Wn is proportional to IR, an

adjustment of the relaxation rates can be achieved by temperature variation. According to
the Debye-Einstein equation the rotational correlation time is determined by the effective

molecular volume Veff , the viscosity 1], and the temperature T: 12)

TR = Veg n/(kB T). [1-361

38

 

As the temperature decreases and the viscosity increases, We will become smaller while

Wn will become larger. Hence, the optimization of the ENDOR experiment can be done

by selecting appropriate temperature and solvent viscosity. For example, for protons,

where W u << We, optimum ENDOR signals in solvents of low viscosity (such as toluene

or tetrahydrofuran) are observed near the freezing points of the solvents. For high
viscosity solvents the optimum temperature is close to the room temperature.

If We and Wn are not of comparable magnitudes the cross-relaxation processes

must be effective for a successful ENDOR experiment. This is the case of paramagnetic

defects in solids or transition metal ions in crystals, where Wn << Wx < We and an
alternate relaxation pathway that involves WX is predominant in generating an ENDOR

response.

1.3.3. Factors influencing ENDOR signal intensity

The relaxation properties of the particular nuclei in the different molecular
positions are deterministic of the ENDOR signal intensity. Therefore, the information
from the intensity distribution in an ENDOR spectrum is not meaningfiil. Additional
effects may obscure any conclusion from ENDOR signal intensities. One of the

difficulties in analyzing the intensities comes from fact that the radiofrequency power is

not constant over the scanned frequency range. This problem can usually be corrected for

in studies of ENDOR line intensities. Another effect is the systematic decrease of the
signal intensities in the case of small hyperfine couplings. Signals close to the free

nuclear frequency are generally weak even if they are generated by many equivalent

nuclei. This originates from the incomplete hyperfine line separation. When the hyperfine

39

F:

v-h'
«

 

 

separation is of the order of the homogeneous EPR linewidth (given by the inverse of the

electron spin-spin relaxation time, 1/T2e) the saturation of one hyperfine line may lead to

partial saturation of other lines, because of the overlap. The result is a reduction of the
ENDOR enhancement. The ENDOR signal intensity is also influenced by the so called
hyperfine enhancement eflect. The nuclear spin interacts with an effective oscillating field
that is the external radiofrequency field at the nucleus modified by the hyperfine field. As
a result, the probability for the NMR transition will be proportional to the hyperfine

enhancement factor given (for isotropic solutions) by VENDOR/W; i. e., the intensity will

be increased with increasing ENDOR detection frequency. Therefore, the high-frequency
component of an ENDOR line pair will be more intense than the low—frequency one at
the same radiofrequency power. The hyperfine enhancement effect becomes more
pronounced as the difference between the two components increases. In solid state

ENDOR, the resonance frequency, VENDOR, and the hyperfine enhancement factor are

governed by different anisotropic hyperfine components. For instance, if the z axis is
parallel to the static magnetic field B0 the ENDOR resonance frequency is determined by
the element Axx of the hyperfine tensor, whereas the transition moment is governed by
the A22 tensor component. This leads to unexpected intensity patterns of low- and high-
frequency lines in the solid state ENDOR spectra.

Since the intensity distribution of an ENDOR spectrum does not reflect the
multiplicity, i. e., the number of equivalent nuclei belonging to each set, other techniques
are used to determine the number of equivalent nuclei belonging to a particular hyperfine
constant. One of the methods uses specific isotopic labeling, e. g, selective deuteration.

While selective deuteration increases the density of spectral lines in EPR, thus decreasing

40

1'

the resolution, replacement of a proton by a deuteron removes its contribution to the
ENDOR spectrum because the proton and deuteron ENDOR transitions occur in different

spectral regions.

1.3.4. ENDOR lineshapes
It is convenient to express the NMR (ENDOR) resonance condition, Equation 1-

32, in a more general form,

VNMR (M1, M] + l) = I - Vn + MS Aisol' [1-37]

In this form, MS is retained explicitly, which allows assignment ofa hyperfine constant
to one ofthe MS states ifthe sign of A150 is known. The relation is precise only to first

order and holds for nuclei that exhibit small hyperfine constants, e. g, protons in organic
it radicals. Second-order effects that lead to line shifting or even splitting have to be
considered iflarge (above 30 MHz for X-band EPR) hyperfine constants are present.

If anisotropic hyperfine effects are present due to orientation dependent electron-
dipole-nuclear-dipole interaction. the ENDOR frequencies are given in the strong field

approximation by an expression similar to Equation 1-3 7,

VENDOR (Mi <-> Mi+i) = | “’11 + Ms R|~ [1-38]

where

R = (AZ’X'2 + A2312 + AZ,Z.2)l/2 [1—39]

41

W‘_-mu. . A

is the effective hyperfine coupling for a particular orientation of the magnetic field with
respect to the axes of a laboratory coordinate system x’y’z’ (usually defined according to
the geometry of the radical or the crystal). If A is diagonal in the laboratory frame R is

reduced to R = Azxzx. The above formula can be used to obtain all components of the

hyperfine tensor A by measuring the observed hyperfine splitting R versus the angle of

rotation about three mutually perpendicular axes.

In the principal axis system xyz ofthe hyperfine tensor A,

R = (Axx2 1x2 + Ayyz 1V2 + A222 122)l/2 ‘ [1-40]
where Ix, lv~ and 12 are the direction cosines of the field B0 with respect to the axes x, y,
and 2.

Generally, the diagonal elements of the hyperfine tensor contain the isotropic
(Fermi contact) interaction Also and the traceless dipolar interaction component B“:

Bii = A“ - A150, 1 = x, y, 2. [1-41]
For small anisotropies, lBiil << |Ai50|, and R can be approximated as

R = Am, + Bxx 1,,2 + 13yy 1,2 + BZZ 1,2 . [142]

For the common case of axial symmetry around 2

42

W~_n—‘M_i.- 0‘. I W

Bxx = By}, = B j. [1-4321]
1322 = B” , and [1-43b]

B“ = -2 B j . [1-43c]

These relations result in the following expression for R:

R = Am, + B” [3 «132(9) - 11/2. [1-44]

where 0 is the angle between Bo and the symmetry axis 2.

For nuclei with I > 1/2, the quadrupole interaction gives rise to additional
Splittings ofthe ENDOR signals. In the simple case in which the hyperfine and
quadrupole tensors have the same principal axes, |Q| << |A|, and the magnetic field is

aligned along a principal axis (e. g., the z axis) the resonance condition is given by

VENDOR (Mi <-> M1+1)= l 'Vn + Ms A11 + 3/2 Q11 (2M1 + 1)l- [1-45]

Figure 1-1 I shows the energy level diagram for a S = 1/2, I = 1 spin system, e. g,
a deuteron coupled to an unpaired electron. It is clear from the diagram that if the
quadrupole interaction is negligible, the same two ENDOR transitions are observed for

each ofthe three EPR lines (AMS = 0; AM] = I, 0, -l). However, with a quadrupole

interaction ofa significant magnitude two ENDOR lines will be observed for the AM] = -

M5 M1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+1/2 +1 1, A A ll
v1 = |A/2+vn+ Q|
IA/2+an
+I/2 0 ‘ ‘
1 ll 1 ll
l 1mm. l v2 = lA/2+Vn- QI
+1/2 -1 11‘ ll
EPR EPR
-1/2 -1 ‘ ll
A lA/Z-an V3 = lA/Z‘Vn+ Ql
-1/2 0
“ IA/2-vnl 1g}. V4 ._. Wz'vn' Ql
-1/2 +1 ‘ ‘
a b

 

Figure 1-11: Energy-level diagram for S = 1/2, I = 1 spin system showing EPR and
ENDOR transitions in the absence (a) and presence (b) of quadrupole coupling. (After

Ref. 11)

 

 

 

1 EPR transition, two different ENDOR signals will be observed for the AM] = 1 EPR
line, and four ENDOR lines are expected for the AM] = 0 EPR line. 1 1)

1n disordered solids, such as those studied here, due to averaging the absorptions
from different orientations of the paramagnetic species with respect to the external

magnetic field, the narrow liquid phase ENDOR lines broaden and may become weak,

Figure 1-12.1 123) In the special case when the shape ofthe EPR spectrum is dominated

44

(a) (b)
Aisozoa All/ A;: '7- Aiso + A‘

 

 

 

 

 

 

Figure l-12: ENDOR lineshapes (absorption: top, first derivative: bottom) resulting

from an axially symmetric hyperfine tensor with (a) zero trace (purely dipolar
hyperfine interaction) and (b) A150 at 0. The bottom parts illustrate the procedure for

determining A“ and Al. (From Ref. 12)

 

 

 

by a particular dipolar interaction, e. g, large g anisotropy or pronounced hyperfine
anisotropy of one nucleus, single-crystal-type ENDOR spectra can be recorded from
powders with randomly oriented paramagnetic species. By using appropriate EPR field
settings orientation selection of paramagnetic species can be performed and the hyperfine
tensor components of other nuclei can be detected relative to the tensor axes ofthe
dominating interaction. In the absence ofa dominating dipolar interaction no orientation
selection in an ENDOR experiment is possible and a powder-type spectrum is obtained.

The ENDOR absorptions are spread over the range ofthe hyperfine coupling values with

some buildup of intensity at three values corresponding to those paramagnetic species
that have one of their respective principal axes oriented along the magnetic field (i. e., at
canonical orientations). Ifthe hyperfine anisotropy pertaining to the nucleus is small,

narrower and stronger powder ENDOR signals are obtained. Thus, for an or proton that is

bonded directly to the sp2 hybridized carbon of an organic rt radical the anisotropy

amounts to about half of A150 and the principal hyperfine tensor values occur near
1/2Aiso, A150, and 3/2Aiso- On the other hand, B-protons whose hyperfine tensor has
approximately axial symmetry with anisotropy amounting to about 10% of A150 exhibit

quite strong ENDOR lines in disordered solids. l 1)

Another feature in the ENDOR spectra of most solid disordered systems is the
matrix line occurring at the free nuclear Larmor frequency. It is due to a remote, purely
dipolar interaction between an unpaired electron and surrounding magnetic nuclei in the
matrix. This interaction is averaged to zero in liquids by the rapid tumbling ofthe
paramagnetic species. Hence, the matrix line can be used to probe the amount of
molecular motion as a function of the temperature as well as to compare the amount of
molecular motion in different phases and matrices at the same temperature. The
appearance of this line also depends on the magnetic nuclei in the local environment of
the unpaired spin. For example, ifa radical site is located in a protein structure, both
protons in the protein structure and the solvent molecules will contribute to a proton

matrix line.

46

I.4. Principles of the Electron Spin Echo Envelope Modulation (ESEEM)

Spectroscopy

Electron spin echo envelope modulation (ESEEM) technique of pulsed electron

paramagnetic resonance (EPR) is a powerful technique capable of measuring small
hyperfine couplings in systems with large inhomogeneously broadened EPR lines.3‘4-l3'

162446) The inhomogeneity in an EPR line originates from the presence of multiple
anisotropic interactions in the paramagnetic powder system. Due to these interactions the
electron is subjected to the effect of slightly different local fields which results in that
only a small fraction of the electron spins is at resonance at any given time. The
superposition of these spin packets yields the observed EPR spectrum, Figure I-13. The
inhomogeneous broadening of the EPR lineshape masks the details of the EPR spectra
and reduces the resolution to a few tens of gauss. The ESEEM spectroscopy circumvents
the inhomogeneity problem by directly recording the time evolution ofthe spin system
which allows observation ofthe individual spin packets. Unlike the continuous wave
(CW) EPR, which is a frequency domain spectroscopy, ESEEM is a time domain
technique based on the phenomenon of the electron spin echo (ESE). In ESEEM
experiments the spin system is probed by high energy resonant microwave pulses of
nanosecond-range duration while keeping the static magnetic field constant. The short
microwave pulses are able to excite only a small portion ofthe inhomogeneously
broadened EPR spectrum. The paramagnetic sample response to these pulses consists in
spontaneous emission of microwave energy, called the spin echo. The integrated intensity

ofthe echo is measured as a function ofthe time separation between some ofthe pulses.

47

Ann-A-" . 2541‘.“-

(a)

 

 

 

 

AB a’“\
0 // \\
\\
/ \\
/ \
/ \
l/ \\
’ \
./ L
B0,av g
(b)
(”0

«>1 l mi
“1111.

 

 

 

Figure I-l3: Inhomogeneously broadened EPR lineshape (total linewidth 10 to

10000 gauss). (a) BO,avg is the mean value of the resonant magnetic field. B0 is the
linewidth of the portion of the spectrum excited by a microwave pulse. (b) The

individual spin packets (linewidth of the order of 10'3 gauss) have magnetization

components precessing independently of each other at frequencies (oi, coo, (oj.

 

 

48

“may: rule‘s—(Com

The superhyperfine interactions manifest themselves as modulations ofthe electron spin
echo envelope whose periods are related to the nuclear magnetic resonance (NMR)
transition frequencies of the sample.

In this Section a semiclassical picture ofthe different ESEEM variations for an S
= 1/2, I = 1/2 spin system will be given, followed by a quantum mechanical description

of the ESEEM experiment.

1.4.1. Pulses of microwave radiation and their effects

When a paramagnetic material is placed in a static external magnetic field B0

along the z axis ofa laboratory coordinate system, the magnetic moments associated with
the individual spins obtain preferred orientations, precessing around the axis of the

external field at angular frequency (.00. The precession cones are oriented either parallel
(spin 0t) or antiparallel (spin [3) with respect to Bo. For electrons the B spin state has

lower energy than the or spin state, therefore, higher population (according to
Boltzmann's law). Because of the population difference, the superposition ofindividual

magnetic moments results in a total macroscopic magnetization M, parallel to B0. In an

ESE experiment a linearly polarized oscillating microwave electromagnetic field, whose

magnetic component, B], is perpendicular to the static magnetic field B0 (1. e., along the

x axis of the laboratory coordinate system), is applied at frequency to during the pulses

(Figure 1-14):

Bx(t) = 2 B] cos(w t). [1-46]

49

 

 

 

 

*— 2/ip —*‘* V

V
p

A,

 

 

Figure l-l4: (a) A microwave pulse is a burst of monochromatic microwave

radiation of duration tp. (b) The frequency spectrum of a pulse gives the spectral

 

density of the field at the sample. (From Ref. 3) J

 

It is most useful to analyze the effect ofthis linearly polarized oscillating field by

decomposing it into two circularly polarized components, B, and B], that rotate in the

plane perpendicular to B0 in directions opposite to one another (Figure I-15):3’27)

B,. = B1 [x cos(m t) + y sin((o t)], [1-47a]

3] = Bl [x cos((1)t)- y sin((o t)]. [I-47b]

50

 

‘Im

Since one component (e. g, Br) rotates in the same sense as the precession of the electron
spins and the other in the opposite sense, near resonance (to E (00) the counter-rotating

component will have little effect on the resonance experiment and will, therefore, be

neglected.

The time dependency of B 1 can be eliminated by introducing a coordinate system
XYZ, rotating about the axis ofthe laboratory static field Bo at angular frequency (1)

equal to the carrier frequency of the pulse. In the rotating reference frame B] will be

 

 

 

 

Figure 1-15: Decomposition ofa linearly polarized oscillating magnetic field, Bx(t),

into two counter-rotating circularly-polarized components, Br and B].

 

 

 

”“mm.s

static. Its direction will be taken to define the X axis in the rotating frame, thus B1 = B]
x. Since the axis of rotation coincide with the direction ofthe laboratory field, B0 will
also be static in the rotating frame, directed along the Z axis. In the absence ofBl the
magnetization in the rotating coordinate system appears to precess about B0 at a
frequency ((00 - (1)) corresponding to a magnetic field of magnitude ((00 - m)/y and
direction along the Z axis. The combination of the microwave field B l and the laboratory

field 2(m0 - (n)/y yields an effective magnetic field

B = B1 x + [(0)0 - (D)/(DO] B0 2. [1-48]

When the microwave pulse is applied for a period oftime tp the effective magnetic field

torques the magnetization M in the reference frame as described quantitatively by the

fundamental Bloch equation:

dM
71}— - 7(13 x M). [1-49]

The result is a precession ofthe magnetization about B at a frequency yB. At exact

resonance, B = Bl = B 1 x., and the magnetization precesses about B] at angular
frequency 031 = yB]. The magnetization before and after the microwave field is switched

on is obtained by solving the Bloch equations that describe the time dependent behavior

52

of the magnetization. At time t = 0 when the microwave field is switched on, the

solutions are

M2 = M0 cos((o1 t) [1-50a]

My = M0 Slfl(0)] t), [1-50b]

where (01 = 7B] and M0 is the magnitude ofthe magnetization at thermal equilibrium (1.

 

e., at time t = 0 when the magnetization has been aligned with the Z axis and microwave '
field has not been applied yet). These solutions describe a circle in the YZ plane. At the

end of the pulse, t = tp, the components of the magnetization are

MZ(tp) = M0 COS(C1)1 tp) [I-SIa]

MY (tp) = M0 sin(tol tp). [1-51b]

If the duration and the power of the microwave pulse are selected such that (1)11 = rt/2

P

then

MZ(tp) = 0, MY (tp) : M0~ [1'52]

indicating that the magnetization has been rotated by rt/2 and lies, with its entire

equilibrium value, along the Y axis. Applying a rt pulse, for which toltp = rt, yields

53.

Mzttp) = - Mo. My up) = 0. 11-531

meaning that the magnetization has been wholly aligned along the -Z axis.
In pulsed EPR techniques, short pulses (tens of nanoseconds) are necessary,
which make possible neglecting the effects of electron spin relaxation while ensuring a

reasonable spectral width. Generation of a rt/2 pulse of duration 10 ns requires a

microwave magnetic field equal to about 9 gauss.3) This represents a large amount of

microwave power, which is difficult to achieve. On the other hand, a microwave pulse of

finite length can excite only a portion of the inhomogeneously broadened EPR line. The

excitation bandwidth is inversely proportional to the pulse duration tp, Av = 1/tp. Hence,
a specific flip angle can be achieved by either increasing tp and simultaneously
decreasing B1 (decreasing the microwave power), thus exciting a wider portion of the
EPR line (making the pulse more selective); or vice versa, decreasing tp and
simultaneously increasing B1, thus making the pulse less selective. However, in the latter
case values oftp and B] are subjected to limitations imposed by the technological

difficulties associated with fast switching of large microwave powers.

1.4.2. Two-pulse electron spin echo

In the simplest ESE experiment, a two-pulse sequence (denoted as rt/2 - 'c - rt - t)

is employed to generate a spin echo, Figure 1-16. The duration tp and the amplitude of the
pulses are chosen so that the flip angle 0 = 0311p is 90° for the first pulse and 180° for the

second pulse. 1f the time interval between the pulses is t, the echo is observed at time t

54

afier the second pulse. The plot of the echo intensity as a function oft shows an overall

decay of the electron spin magnetization (characterized by the phase memory time, TM or
T2*) that is modulated by the electron-nuclear hyperfine interactions.

A vector diagram for the two-pulse experiment is depicted in Figure 147.26)

Following the first pulse, the magnetization is brought into the plane perpendicular to z

 

 

 

echo ampl. (a.u.)

 

I (usec)

 

Figure 1-16: Two-pulse electron spin echo sequence and an exemplary two-pulse

ESEEM time-domain data set collected for the Ni(III)(CN)4(HzO)2' complex in a

 

50% v/v water/ethylene glycol glass. (From Ref. 24)

 

 

55

_,_-_n ...n-‘~
.

axis. In the laboratory frame the magnetization rotates about 2 at angular frequency (130

but in the rotating frame it appears static. directed along the -Y axis. Because the
individual spin packets (i. e., groups of spins that have different local magnetic
environments) precess at different frequencies, they will fan out in the transverse plane
during the free precession period t, which results in loss ofthe macroscopic
magnetization. During the time t spin packets that have precession frequencies larger

than 0.10 (e. g., spin packets labeled 2, 3 and 4) will accumulate positive phase angles with
respect to the -Y axis while spin packets with an effective local field weaker than 130 (e.

g., spin packets labeled 5, 6, and 7) will develop negative phase angles. Thus, the
presence ofinhomogeneities in the spin system is essential for the echo phenomenon. The
second pulse torques the magnetization of every spin packet about the X axis through an
angle of 180°. Since the original angular frequencies and directions of precession ofthe
individual spin packets remain unaltered. the spin packets rephase into a microscopic
magnetic moment along the Y axis after time I following the second pulse. Refocusing of

the magnetization results in an emission of microwave radiation by the sample and is

called the spin echo.

1.4.3. Three-pulse electron spin echo (stimulated echo)
The three pulse sequence (rt/2 - t - rt/2 - T - rt/2 - t) creates a stimulated echo at
time t after the third pulse. Figure 1-18 shows the vector diagram for the 3-pulse

experiment.26) The first pulse rotates the magnetization about the X axis so that it

becomes aligned along the -Y axis. This is followed by dephasing ofthe magnetization in

56

 

 

Figure I-l7: Vector diagram illustrating the formation of the two—pulse electron spin
echo. (a) two-pulse electron spin echo sequence; (b) at thermal equilibrium the

magnetization M is aligned with the external magnetic field B0; (c) the first (rt/2)

pulse has torqued M onto the XY plane ofthe rotating frame; (d) M is a
superposition of spin packets that dephase due to the differences in their precession
frequencies; (e) the second pulse rotates the spin packets about the X axis through
angle rt. The direction of precession of each spin packet is conserved. (f) the

individual spin packets refocus along Y to reform M, thus generating an echo. (After

Ref. 26)

 

 

n0 n

 

 

 

0H 4——> i

 

 

 

 

 

’1' T

i=0-

c AZ d ‘2
(DOKJ wOK/f

Y
A ,
'4, X

t=0+ t=T

e 1‘ z r l 2
010K.) moKJ

 

 

 

t=21
Figure 1-17

58

 

 

Figure 1-18: Vector diagram illustrating the formation of the three-pulse electron spin
echo. (a) three-pulse electron spin echo sequence; (b), (c) same events as in Figure 1-
17; (d) the second rt/2 pulse converts the transversal magnetization into a longitudinal
one; (e) the magnetization components precess about Z; (f), (g) the third rt/2 pulse
rotates the surviving magnetization components (directed along Z) onto the XY plane;

(h) the spin packets refocus along Y to reform M, thus generating a stimulated echo.

(After Ref. 26)

 

5‘)

 

 

 

 

 

 

 

 

 

 

 

Figure 1-18

60

 

 

t = 21+T

awn

 

m1

 

the transverse plane as described above for the primary echo. The second pulse rotates
the Y components of the dephased magnetization by 90° storing them along the -Z axis

during the waiting time T. Ifthe free precession period T satisfies the condition T2e << T
< Tje , where T2e and Tle are the transversal and longitudinal relaxation times ofthe

electron, respectively, the magnetization in the transverse plane will fully decay during

the free precession period T and only the longitudinal magnetization MZ will survive.

The third 90° pulse transfers this polarization pattern to magnetization in the XY plane,

which, after time 1 following the third pulse refocuses along the Y axis, yielding the

“'1'?"

stimulated echo. It should be noted that owing to the incomplete refocusing of the

magnetization vectors, the stimulated echo has a "diffused" magnetization pattern, which

reduces the intensity of the echo to about half the intensity of the two pulse echo. 14)

1.4.4. Four-pulse electron gpin echo

The four pulse sequence (rt/2 - t - rt/2 - t1 - rt - t2 - rt/2 - t) utilized in the
HYSCORE experiment (cf. Chapter III) is essentially the stimulated echo pulse scheme
with an additional rt pulse inserted between the second and third rt/2 pulses. This
additional pulse inverts the magnetization, while interchanging spin packets that belong
to the opposite electronic manifolds. This results in mixing, or correlating, hyperfine

frequencies that arise from the same coupling. Consider a spin packet denoted as 5M2

that lies along the -Z axis after the second rt/2 pulse, Figure 149.28) The rt (mixing) pulse

inverts 5M2 onto the +2 axis. The spin packet is rotated onto the -Y axis by the last rt/2

pulse, where it starts precessing about the Z axis. The different components refocus to

61

5M

 

 

 

 

 

.2
09
JZ
v ‘<
a
..<

 

 

ii'<

 

 

 

 

 

Figure 1-19: Vector diagram illustrating the formation ofthe four-pulse electron

spin echo. (a) after the second rt/2 pulse the magnetization 6MZ associated with a
particular spin packet is brought along the Z axis; (b) the it pulse inverts 6M2; (c) the
fourth (rt/2) pulse rotates 5MZ onto the XY plane; (d) spin packets start precess

about Z; (e) during a time period t after the last pulse various spin packets attain the

position shown, which creates the echo along the -Y axis. (After Ref. 28)

 

62

 

form an echo after a waiting period t, following the fourth pulse.

1.4.5. Origin ofESEEM
The origin ofthe modulation phenomenon can be qualitatively understood by
introducing a semi-classical description combining the classical vector model of echo

formation with the quantum mechanical treatment ofa simple anisotropic system

consisting of one electron coupled to a spin 1/2 nucleus.24) The spin Hamiltonian of such
system consists of electron Zeeman, nuclear Zeeman, and electron—nuclear hyperfine

interaction terms:

H/h=ms SZ+AZZ sZ 12+AxZ sZ lx-to] 12, [1-541

where AZZ = A = A“ cosz(0) + AI sin-2(0), Ax2 = B = (AH - AI) cos(0) sin(0), 03S =g “B
B0 / h, and to] =gn “Bn B0 / it. A“ and A1 are the principal values of an axially
symmetric hyperfine tensor that can be described in terms ofa Fermi contact coupling
Aiso and a traceless dipole-dipole coupling term, T = g gn 11B “Bo/r3» with A” = Aiso
+2T and Al = Aiso - T. The angle 0 describes the orientation ofthe principal axes ofthe
hyperfine tensor with respect to the laboratory field B0. The remaining terms have their

usual meaning. Eigenvalues and eigenvectors ofthe above Hamiltonian can be obtained
easily after constructing the Hamiltonian matrix in the uncoupled basis set consisting of

electron and nuclear spin product states, |MS, MP. The diagonalization can be managed

 

independently for the two electron spin manifolds since the only term in it that gives rise
to off-diagonal elements is that involving Ix. The results are summarized in the energy
level scheme of Figure 1-20, where tog = (110 and the normalized probability amplitudes

for the EPR transitions are given by

 

Ia> = cos(r1/2)|++> + sin(ri/2)|+->

 

 

 

 

'° 1 i A, ............
lb) H i i ‘ a l lb>=-Sin(n/2)|++>+COS(n/2)|+->
Elul EIVI EIVI iiui ms
lC> * i j i ll c>=cos(§/2)l-+>+sin(§/2)|-->
5 E 0013 ..... 1!...
l r

 

ET.
V

 

ld> = -sin( E./2)l++> + cos(§/2)|-->

w, = [(0), - A/2)2 + 82/4]”2

wt; = [001+ A/2)2 + 132/41“2

 

 

 

Figure 1-20: Energy-level diagram for an S = 1/2, I = 1/2 spin system described by

 

the Hamiltonian oquuation [1-54].

 

 

 

64

‘5'

t
l
i
l
b

 

 

 

 

<b S, c> f - 7
|u|=2 l -‘l =sinl” él [L553]
gHBBi 2 1
<a S c> _
|v|= 2——|—y—B‘——:cos[”2§] [1-55b]
£11131

The angles 11 and 8, define the axes of quantization for the or and [3 spin manifolds,

4."
respectively, and are given by sinm) = B/2wa and sin(§) = B/ZmB. In general, due to the
anisotropic nature ofthe electron-nuclear spin interaction, which mixes the nuclear spin !
states all four ofthe possible EPR transitions for the S = 1/2, I = 1/2 spin system are i

allowed. They can be excited coherently in a pulsed EPR experiment, provided that the
microwave pulses have sufficient bandwidth. Thus, the microwave pulse bandwidth
places an experimental constraint on the ESEEM experiment. The quantum mechanical
effect that is responsible for the nuclear modulation phenomenon is the so called
"branching oftransitions", i. e., the fact that the microwave pulses can induce transitions
that start at one energy level but end at more than one distinct levels. The semi-classical

picture illustrating this effect is shown in Figure 1-21. The microwave frequency (.00 is
taken to be equal to (”S ofFigure 1-20. The four partially allowed transitions are labeled

A, B, (7, and D. The discussion will focus on transitions A and C. After the application of
the first rt/2 pulse, the transverse magnetization that corresponds to transition A has fallen

behind the frame precession (since toA < (110). Thus in the rotating frame, spin packet A
has acquired a negative phase with respect to the Y axis, ((DA - w0)t, during the free

p[.5-ce’ssion period t. In a two-pulse experiment. the second pulse not only torques the spin

65

 

 

Figure 1-21: Vector model showing the interference between electron spin packets
that result from transition "branching" in a two-pulse ESEEM experiment. The upper
left insert represents the energy-level diagram of Figure 1-20, while the upper right
insert shows the spin packets across the inhomogeneous line. (a) after the first pulse

spin packet A precesses in the XY plane at frequency 03A < (00 acquiring phase (01A -
w0)t during time t; (b) the second pulse flips spin packet A about X and induces its
branching into two portions that precess at frequencies to A < mg and 03C > (110 ; (c)

spin packet A is refocused along Y contributing fully to the spin echo, while spin

packet C is refocused at an angle 0 = (03A - 03(7)t with respect to Y, giving a

 

jiomribution to the echo weighted by cos(0).

66

 

‘T‘H

‘- 't' 1. -

 

 

 

rt pulse _ y/

 

 

 

(Dc

 

Sea/x
k/

 

C

/

t=2t

A

C0C
Y 0
r K

 

Figure l-21

 

 

packet A by 180° about X, but since it excites all transitions simultaneously, it will induce

"branching" ofA into two portions, precessing at 03A and (or. Because the new spin
packet C has a precession frequency larger than too, it will precess in the opposite
direction from the packet that maintains the (DA precession frequency. Hence, while the

spin packet A refocuses wholly along Y axis after time t following the second pulse, spin

p
packet C will be at an angle (to/1 - (1)(~)t with respect to Y axis. Both "branched" portions, L
A and (.7, will interfere with the echo formation. however to a different extent depending ‘1

I
on the projection ofthe "branched" spin packet onto the Y axis. While packet A L

contributes fully to the echo, the contribution ofC is reduced by COS[((DA - coat] =

cos(mat), where (11a is the NMR frequency in the |a> electron spin manifold (the

difference between levels |a> and lb>), and weighted by the probability for "branching", k
(the fraction of the magnetization split from spin packet A upon the second pulse). It is
evident that the maximum contribution ofthe magnetization vector ofthe C spin packet is

obtained only if((oA - (D(")‘[ = 2rtn, for n = 0, 1, 2, Therefore, the modulation of the

echo envelope as a function oft will be given by

Emod“) = l - k cos(ooat), [1-56]

Thus the echo amplitude as a function oft will be modulated by the frequency ma and

will depend on the extent of "branching" k (the modulation depth). The same reasoning

[70 [£15 for all other combinations of spin packets formed by branching oftransitions. For

68

   

 

 

instance, the pair of transitions B and D will result in (DB being a modulation frequency as

well.

The detailed quantum mechanical treatment outlined later shows that for a S =
1/2, I = 1/2 spin system the primary echo is modulated at the fundamental hyperfine
frequencies (1)0l and mg, as well as at their sum and difference combinations, ma +

r
(9,329.30) ,

Emod(t) = l - (k/4){2 - 2COS((1)a‘t) - 2cos((opt) + cos[(toa + (DB)T]

+ cos[(toCl - wB)t]}. [1-57]

The modulation depth parameter, k, which is related to the product of the transition

probabilities, |ul2|v|2, for the two different EPR transitions associated with "branching" is

given by
k = sin2(r] — 25,) = [ij/(mawfiflz. [1—58]

The modulation frequencies can be resolved by Fourier transformation of the echo
envelope function. It should be pointed out that since the combination frequencies have
opposite phase to the fundamental ones (cf. Equation 1-57), negative components can also

a p p ear in the two-pulse ESEEM spectra. The Fourier transformation is usually preceded

by a dead-time reconstruction procedure, according to the algorithm given by Mims,3 l)

[a fgduce the lineshape distortions introduced by the spectrometer dead-time (ca. 150 ns).

69

 

 

 

 

The experimentally observed ESEEM function can be represented as a product of

the quantum mechanically derived modulation fiinction, Emod(T)~ and a decay function,

Edeeavfi), that describes the loss of magnetization due to spin relaxation:
E(t) = Edecay“) Em0d(‘t) . [1-59]

Edecav“) is usually modeled with exponentials ofthe type exp(-t/t0)“, where n = 1, 2, or

U232) In the two-pulse ESEEM, the magnetization decays in the transverse plane,
primarily due to the spin-spin relaxation characterized by the (homogeneous) relaxation
time, T2* (TM), which is of the order of 1 us for most systems ofinterest. The rapid
background decay broadens the peaks and reduces the frequency resolution of the two-
pulse ESEEM measurement. A fiirther complexity of the ESEEM experiment is added
when N nuclei that are coupled to a single paramagnetic center contribute to the
modulation pattern. In this case, the modulation function is a product of modulation

functions for the individual nuclei,l6~.24,33.34)

N .
5(7) = Edeea}, (1)1] E“) d (1). [1-60]

mo
1:]
The result oftaking the product of functions E(l)m0d(t), each of which is given by
Equation 1-57, will contain not only the fundamental (AMI = i l) frequencies and

b i nation fre uencies for h ' ' '
”0,77 q eac nucleus, but also frequenc1es that are combinations of

70

 

 

the frequencies arising from different nuclei. Therefore, the two-pulse ESEEM data (or
the corresponding ESEEM frequency spectrum obtained from Fourier transformation of
the time domain data31) may become very complex even when only a few nuclei
contribute to the echo modulation.

The product rule, Equation 1-60, is the basis of an approach to analyzing complex
ESEEM data. The contributions from various nuclei are sorted out by isotopically
substituting one nucleus, then dividing the ESEEM functions for the original (non- i
labeled) and isotopically substituted sample. Since the modulation function of several
nuclei is the product ofthe modulation fiinctions of the individual nuclei the division of L
the modulation functions for both samples cancels out all individual nuclei functions,
except for the modulation functions ofthe two isotopic nuclei. For example, the ratio of
the ESEEM fiinctions for a sample in which one hydrogen is replaced by deuterium and

the ordinary (non-labeled) sample is given by
Edivtr) = EDm/EHo). [1-61]

Due to the lack of nuclear quadrupole interaction of H (I = 1/2), EH(t) features very
small modulation depth compared with ED(t), so Ediv(T) to a very good approximation is

identical to the deuterium modulation function, and can be analyzed by numerical
5 i m ulations. Although this rule is strictly correct only for two-pulse single-crystal
ESEEM, it has also been found applicable to disordered samples. An application ofthis

approaCh is outlined in Chapter II.

71

 

k

 

The problems ofthe increased complexity and decreased frequency resolution of

the two-pulse ESEEM experiment, which complicate the data analysis, are alleviated in
the three-pulse ESEEM experiment. In the 3-pulse ESEEM t is kept constant and the
amplitude ofthe spin echo is measured as a function ofT (or, equivalently, T + t). The

explicit form ofthe three-pulse envelope modulation function in the case ofa S = 1/2, 1 =

1/2 spin system 157-930)

Em0d(‘t, T) = I - (k/4){[l - cos(wat)] [I - cos(mfit + wBT)]

+ [l - COS(0)BT)] [l - COS(CL)aT + maT)]}. [1-62]

This equation shows that only the fundamental hyperfine frequencies contribute to the
modulation, which leads to simpler spectra in the three-pulse ESEEM. Since the
background decay for the three pulse sequence is governed by electron spin-lattice
relaxation, electron cross relaxation, and nuclear spin-spin relaxation, all of which are
characterized by relaxation times much longer than the electron spin-spin relaxation time,
the modulations extend over longer periods. This fact results in better resolution in the
frequency domain for three-pulse ESEEM spectra than for two-pulse ESEEM spectra.
Equation 1-62 also shows that because the stimulated ESEEM function depends on T as a
parameter, it is possible to enhance or suppress certain frequencies by varying t. This
effect, known as the t-suppression effect, is useful in making spectral assignments. lt
m3,V lead to blind spots in the three-pulse ESEEM spectra. which may yield lineshape
diS tortion in disordered systein525-3O~35). The product rule for the overall modulation

[17” c t i on, when multiple nuclei are coupled to the paramagnetic center, is less complex

72

 

than in the case of the two-pulse experiment since the products are taken only between

the frequencies belonging to the same electron spin manifold24~25)

E- .(T) N . N .
———“““a’ ”Egi)od.a(T~T)+“Bigodfifi’n‘ ““631
j=l

i=1

15(1, T) =

1.4.6. Density matrix description of ESEEM

The density operator formalism provides a powerful method for calculating the
properties of ensembles in statistical mechanics36) It has proven especially usefiil to

describe the time evolution of ensembles of spins in magnetic resonance-322737) Here the

derivation of the modulation formula for the two pulse ESEEM experiment will be
outlined, following Mims.29) The same derivation steps are followed in Chapter 111,
where an expression for the two-dimensional echo envelope modulation effect in a four-
pulse spin echo experiment is obtained.

The state of the system described by the vector |‘1’(t)> can be expressed by an

expansion in terms of a complete orthonormal set of functions |¢k> with coefficients ck(t)

|‘P(t) >=ch(t)|d>k) [1-64]
It

The density operator, p, which describes the projection of one basis set onto another, is

given by

73

 

00) = l‘1’(t)><‘1’(t)lt [1-651
and the corresponding matrix has elements
[1-66]

Dij = <¢1lp(t)l¢j>.

The expectation value of an macroscopic observable represented by the operator O is

obtained in quantum statistics by taking an ensemble average over <‘PIOI‘I’>,
<0) = <‘P IOI‘I’) [1-67]
From Equations 1-64 - 1-67 it follows that
<O>(t) = Tr{ p(t)-O}. [1-68]
T h i 5 equation makes possible the calculation ofthe properties of ensembles, provided
t h at the density matrix is known. In an electron spin echo experiment the expectation

a l we ofinterest is the magnetization which is detected along the Y axis. Since it is

p r0 portional to the Y-component of the electron spin, Sy, the normalized echo amplitude

l S given by

74

 

 

"H

new." m; ’r‘

 

Tr{PESY}
E =————, [1-69]
Tr{PoSY}

where 9E is the density matrix at the time of echo formation and p0 is the density matrix

before the application ofthe pulse sequence.

The equation ofmotion for the density matrix can be derived from the time

dependent Schrodinger equation, and takes the form
(1 i
5pm = glp(t)fl(t)l, {1.70}

Where H(t) is the time dependent Hamiltonian ofthe system. Integration of this
differential equation allows determination ofthe density matrix at time If, p(tf), in terms

of the density matrix p(ti) at an initial time ti?
000 = eXPl- 1' HW- t11ml 0(11) eXPII' HW- tMr]- [1-711

Thus, the density matrix PE at the time of appearance ofthe echo can be obtained from
the initial, thermal equilibrium density matrix 90-

The system Hamiltonian consists ofa time dependent and a time independent

component,

H = H0 + Hm). [1-72]

75

 

The Hamiltonian H0 describes the static interactions such as the electronic Zeeman,

nuclear Zeeman, electron-nuclear hyperfine, and nuclear quadrupole interactions

H0 = HeZ + Hmz + HHFi + ”Norm [1-731

zep-

if] is the portion ofthe total Hamiltonian that describes the interaction ofthe spin system

with the microwave resonance field.

WHO-“sh“.uonnn

The trace Tr{pSy} is obtained by first taking the sum over the loq> and lBj> states

of each quantized system, which yields the envelope modulation function, then summing
over the systems that make up the inhomogeneously broadened EPR line, which gives the

form of the spin echo signal, Figure 1-22. These two summations can be carried out

independently, ifthe distribution of values of H0 .

“or = Haav + “(or . [1-74]

about a mean value, Home is such that the spread in the inhomogeneous shifts, AHQk, is

large compared with the hyperfine interlevel spacings within each ofthe 0t and [3 electron

Spin manifolds. Another assumption is that AHQk only varies the spacing between 0t and

B eleCtron spin manifolds but does not cause an inhomogeneous distribution ofthe

'"IerVais within each manifold.

76

 

 

°"> ll 1 I

 

 

 

 

 

 

 

 

 

”3? i W __L_

 

 

Figure 1-22: Energy levels of a spin system and transitions involved in the

generation of electron spin echo signals. The resonance field at frequency w is able

 

 

to induce transitions in all intervals (Da’i - (DB j'

 

 

To calculate pE the integrated form of the equation of motion, Equation 1-71, is
applied to the successive periods (tf - 11) of nutation and free precession that make up the

Spin echo sequence, Figure 1-23. In the case of a S = 1/2 spin system the calculation can

be performed in terms of submatrices for the or and B electron spin manifolds. For the

free precession portions of the echo experiment, it = H0 , i. e., there is no time

dependency in the Hamiltonian, and the solutions of Equation l-70 can be obtained in a

S'mDIe form. In the representation that diagonalizes HO the transformation matrices

77

a Primary
TI/2 7t Spin Eclio

 

 

 

Stimulated
/2 Spin Echo

iiii hhe

T tpir T tp111 T +1

 

 

tpj

Stimulated
Tt/2 71/2 “it Spin Echo

Jill llJL

>‘———‘——"<——>
tpi T tpii t1 tp111 t2 tpiv T+I

 

 

 

 

 

 

 

 

Figure 1-23: Various electron spin echo pulse sequences. Each sequence consists of
Successive periods of nutation and free precession. (a) two-pulse sequence, rt/2 - t - rt
‘ T; (b) three-pulse sequence, rt/2 - T - rt/2 - T - rt/2 - t; (c) four-pulse sequence, 1t/2 - t

-rt/2-t]-rt-t2-rt/2-t.

X

 

expli i H0(tf- ti)/l1] are diagonal with elements exp[i 030_i(if- ti)/lr], exp[i wBiUf- ti)/l1].

ConSequently, the transformation results in the off-diagonal elements ofp being

78

 

 

A...
v 15.8 n - v. 0 ,

multiplied by phase factors exp[i (tom - ijxtf‘ li)/ll], where (”at and (ij are the nuclear

transition frequencies in the (1 and B electron spin manifolds, respectively.

During the pulses the system evolves under the influence of both H0 and Hj(t).

The interaction ofthe spin system with the magnetic component ofthe oscillating

radiation field is given by the time dependent Hamiltonian

H10) = 2 RN cos((o t) = HN [exp(i to t) + exp(-i to 0], [1-75]

where (D is the frequency ofthe oscillating field and the Hermitian operator HN consists

0f the singled-out time independent factors that connect states from different electron

 

Spin manifolds. 1n the basis consisting of states |a>, 61>, (i. e., in the He] + HnZ

representation) the matrix ofthis Hamiltonian can be partitioned into four submatrices,

la? |l3j>
0 RN exp(-i(o t)
t = . 1-76
H“) Hg] exp(iwt) 0 [ ]

The time dependency can be removed from H] by the following similarity

tranSformation (which is equivalent to introducing a frame rotating about 2 at angular

freCluency to):

H] = exp(i (1) :2 t/2) H10) exp(-i (r) 22 U2). [1-77]

79

IA! ..

 

The matrix 22 has the meaning ofthe operator 82. It is composed (in submatrix form) of

identity matrices I of dimension equal to the number ofthe nuclear spin states (i. e., equal

to 21 + 1, where I is the nuclear spin)),

1 o
zz—[O 4]. [1-78]

Substitution of Equations 1-76 and 1-78 into Equation 1-77 givesz9)

[1—79]

H1: 0 <ailHNlBj>
<BjIHN+Iai> 0 ‘

After applying analogous transformations to H0 and p the whole problem is restated in

the rotating frame of reference.

The appropriate rotation operators (propagators) for the nutation period p (of

duration tN,p) and the free precession period 1 (of duration t1 ) are then expressed as

RN,p = exp[i (H0 + %1)tN,p/h]i [1-80]

Rt.l = exp[i H0 tj/li]. [1-81]

consecutively, the evolution ofthe density matrix can be cast in the form

80

pE = R" 00 R, [1-83]

where the general operator R is composed of products of RNp and Rt! for the different

nutation and free precession periods ofthe spin echo sequence. Since H0 and H] are

Hermitian and RN,p and Rt! unitary operators (R‘1 = R+), pE can be written out as

pE = R+ p0 R. [1-831

H#&----‘- I I . fl

The initial density matrix p0 describes the spin system at thermal equilibrium in an
applied static field B0. It is diagonal in the representation which diagonalizes $2, with
elements given by the Boltzmann populations piio. With the assumption that the initial
Boltzmann populations of all sublevels in a given electron spin manifold are the same, p0

can be written out using the submatrices pa0 = a], p30 = bl as

0
p 0 a] 0
p0: °‘ 0 = _ [1-84]
0 pl3 0 b]

The rotation operators can also be written in terms of submatrices for the or and [3

electron spin states. Thus, the free precession operator, which contains only the static

(HO) Hamiltonian is

81

Pt.l O
Ru = ' . [1-85]

while the nutation operator is expressed as

T U
Rsz Np Np. new
i VN,p WN‘p
The diagonal matrices P and Q for the free precession have elements
(PJ-th = exp[ I' ( coal- - co/2 )t] ], [1-87a]
(ij)t.l = exp[ i ( mm + 0V?- )111- l1-87bl

P and Q are influenced by the inhomogeneous broadening term, AHOk as they are
related to the static Hamiltonian H0. 1n the Hal + Hmz representation AHOJ< is given

by the diagonal matrix

 

HM : hAmk [I 0 ] . [1-88]

Hence, the nuclear sublevel shifts Awk generated by the inhomogeneous broadening term
appear as part ofthe NlV[R frequencies (our (”Bi As a result, scalar factors ofthe type

exp(iAwk) are introduced into P and Q and, subsequently, into PE and the modulation

82

 

function B. When accumulated over the inhomogeneously broadened line, these phase
factors give rise to free induction signals that appear immediately after a pulse and last
for a relatively short time. However, they do not contribute to the modulation of the
electron spin echo. It is therefore permissible to keep only those matrix product terms in

the trace Tr{ pESY}, in which the scalar factors cancel out upon carrying out the

multiplication ofthe rotation matrices.29)

A major simplifying assumption in the Mims approach to deriving the echo

modulation function is that H0 << H], which is analogous to the common assumption
that the excitation bandwidth VH1 is much larger than the EPR linewidth. It should be
noted, however, that the condition H0 << H1 is not always satisfied since some of the

matrix elements in H] may be small due to the partially forbidden nature ofthe
transitions concerned. With this assumption, however, it is relatively simple to obtain the
nutation matrices RN43» or, equivalently, T, U, V, and W. Since H0 << H], RN,p = exp(i
HltN’p/h), and the inhomogeneous broadening term AHOJ< does not appear in the

nutation matrices.
It is convenient to carry out the nutation matrix manipulations in the

representation in which H0 is diagonal (the "interaction representation").29) In a basis of

vectors IMS, M]>, where M5, M1 are the electron and nuclear magnetic quantum numbers

(i. e., in the representation of the combined electronic Zeeman and nuclear Zeeman

interactions) the Hamiltonian H0 is block diagonal. The unitary transformation that

completely diagonalizes H0 is represented in submatrix form as

83

HOD: 0 M+ Roi 0 MB] [1-89]

where Mon and MB are unitary matrices of dimension (2] + l), which describe the state

mixing caused by the hyperfine interaction in the 0t and B electron spin manifolds. Thus,

Ma and MB are the matrices diagonalizing the blocks ofthe block-diagonal Hamiltonian.

1n the interaction representation H] and Sy take the form

 

th 0 M

= , 1-90

5 —i O 'M [191]
Y 2 M+ 0 ’

where M = Ma+MB is also a unitary matrix. The above form for H1, along with the

assumption H0 << H], leads to major simplification in the nutation matrices. The

operator RN43 = exp(i Hlle/h) can be expanded to yield

 

_ 1 O . O M _ 7
RN,p — O l cos(mNtN‘p/2)+I M+ O sm(u)NtN.p/,_). [1-92]

The submatrices T, U, V, and W then take the form

84

-:-. ¢-‘

“.5 r 1““; -7'"_

TN,p = WN,p =1COS( CON tN‘p/Z ) , [1-933]
UNI) = i M sin( ‘DN tN,p/2 ) , [I-93b]

VN,p = I'M+ sin( (9N tN,p/2 ) . [I-93c]

Thus, given a specific spin system Hamiltonian, H0, the echo amplitude can be

obtained with the above free precession and nutation matrices for any particular spin echo

sequence.

For a two pulse sequence PE at time 2t + t, where t is a variable time after a

waiting period 1’. following the last pulse, is evaluated according to

PE = Rt+t+ Rm]+ R5" RNJ+ Po RNJ Rx RN," Rt+t~ [1-94]
with
R T] U' [1 95 ]
z - a
N] v] w]
T U
Run =[ n n] [1-95b]
’ V11 W11
R _ PI 0 1 96
T — 0 Q1 , l ' a]

85

P 0
I“ l , [l-96b]

R 2
1+1 l0 Qt+t

and p0 defined by Equation 1-84. The evaluation of Tr{pESy} by multiplying matrices

given by Equations 1-84, 1-91, 1-95, and 1-96 results in a sum of sixteen product terms.

 

However, the phase factors associated with inhomogeneous broadening cancel out in only FT:
four ofthem. The phase factor cancellation constraint requires that, for a term to be '
retained in the sum, each occurrence ofa matrix P in the product must be accompanied

by the presence of either a corresponding matrix Q or the adjoint of P, P+; and, i

conversely, each occurrence of a matrix Q must have a corresponding occurrence of an

appropriate matrix P or the matrix Q+. For example, the term

Qt+t+ Wu+ 01+ U1+ Pa0 TI 1’: T11 Pm M

which appears in the expression for the trace will lead to accumulation of positive phase
factors from the matrices QT+1+, QT+, PI, and PT“, and should be excluded from the sum.

On the other hand, in the term

Qt+t+ Un+ 131+ Tl+ Duo Ur Q: V11 Pm M

the positive phase factors introduced by QT+t+ and PTH are eliminated by the negative

factors introduced by PT+ and Q1. It is evident that exact cancellation of the phase factors

86

occurs when t :— O, i. e., the maximum ofthe echo signal is observed when the two pulses
and the echo are equally spaced. Therefore, t will be set to zero in the subsequent

considerations.

After elimination ofthe unwanted terms, the expression for the trace Tr{pESy},

 

l:
TripESY} : ’72 Tr{ ' Qt+t+ Ull+ PT+ Tl+ paO U] QT Vll PI+t M

+ l)IthJr Vll+ QI+ 1ler pao Tl Pt UII Qt+t M+

- Qt+t+ U11+ Pi V 1+ Pp” W1 Q: V11 Pm M w

+ pI+t+ Vll+ QI+ “11+ 9B0 VI PT Ull Qt+t M+i~ [1'97]

contains both product terms and their Hermitian conjugates. Combining each term with
its Hermitian conjugate and substituting matrices pao, p30, T, U, V, and W according to

Equations 1-84 and 1-93 one obtains the general expression for the (unnormalized) two-

pulse echo modulation function:

13(1) = (1/2) (a - b) sin(mN tpl) sin2(wN tpu/Z) ><
Tr{ Qt+t+ lVl+ Pt+ M Qt M+ Pt+t M

-Qt+t+ W P: M QT M+ PM M }. [1-98]

The normalization factor Tr{ p0 Sy} for the envelope modulation function is given by the

echo amplitude at t—>O and can be found by setting all free precession matrices P and Q

87

equal to the identity matrix]. Under these conditions the trace becomes Tr{l}, which
equals the number of hyperfine levels (i. e., 21 + 1, where l is the nuclear spin) in each

electron spin manifold. The normalized two-pulse echo modulation function is then

Enm = Tr{ ofifi W P: M QT M+ PI+t M

- om+ W P: M QT M+ PT+t M} /Tr{I}. [1-99]

For a four-level electron-nuclear system, Figure l-l7, described by the Hamiltonian given

by Equation 1-54, the unitary transformation matrix M has a simple form:

v u
M l j [1-100]
-U* V*
and the normalized echo modulation function takes the form

En(‘C) = M4 + |u|4 + |v|2|ul2 {2 cos(mat) + 2 cos(wBt)

- cos[(coOL - wB)t] - cos[(ma + wB)t]}, [l-lOl]

where ma = ma - 03b, COB = we - cod. The matrix elements lul and IV] that describe the

extent to which the branching transitions are allowed or forbidden can be determined by
applying transformations, which can be described as rotations ofthe electron and nuclear
coordinate systems. By diagonalizing the electron Zeeman and electron-nuclear portions

ofa general Hamiltonian H0 in the basis of eigenvectors ofthe electron spin operator SZ,

88

 

the electron z axis is rotated along the direction of quantization ofthe electron spin. The
nuclear spin coordinate system does not have to be the same as that for the electron spin.

It can be defined through the basis of eigenvectors ofthe nuclear spin operator 12, in

which the nuclear Zeeman term is diagonal. A rotation ofthe nuclear xy axes about the

nuclear z axis can be performed to eliminate the 1y term. One thus obtains the following

two Hamiltonians, whose combination is equivalent to the Hamiltonian in Equation 1-54,

‘Ha/h=co] 12+1/2A12+ V231,, [1-10221]

HB/h=w]12- 1/2A12- 1/2le. [1-102b]

The eigenfrequencies of these Hamiltonians are

03a = [(0)] — A/2)2 + (B/2)2]1/2 , [1-103a]

cup = [(w] + A/2)2 + (B/2)2]1/2 , [1-103b]

and the corresponding eigenvectors determine the transition probabilities, or the elements

ofthe transformation matrices M = Ma+MB ,

u = sin[(n - §)/2], [l-lO4a]

v = cos[(n - &)/2], [I-lO4b]

where n and i are defined by

89

tan(§) = B / (A + 2 (0]), [I-lOSa]

tan(n) = B / (A - 2 (01). [I-lOSb]

The product |v|2|u|2 defines the modulation depth

k = 4 |v|21u|2 = sian — a) = [mlB/(mampflz. [1-106]

After substituting u and v, Equation 1-104, in Equation 1-101 one obtains the final form of
the two-pulse echo modulation function for a S = 1/2, I = 1/2 spin system, Equation 1-57.
The Fourier“) or parametric38) analysis ofthe ESEEM time domain data reveals
information on hyperfine interactions that is identical to that obtained in an ENDOR
experiment. The two methods are often considered to be complementary to each other.
Because of the constraints placed on ESEEM by the requirements of nuclear state mixing
and microwave pulse bandwidth, the technique is generally more suitable for measuring
weak hyperfine couplings of nuclei with small magnetic moments. The ENDOR
experiments on such systems are typically difficult. Unlike in ENDOR, the amplitudes of
the lines in an ESEEM spectrum can be used to quantitate the number of nuclei giving
rise to an interaction once the coupling parameters have been determined.39‘41)
However, the ESEEM data are more difficult to analyze and often require computer
simulations to extract all ofthe information on magnetic couplings contained in the

spectrum. Part ofthe reason for the greater complexity ofthe ESEEM data analysis is

illustrated in Figure 124.24) Trace (a) shows the simulated powder ENDOR spectrum for

an S = 1/2, 1 = 1/2 system with an axial hyperfine spectrum. In this case the tensor

90

(a)

 

 

J l _J

O 2 4 6 8 10 12
frequency (MHz)

E (b)

 

l l l J l

O 2 4 6 8 10 12
frequency (MHz)

 

 

 

Figure l-24: Simulations of(a) powder ENDOR spectrum and (b) a three-pulse

ESEEM spectrum for an S = 1/2, 1 = 1/2 spin system. Parameters: g = 2.004, gn =
2.261 (311)), AH = 7.0 MHz, Al = 2.4 MHz, B0 = 3200 G; r = 200 ns; dead-time, 240

ns. (From Ref. 24)

 

9l

 

symmetry and principal values can be readily determined from the frequencies ofthe

turning points and lineshape singularities42) The corresponding ESEEM spectrum
displayed in trace (b) shows no lineshape features, because the intensity ofthe ESEEM is
determined by the product of the orientation dependent coupling parameter (which gives
rise to the classical lineshape seen in (a)) with the orientation dependent modulation
depth parameter, k. k goes to zero at the canonical orientations (the turning points and

lineshape singularities) because one of the EPR transition probability amplitudes,

 

u| or
M, becomes zero.43) Thus, the information on the hyperfine interactions is contained in
the frequencies, amplitudes, and dumping characteristics of the modulations, which

necessitates the use of computer simulations ofthe ESEEM data.

92

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Kevan, L.; Bowman M. K., eds, Willey-lnterscience: New York, 1990; Chapter 2.

. Feynman, R. P. Statistical Mechanics: A set of Lecture Notes, Benjamin: Reading,

Mass, 1972.
Abragam, A. The Principles of Nuclear Magnetism, Oxford University Press, 1961.

DeBeer, R.; Van Ormondt, D.; Punappel, W. W. F.; van der Veen, J. W. C., 1s. J.
Chem. 1988, 28, 249.

. Kevan, L.; Bowman M. K.; Narayana, P. A.; Boeckman, R. K. J. Chem. Phys. 1975,

63, 409.
Mims, W. B.; Peisach, J.; Davis, J. L. J. Chem. Phys. 1977, 66, 5536.

McCracken, J.; Pember, S.; Benkovic, S. J.', Villafranca, J. J.; Miller, R. J.', Peisach, J.
J. Am. Chem. Soc. 1988, 110, 1069.

Blinder, S. M. J. Chem. Phys. 1960, 33, 748.

DeGroot, A.; Evelo, R.; Hoff, A. J. J. Magn. Res. 1986, 66, 331.

Chapter 1]

CW-EPR, ENDOR and ESEEM Studies of PyruvatezFerredoxin Oxidoreductase

(PFOR) Reaction Intermediates

11.]. Introduction

PyruvatezFerredoxin Oxidoreductase (PFOR) belongs to the class of redox
enzymes. 1’2) Such enzymes are defined as those that catalyze a reaction with an associated
electron transfer event, wherein an external electron carrier is either reduced or oxidized.
Enzymes that belong to this group are termed oxidoreductases, reductases, oxidases, or
dehydrogenases, often for historical reasons. The main distinction between
oxidoreductases and dehydrogenases lies in the nature ofthe electron carrier that the
enzymes use. A characteristic of the oxidoreductases is the presence of metal-containing
centers, which are typically iron-based. These centers can either function directly in
substrate activation or, more typically, participate in the intra- and intermolecular transfer
of electrons to or from an external electron donor. In contrast, the dehydrogenases are
enzymes that make use of nicotinamide nucleotides as electron carriers. They usually do
not contain a metal center that undergoes a redox reaction. Both dehydrogenases and
oxidoreductases play role in the anaerobic fermentative metabolism.

In this Chapter an introduction to the 2-keto oxidoreductase enzymes is given.
followed by a summary ofthe general, structural and functional properties of PFOR and

the proposed reaction mechanism. The results ofa CW-EPR, ENDOR, and ESEEM study

96

ofthe PFOR reaction intermediates are presented and discussed with an aim of elucidating

some aspects ofthe reaction mechanism.

11.1.1. 2-Keto oxidoreductases
Common substrates in the anaerobic catabolism are the 2-keto carboxylic acids.
Enzymes known as 2-keto oxidoreductases catalyze the oxidative decarboxylation of 2-

keto acids with the transfer ofthe acyl moiety to coenzyme A (CoASH) as shown in

Equation II-1.2)

RCOCOOH + CoASH —) RCOSCOA + C02 + 2H+ + 2e‘ [II-l].

The electrons from this reaction are transferred to low-potential redox-proteins such as
ferredoxin or flavodoxin to be either disposed as H2 or included in an organic compound.
Four types of 2-keto acid oxidoreductases have been characterized and studied in
hyperthermophilic (i. e., microorganisms that grow at or above 900 C) and mezophilic
microorganisms?) They are classified and named according to the substrate used in their
purification: POR (pyruvate substrate),3~4) IOR (indole pyruvate substrate),5) VOR (2-
ketoisovalerate substrate),6) KGOR (2-ketoglutarate substrate).7) All 2-keto acid
oxidoreductases appear to be composed oftwo "catalytic units" of Mr ~ 120,000. In
enzymes from different sources a catalytic unit either exists as a single large subunit or
consists oftwo or four subunits?) For example, a single large subunit, denoted as subunit
A, constitutes a catalytic unit of mesophilic bacterial and eucaryotic enzymes. Mesophilic

archaeon Hm. halobiurn and hyperthermophilic IOR's have catalytic units consisting of

97

two subunits, ab. The catalytic unit in all other hyperthermophilic enzymes exists as a set
of aByb subunits. There exists homology between a and oz subunits and between b and B
or y subunits. The single subunit of the mesophilic enzymes also resembles the composite
subunit in the other enzymes in that it contains (1133/6 domains. All ofthe 2-keto acid
oxidoreductases contain iron-sulfur clusters and thiamin pyrophosphate (TPP), although in
different amounts. Typical TPP content is less than 1 mol per 120 kDa unit. The iron
content varies from 3.5 to 12 atoms per 120 kDa unit. The iron content has been found to
decrease upon exposure of the enzyme to oxygen due of the damage to the iron-sulfur
clusters by 02. Analyses of the 2-keto acid oxidoreductases by EPR spectroscopy have
indicated that the enzymes contain two or more [Fe4S4] clusters of the type found in 4Fe
ferredoxins.2) Thus, POR enzymes contain one iron—sulfur cluster per 120 kDa unit. Since
the 2-keto acid oxidoreductases have the same fundamental structure and cofactor content
(as shown by sequence analyses), they are expected to differ only in substrate specificity
but not in the fundamental mechanism of catalysis.

Studies of the mechanism of 2-keto acid oxidation by oxidoreductase enzymes are
based on the pioneering investigation of Oesterhelt and co-workers (1980) with the POR
from Hm. halobium (Halobacterium salinarium).8'l 1) They have detected a stable free
radical by EPR spectroscopy in pure preparations of the enzyme, Figure 11-1. The intensity
of the radical signal has been found to increase upon addition of pyruvate, and to
disappear with the addition of coenzyme A89) It has been shown that the reaction with
pyruvate has lead to the reduction of a [Fe4S4] cluster as well as radical formation, and to
the tight binding of the decarboxylated substrate to the enzyme. The observation of spin

coupling between the radical and the cluster has indicated that they must be in

98

g-value
2.03 2.02 . 2,01 . 2.00 1.99

j I T

l ' I

   

HJ:\C id)"
3/ 2

 

H\ _
"lg-)C C
H\ u _
vi7C—C—CUZ
J a J a l i l
3360 3380 3400 3420
Magnetic field (G)

 

 

Figure Il-I: First-derivative EPR spectra of PFOR from Hm. Halobium. (From

Ref. 11)

 

99

 

close proximity (£10 A). The authors have therefore proposed that in the first step of
catalysis pyruvate is bound covalently by its C-2 atom to the C-2 atom of TPP generating

hydroxyethyl-TPP (HE-TPP), while the C-1 carboxyl group is released as C0210) The

(oxidized) [F6484]2+ cluster then oxidizes HE-TPP to form a stable TPP=C-O'-R radical
intermediate and the reduced cluster. Latter studies have shown that the addition of the 2-
keto acid substrate to the oxidized form also leads to the detection of a stable, organic
radical in POR,4) lOR,5) VOR,6) and KGOR7) from different sources. On the other hand,
no stable radical has been observed on pyruvate addition to the POR from some
sources,4.~12) while with VOR6) and KGOR,” the formation of stable radical has been
found to be dependent on the addition of TPP as well as the substrate and accompanied by
the appearance of an EPR signal from a reduced [Fe4S4] cluster. The TPP addition

dependency suggests that these results may be due to loss of TPP during enzyme

purification.

The current model for the structure of the 2-keto acid oxidoreductases and the
proposed pathway of electron flow during catalysis is shown in Figure II-2.2) The two sets
of heterotetramers, 0t, B, y, and 6, that constitute the holoenzymes are assumed to be
catalytically independent. A 2-keto acid reducible [Fe4S4] cluster is located in the B
subunit, whereas two other [Fe4S4] clusters are assigned to the 6 subunit. 1n the absence
of exogenous electron acceptor and in the presence of excess coenzyme A (CoA) and 2-
keto acid, acyl-CoA is produced and the two [Fe4S4] centers in the 6 subunit become
reduced, presumably one electron at a time via the B subunit [Fe4S4] center. A second

molecule ofthe 2-keto acid reacts to generate TPP—based radical and a reduced B subunit

100

R—CO-COOH R-CO + co2

I (A f Yd

 

 

 

 

 

 

 

I

 

 

 

L 5L 3
)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

rB \ / f {H2484 » erl
4 L__3

_ Fe 8 ff 6
L lTPPfMg H 4 4J<3L [Fe4S4 E

 

CoA

 

Figure II-2: Four subunit catalytic model of 2-keto acid oxidoreductases. (From

Ref. 2)

 

 

 

—- ——o ‘—

[Fe4S4] center. This form of the enzyme contains four unpaired electrons per

heterotetramer. The enzymes that lack the 6 subunit, e. g., Hm. Halobium POR reduce
ferredoxin via the B subunit/domain.

Rationalizing the mechanism of the 2-keto acid oxidoreductase reaction lacks
proper understanding of how these enzymes catalyze the reaction between two
nucleophiles, hydroxyacyl-TPP and coenzyme A. In the well-characterized pyruvate

dehydrogenase (PDH) complex found in aerobic organisms, the reaction between the PDH

ltll

TPP and coenzyme A is mediated by lipoic acid. (The PDH complex is similar to POR in
that it catalyzes the same reaction - the oxidative decarboxylation of pyruvate to acetyl-
CoA; however it differs from oxidoreductases in that it lacks iron-sulfur clusters, contains
flavin and lipoic acids, and uses nicotinamid dinucleotide (NAD) as an electron carrier.)l3)
The mechanism of pyruvate oxidation by PDH involves formation of an intermediate
hydroxyethyl-TPP anion instead of a HE-TPP radical. The anion reacts with the oxidized
form of lipoic acid to form acetyllipoic acid, which then reacts with coenzyme A to
generate acetyl-CoA. With the mezophilic oxidoreductases, which have been shown to
exhibit the TPP radical signal (e. g., Hm. halobium), two types of mechanisms have been
proposed for the reaction of coenzyme A with the hydroxyacyl-TPP radical and the
reduced [Fe4S4] clusters. According to the mechanism given by Kerscher and
Oesterhelt,9) the processes of decarboxylation, radical formation, and reaction with
coenzyme A to yield acyl-CoA all take place at the same enzyme site. The [Fe4S4] cluster
is first oxidized by the external electron acceptor. Coenzyme A then reacts with
hydroxyacyl-TPP, causing transfer of an electron to the oxidized [Fe4S4] cluster, while the
coenzyme A accepts the acyl group. Docampo et al. (1987) have proposed an alternative
mechanism based on their observation of a second intermediate radical. 14) This species
has been assigned to a thiyl derivative of coenzyme A, CoAS-, generated by a direct
reaction of coenzyme A with an oxidized [Fe4S4] cluster. The thyil radical then reacts
with the hydroxyacyl-TPP radical to form acyl-CoA and TPP.

Whether actual differences in the catalytic mechanism of 2-keto acid
oxidoreductases exist or the reported variations reflect different methods of enzyme

purification and/or sample preparation, is yet to be determined.

102

11.1.2. Mechanism of the oxidative decarboxylation of pyruvate by PFOR

PyruvatezFerredoxin Oxidoreductase (PFOR) is a member of the 2-keto acid
oxidoreductase family, which plays a role in the anaerobic fermentative metabolism. l5) In
its function, it is similar to enzymes such as pyruvate dehydrogenase (PDH), pyruvate
decarboxylase (PDC), pyruvate oxidase, and pyruvatezformate lyase. All these enzymes
can initiate pyruvate catabolism. For example, PDH and PFOR both catalyze the oxidative
decarboxylation of pyruvate to acetyl-CoA and C02. However, unlike PDH, PFOR lacks
lipoamide and is able to reduce a number of electron carriers such as ferredoxin (Fd),
flavodoxin, and viologens, but not pyridine nucleotides.

The oxidative decarboxylation of pyruvate by PFOR occurs according to the

following half-reaction: l6)

_ E =-540m¥
CH3COCOO + CoASH v—

CH COSCoA + co +H++ 2e '
3 2 [11-2]

 

1n anaerobic acetogenic bacteria such as C lostridiunr thernroaceticum, C02 is reduced to
CO by a bifunctional enzyme, CO dehydrogenase/acetyl-CoA synthase (CODH/ACS). CO
generated in situ combines with the acetyl-CoA synthase active site to form a
paramagnetic adduct, called the NiFeC species, which, in turn, is condensed with a bound

methyl group and coenzyme A to generate acetyl-CoA. The acetyl-CoA is used both as a

carbon and energy source by acetogenic bacteria. 17-18)

103

However, the cofactor content and the mechanism of PFOR remain controversial.
Although the number of [Fe4S4] clusters may vary in the different PFORs, apparently only
two prosthetic groups are required for decarboxylation: TPP, Figure II-3, and
[Fe4S4] clusters. 19) Recently, Menon and Ragsdale16) have used a combination of rapid
freeze-quench EPR and stopped-flow spectroscopy to elucidate and quantify the
elementary steps in the reaction mechanism of Clostr'idium thermoaceticum PFOR. Their
kinetic data reveal the intermediacy of a radical, which has been identified as the
hydroxyethyl thiamin pyrophosphate radical (HE-TPP), and proposed as a common

transient intermediate in the catalytic reaction of PFORs from different sources. The

__ of”:

R

——N+\/S 0'

 

Figure Il-3: Thiamin pyrophosphate prostetic group of PFOR.

 

 

 

l ()4

mechanism for the oxidation of pyruvate by PFOR is illustrated in Figure II-4 and is
similar to that of Hm. halobium PFOR proposed by Oesterhelt and co-workers Thus, it
complies with the idea that PFORs with different subunit composition and different cluster
compositions should have essentially the same catalytic mechanism. 19) The first two steps
in the reaction mechanism are common for PFOR, PDH, PDC, and thiamine
pyrophosphate (TPP) in solution. The enzyme reacts with pyruvate to form a pyruvoil-
TPP adduct (step 1) which decarboxylates to yield hydroxyethylidine-TPP intermediate
(step 2). At step 3, one electron is transferred from hydroxyethylidine-TPP to one of the
two [Fe4S4] clusters generating a pyruvate-derived radical, the hydroxyethyl-TPP (HE-
TPP) radical. Steps 4 and 5 involve transfer of one electron from the FIE-TPP radical to
another [Fe4S4] cluster leaving an acetyl-TPP intermediate that undergoes cleavage by
coenzyme A to form acetyl-CoA. These steps leave the enzyme in the two-electron
reduced state. with both [Fe4S4] clusters reduced. Completion ofthe catalytic cycle (step
6) requires two-electron oxidation of PFOR by external electron acceptors, such as
ferredoxin (F d) or flavodoxin, CODH/ACS, or even protons when electron acceptors are
limiting. The intermediacy of the FEE-TPP radical has been assumed on the basis of the
fact that an EPR signal arises at g = 2.008 after the TPP-dependent decarboxylation of
pyruvate, but before coenzyme A takes part in the reaction. However, no direct
spectroscopic evidence for the presence ofthe TPP in the spin system has been found.
There is controversy surrounding even the existence of this radical since it has not been
detected with all PFORs.

The EPR spectra of frozen PFOR intermediates lack resolution, even when low

modulation amplitude is used, because ofthe inhomogeneous line broadening (cf.

1 ()5

    

H3C (‘3 + CoASH
O“
O
Jk ,0

H3O ‘ C",-

1 1‘6 5 .1-1

. O 8.6x10 M s

X
—N/ S [F9484]?

Pd,“
CODHM
Flavodoxinnd

SCoA

/9\ k, ..
s
N / s A
+ —-———>
> < 1.1 x10‘ M‘s"

[139.84]; E]

[F9484]:

Flavodoxtno,

0
F9 k
{ come} HaC

 

 

O

A

H3C SCoA + co? + H’ + 2 9'

[Feisag‘ [Fasdg
[F94SAJTA‘ [F848412A.
\ / co. \ /
+ — + —
Y fast
c CO
0 /
H3C// \CT' H3C /
H0 (131,9 HO

10.8 s"l 108 s"

E]

[F951,]; [F9454]:
- (Fast; (Fmsii‘;
\ ‘/ CoASH \‘ f
+ 1.6x105M"s" — S
"'—N \ S ___. """N
Y 7.4 s'1 |

.008 s“

l < [F 945‘];
-— N S ,
I [F9454];

HJC o

C
H C 0°
H3c// \SCOA [3 3
HO 1L slow

5..
-
.....

 

 

Figure I]-4: Mechanism of the PFOR catalyzed reaction. Steps: (1) pyruvate binding;

(2) formation of hydroxyethylidene-TPP intermediate; (3) formation of HE-TPP radical

and reduction of cluster A; (4) CoA binding and reduction of cluster B; (5) formation

of acetyl-CoA and regeneration of TPP anion; (6) reduction of external electron

acceptors. (From Ref 16)

 

106

 

Chapters 1). The inhomogeneous spectral broadening masks the details of the EPR
spectrum and reduces the certainty in the determination of magnetic properties for

identification and characterization of the paramagnetic species in question. Figure Il-S

"B" %

/1.94

1,289,

2500 3000 35100 4000
Gauss

 

 

 

 

 

 

 

U l

 

 

Figure Il-S: First-derivative EPR spectra of Clostridium Therrrroaceticum PFOR
incubated with (A) sodium dithionite, (B) pyruvate and CoA, (C) CoA, or (D)
pyruvate. EPR parameters: spectral width, 2000 G; field center, 3400 G; modulation
frequency, 100 kHz; modulation amplitude, 10 G; temperature, 10 K; microwave

power, 2 mW; microwave frequency, 9.447 GHz. (From Ref. 16)

 

 

 

107

shows the EPR spectra reported in Ref. 16. which are obtained from PFOR under different
conditions. PFOR as isolated is EPR silent. When reduced by dithionite at pH 9.0, a
complex EPR spectrum has been recorded, Figure II-5 (A). The observed spectrum, which
cannot be explained by simple rhombic signals has been attributed to electron spin coupled
[Fe4S4] clusters that are within approximately 10 A of each other (i. e., arising from a
through-space dipolar magnetic interaction). The double integral ofthe spectrum has
indicated that the [Fe4S4] clusters are fully reduced. A similar spectrum has been obtained
after reacting the enzyme with pyruvate and coenzyme A, Figure Il-S (B). Reaction of
PFOR with coenzyme A alone has yielded the EPR spectrum shown in Figure II-5 (C),
with g values at 2.04, 1.94 and 1.89. The signal intensity has indicated that half of the
[Fe4S4] centers have been reduced. An EPR spectrum which consists of an isotropic
radical signal centered at 2.008 and a rhombic signal similar to that in the previous case
has been recorded upon reacting PFOR with pyruvate alone, Figure II-5 (D). The signal
intensity corresponds to two spins per monomeric unit of the enzyme. It has therefore
been concluded that half of the spins reside in an [Fe4S4] cluster and half in the radical.
The complex EPR lineshape for the cluster has indicated that the reduced [Fe4S4] cluster
and the radical are close enough to experience magnetic dipolar interactions. The radical
signal has disappeared after addition of coenzyme A, which has been interpreted as an
indirect evidence that the radical is substrate-derived.

The EPR spectrum of the radical scanned at low modulation amplitudes, in a
narrow field range around g = 2.0, has demonstrated some hyperfine structure, Figure I]-
6.16) The predominant splittings observed in the pyruvate reacted enzyme have been

altered when the three protons on carbon 3 of pyruvate have been substituted with

108

 

deuterons, implying that the radical signal is substrate-derived. A comparison of the two
EPR spectra in Figure 11-6 shows that the EPR line for the sample with deuterated
substrate is narrower and contains less features than the one for the unlabeled sample.
Spectral features that appear to remain after the isotopic substitution are assumed to arise

from interaction of the unpaired electron with other nuclear spins (such as the thiazole

nitrogen). 16)

 

0" l

 

3325 3330 33175 3400
Gauss

 

Figure Il-6: First-derivative EPR spectra of Clostridium Thernroaceticum PFOR
incubated with (A) pyruvate, and (B) CD3-labeled pyruvate. EPR parameters: spectral
width, 100 G; field center, 3360 G; modulation frequency, 100 kHz; modulation

amplitude, 0.5 G; temperature, 10 K; microwave power, 2 mW; microwave frequency,

9.446 GHz. (From Ref. 16)

 

109

 

A dependency of the EPR signal of the radical intermediate on the number of
protons at the C-3 position of the 2-oxoacid substrate has been observed by Kersher and
Oesterhelt1 ‘1 in their study of Hm. halobium PFOR, Figure II—l. Apparently, the radical
EPR signal becomes narrower and gradually loses hyperfine structure upon decreasing the
number of the substrate C- 3 bonded protons. The hyperfine pattern has therefore been
attributed to interactions between the unpaired electron and the three protons on carbon 3
of pyruvate. However, neither of the studies reports on values of electron-nuclearcoupling
constants for the emerging radical species. Since the hyperfine structure of the radical EPR
signal is not resolved it is of little use in determining the hyperfine coupling parameters.
Hence, no reliable conclusions about the substrate nature of the enzyme can be drawn.
The application of advanced EPR methods such as ENDOR and ESEEM, which can
provide high resolution in detecting weak electron-nuclear magnetic interaction in samples
of randomly oriented paramagnetic species, seems to be appropriate to the study of
paramagnetic PFOR reaction intermediates. The present study was aimed at determining
the magnetic and structural properties of the reaction intermediates in the PFOR enzyme,

which would allow elucidating some aspects ofthe reaction mechanism.

110

[1.2. Application of Advanced EPR Methods to the Study of Clostridium

thermoaceticum PFOR Reaction Intermediates

11.2.1. Exfiperimental

 

Samples of (.‘lostridium thermoaceticum PFOR with different substrates have been
provided by Dr. S. Ragsdale from the University of Nebraska. They have been prepared
according to the procedure described in Ref. 16. The samples represent freeze quenched
reactions between the enzyme and substrates in aqueous buffer solutions. As indicated in
Ref. 16, the data of the metal, sulfide, and protein analysis of the Clostridium
thermoaceticum PFOR have shown that it is a dimeric protein containing two [Fe4S4]
clusters per monomer. The 2-keto acid substrates used in the preparation of the samples
include pyruvate, l3C-2 (carbonyl) labeled pyruvate, l3C-3 (methyl) labeled pyruvate,
2H3C-pyruvate in deuterated (ZHzO) buffer, 3-methyl-2-oxobutyrate, and 2-oxobutyrate.
Each of the substrates has been reacted with PFOR and the reaction has been stopped by
freezing the samples in liquid nitrogen.

The EPR and ENDOR spectra were recorded on a Bruker ESP300E spectrometer,
equipped with a Bruker ESP 360 DICE ENDOR assembly, Oxford ESR-900 cryostat with
an Oxford ITC 502 temperature controller, Bruker ER035M NMR Gaussmeter, and EIP
25 B frequency counter. The radio frequency (r1) in the ENDOR measurements was
amplified by an ENI A-300 amplifier. ENDOR spectra were collected by sweeping the rf
field in the range 0.5 MHz to 35 MHZ. The ESEEM measurements were performed on a
homebuilt pulsed EPR spectrometer described in Ref. 20. The microwave cavity system

used for ESEEM measurements employed a slotted—tube resonator”) combined with a

111

Gordon coupler arrangement”) Both two-pulse (rt/2 - t - 7t) and (predominantly) three-

pulse (tr/2 - I - 7t/2 - T - rt/2) microwave pulse sequences were employed to generate the

ESEEM data.

I]. 2.2. Results

 

The EPR spectra ofthe samples at 4 K, Figure 11-7, are similar to those described
in Ref. 16. An intense line at g = 2.0056, attributed to a reaction radical intermediate,16) is
present in all ofthem. This signal is superimposed on the broad, complex EPR lineshape
with extrema at g = 2.046, g = 1.948, and g = 1.861 This complex signal, which is only
observed at temperatures below ca. 20 K, is due to [Fe4S4] clusters in the protein
structure. The deviation of the spectral morphology of the signal from a rhombic lineshape
has been attributed to dipolar through-space electron spin-spin interaction which involves
the unpaired electrons of the [Fe4S4] clusters and, possibly, the radical. 16)

Figure II-8 gives a detailed view ofthe EPR line at g = 2.0056. A hyperfine
structure similar to that described in Ref. 16 is observed. Because this EPR signal is easily
saturated at low temperatires, the spectra appear to demonstrate an enhancement in
resolution at T = 60 K in comparison to that at T = 9. l K. The peak-to-peak linewidth of
the signal is ca. 20 gauss but the line extends over a range of about 70 gauss.

The EPR spectra of PFOR reacted with l3C-2 and 13C-3 labeled pyruvate at 9.0 K
are shown in Figure II-9. They are similar to the EPR spectrum of PFOR with unlabeled
substrate, Figure 11-9 (a). However, different features are observed in the g = 2.00 region,

Figure II-lO. The spectrum ofPFOR/l3C-2 pyruvate, shown in Figure 11-10 (b),

112

 

 

Figure 11-7: First-derivative EPR spectra of PFOR with pyruvate, (a), 2H3C-
pyruvate, (b), 3-methyl-2-oxobutyrate, (c), and 2—oxobutyrate, ((1). Experimental
parameters: field center, 3376 G; field sweep width, 1000 G; modulation frequency,
100 kHz; modulation amplitude, 5.0 G; time constant, 10 ms; microwave power, 0.1

mW; microwave frequency, 9.468 GHz; temperature, 4 K.

 

113

 

 

 

 

PFOR/PyruvaL/J

 

 

 

PFOR / 2H3C-pyruvate/\J

 

 

 

 

PFOR/
3-methyI-2-oxobutyrate
A - 1

 

fl

 

 

 

 

PFOR / 2-oxobuty:11/J
l

I l l l
3000 3200 3400 3600 3800
Magnetic Field (Gauss)

Figure I]-7

114

 

 

 

EPR of PFOR/pyruvate

9.1 K

60K

 

l l l l l
3340 3360 3380 3400 3420

Magnetic field (Gauss)

 

 

Figure Il-8: First-derivative EPR spectra of PFOR reacted with pyruvate.
Experimental parameters: field center , 3377.2 G; field sweep width, 100 G;
modulation frequency, 100 kHz; modulation amplitude, 1.0 G; time constant, 10

ms; microwave power, 0.05 mW; microwave frequency, 9.482 GHz; temperature:

9.1 K, (a), and 60 K, (b).

 

115

 

 

 

 

Figure Il-9: F irst-derivative EPR spectra of PFOR reacted with pyruvate, (a), 13C-2
labeled pyruvate, (b), and 13C-3 labeled pyruvate, (c). Experimental parameters: field
center, 3377 G; field sweep width, 1000 G; modulation frequency, 100 kHz;
modulation amplitude, 10.0 G; time constant, 10 ms; microwave power, 0.05 mW;

microwave frequency, 9.481 GHz; temperature, 9.0 K.

 

116

 

 

EPR of PFOR/pyruvate

PFOR/
pyruvate

 

 

 

PFOR /
13C-2 pyruvate

 

 

 

 

 
   
 

PFOR/
13C-3 pyruvate

 

 

 

 

 

 

l T T 1 l J l
2600 2800 3000 3200 3400 3600 3800 4000
Magnetic Field (Gauss)

Figure [1-9

117

exhibits an intense, narrow (0.5 G peak to peak linewidth) EPR line at g = 2.0025
superimposed on the line at g = 2.0056. Two distinct narrow (~05 G peak to peak
linewidth) EPR lines at g = 2.0025 and g = 2.0008 are observed in the spectrum of 13C-3
pyruvate reacted enzyme. These additional features in the spectra of PFOR with 13C
labeled substrates are clearly due to hyperfine interactions of carbon-l 3. It is worth noting
that besides the sharp lines due to 13C hyperfine coupling, the hyperfine structure of the
line at 2.0056 is different for all of the three spectra in Figure II-10. The hyperfine pattern
is most pronounced for PFOR reacted with l3C-3 pyruvate. The difference in the
hyperfine patterns indicates that there exist more 13C hyperfine components that overlap
with the EPR line at g = 2.0056. This conclusion is supported by the fact that the
linewidth of the g = 2.0056 EPR signal is larger in the case of 13C labeled samples relative
to the linewidth for the unlabeled sample.

ENDOR spectra of the samples were collected at temperatures, ranging from 4K
to 200K, with the maximum ENDOR response being found at 60 K. To distinguish the
contributions of the radical species from those of the paramagnetic iron-sulfiir center,
experiments were performed at different magnetic field strengths corresponding to
different g values. An ENDOR spectrum of PFOR with added pyruvate, which was
recorded at g = 2.0056 (the maximum EPR resonance effect for the radical), is shown in
Figure 11-1 1. A broad line due to matrix protons appears at ca. 14.2 MHz. A pair of
intense lines is resolved at 5.48 MHz and 5.99 MHz. These frequencies are in the close
proximity of the Larmor precession frequency of 3 1P (5.77 MHz at 3349 G). They are,
therefore, attributed to a long range hyperfine interaction of the radical unpaired electron

with the HE-TPP phosphorus nuclei. The almost symmetrical lineshape of both signals

118

 

 

Figure [1-10: F irst-derivative EPR spectra of PFOR reacted with pyruvate, (a), 13C-
2 labeled pyruvate, (b), and 13C-3 labeled pyruvate, (c). Experimental parameters:
field center, 3377.2 G; field sweep width, 100 G; modulation frequency, 100 kHz;
modulation amplitude, 1.0 G; time constant, 10 ms; microwave power, 0.05 mW;

microwave frequency, 9.481 GHz; temperature, 60.0 K.

 

119

 

 

 

PFOR/
pyruvate

PFOR/
13C-2 pyruvate

IWKDR/
13C-3 pyruvate

EPR of PFOR/pyruvate

 
 
   

 

 

 

l j j l 1
3340 3360 3380 3400 3420
Magnetic Field (Gauss)

Figure 11-1 0

120

 

 

 

ENDOR of PFOR/pyruvate

 

 

 

 

 

 

 

 

—

1 1 1 l
5 10 15 20 25

Frequency (MHz)

 

 

Figure IL] 1: ENDOR spectrum of PFOR/pyruvate. Experimental parameters: static
magnetic field, 3349 G; microwave frequency, 9.400 GHz; microwave power, 10 mW;
rfsweep width, 5.5 MHz; rffin modulation depth, 100 kHz; rf power, 220 W; time

constant, 10 ms; temperature, 60 K.

 

121

 

 

indicates that the hyperfine coupling is mainly isotropic with Aiso = 0.51 MHz. Figure I]-
12 shows the ENDOR spectrum obtained by averaging a large number (> 300) of scans in
a narrow frequency range around the Larmor frequency of 3 1P. However, the lineshapes
still do not reveal distinct anisotropic components. This result is surprising since the TPP
perphosphate fragment is o-bonded via an ethylene bridge to the thiazole ring, and the
only interaction between the radical unpaired electron and 31P would be via a dipolar,
through-space mechanism. The high-frequency region ofthe spectrum in Figure II-l 1
shows two overlapping proton powder type ENDOR patterns. The lineshape of these
patterns is characteristic of axial hyperfine interaction oftwo sets of protons. The peaks in
the patterns are positioned at 20.23 and 22.64 (set 1), and 21.50 and 23.85 MHz (set 2).
The corresponding low-frequency signals are distorted because of their overlap with the
31P lines at 5.48 MHz and 5.99 MHz. Low-intensity peaks at 16.50 MHz, and l 1.84
MHz, are also resolved. From the proton ENDOR components, the magnitudes of proton

hyperfine couplings were obtained. The results are summarized in Table II-l.

Table Il-I: Hyperfine coupling constants from 1H ENDOR of Clostridium

T lrermoaceticum PFOR reaction intermediates.

H set Aiso~ MHz B”, MHz B i, MHz
1 13.75 3.60 -1.80
2 16.33 3.33 -l.67
3 4.66 - _

 

 

J ENDOR of PFOR/ H3C-pyruvate

 

 

{ T=6OI<

 

 

 

 

 

 

 

 

 

 

I l 7 l I
4 5 6 7 8
Frequency (MI-12)

 

 

Figure Il-12: ENDOR spectrum of PFOR/pyruvate. Experimental parameters:
static magnetic field, 3349 G; microwave frequency, 9.400 GHz; microwave
power, 10 mW; rf sweep width, 5 MHz; rf fm modulation depth, 100 kHz; rf

power, 220 W; time constant, 10 ms; temperature, 60 K. 300 scans were averaged.

 

 

123

No significant changes in the observed spectral pattern and the lineshapes ofthe
signals occurred as the temperature was varied between 4K and 200K (Figure Il-13).

To check for contributions from the [Fe4S4] clusters, ENDOR experiments were
attempted at g = 2.0218, g = 1.9871 and g = 1.9293. At 60K no ENDOR signal was
detected with those g values. Upon lowering the temperature to 4 K, a broad line
corresponding to matrix protons emerged, Figure lI-l4', however, the rest of the ENDOR
signals observed at g = 2.0056 (cf Figure 11-11) were not detected.

The ENDOR spectrum of PFOR reacted with 2H3C—pyruvate at 60 K, Figure 11-
15, shows the proton matrix line at ~14.2 MHz and the two 31P peaks at 5.48 MHz and
5.99 MHz, whereas the powder proton lines are strongly suppressed. An additional feature
is resolved at 3.34 MHz and is assigned to the high-frequency deuteron hyperfine
component. Figure ll-16 shows an ENDOR spectrum collected in a narrow frequency
range around the deuterium signal. This ENDOR signal has a characteristic lineshape due
to the combined effect of nuclear quadrupole and electron-nuclear dipolar interactions.
The detection ofthe corresponding low-frequency hyperfine component is obscured by
baseline artifacts present in the 1 MHz region. This line is partially resolved at ~ 1 MHz.

Figure 11-17 (a) shows the ENDOR spectrum of PFOR reacted with l3C-3
pyruvate at g = 2.0048. ENDOR signals at 9.0 MHz and 9.5 MHz, not observed in the
case of unlabeled substrate, Figure 11-1 1, are detected. However, no matching signal
components are found either symmetrically situated relative to the 13C nuclear Larmor
frequency (v](l3C) = 3.58 MHz at 3349 G), or offset by i2v](]3C). No additional
features are observed in the ENDOR spectrum of PFOR reacted with 13C-2 pyruvate,

Figure 11-17 (b), when compared with the spectrum of PFOR/pyruvate, Figure II-l l. The

124

 

 

Figure Il—l3: ENDOR spectrum of PFOR/pyruvate. Experimental parameters: static
magnetic field, 3349 G; microwave frequency, 9.400 GHz; microwave power, 20
mW; rfsweep width, 27 MHz; rffm modulation depth, 280 kHz; rfpower, 220 W;

time constant, 10 ms; temperature: 4K, (a), 77K, (b), 200K, (c).

 

125

 

 

ENDOR of PFOR /pyruvate

 

 

 

 

 

T=77K

 

 

 

 

 

 

 

 

 

l l l l 1
5 10 15 20 25

Frequency (MHZ)

Figure I]-13

126

 

 

 

 

 

 

ENDOR of PFOR/pyruvate
at 3322 G
T = 4 K
1 1 7 I l
5 10 15 20 25
Frequency (MHz)

 

 

Figure Il-l4: ENDOR spectrum of PFOR/pyruvate. Experimental parameters: static
magnetic field, 3322 G;microwave frequency, 9.400 GHz; microwave power, 1 mW; rf
sweep width, 27 MHz; rf fm modulation depth, 280 kHz; rf power, 220 W; time

constant, 10 ms; temperature: 4K.

 

127

 

 

 

ENDOR of PFOR/2H3C-pyruvate

 

 

 

 

 

 

 

 

 

l l l l 7
5 10 15 20 25

Frequency (MI-12)

 

 

Figure Il-15: ENDOR spectrum of PFOR/2H3C-pyruvate. Experimental

parameters: static magnetic field, 3349 G; microwave frequency, 9.400 GHz;
microwave power, 5 mW; rf sweep width, 27 MHz; rf frn modulation depth, 100

kHz; rf power, 220 W; time constant, 10 ms; temperature, 60 K.

 

128

 

 

ENDOR of PFOR/2H3C-pyruvate

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 l l l
1 2 3 4 5 6
Frequency (MHz)

——4
_
\l—

 

 

Figure Il-l6: ENDOR spectrum of PFOR/2H3C-pyruvate. Experimental parameters:
static magnetic field, 3349 G; microwave frequency, 9.400 GHz; microwave power, 5

mW; rf sweep width, 6 MHz; rf frn modulation depth, 100 kHz; rf power, 220 W; time

constant, 10 ms; temperature, 60 K.

 

129

 

 

 

Figure Il-l7: ENDOR spectrum of PFOR reacted with 13C-3 labeled pyruvate, (a),
and 13C-2 labeled pyruvate, (b). Experimental parameters: static magnetic field,
3348.5 G; microwave frequency, 9.396 GHz; microwave power, 1 mW; rf sweep
width, 35 MHz; rffin modulation depth, 158.5 kHz; rfpower, 220 W; time constant,

41 ms; temperature, 60 K.

 

130

 

 

 

PFOR/H31 3C-pyruvate

 

 

 

 

 

_

1O

1 l 3 I
15 20 25 30

Frequency (MHz)

Figure 11-17 (a)

 

 

 

PFOR/H30-1 3CO-pyruvate

 

 

 

 

 

 

l l 1 l 1
1O 15 20 25 30

Frequency (MHz)

Figure [1-17 (b)

132

35

reason for the lack of 13C characteristic features is most probably in that the values of the
13C hyperfine couplings extend beyond the employed rf scan range of35 MHz (12.5 G).

ENDOR spectra of PFOR/3-methyl-2-oxobutyrate and PFOR/2-oxobutyrate at
60K are given in Figure 11-18. 1H ENDOR features analogous to those listed in Table 11-1
are not observed for either ofthe substrate analogs.

ESEEM data were collected using a three-pulse (tr/2 - ‘t — 7r/2 - T - rt/2 - t)
microwave pulse sequence. t-values were varied between 180 and 500 ns, so that the t-
suppression effect on the resolved modulation frequency components could be
established-23) Frequency spectra were obtained from the time domain by Fourier
transformation, using the dead time reconstruction algorithm described by Mims24) Since
the spin-lattice relaxation time ofthe radical species is longer than that ofthe [Fe4S4]
clusters, pulse sequence repetition rates of 40 Hz or less were employed in order to
maximize contributions from the radical species to the echo amplitude. Figure Il-19
represents three-pulse ESE-derived EPR spectra of PFOR reacted with pyruvate, which
illustrate this dependency. The ratio between the maxima ofthe radical species peak at g =
2.0056 and the [Fe4S4] cluster-derived peak at g = 1931 changes insignificantly, from
1.06 at pulse sequence repetition rate 1 Hz to 0.97 at repetition rate 40 Hz. This implies
the proximity ofthe [Fe4S4] cluster to the radical, which agrees with the conclusion of
Oesterhelt et al. that the radical and the cluster are in close proximity (£10 A).

Figure 11-20 (a) shows the time domain stimulated ESEEM data collected for
PFOR/pyruvate at g = 2.0003. Shallow modulations, indicative of weak hyperfine
interactions are observed. Examination ofthe frequency domain data, Figure 11-20 (b),

shows that the spectrum is dominated by the proton modulation line at 14.6 MHz.

133

 

 

Figure Il-l8: ENDOR spectrum of PFOR/3-methyl-2-oxobutyrate, (a). Experimental
parameters: static magnetic field, 3349 G; microwave frequency, 9.410 GHz;
microwave power, 2 mW; rf sweep width, 27 MHz; rf fm modulation depth, 100 kHz;
rfpower, 220 W; time constant, 10 ms; temperature, 60 K. ENDOR spectrum of
PFOR/2-oxobutyrate, (b). Experimental parameters: static magnetic field, 3349 G;
microwave frequency, 9.410 GHz; microwave power, 2 mW; rf sweep width, 27 MHz;
rffm modulation depth, 100 kHz; rfpower, 220 W; time constant, 10 ms; temperature,

60 K.

 

134

 

 

 

ENDOR of
PFOR /3-methy1-2-oxobu tyrate

 

 

 

 

 

 

 

 

 

——t
_l

l I
5 10 15 20

Frequency (MHz)

Figure Il-l8 (a)

135

25

 

 

 

ENDOR of PFOR/Z-oxobutyrate

 

 

 

 

 

 

 

 

l l 1 1 l
5 10 15 20 25

Frequency (MHz)

Figure 11-18 (h)

136

 

 

 

 

 

ESE EPR of PFOR/ pyruvate

 

 

 

 

 

l 1 I 1
3200 3400 3600 3800
Magnetic Field (Gauss)

 

 

Figure Il-l9: ESE—EPR spectra of PFOR/pyruvate. Experimental parameters:
magnetic field sweep width, 900 G; microwave frequency, 9.600 GHz; pulse
duration, 17 ns; I value, 205 ns; T value, 600 ns; temperature, 4.2 K; pulse

sequence repetition rate: 1 Hz, (a), and 40 Hz, (b),

 

 

 

 

 

Figure Il-ZO: Stimulated time domain ESEEM data for PFOR/pyruvate, (a).
Experimental parameters: magnetic field strength, 3429 G; microwave frequency,
9.600 GHz; pulse duration, 17 ns; pulse sequence repetition rate, 10 Hz; 1 value, 205
ns; initial T value, 100 ns; sample temperature, 4.2 K; number of data points, 1024;
number of events averaged for each data point, 14; number of scans, 2. Corresponding

frequency domain spectrum obtained by Fourier transformation of the time domain

data, (b).

 

138

 

 

 

Stimulated ESEEM of PFOR/pyruvate

(a)

 

—

l
4

t + T (usec)

Figure Il-20 (a)

139

—-1

—

 

 

 

 

 

 

 

 

 

 

 

Stimulated ESEEM of PFOR/pyruvate

(b)

 

-

—i

d

l l 1 7 7 l l l
10 12 14 16 18 20 22 24

Frequency (MHz)

Figure Il-20 (b)

140

 

However, there are low-frequency peaks at 0.8, 1.9, 3.1, 3.9, and 4.4 MHz, due to I4N
modulations. It is apparent that the relative intensity ofthe different frequency components
changes with the I value (Figure 1.1-21) the component at 1.9 MHz becoming the most
intense amongst the low-frequency lines at T = 275 ns. 1 values of 205 ns and 275 ns
correspond to proton modulation suppression condition, while I = 240 ns maximizes the
amplitude ofthe proton modulations. Comparison ofthese spectra with a set of stimulated
ESEEM data collected for PFOR/pyruvate at g = 1.931, Figure 11-22, reveals the
similarity ofthe corresponding pairs ofspectra under similar experimental
conditions. Absent from the spectra in Figure 11-22 is the frequency component at 0.8
MHz. In addition, lines in these spectra are less intense and not well resolved.

The effect ofthe pulse sequence repetition rate on the three-pulse ESEEM at g =
2.00 is illustrated in Figure 11-23. Lowering the repetition rate is expected to raise the
relative intensity ofthe modulation frequencies associated with the nuclei in the structure
of the radical due to the slower electron spin relaxation. Such effect could not be observed
with certainty in the range from 40 Hz to 1 Hz, due to the low echo modulation amplitude
(low intensity of the observed peaks) as well as the electron spin coupling between the
radical and nearby [Fe4S4] center, which increases the spin-lattice relaxation rate for the
radical.

Typical stimulated ESEEM data for PFOR reacted with 2H3C-pyruvate is given in
Figure 11—24. Pronounced deuterium modulations are present, inasmuch as the I value
selected, 205 ns, is significantly different from the deuterium suppression I value of 445 ns
determined by the inverse ofthe 2H Larmor frequency (2.24 MHz at 3429 G). To single

out the contribution from deuterium modulations the approach described in

141

 

 

Figure I]-21: Stimulated ESEEM spectra of PFOR/pyruvate. Experimental
parameters: magnetic field strength, 3429 G; microwave frequency, 9.600 GHz; pulse
duration, 17 ns; pulse sequence repetition rate, 40 Hz; initial T value, 100 ns; sample
temperature, 4.2 K; number of data points, 1024; number of events averaged for each
data point, 34; number of scans, 2; I value: 205 ns, (a); 240 ns, (b); 275 ns, (c); 340 ns,

(d); 480 ns, (e).

 

142

 

 

 

 

 

 

Stimulated ESEEM of PFOR/pyruvate

 

t = 205 ns

”C = 240 ns

”C = 275 ns

t=340ns

1: = 480 ns

 

__l

l l 1 j l
10 12 14 16 18

Frequency (MHz)

Figure Il-21

143

22 24

 

 

 

Figure Il-22: Stimulated ESEEM spectra of PFOR/pyruvate. Experimental
parameters: magnetic field strength, 3553 G; microwave frequency, 9.600 GHz; pulse
duration, 17 ns; pulse sequence repetition rate, 40 Hz; initial T value, 100 ns; sample
temperature, 4.2 K; number of data points, 1024; number of events averaged for each
data point, 12; number of scans, 2; I value: 203 ns, (a); 240 ns, (b); 340 ns, (c); 480 ns,

(d).

 

144

 

 

 

 

 

 

 

 

 

Stimulated ESEEM of PFOR/pyruvate
at g = 1.931
t = 203 ns
‘C = 240 ns
t = 340 ns
t = 480 ns
1 1 l 1
10 15 20 25
Frequency (MHz)

Figure I]-22

145

 

 

Figure Il-23: Stimulated ESEEM spectra of PFOR/pyruvate. Experimental
parameters: magnetic field strength, 3429 G; microwave frequency, 9.600 GHz;
pulse duration, 17 ns; initial T value, 100 ns; I value, 203 ns; sample temperature,
4.2 K; number of data points, 1024; number of events averaged for each data point,

12; pulse sequence repetition rate: 1 Hz, (a), and 40 Hz, (b).

 

146

 

 

Stimulated ESEEM of PFOR/pyruvate

 

 

 

 

 

 

 

 

1H2

 

40 Hz
1 T 1 1 l l 1 1 1 l I I
2 4 6 8 10 12 14 16 18 20 22 24
Frequency (MHz)

Figure 11-23

147

 

 

 

Figure Il-24: Stimulated ESEEM data for PFOR/2H3C-pyruvate. (a) Time-domain
data; (b) The corresponding frequency-domain data obtained by Fourier transformation
of trace (a). Experimental parameters: magnetic field strength, 3429 G; microwave
frequency, 9.600 GHz; pulse duration, 17 ns; initial T value, 100 ns; pulse sequence
repetition rate, 10 Hz; sample temperature, 4.2 K; number of data points, 1024;

number of events averaged for each data point, 14; number of scans averaged, 2; I

value, 203 ns, (b), and 444 ns, (c).

 

148

 

 

 

 

Stimulated ESEEM of PFOR/2H3C-pyruvate

 

_

1
4 6

t + T (usec)

—

Figure I]—24 (a)

149

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stimulated ESEEM of PFOR/2H3C-pyruvate

t=203ns

t=444ns

WWW

 

 

 

 

l l l 1
5 10 15 20 25

Frequency (MHz)

Figure Il-24 (b, c)

150

Chapter I was used. The ESEEM time-domain data set for PFOR/2H3C-py1uvate sample
(Figure 11-24) is divided by the data set collected for PFOR/pyruvate (Figure 11-20) under
similar experimental conditions. The Fourier transformation ofthe resulting data set is
shown in Figure 11-25. It is evident from the figure that, except for the deuterium
modulation at 2.3 MHz, the contribution from all ofthe other modulations is almost
completely canceled.

Fourier transformations ofthe three pulse ESEEM data for PFOR reacted with 3-
methyl-2-oxobutyrate and 2-oxobutyrate are represented in Figure II-26, respectively.
They do not demonstrate any significant difference from the data for PFOR with added
pyruvate. This is to be expected since the three samples differ essentially in the number of
substrate protons, which does not affects the ESEEM spectrum below the proton Larmor

frequency.

11.2.3. Discussion

 

The application of advanced EPR techniques capable of resolving weak electron-
nuclear hyperfine couplings in disordered systems allows characterization of the magnetic
and structural properties ofthe PFOR paramagnetic intermediates.

The ENDOR data presented here clearly show that the narrow EPR signal at g =
2.0056 corresponds to a substrate-derived catalytic intermediate. The presence of proton
hyperfine transitions with coupling constants All“): 17.35 MHz, A1“) = 1 1.95 MHz,
Alla) = 19.66 MHz, and Ale) = 14.66 MHz, in the spectrum of PFOR/pyruvate, and
their sensitivity to deuterium substitution, confirms the conclusion that the proton signals

are due to the substrate hydrogens. In support ofthis conclusion is the appearance of

 

 

Stimulated ESEEM of
PFOR / 2I-I3C-pyruvate vs. PFOR / pyruvate

 

 

 

 

 

 

I 1 1 1 l I l l 1 l 1 l
2 4 6 8 10 12 14 16 18 20 22 24
Frequency (MHz)

 

 

Figure Il-ZS: Fourier transform of the time—domain ratio of the two data sets shown in

Figure 1-20 and Figure 1-24 (a).

 

152

 

 

 

 

Figure [1-26: Stimulated ESEEM spectrum of PFOR/3-methyl-2-oxobutyrate, (a).
Experimental parameters: magnetic field strength, 3429 G; microwave frequency,
9.600 GHz; pulse duration, 17 ns; initial T value, 100 ns; I value, 205 ns; pulse
sequence repetition rate, 40 Hz; sample temperature, 4.2 K; number of data points,
1024; number of events averaged for each data point, 34; number of scans averaged, 4.
Stimulated ESEEM spectrum of PFOR/2-oxobutyrate, (b). Experimental parameters:
magnetic field strength, 3429 G; microwave frequency, 9.600 GHz; pulse duration, 17
ns; initial T value, 100 ns; I value, 205 ns; pulse sequence repetition rate, 10 Hz;
sample temperature. 4.2 K; number of data points, 1024; number of events averaged

for each data point, 34; number of scans averaged, 4.

 

 

 

 

 

 

 

 

 

 

 

 

Stimulated ESEEM of
PFOR/ substrate analogs

3-methy1 2-oxobutyrate

2-oxobutyrate

 

 

l l —l
10 15 20

Frequency (MHz)

Figure H-26

154

25

corresponding deuteron ENDOR lines upon the isotopic substitution ofthe methyl protons
of pyruvate. In addition, the ESEEM data on Figure 11-25 shows the net contribution of
the deuterium modulations arising from the substrate deuterons in the isotopically
substituted pyruvate. The substrate origin ofthe EPR signal at g = 2.0056 is also indicated
by the observed broadening ofthe signal upon a 13C labeling ofthe substrate.

To justify the hypothesis that the detected 1H ENDOR transitions are due to two
sets of substrate protons, numerical simulations aimed at reproducing the experimental
peak frequencies and lineshapes have been performed using the MATLAB scripting
language35) program "H12.m" .35-54) One or two sets of proton spin Hamiltonian
parameters have been used as input. Frequency histograms have been computed by
diagonalizing the spin Hamiltonian and finding the AM] = 1 transitions for both electron
spin manifolds. No weightings for nuclear state mixing have been included in the
calculation. The amplitudes ofthe computed superhyperfine frequencies have been given a
sin(0) weighting, where 0 is the angle between the principal axis of the electron-nucleus
hyperfine coupling tensor and the laboratory magnetic field. The integration over all
possible orientations of the laboratory field, with respect to the hyperfine tensor principal
axes has been done in angle increments of either 1.10 or 2.20. Each "stick" corresponding
to a particular orientation has been convoluted with a Gaussian line function having a full
width at half-height between 0.3 MHz and 0.4 MHz to obtain smooth powder-type
lineshapes. The powder patterns for each proton set have been differentiated numerically
and added together to yield the simulated spectrum. A polynomial fit of experimental
baseline points has been introduced to account for the baseline distortion that might

possibly affect the appearance ofthe ENDOR peaks. Five equally spaced experimental

I55

baseline points have been picked on either side ofthe lH ENDOR signals, and along with
two additional intermediate experimental points have been fit with a fourth-degree
polynomial. The polynomial function has been added as a correction factor to the
derivative function representing the simulated spectrum. The above procedure has also
been applied to simulate 2H and 31P ENDOR spectra, as described later in this Section. It
should be underlined that these simulations concern only the frequencies and the
lineshapes but not the intensities of the ENDOR lines. The 1H ENDOR experimental and
simulated spectra are shown in Figure II-27.

In all cases, the frequencies of the corresponding peaks agree within i 0.2 MHz.
However, the correspondence between the experimental (solid lines) and simulated
(dotted lines) spectra with respect to the lineshapes is definitely closer for traces (a) and
(b), where two sets of axially symmetric coupling parameters have been assumed. Trace
(c), which has been obtained considering only one set of protons with a hyperfine tensor of
rhombic symmetry shows poorer agreement with the experimental lineshape. On the other
hand, the results ofthe simulations give little indication on whether the two sets of protons
have very similar (trace (a)) or very different (trace (b)) anisotropic hyperfine interactions.
In both cases, the values of the proton simulation parameters correspond closely to the
ones measured directly from the experimental data set. The consideration of two sets of
protons with very similar anisotropic couplings will be adopted tentatively as a working
hypothesis for reasons outlined later on in this discussion.

The two hyperfine tensors extracted from the ENDOR data, Table II-1, are thus

associated with two sets of substrate methyl protons. The anisotropic dipolar coupling

156

 

 

Figure [127: Simulated lH ENDOR spectra for PFOR paramagnetic reaction
intermediate. Each simulation data set is plotted using dotted lines and shown in
comparison with the experimental spectrum (solid line). Simulation parameters: g =
5.5856012, B = 3349 G; (a) Am“) = An“) = 11.95 MHz,AZZ(l)=16.90 MHz,
AXXQ) = A3312) = 14.66 MHz, A2712) = 19.10 MHz, number of0 increments in the
range 0° - 90°, 80, Gaussian linewidth, 0.40 MHz; (b) Axxtl) = Aw“) = 11.95 MHz,
A220) = 19.10 MHz, Axxfl) = Anti?) = 14.66 MHz, A220) = 16.90 MHz, number
of0 increments in the range 0° - 90°, 80, Gaussian linewidth, 0.40 MHz; (c) Axx =

I 1.65 MHz, A“, = 15.50 MHz, AZZ = 19.10 MHz, number of0 increments in the
range 00 - 90°, 40, number oftp increments in the range 00 - 90°, 40, Gaussian

linewidth, 0.30 MHz.

 

157

 

 

.....

 

 

I ' I ' 1 ' 1 T
18 20 22 24 26
Frequency (IVIHZ)

Figure 11-27

 

constants are only small fractions ofthe respective isotropic constants. Such a hyperfine
pattern is characteristic ofthe interaction ofa unpaired electron with B-protons (cf.
Chapter I). The small difference between the values of the hyperfine isotropic couplings
indicate that the corresponding sets of B-protons are nearly equivalent. B-couplings of
three methyl protons to an unpaired electron would hypothetically give rise to eight lines
in the EPR spectrum and three line pairs in the ENDOR spectrum, provided that the three
protons were non-equivalent. Such spectra would be expected at sufficiently low
temperatures, at which the rotation of the methyl group is frozen. However, if the internal
rotation of the methyl group about the Ca‘CB bond is fast enough, so that the frequency
of rotation is high in comparison with the hyperfine precession frequency of the protons,
the proton couplings will be equalized.25) The EPR spectrum of the methyl group will
then consist ofa 1:32321 quartet, while the corresponding ENDOR spectrum will be a
single pair oflines with small anisotropy characteristic ofB protons. This situation is
encountered in solutions and even in solids at sufficiently high temperatures. It is well

known that significant rotation ofthe CH3-group is present even at temperatures as low as

4.2 K2631) For instance, the methyl group in the CH3C'(COOH)2 radical, which can be
observed in a methylmalonic acid crystal, undergoes almost free internal rotation at 4.2
K26) In addition, at low temperatures (e. g., below 77 K) the methyl group may execute
restricted rotation through a quantum mechanical barrier-tunneling process that exchanges
the methyl protons.28'3l) The tunneling rotational motion ofthe methyl group affects the
energies ofthe spin states and leads to an additional term in the spin Hamiltonian, which

introduces a so called tunneling splitting. The tunneling frequency ofa methyl group varies

greatly from radical to radical. For the CH3C'(COOH)2 radical in methylmalonic acid at
4.2 K a methyl tunneling frequency of 192 MHZ has been found3O)

The detection of only two pairs of proton hyperfine lines in the ENDOR spectrum
of PFOR reacted with pyruvate cannot be accounted for by the hyperfine effects of a
frozen, stationary methyl group (which would give rise to three ENDOR pairs). On the
other hand, raising the temperature would lower the potential barrier to the internal
rotation and the ENDOR lines for the non-equivalent, frozen protons would collapse into
a single pair. However, such effects were not observed in this study. The invariance of the
methyl proton ENDOR lineshapes with respect to the temperature (of. Figure II-13)
indicates that the pyruvate methyl group must be rapidly rotating in a broad temperature
range, even at temperatures as low as 4.2 K. The two pairs of B-proton ENDOR signals
that correspond to two sets of almost equivalent methyl protons then should originate
from two types of radical species that differ slightly in their structure, most likely in their
conformation. The reason for having two radical species most probably lies in the sample
preparation procedure, which includes quenching the reaction by rapidly freezing the
sample in liquid nitrogen.

The third proton coupling constant listed in Table 11-1, Aiso = 4.66 MHZ,
characterizes a more distant proton hyperfine interaction. It is known that more distant
protons exhibit a nearly pure dipolar coupling, in which the maximum anisotropy is
smallzg) Therefore, this coupling can be assigned to y-proton hyperfine interaction in the
radical intermediate. As mentioned in Chapter 1 the typical coupling constants for y-
protons are in the range ofa few 64112253233) For example, the acetoxyl radical

(CH3COO-) whose structure resembles the hydroxyethyl fragment ofthe proposed HE-

] 60

TPP radical intermediate, has y-proton isotropic hyperfine coupling of 1.7 i 0.2 G, i. e.,
about 4.8 M11234l , which is in very good agreement with the one for the PFOR
intermediate.

The isotopic replacement of the pyruvate methyl hydrogens by deuterium causes
the observed ENDOR hyperfine lines to appear in a different spectral region - around the
deuteron Larmor precession frequency (2.19 MHZ at 3349 G). On account ofthe
gyromagnetic ratios for protons and deuterons the isotropic hyperfine constant for the
methyl protons is reduced by a factor gn(lH)/gn(2H) = 6.51 upon the isotopic
substitution. Thus the isotropic constants for the three sets of protons listed in Table IV-l
(221,500) = 13.75 M112, 21,5012) = 16.33, and 21,5013) = 4.66 MHZ) are expected to be
scaled down to 2.1 1, 2.50, and 0.72 MHZ, respectively. However, the values for the
deuteron hyperfine couplings are expected to be modified by the nuclear quadrupole
interaction. Using the MATLAB scripting language program "D12.m",54) numerical
simulations have been performed to reproduce the frequencies and lineshapes of the
experimentally observed 2H ENDOR lines. The simulation procedure outlined above for
the case of ]H ENDOR has been followed to yield the simulated spectra shown in Figure
II-28.

The values ofthe hyperfine coupling parameters used in the 1H ENDOR
simulations, Figure 11-27(a-c), have been scaled down by a factor of approximately 6.5
and used as input data to yield the corresponding 2H ENDOR simulated traces (a-c) in
Figure 11-28 (dotted lines). These hyperfine parameters have been combined with a nuclear

quadrupole coupling constant, eZqQ/h, with values in the range 40 kHz to 50

I61

 

 

Figure Il-28: Simulated 2H ENDOR spectra for PFOR paramagnetic reaction
intermediate. Each simulation data set is plotted using dotted lines and shown in
comparison with the experimental spectrum (solid line). Simulation parameters: g =
0.85739, B = 3349 G; (a) Am“) = 4,3,“) = 1.80 MHZ,AZZ(1)= 2.60 MHZ, e2qQ(l) =
0.05 MHZ, AXXQ) = 4,312): 2.2 MHz, A2212) = 2.965 MHz, e2qo(2) = 0.04 MHz,
11“) = r112) = 0.1, number of0 increments in the range 0° - 90°, 40, number oftp
increments in the range 0° - 90°, 40, Gaussian linewidth, 0.092 MHz; (b) Axx“) =
Aw“) = 1.83 MHz, A2211) = 2.93 MHz, AXXQ) = Ant?) = 2.25 MHZ, A2212) = 2.47
MHZ, e2qQ(l) = e2qQ(7-) = 0.05 MHz, 11“) = n12) = 0.1, number ofB increments in
the range 0° - 90°, 40, number 0pr increments in the range 0° - 90°, 40, Gaussian
linewidth, 0.0925 MHz; (c) Axx = 1.74 MHz, A}? = 2.30 MHz, AZZ = 2.934 MHZ,
equ = 0.05, n: 0.1, number of0 increments in the range 0° - 90°, 40, number of(p

increments in the range 0° - 90°, 40, Gaussian linewidth. 0.085 MHz.

 

162

 

 

 

 

 

2.5 3.0 3.5
Frequency (MHZ)

Figure 11-28

I ('1 3

 

4.5

kHz, and a small assymetry parameter. n ~ 0.1. (Due to the small value of e2qQ for
deuterons, the asymmetry parameter has been found to not influence the results
significantly.) The values for the quadrupole coupling constant are within the range of
reported magnitudes for the quadrupole interaction in organic compounds with covalently
bonded deuterons32~36‘38) In all of the three cases, the frequencies of the corresponding
experimental and simulated peaks agree within i 0.1 MHZ, while it is difficult to assess the
degree of agreement between the experimental and simulated lineshapes. It appears that
traces (a) and (c) correspond better to the experimental spectrum with respect to the
lineshape. However, only the simulated spectrum in Figure II—28(a) has a corresponding
lH ENDOR simulated spectrum that is in satisfactory agreement with the experiment,
Figure II-27(a). This observation is supportive of the assumption that the complex lH
ENDOR lineshape is due to hyperfine interactions of two sets of protons with similar
hyperfine parameters.

Surprisingly, no corresponding deuterium modulation peaks are observed in the
ESEEM experiment, Figure 11-24. This is most probably due to the fact that the ESEEM
spectrum is dominated by a strong deuterium Larmor line at 2.24 MHZ arising from matrix
deuterons.

The hyperfine parameters for the B-proton hyperfine interaction in the PFOR

reaction intermediate are very similar to the corresponding parameters found for the

protons in polycrystalline acetyl radical (CH3'C=O).39) The acetyl radical is relevant to
the PFOR catalyzed reaction as it can potentially emerge as a product of the pyruvate
decarboxylation. The principal values of the proton hyperfine coupling tensor reported by

Bennet and Mile39) from their carbon-13 and proton EPR studies of polycrystalline acetyl

164

radical are A j = 13.0 MHZ and A” = 16.9 MHZ, overall error being estimated at i4 MHZ.
Thus, the isotropic component is Also = 14.3 MHZ, and the purely anisotropic
components are B” = 2.6 MHZ, Bi = -l .3 MHZ, where the symmetry axis lies close to the
Ca‘CB bond direction. The authors have concluded that the acetyl radical is a o-type
radical (cf. Chapter I) with a valence angle CB‘Ca:O equal to approximately 130°. Their
analysis shows that the unpaired electron is located primarily in a sp-hybrid orbital on the
carbonyl carbon atom, but that there is also an appreciable spin density on the adjacent
carbon and on the oxygen atom. The unpaired spin density on the two carbons has been
calculated by using the obtained values for the principal elements of the 13C axially
symmetric hyperfine tensors and the theoretical values of the hyperfine coupling constants
for the fully occupied 25- and 2p-orbitals to find the corresponding fractions of the
unpaired spin density in the 2s— and 2p-orbitals, which then have been summed. The
reported total unpaired spin densities are as follows: 0.27 for the methyl carbon and 0.52

for the carbonyl carbon atom. The similarity of the total spin density on the methyl carbon

atom to that on the hydrogen atom in H'CO4O) has suggested that there is a participation
of the excited state, [H3C-:C=O], in the overall electronic structure of acetyl radical
comparable to that proposed for the formyl radical (cf. Chapter 1). Supporting evidence
for the participation of this resonance structure has been found in the low C-C bond
strength in the acetyl radical (50 kJ/mol).39) As pointed out by Bennet and Mile,39)
however, it is not necessary to postulate such delocalization of the unpaired electron since
the observed isotropic methyl coupling constant (14.3 MHZ) can arise from
hyperconjugation (cf. Chapter I). Hyperconjugation results in a positive isotropic

hyperfine coupling constant. In the acetyl radical, the delocalization ofthe unpaired

165

electron on the methyl carbon will produce a negative contribution to the hyperfine
coupling and thus will reduce that caused by hyperconjugation which is positive. In
addition, the orbital overlap due to hyperconjugation is less because ofthe elongated (as
concluded from the bond energy) C-C bond. These two factors account for the
observation that Aiso for the methyl protons in acetyl is much smaller than the isotropic
hyperfine couplings measured for methyl protons in other 0- and rt-radicals (45-80
M}1Z).25332r41) The smaller magnitudes of the anisotropic hyperfine components for
acetyl radical compared to those observed for a freely rotating methyl group in n-radicals
(Bll = 6 MHZ, 81 = -3 I\/1Hz)4l) has been attributed to differences in the spatial
configuration and also the lower spin density (0.52) on the carbonyl carbon atom.
Applying a reasoning similar to the one given by Bennet and Mile39) for the acetyl
radical, towards the PFOR radical intermediate would lead to the conclusion that there is a
pyruvate derived acetyl radical that may be bound to the TPP by a weak, non-covalent
bond. This conclusion is supported by the fact that the nitrogen modulations observed in
ESEEM at g = 2.003 are weak indicating a small unpaired electron spin density on the
nitrogen atom. (If the radical intermediate was the HE-TPP radical, in which the
hydroxyethyl fragment is covalently bound to TPP and the unpaired electron occupies the
Con 2p,t orbital, more significant spin density on the TPP nitrogen would be expected
because of the effect of 71 delocalization over the thiazole ring). Within the frame of such a
model, the small isotropic 31P coupling observed in ENDOR can be explained by the

proximity of the loosely bound radical and a phosphorus nucleus from the pyrophosphate

fragment.

166

On the other hand, the results ofthe ENDOR and ESEEM experiments can also be
explained within the frame ofa 7t-type radical model with a rapidly rotating methyl group.
The typical values for isotropic B- coupling of methyl protons in rt-type radicals with a
rapidly rotating methyl group are between 65 MHZ and 80 MHz.25532~41‘49) However, in
the present study no ENDOR frequencies were detected beyond 23 MHZ with the
magnetic field being set at different values that correspond to different resonance positions
in the inhomogeneously broaden radical EPR line. The deviation of the measured
hyperfine couplings from the typical values for B couplings reported in the literature for
alkyl and acyl radicals can be accounted for by a possible unpaired electron delocalization,
which leads to a distribution of the unpaired electron spin density over the rt-orbital
system of the intermediate. The proposed PFOR intermediate, the HE-TPP radical (Figure
II—29), is a conjugated system in which a significant electron delocalization may exist.
Figure 11-30 shows three of the possible resonance structures for the HZE-TPP radical, the
superposition of which can explain the observed B- and y-proton hyperfine couplings.

y -proton couplings are more likely to arise from the magnetic interaction of the
methyl protons with the unpaired spin density on the TPP carbon (resonance structure 1)
than from their interaction with the unpaired electron centered on the hydroxyethyl oxygen
since alkoxy—radicals, in which the unpaired spin is mainly concentrated on the oxygen
atom, usually do not show hyperfine interaction with the alkyl protons-50) Additional
resonant structures which give rise to nitrogen hyperfine couplings are also relevant to the
HE-TPP structure. This idea is in agreement with the conclusion ofMenon and

Ragsdalel6) that the FIE-TPP radical is not purely oxygen centered, but that there

167

 

Figure Il-29: Hydroxyethyl thiaminpyrophosphate radical (HE-TPP).

 

 

 

must be significant spin density among a number of atoms in the radical. The presence of
some electron spin density on the TPP nitrogen, as indicated by the weak nitrogen
ESEEM modulations at g = 2.003, can thus be related to the delocalization of the
unpaired electron over the thiazole ring system. The unpaired electron delocalization may
also be responsible for the remote 31P hyperfine interaction observed in the ENDOR

spectra of the intermediate radical.

168

O O S O \‘ O/QOS \0
_ +\ H _ N . C,\.....n
fl CA a 7
\ a a a n

 

 

Figure 11-30: Resonance structures for the HE-TPP radical.

 

 

169

With the assumption ofa 71 type radical with a rapidly rotating methyl group, the
unpaired electron density at the Qt carbon atom, pnCO‘ , can be obtained using the well

known relationship (cf. Chapter 1)

AiSOBJot _—_ pnch Q13 <c0520> . [113]

where 0 is the dihedral angle between the plane ofthe unpaired electron 2p,r orbital and
the projection ofa C-H bond, <c0320> = 0.5 for a rotating methyl group, and Q13 = 164
MHZ.25) The calculated p7,COL is 0.168 for species 1 and 0.199 for species 2. This result
indicates that most of the spin density (approximately 0.8) is concentrated not on the
carbonyl carbon atom but that it is distributed over the rest of the atoms in the conjugated
system. There is little spin density on the TPP nitrogen and the hydroxyethyl oxygen most
probably carries the largest fraction of the unpaired electron population. However, a
considerable spin density may also be present at the thiazole carbon atom, to which the
pyruvate acyl fragment is bound by a covalent bond, as well as at the thiazole sulfur. The
question ofthe unpaired electron distribution over the atoms in the HE-TPP intermediate
can be elucidated by carrying out an experiment with an l7O-labeled pyruvate, which
would allow unambiguous determination ofthe unpaired spin density at the carbonyl
oxygen atom. By using the calculated unpaired electron populations on the or-carbon atom
and the dipolar field value obtained from A“ and A1 (cf. Chapter I), the distance between
the H13 nuclear dipole and the Ca electron dipole has been calculated. For species 1, the
dipolar distance is 1.95 A, while for species 2 it is 2.1 l A. These values are in good

correspondence (within 10 %) with the molecular geometry average distance (2.150 A)

170

between the methyl hydrogens and the carboxyl carbon in H3CCOOH.51) The agreement
shows that the rt-radical model is self-consistent.

The EPR spectrum of PFOR reacted with 13C labeled substrates shows that there
is significant spin density on the carbonyl carbon so as to perturb the lineshape ofthe
radical EPR signal. The EPR spectra lack sufficient resolution to allow determination of
13C hyperfine couplings. Since the hyperfine patterns ofthe g = 2.0056 EPR signal in the
spectra of PFOR/puruvate, PFOIU13C-2 pyruvate and PFOR/1303 pyruvate are different
(Figure 11-10), it may be concluded that 13C hyperfine components are present within the
range ofthe EPR powder lineshape at g = 2.0056 but masked by the inhomogeneous line
broadening. The presence of narrow EPR lines at the g value for the free electron (2.0023)
can be associated with a dynamic averaging of hyperfine couplings and evidences the
presence of a less bound, freely moving paramagnetic species. The absence of 13C
ENDOR signals in the spectrum of PFOR/13C-2 pyruvate indicates that, most probably,
the 13C ENDOR spectrum occurs above the radiofrequency upper bound (35 MHZ). If a
free acetyl-like o-type radical is assumed, the total unpaired spin density on the
isotopically substituted Ca atom would be close to 052,39) which would give rise to
hyperfine splittings on the order of 300 to 450 MHz (approximately 100 to 160 gauss).
Such splittings exceed the full width ofthe inhomogeneously broadened EPR line at g =
2.0056. However, in the present study, no distinct EPR lines extending beyond the field
range ofthe EPR powder line at g = 2.0056 were detected at 60 K. This indicates that the
value ofthe 13C,l hyperfine coupling has an upper bound of approximately 70 gauss (ca.

200 MHZ) and that the unpaired spin density on 13CO, is less than 0.52.

171

The derivative-like ENDOR lineshapes at 9.0 MHz and 9.5 MHZ observed in the
ENDOR spectrum of PFOR/1303 pyruvate can be assigned to the perpendicular edges of
two anisotropic powder-type hyperfine lines that are associated with two sets of almost
equivalent l3CB nuclei. It is well known that 13C hyperfine interactions usually exhibit
large anisotropy.25-32-39) It is therefore possible that a single l3C anisotropic hyperfine
powder line covers a frequency range that is equal to or larger than the scanned range (i.
e., 3T 2 35 MHZ). Thus, in the study ofBennet and Mile,39) T = -21 MHZ for the methyl
'3Cp hyperfine interaction. High-frequency ENDOR studies of 13C hyperfine interactions
in PFOR with 13C labeled substrates are necessary to allow an independent determination
of the unpaired spin density on Ca and C13 carbons of pyruvate and an unambiguous
assignment of a structure to the radical intermediate.

The observed ESEEM frequencies in the range 0.7 MHZ - 5 MHZ are due to 14N
modulations that arise from nuclear hyperfine and quadrupole interactions. These
modulations are present in the ESEEM experiments at different conditions, which
indicates that their origin is not solely the thiamin nitrogen. [Fe4S4] clusters that are
encased in the protein structure show 14N modulations due to [N-H S]-type hydrogen
bonding between the protein amino groups and the [Fe4S4] cluster sulfur. Comparison of
the ESEEM spectra obtained at different g values, Figure 11-21 and Figure II—22, shows
that the modulation frequency component at 0.8 MHz with g = 2.003 is characteristic of
the TPP nitrogen. To extract information on the nitrogen magnetic coupling contained in
the stimulated ESEEM data computer simulations with the FORTRAN program "sepacl "
have been performed. A simulated frequency-domain ESEEM spectrum is shown in Figure

11-31. The correspondence between the experimentally obtained and calculated ESEEM

172

 

 

 

 

 

Echo Amplitude

 

 

 

 

 

 

 

0.74 r = 205 ns
1.88
1.1
11
l“ 3.9
k 4.48
I 1 l l J l L l I i l l 1 l 1 l 1 J I I l l l l
0 5 10 15 20 25

Frequency (MHZ)

 

Figure I]-31: Simulated 14N ESEEM frequency domain spectrum. Simulation
parameters: nuclear Larmor frequency, v] = 1.05 MHz; A1 = 1.36 MHZ, A” = 2.36
MHz; e2qQ = 1.9 MHZ, n = 0.74; number of 0 increments in the range O-90°, 60,

number oftp increments in the range 0-90°, 40; t = 205 ns.

 

 

frequencies is satisfactory ($0.1 MHZ). However, there is some discrepancy in the
intensities of the low-frequency peaks indicating that the Hamiltonian parameters used in
the simulation are not optimal. The 14N spin Hamiltonian parameters used for the
simulation ofFigure 11—31 were Aj = 1.36 MHZ and A” = 2.36 MHZ, e2qQ = 1.9 MHZ,

and n = 0.74, indicating that the superhyperfine couplings are dominated by 14N nuclear

quadrupole interactions. The hyperfine and nuclear quadrupole parameters are comparable
to the ones reported for nitrogen couplings in heterocyclic systems32~38~52l The large
value of the asymmetry parameter reflects an uneven electronic charge distribution around
the nitrogen nucleus due to a more localized (C=N) double bonding in the thiazole ring
and the low local molecular symmetry. The parameters estimated via the simulation
illustrate one of the reasons for not observing nitrogen hyperfine transitions in the
ENDOR experiments. The small values of the hyperfine coupling constants combined with
the exceptionally low gyromagnetic ratio of 14N relative to the one for 1H

(g,,( lH)/gn( 14N) = 13.85) cause the 14N ENDOR lines to appear in the ~1 MHZ region,
where the detection is impeded for instrumental reasons.

An interesting feature in the ENDOR spectra of the radical intermediate in the
PFOR catalyzed reaction are the 31P signals. The lineshapes of these signals are
characteristic of a predominantly isotropic hyperfine interaction of 31P nucleus with the
unpaired electron in the radical, which implies proximity of the phosphorus and the
unpaired electron. This is supported by the 3 ]P ENDOR simulation results shown in
Figure 11-32. 54)

The simulation procedure described for 1H ENDOR has been followed, with the
assumption of an axially symmetric anisotropic hyperfine interaction. No baseline
correction has been attempted. The best agreement with the experimental spectrum is
obtained for the cases of either a purely isotropic hyperfine interaction, Figure II-32(a), or
a predominantly isotropic hyperfine interaction, Aiso >> T, where T denotes the dipolar
part of the axially symmetric hyperfine tensor, Figure II-32(d). It is not clear how such an

isotropic interaction can arise since the pyrophosphate phosphorus nuclei and the substrate

174

remainder that carries the unpaired electron are separated by a number ofbonds. There is
little possibility for delocalization of the unpaired electron as the pyrophosphate group is
bonded to the thiazole ring via an ethylene bridge. The most probable cause for the
observed weak (~05 MHZ) 31P hyperfine interaction is the hydrogen bonding between the
carbonyl oxygen in the decarboxylated pyruvate and the pyrophosphate part of the
molecule, with the participation of solvent molecules (H20).

However, there exist possibility that the 31F ENDOR signals are primarily due to
remote, through-space dipolar electron-nuclear magnetic interactions. Trace (b) in Figure
11-32 represents the simulated 31P ENDOR spectrum for the case of a purely anisotropic
hyperfine interaction. Similar lineshapes are obtained when the dipolar coupling is
combined with a smaller isotropic component. Apparently, the correspondence between
the experimental and simulated lineshapes is less satisfactory in this case relative to the
case of a dominating isotropic hyperfine interaction.

A third interpretation can be considered, assuming that the observed 31P ENDOR
signals represent the perpendicular edges of two broad 31P hyperfine powder patterns
whose low-intensity parallel edges either span beyond the scanned frequency region, or
overlap with the proton matrix line. This assumption results in trace (c) of Figure II-32.
Multiple simulated spectra of type (c) can be obtained with various combinations of Aiso
and T. For example, the combination of A150 = 10.53 MHz and T = 10.00 MHZ which
ensures the appearance ofthe parallel edges outside the region 1 MHz — 30 MHZ, leads to
a simulated spectrum that is very similar to that shown in Figure II-32(c). As in the case of
Aiso = 0, simulated lineshapes do not agree well with the experimental ones. Moreover,

larger values of Aiso and T are even more difficult to be accounted for, taking

 

 

Figure [1-32: Simulated 31P ENDOR spectra for PFOR paramagnetic reaction
intermediate. Each simulation data set is plotted using dotted lines and shown in
comparison with the experimental spectrum (solid line). Simulation parameters: g =
2.2633, B = 3345 G; (a) Also = 0.53 MHz, T = 0 MHZ, number of0 increments in
the range 0° - 90°, 80, Gaussian linewidth, 0.09 MHz; (b) Aiso = 0 MHZ, T = 0.59
MHZ, number of0 increments in the range 0° - 90°, 80, Gaussian linewidth, 0.08
MHz; (c) Also = 6.15 MHZ, T = 5.725 MHz, number of0 increments in the range 0°
- 90°, 160, Gaussian linewidth, 0.09 MHz; (d) Aiso = 0.53 MHZ, T = 0.12 MHZ,

number ofB increments in the range 0° - 90°, 80, Gaussian linewidth, 0.07 MHZ.

 

176

 

 

..........

.........

 

ccccccccc

 

Frequency (MHZ)

Figure II-32

I77

 

into consideration the remoteness ofthe phosphorus nucleus relative to the paramagnetic
center.

Molecular mechanics computations have been carried out to estimate a reasonable
distance between the phosphorus (labeled as P2) in the structure of HE-TPP radical and
the hydroxyethyl oxygen atom carrying most ofthe unpaired electron density. Spartan 4.0
with the Sibyl force field has been used to perform the computations54) The molecular
geometry has been first optimized to find a minimum on the potential energy surface. The
resulting conformation has a planar thiamine ring and an unfolded pyrophosphate chain,

with both phosphorus atoms being in the opposite end with respect to the hydroxyethyl

 

oxygen. The optimized molecular conformation has been used as a starting geometry for
the next computations. All bond lengths and bond angles have been constrained to their
optimized values. The ring system has also been constrained to remain flat by fixing the
relevant dihedral angles. A force constant (SIGMA) equal to 100 for each of the
constrained parameters has been used. Several partial optimizations of the constrained
system have been performed at fixed distances between the hydroxyethyl oxygen and P2.
The resulting conformations have been visually monitored for unrealistic distortions and
some of the values for the interatornic distances (e. g., between oxygens of the
pyrophosphate remainder and the thiamine sulfur) have been examined for consistency. 2.5
A has been found to be a reasonable estimate for the smallest Pz-O distance at which no
significant distortions ofthe rest ofthe molecule occur (Figure II-33). Such a distance is
not unrealistic, considering that the TPP is contained within the protein structure which
may place constraints on the TPP conformations. Clearly, a distance in the range 2.5 - 3 A

is sufficient for an efficient, through-space electron-nuclear magnetic interaction to take

178

 

 

 

Figure Il-33: A constrained conformation of the HE-TPP radical. All valence bond
lengths and valence angles are set to their equilibrium values in the optimal
conformation. P2 - O distance is fixed at 2.5 A. Optimization of the molecular

geometry has been performed by adjusting dihedral angles.

 

 

place. Ifa purely dipolar electron-nuclear hyperfine interaction is assumed (A,SO = 0), so
that the two 3 1P ENDOR components overlap as shown in Figure 1-12 (a), the unpaired
spin density on the pyruvate oxygen, p0, can be estimated. With A1 = 2T = 0.5 MHZ and
T = pO (g gn “B “Bn / r3), the calculated unpaired electron density on the pyruvate

oxygen is pO = 0.2 at an electron dipole-nuclear dipole distance r(O-P2) = 3.0 A. On the

other hand, if p0 is assumed to be p0 ~ 0.8, a limiting value in accordance with the model

179

. ‘" : ‘Cflwt- I"

 

ofa it-radical, the corresponding dipolar distance is r(O-P2) = 4.7 A. With T = 0.12 MHZ,
i. e., the dipolar coupling from the simulated spectrum that most adequately reproduces
the experimental lineshape (Figure II-32(d)), the 2p-unpaired electron density on the
pyruvate oxygen is found to be p0 = 0.1 at r(O-P2) = 3.0 A, while the dipolar distance
turns out to be r(O-P2) = 5.98 A for p0 ~ 0.8. It can be concluded that the estimated
range of electron nuclear dipolar distances, 3.0-6.0 A, correlates well with the expected

range of unpaired spin densities on the pyruvate oxygen.

11.2.4. Conclusion

 

The study of PFOR paramagnetic intermediates by EPR, ENDOR and ESEEM has
brought some insight into the nature and magnetic properties ofthe reaction intermediates.
It has been shown unambiguously that the EPR signal detected at g = 2.00 is due to a
substrate-derived radical. A number of hyperfine couplings have been determined from the
spectra. The results can be explained equally well within the frame oftwo models. The 0-
type radical model postulates a pyruvate-derived acetyl radical which is not covalently
bound to TPP, but is in proximity of(or weakly bound to) both the thiazole nitrogen and
the pyrophosphate, i. e., it forms an adduct with TPP. The 1t -type radical model adopts
the proposed HE-TPP radical as the reaction intermediate. The results show that the

reaction intermediate is related to the enzyme TPP prosthetic group.

180

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44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

. Bennet, J. E.; Mile, B. 'l'rarrs. baraday Soc, 1971, 67, 1587-1597.

Cochran, E. L.; Adrian, F. J.; Bowers, V. A. J. Chem. Phys. 1966, 44, 4626.

. Ayscough, P.B. In Electron Spin Resonance in Chemistry, Methuen: London, 1967.

Read, S. F. J.; Whiffen, D. H. Mol. Phys, 1967, 12, 159-164.

. Morton, J. R.; Horsfield, A. J. Chem. Phys. 1961, 35, 1 142-1 143.

Morton, J. R., Chem. Rev. 1964, 64, 453.

Wells, J. W.; Box, H. C. J. Chem. Phys. 1966, 35, 2935-2938.

Kwiram, A. J. Chem. Phys. 1968, 49, 2860-2861.

Box, H. C.; Budzinski, E. E.; Lilga, K. T. J. Chem. Phys. 1972, 57, 4295-4298.
Brustolon, M.; Cassol, T.; Micheletti, L.; Serge, U. Mol. Phys, 1986, 57, 1005-1014.
Atherton, N. M.; Oliver, C. E. J. Chem. Soc. Faraday Trans. 1, 1988, 84, 3257-3262.

Ayscough, P.B. In Electron Spin Resonance in Chemistry, Methuen: London, 1967,
pp. 347-348.

Tabor. w. 1. .1. Chem. Phys. 1957, 26, 974-975.

Wamcke, K.; Brooks, H. B.; Lee, H.-I.; Davidson, V. L.; Babcock, G. T.;
McCracken, J. J. Am. Chem. Soc. 1995, 117, 10063-10075.

Wavefiinction, Inc. Spartan. [Online] Available
http://www.wavefun.com/index.html, August 6, 1998.

Simulations of ENDOR Frequencies for PFOR Reaction Intermediates. [Online]
Available

http://www.cem.msu.edu/~bouchev/simulations/ENDOR/ENDORSimulations.html,
April 25, 1999.

183

Chapter 111

Hyperfine Sublevel Correlation Spectroscopy (HYSCORE)

ofS = 1/2, 1 = 1 Spin Systems

111.1. Introduction

Two-dimensional (2D) ESEEM techniques have proved to be useful for
disentangling complicated ESEEM spectra by correlating pairs of transitions between
hyperfine levels, determining the relative sign of different hyperfine couplings, and
separating ESEEM lines belonging to different paramagnetic species. The first 2D Fourier
transform (FT) ESEEM experiment proposed by Merks and de Beer” is based on the
three-pulse sequence. It is essentially a three-pulse ESEEM experiment in which the time-
domain data points are systematically collected in both I- and T-dirnensions to aid in
spectral assignment. A single 2D Fourier transform thus contains the precise information
that is available from a large number of 1D three-pulse ESEEM spectra. For an S=1/2,
1=1/2 spin system the 2D spectrum is symmetrical relative to the diagonal (03] = (112) and
consists of peaks ((01, 002) at (0, 0), (0301» 0), (0, (0a), ((DB, 0), (0, 005), (mu, (05), (005,
(’30.)- l~2) 1n the absolute value Fourier transform spectrum, the amplitude of all peaks
(except that ofthe peak at (0, 0)) is the same and no suppression effect typical ofthe 1D
stimulated ESEEM is observed. However, the use ofthe three pulse sequence for 2D
ESEEM is limited by the fact that the decay ofthe electron spin echo is governed by

different relaxation times in both I- and T- time dimensions. Since the time ofthe primary

184

echo decay is much shorter than that ofthe stimulated echo, the resolution along the
different frequency axes may differ by orders of magnitude. An alternative method that
overcomes the disadvantages of the three-pulse 2D ESEEM is the HYSCORE (hyperfine
sublevel correlation spectroscopy) technique proposed by Hofer et al.3)

The simplest pulse scheme for HYSCORE utilizes a four-pulse sequence (rt/2 - I -

7t/2 - t] - 71 - t2 - 7t/2) to generate a stimulated echo at time I after the third 7t/2 microwave

pulse, Figure III-l. The additional 7: pulse inserted in the three pulse sequence that is
normally used in the 1D stimulated ESEEM experiment, mixes, or correlates, hyperfine
frequencies that arise from the same coupling. The amplitude of the echo at fixed I is
measured as a function of the two time periods, t1 and t2, which are systematically varied

to build up a two-dimensional data set, Figure III-2 (a). The linewidth in both dimensions

is determined by the electron spin-lattice relaxation time, T16. The subsequent 2D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stimulated
71/2 112/2 71 11/2 Spin Echo
~—> <——>i 4 1 4—> t
I I1 t2 ‘ T
Preparation Evolution Mixing Detection

 

Figure III-1: Sequence of events during a four-pulse ESEEM experiment. The

 

amplitude ofthe four-pulse echo is measured as a function oft] and t2.

 

 

185

 

 

 

 

 

Figure III-2: (a) An exemplary 2D time-domain data matrix, with only 33 of all the
128 tl'SllCCS shown. (b) 3D representation of the HYSCORE frequency-domain
magnitude spectrum obtained by 2D Fast Fourier Transformation of the time-domain
data matrix and taking the absolute value ofthe resulting complex matrix. (c) Contour

plot ofthe above spectrum. v1 = (0 l/27t, v2 = (02/27:. (After Ref. 21)

 

I 86

 

 

r ,.
! a,”
11018) 4 "I

3 M

.—
N
A
I

u:
v
may

    

 

1 F 1 I
1.0 1.5 2.0 2.5 3.0 3.5
v] (MHZ)

 

 

Figure III-2

187

Fourier transformation yields the HYSCORE spectrum in frequency-domain, Figure III-2
(b), which is more conveniently represented as a contour plot, Figure III-2 (c). In a
HYSCORE experiment each data set is collected with a fixed value of I, which is to be
adjusted according to the spectral properties and the desired information (cf. Section III-
3).

HYSCORE is a relatively new technique with a limited number of applications
reported in the literature. However, it is becoming increasingly popular as the
experimental data demonstrate its advantages. The resolution and information
enhancement that can be gained via the correlation of nuclear spin transitionslr3) or by
correlating the electron spin transitions with the nuclear spin transitions4~5) has been
demonstrated in a number of single-crystal applications. Poppl and coworkers have used
HYSCORE to analyze the homogeneous and inhomogeneous line broadening effects of
proton ESEEM signals in single crystals61 The potential of HYSCORE applied to
disordered systems has been explored in studies on a oxovanadium complex with nitrogen-
containing ligands.7~8) Dikanov and coworkers have analyzed the HYSCORE contour
lineshapes in an experiment on imidazole and histidine complexes of V02+.9) HYSCORE
has been utilized to separate the ESEEM contributions of weakly coupled nitrogens from
those of strongly coupled ones in a bacterial photosynthetic reaction center. 10) Another
application of HYSCORE to the study of systems of biological interest includes
correlating pairs of ESEEM frequencies belonging to certain l4N couplings in a Fe-S
protein. 1 l) Hofer has illustrated the suppression effect and the interpretation of
HYSCORE powder patterns of S = 1/2, I = 1/2 systems and proposed a 3D version of

ESEEM to completely eliminate the suppression effect. 12) Other developments ofthe

I88

correlation spectroscopy includes a six-pulse 2D ESEEM technique proposed by Pilbrow
and coworkers,13) which offers enhancement ofthe intensity ofthe cross peaks relative to
that ofthe diagonal peaks due to the increased modulation depth”)

In this Chapter. some aspects ofthe analysis of HYSCORE data will be discussed.
First, the theoretical background and computational aspects of the HYSCORE experiment
will be considered, followed by the derivation ofthe four pulse echo envelope modulation
function for a S = 1/2, 1 = 1 system. Finally, an application ofthe derived formula to the
analysis of HYSCORE spectra of randomly oriented 3,5-2H labeled tyrosyl radical species

will be presented.
111.2. Principles of HYSCORE

Gernperle et al. '5) have derived a HYSCORE modulation formula for the S=1/2,
I=l/2 spin system, with the assumption of non-selective, ideal 7I/2 and 7t pulses. The spin
system is described in the high field approximation by the Hamiltonian given by Equation
1-54. The amplitude ofthe four-pulse echo has been obtained by using the density matrix

approach described in Chapter 1. The result is given by the following formula:

S(t1.12)= 1 —%{C0 +Ca[cos(wat] +qu/2)+COS(0)a12 +c0aI/2)]
+Cplcos(u)gt1 +(uBI/2)+ cos(0)pt2 +(DBI/2)]
+CC c2cos((0at] +wBt2 +60+T/2)+C2COS((.OBI] +01at2 +(0+I/2)

+s2cos(0)atl —60[312 +w_T/2)+SZCOS(wB11—(Da12 +(0_‘C/2)]}

[III-1a]

189

with the amplitudes

C0 : 3 — cos(w‘3t) — cos(03at)— s2 COS(0.)+T)— c2 cos((0_I) [III-lb]
Ca 2 c2 cos(mBI—03at/2)+s2 COS(0)BT+C0aT/2)—COS(CDaT/2) [III-1c]
C13 : c2 COS((DO_I-0)BT/2)+SZ cos(maI+wBt/2)—cos(wBt/2) [III-1d]
C0 : ~2sin(maI/2)sin(wBI/2), [III-1e]

the sum and difference frequencies c0+ = ma + (05 and (0- = (.00[ - (0‘3, 32 = sin2(6/2), c2 =
cosz(6/2), and the modulation depth parameter k = 4 sin7-(6/2) cos7-(6/2). 6 corresponds to

the angle between the two effective magnetic fields at the nucleus with MS = 1/2 and M5

= -1/2, and is defined by

2 2 1
c0 —[((0 + w ) /4]
sin 2 (6 r2) = l a B ' [III-2a]

wawB

2 wIZ—[(wa—wB)2/4]i
cos (6 /2) : ’ _ [III-2b]
mama

 

190

C0 in Equation III-1 is a constant term that depends on I only and does not contribute to
the echo modulation. The second and third terms in Equation III-I proportional to Ca and
CB contain the modulation frequencies (00, and (013 in either ofthe t1 or t2 time domains. In
the frequency domain this gives rise to peaks at (0, 00a), (wa, 0), (0, (05), ((05, 0). The last
term with coefficient CC (Equation III-la) contains cosine functions with both time
variables simultaneously in the argument. It yields cross peaks in the 2D spectrum at (ma,

00B) and (0)3, 600,). Thus, for a S=1/2, 1=1/2 spin system, a 2D FT ESEEM spectrum,

 

 

 

 

 

 

 

 

Cl)2

 

 

Figure III-3: Schematic HYSCORE 2D spectrum for an S = 1/2, 1 = 1/2 spin system.

Solid squares: peaks observed for ideal pulses. Open squares: diagonal peaks that are

 

observed only for non-ideal pulses that cause partial excitation. (After Ref. 15)

 

 

191

8(0)], (02), will consist of six peaks as shown schematically in Figure III-3 by the solid
squares. Two pairs of axial peaks with frequencies (0Cl and 033 appear along the axes (01 =
0 and (.02 = 0, forming two identical 1D spectra. The two cross peaks (ma, (DB) and (cup.
(00,) are related by reflection symmetry with respect to the diagonal 00] = (02. Since ideal
pulses are assumed, no diagonal peaks occur. However, in reality the pulses have finite
bandwidth and diagonal peaks do occur (Figure III—3). Equation III-1a shows that the
peaks appear as a mixture of absorption and dispersion type signalsl6) with a variable
phase shift that depends on I. Since phasing is not normally possible, magnitude (absolute

value) spectra are to be plotted The peak amplitudes in a magnitude spectrum are

A(o)a,0)=A(0,coa):

k
: .4. c2 cos((uBI—maT/2)+ 52 cos(wBI+(0aI/2)— cos(waI/2)

[III-3a]
A(m,,,0)= 440.013):
: hie2 cos( c0,1I—0)p,I/2)+ 52 cos(mat + (OBI/2)" cos( (BM/2)
[III-3b]
Alwa’wB) : %sin((13(),I/2)sin((13‘3I/2)l(2C4 + 25411/2
[III-3c]

. c) . .
Dependrng on the actual values of 010,, (up, I, 52 and c4, blind spots may occur, at which

the intensity of pairs of peaks drops to zero. Ifthe microwave field strength ofthe pulses.

B1, is not sufficient to fulfill the condition of complete excitation (i. e., If] >> H0, or,

equivalently to] >> (00,. (09, where (01 = g “B Bllh), the two allowed and two forbidden
transitions are no longer equally excited. Consequently, the Hamiltonian of Equation 1-54
cannot be neglected during the pulsesl7~18) and the problem must be solved numerically.
A non-ideal mixing 7I-pulse also causes an incomplete coherence exchange between the
two nuclear transitions ma and dip, which results in the appearance of two diagonal peaks
at (010,, (11a) and (£03, 003). In this case the above formulae for the peak intensities the
modulation depth parameter, k, are not valid anymore. Another difficulty arising from a
non-ideal excitation is formation of all possible two-, three- and four-pulse echoes, which
necessitates the elimination of the unwanted echoes by phase-cycling.

As already pointed out, the properties of a HYSCORE spectrum, S((oa, (DB), can
be inferred from the 2D Fourier transform (FT) of the time-domain data, S(t ], t2). A 2D
Fourier transform is performed by consecutively transforming S(tl, t2) with respect to
each of the independent time variables. A real or complex Fourier transformation of the
data set with respect to a particular time variable can be carried out, which leads to
different spectral representations as well as different spectral densities?) Hofer has
analyzed the cases of amplitude modulation and phase modulation of 2D ESEEM
signals. 19)

In a 2D experiment, both the phase and the amplitude of a signal observed during a
time t2 can be modulated as a function of a previous time interval t1.19) In the ESEEM

experiments non-quadrature detection is normally utilized and the detected signal contains

193

both absorption and dispersion components. Consider a simplified, exemplary 2D time

domain signal described as

S(t], t2) = cos(wa t1) cos(mb t1 + (0C 12). [111'41

(The above expression is oversimplified in that the relaxation and amplitude factors have
been neglected and the constant phase shifts arising from the spectrometer dead time have
been omitted.) The frequency (0C in S(t], t2) is detected during the time t2. The signal
S(t], t2) as a function oft] is modulated by the two frequencies (pa and (0b, where ma
affects the amplitude and cob the phase ofthe signal S(tl). A complex Fourier
transformation performed in the t2 time domain will generate a real- and imaginary part
spectrum F(0)2) = A0112) + i D002), containing the absorption (A) and dispersion (D)
lineshape, respectively. For a phase modulated signal, such decomposition of F into two
parts is only valid for t] = 0 (i. e., for the first slice in the t] time domain). After the

Fourier transformation with respect to 12, the signal S(t], 002) can be written as

S(t], (02) = cos(uoa t1) exp(i (0b t] )F(0)2 = CDC)

= (1/2) F0112 = 03C) {exp[i (60a + (0b) t1] + exp[i (cob - ma) t1]}. [III-5]
Ifthe signal S as a function oftime t2 is only modulated in amplitude (60b = 0), no

information about the sign ofthe modulation frequency is present. A complex FT in the t]

domain will then produce a pair oflines at the positions ((03. (0C) and («03, 00C). Since only

194

 

the real part signal in t2 domain is recorded. the complex FT with respect to 12 also
generates two lines at 03c and '(DC and the calculation ofthe 2D Fourier transform results
in four lines containing equivalent information. Thus, for an amplitude modulated real part
signal only the frequency range to] > 0, 012 > 0 has to be considered. Ifthe signal is only
phase-rnodulated (ma = 0), the complex FT with respect to t1 will preserve the sign ofthe
modulation frequency, which results in a single line at (60b, (be). In the most general case,
when both amplitude and phase of S(t], t2) are modulated, the FT in the t1 domain results
in a pair oflines at positions (ma + cob, (0C) and (03b - (0a, (be), similar to the case of
exclusive amplitude modulation. However, both positive and negative frequencies have to
be considered in the (0] domain, while it suffices to deal only with the positive (02
frequencies. Since the lineshapes obtained after a 2D Fourier transformation are normally
a mixture of absorption and dispersion lines,l6) the absolute value (modulus, or

magnitude) spectrum defined by

so], 12) =[Re2((0], (1)2)+1m2((0], 62)]1/2 [III-6]

is usually used in practice.
The term of most interest in the HYSCORE modulation function for a S = 1/2, I =

1/2 spin system, Equation III-1, is the one that yields cross peaks after the Fourier

transformation,

k
S(t],t?_):—4—CC[C2 cos(toatl +6)th +(p+)
+ c2 cos((ogtl +(Da12 +tp+)
+32 cos(watl —wgt2 +tp_)

+ 52 COS((DI311—(Da12 + tp_)]
[III-7]

The amplitude factor CC and the phase constants (12+ and (,0, depend only on the time
separation I between the first and the second pulses. The t1 dependence influences only
the phase of the signal detected in t2. Therefore, if the time domain data are processed by
taking a cosine Fourier transform in the t2 dimension followed by a complex Fourier
transform in the t 1 dimension, the cross peaks will separate into two different frequency
quadrants according to the sign of the dominant phase of S(tl, t2). For weak anisotropic

hyperfine interactions the nuclear transition frequencies can be approximated by

(pa = 10)] - A/2! [III-8a]

(up = 160] + N2], [III-8b]

where A denotes the hyperfine coupling constant for a particular orientation and (01 is the

nuclear Larmor precession frequency. With the above expressions the factors c2 and s2 are

c2 = 10312 - (N2)2|/((.0a tug) [111-921]

52 = 0 [III-9b]

I96

for (01 > A/2, and

c2 = 0 [III-10a]
s2 = 16512 - (ix/29146,, (.03) [III-10b]
for (0] < A/2.

The Fourier transform of Equation III-7 in the t2 time dimension results in

S(t], (1)2)= exp(i 03a t1) F(032 = (8‘3) + exp(i (DB t1) F(002 = (0a) [III-1 l]

for to] > N2, and

S(t], (02) = exp(-i (i)Cl t1) F((02 = (11B) + exp(-i (DB t1) F((02 = ma) [III-12]

for (0| < A/2. (The contribution from the time independent phase shift in Equation III-7 to
S(t], 032) has not been taken into account). The sign ofthe phase modulation in t] depends
on the relation of the hyperfine coupling to the nuclear Larmor frequency. The absolute
value spectrum calculated after carrying out the Fourier transformation in the second
dimension contains a pair of cross peaks at (ma, (up ) and (039, (0a ) provided that 0)] >
A/2. In the case of 0)] < A/2, the cross peaks are in the negative (01 region, at (400,, (OD )
and (4.05, (0a ). This is verified by the experimental examples in Figure III-4,19) showing
both (+001, +032) and (4101, +(02) regions of the HY SCORE spectra of radicals prepared
from succinic and malonic acids. In each example there are two pairs of dominant peaks

which originate from different crystal sites. In the succinic acid radical, Figure III—4 (a),

197

    

 

(22 (MHz)

(b1

 

0 (22 (MHZ) 40

 

 

Figure III-4: HYSCORE absolute value spectrum of irradiated (a) succinic acid and

(b) malonic acid after Fourier transformation with respect to t] and t2. Q] = 001/21t,

(22 = (oz/Zn. (From Ref. 19)

 

198

 

both hyperfine couplings are greater than 26)] (at the particular crystal orientation
selected). The corresponding pairs of peaks are thus in the negative (0] region. For the
malonic acid radical, Figure III—4 (b), the hyperfine coupling is Al < 20)] for one crystal
orientation, which leads to cross peaks in the +(01 region, while it is A2 > 20)] for another
crystal orientation leading to appearance of cross peaks in the negative (0 1 region. It is
interesting to note that the diagonal peaks due to an incomplete inversion by the 7: pulse
are mainly confined to the positive (1)] region. The modulation that leads to the diagonal
peaks is therefore a phase modulation in t1 with a positive sign. The HYSCORE spectrum
of malonic acid radical shows residuals of the diagonal peaks and cross peaks in the
corresponding other side of the (02 region, accounted for by the fact that the expressions
for the nuclear transition frequencies, Equations III-8, are approximate. With the exact
expressions for the nuclear frequencies. S2 and c2 will not drop to zero. Therefore, there
will also be a contribution from a positive phase modulation for every negative phase
modulation in t1, and vice versa.

The optimization of the HYSCORE experiment includes adjusting two parameters,
the duration ofthe time period I and the width and amplitude ofthe mixing it pulse. 1115)
The value of I should be selected so that the suppression effect of the cross peaks is
minimized. Hofer has proposed a procedure of finding the optimum I value by recording a
series of three-pulse ESEEM spectra with increasing I, Fourier-transforming it with
respect to T and calculating the absolute value spectrum. The HYSCORE optimum I is
selected to be that value ofI in the three-pulse experiment at which the least suppression

occurs in the frequency region of interest. Since single crystal spectra are characterized by

199

a limited number oflines there may exist several I values that satisfy this condition. In
disordered systems. however, the smallest I at which all lines are present has to be chosen
to minimize line-shape distortions. 12) The typical I values used in practice range from 120
to 200 ns.

Another aspect of the optimization procedure is to improve the amplitude ratio of
the cross peaks to the disturbing diagonal peaks. The appearance of diagonal peaks is due
to an incomplete mixing by the inverting 7t pulse. 15) Ideally, this pulse should be much
shorter than the 7c/2 pulses for a complete mixing to occur. This condition cannot always
be fiilfilled, e. g., in the case of relatively high frequency proton lines, because of the
limited microwave power available. The degree of inversion obtained for certain pulse
widths and amplitudes can be estimated from the appearance of the HYSCORE echo.
With the ability to generate pulses of different amplitudes, one can use a 7: pulse with a
width between 10 ns and 20 ns to achieve almost complete inversion of the spectral region
excited by the 7I/2 pulses, thus efficiently suppressing the diagonal peaks.

The systematic analysis of HYSCORE data allows recovering the hyperfine tensor
principal values and tensor orientation with respect to other magnetic tensors associated
with a paramagnetic center. This information is contained in contour plots ofthe cross
peaks. This is visualized in Figure III-5 by considering first-order hyperfine interactions in
a S = 1/2, I = 1/2 spin system with axial symmetry under the (a) strong- and (b) weak-
coupling limitszo) For the weak coupling condition, A” < 20)], the first- order powder
ENDOR spectrum consists ofa pair of peaks whose lineshape characteristics, singularities,
and turning points are symmetric about the nuclear Larmor frequency. Cross peaks

corresponding to these idealized powder patterns can be constructed by connecting

200

 

 

Figure Ill-5: Schematic HYSCORE contour plots of cross peaks arising from an S =
1/2, I = 1/2 spin system considered at the level of first-order perturbation theory. (a)

(1)] > AH/2; (b) 0)] < Ai/2. f] = OJI/ZTI, f2 = (02/27:. (From Ref. 20)

 

201

 

 

 

 

 

(b)

 

 

 

Figure III-5

202

the corresponding lineshape features ofthe Va peak along the v2 axis with the VB peak
along the v1 axis and vice versa. The cross peaks thus form "ridges" (shaded area in
Figure III-5) perpendicular to the frequency diagonal. The extremes ofthese ridges
provide a measure ofthe parallel and perpendicular components ofthe hyperfine coupling.
For the strong coupling condition, A” > 2a)], the powder ENDOR spectra are no longer
symmetrically positioned about a center frequency, with respect to their parallel turning
points and perpendicular singularities. Similarly to the case of weak coupling, the contour
lines for the cross peaks define ridges that are now parallel to the frequency diagonal.7)
When second order effects are included in the hyperfine interactions or the anisotropy is
increased (i. e., greater T = (g gn “B “BE/’3)» the ridges develop a curvature, as shown
in Figure III-6.1221)

Recently, Dikanov and Bowman have developed simple analytical expressions for
cross-peak contours predicted for disordered S=l/2, 1=1/2 systems7-2) They have
presented a simple graphical method for determining the principal elements ofthe
hyperfine tensor. Plotting of the cross peaks on an axis system where the frequencies to]
and (112 are squared results in "straight-line" where tensor elements can be derived from the
slope and the intercept. The authors have also addressed the case of rhombic hyperfine
couplings, where the arc-shaped contours found for the axial case change to wedge-
shaped (horn-shaped) cross peaks, Figure III-7. The analysis ofthese more complex
shapes can still be performed by plotting the contours in an (1312 vs. (027- coordinate system

and analyzing the triangular shapes to extract the principal elements ofthe hyperfine

1611 SOT.

203

 

 

Figure III-6: Simulated HYSCORE contour plots arising from an S = 1/2, I = 1/2
spin system with an axially symmetric hyperfine tensor. Parameters: v] = 3 MHz; (a)
All = 3.6 MHZ, A1- = 1.2 MHz; (b) A” = 5.2 MHZ, A1 = 0.4 MHZ. f] = 601/27I, f2 =

(oz/Zn. (From Ref. 21)

 

204

 

 

 

 

 

 

 

 

 

6 v . v
5 .
4 .
3 .
2 1
l r
0 A
0 l 2 3
1‘, (MHz)
6 . - .
5.
4 P
3.
2 1»
1.
O 1 1 l
0 l 2 3
t1 (M112)
Figure III-6

205

 

..-

1‘7 ( MH 7.)
(a)

 

 

 

 

o 1 i 1
O 1 2 3

f] (MHZ)

gl—
U!
0'!

 

Figure III-7: Simulated HYSCORE contour plots arising from an S = 1/2, 1 = 1/2 spin
system with a rhombic hyperfine tensor. Parameters: v1 = 3 MHz, Axx = - 0.04 MHz,

A = 1.64 MHZ, AZZ = 4.40 MHz. f1 = (01/27I, f2 = (82/27:. (From Ref. 21)

W

 

 

206

111.3. HYSCORE Modulation Function for an S = 1/2, I = 1 Spin System

While the proton ENDOR is an established technique that achieves high hyperfine
resolution, the ENDOR spectroscopy of nuclei with low gyromagnetic ratios (yN) and
higher nuclear spin is associated with a number of difficulties, especially when nuclei other
than protons exhibit small hyperfine constants.23) Although nuclei with small magnetic
moments are not inherently less sensitive than protons (nuclear transitions are detected
indirectly via the EPR signal), optimum ENDOR signals for these nuclei are usually more
difficult to achieve than for protons. Moreover, the ENDOR resolution for nuclei with
small gyromagnetic ratios is lower than that for the corresponding isotopes with higher
nuclear magnetic moments. For example. the lower gyromagnetic ratios for 2H and 14N
relative to 1H and 15N, respectively, results in smaller hyperfine constants and lower
Larmor frequencies for the former. On the other hand, a large anisotropy in a spin 1 = 1/2
nucleus, e. g., a strong or-proton hyperfine interactions, causes a broad spectral extent,
which may also place the transitions in regions of weak ENDOR enhancement and poor
instrument sensitivity. When ENDOR experiments are carried out on biological samples,
detection difficulties are combined with the typically low paramagnet concentrations.

In contrast, the sensitivity ofthe ESEEM technique is inherently high for nuclei
with low gyromagnetic ratio (y) and increases with nuclear spin I as 21(1 + I).24-25)
ESEEM has been applied extensively to the study of weak hyperfine interactions of nuclei
such as 2H or 14N. 2H ESEEM offers a number of advantages over the proton ESEEM.
Thus, strong 2H hyperfine contributions to ESEEM overwhelmingly dominate

contributions fi'om 1H when coupling to both nuclei is present. The low 7 of 2H leads to a

207

concentration ofanisotropically broadened hyperfine transitions in a relatively narrow
spectral band and assures complete excitationzé) ofthe EPR transitions that connect the
2H nuclear hyperfine sublevels. The narrow 2H linewidths curtail undesired lineshape
distortion arising from the spectrometer dead time.27)

HYSCORE experimental data for S = 1/2, I = 1 spin systems have also appeared in
the literature. However, no 2D ESEEM function describing precisely and adequately the
HYSCORE data for such systems has been reported so far. In this Section, the derivation
of an analytical expression for the echo modulation amplitude in four-pulse echo
experiments (e. g., HYSCORE) for ideal non-selective 7t/2 and 11: pulses will be presented.
The density matrix formalism from Chapter III will be utilized, following Mims24) The
resultant formula will be used in Section 111.4 to simulate the HYSCORE data for a
tyrosyl radical.

The formula for the HYSCORE modulation effect will be derived under the
assumptions and with the approximations described in Chapter I for the case of a two-
pulse ESEEM experiment. The spin system under consideration consists of one electron

spin with S = 1/2 and one nuclear spin 1 = l in an external laboratory magnetic field BO,

and is described by the Hamiltonian

H0 / r2 = (as S2 - (11112 + l-A-S +1-Q.1, [111-13]

with the electron and nuclear Zeeman frequencies 005 = (g “B B0)/h (isotropic g tensor)

and (0] = (gn LIB.“ BO)/h, respectively, the anisotropic hyperfine tensor A, and the nuclear

208

quadrupole tensor Q. The nuclear quadrupole interaction is assumed to be small enough to
be ignored when calculating the unitary matrix M (cf. Chapter I) which determines the
modulation amplitudes. Thus, the applicability ofthe resulting algebraic expression is
expected to be limited to spin 1 = 1 nuclei that possess small quadrupole moments (e. g.,
2H or 14N). The relevant energy-level diagram is displayed in Figure I-22 with the |a>
states labeled a, b, c and the |B> states (1, e, f. Neglecting the nuclear quadrupole term, l-Q
'1, one can obtain the two eigenfrequencies of Ito/71, 0301 and (0(3, which are associated with
the electronic spin states M5 = 1/2 and MS = -1/2, respectively. In the high-field

approximation where the Sx and Sv terms are neglected, the nuclear transition frequencies

with no quadrupolar effects are given by

(00, = nt.((0] l + A/2)-n. [III-14a]

605 = nl-(col l - A/2)-n, [III-14b]

where n is a direction vector aligned with the external magnetic field B0 and I is a 3x3
unit matrix. The corresponding eigenvectors define the elements ofthe 3x3 unitary

transformation matrices Ma, MB‘ and M = MO,+ MB. The calculated matrix M thus i324)

_1

é—[l + cos(n —§)] — £81001" 55) $1] — C0501 " 5)]

M : fisinm — é) cos(n — é) — J—E sin(n — 8,) [III—15]

 

1 l . l
L§[l—cos(n—§)] -\/—._2.-srn(n—§) 311+905111‘5ll

_a

 

209

The difference, 6 = (n - i), determines the angle between the two effective magnetic fields

at the nucleus with MS = 1/2 and MS = -1/2 and is defined as in Chapter I and Section

111.2, by15-24)

2 2
(0 —[(0) +0) ) /4]
sin2(8/2)=l I a B I

 

[III-16a]
wawg

14.2 —1(wa 4612/41

mawB

 

6652 (8 /2) = [III-16b]

The eigenfrequencies are next adjusted to take account of quadrupolar
interactions. This approach ofincluding the quadrupole interactions (a perturbation) only
for calculating the fiequencies but not the modulation amplitudes isjustified by the fact
that small frequency differences are experimentally easier to detect than to make a precise
experimental measurement ofthe modulation amplitudes.24) Quadrupolar corrections to
01a and (”13 are obtained by diagonalizing the nuclear quadrupole term in the Hamiltonian
in Equation III-l3. Since the eigenfrequencies ofI-Q-I are (cf. Chapter 1) Eli = - K(1 i 11),

E0 = 2 K, the corrected nuclear transition frequencies are

”ab = 030, - A] - A3 [III-17a]
(obC = (0a + A2 + A3 [III-17b]
018C = 2 0)CL - A] + A2 [III-17c]
0JdC = (0B - A] - A3 [Ill-17d]

210

(Def: (05 + A2 + A3 [Ill-17C]

(1)de (DB - A] + A2 [Ill-17f]

with A] = K (3 - 11). A2 = K (3 + n). A3 = 2 K n, where K = e2qQ/4.

Introducing a resonance microwave field interaction H] ofthe form

 

H, : th[ 04 M] [III-18]

one can obtain the appropriate rotation operators which determine the evolution of the
density matrix during the pulses and the free precession periods. The rotation operators
for the nutation period p (of duration lN,p) and the free precession period 1 (of duration t])

are expressed according to Equations 1-80 and 1-8], respectively, as

RN,p = exp[i (H0 + H1) tN‘p/I‘t], [Ill-l9]

RU = exp[i H0 tl/h]. [III-20]

The evolution ofthe density matrix is then written out as

pE = W p0 R, [111-21]

where the rotation operator R for the four-pulse sequence shown in Figure 1—23 (c) is

21]

R = RNJ RT RN.” Rt] RNJII th RNJV Rm - [III-22]

The initial density matrix, p0, and the rotation operators RtJ and RN,p are represented in
terms of submatrices pao, pBO, PIJ‘ Qtl» Tva UN,p~ VNp and WN‘p, respectively,
according to Equations 1-84, 1-85, and 1-86.

The amplitude ofthe (unnormalized) stimulated echo in a four pulse experiment, E
= Tr{pESy}, is obtained using PE» given by Equation III-21, and Sy represented by
means of submatrices M and M+, according to Equation 1-91. The matrix multiplication in
symbolic form is conveniently performed by the algebraic computer program
Mathematicazg) The result consists of a sum of a large number of matrix product terms.

After enforcing the phase factor cancellation constraint (cf. Chapter 1, Section 1.4) only

sixteen terms are retained in the sum:

Tr{pESy} = 1' /2 Tr{
QI+t+UIV+Pt2+Tlll+P11+TII+PI+TI+pa0UIQIVIIPt1TIIIPtzTIVPI+tM

- Pt+t+TW+Pt2+Tlll+Pt1+VII+QI+Ul+pa0TIPITlIPt1TIIIPt2UIVQI+tM+

+ Qt+t+wIV+Qt2+Ulll+Pt1+Tll+PI+Tl+paOUIQ1VlIPt1UIIIQIQVIVPHIM

- PI+t+VIV+Qt2+Ulll+Pt1+VII+QI+Ul+pa0TlPITIIPt1UIIIQtzwIVQI+tM+
+ Qt+t+UlV+Pt2+VIII+Qt1+UII+pI+Tl+pa0UIQtWIIQt1VIIIPtzTIVPI+tM

- Pz+t+TIv+Pt2+Vm+Qt1+W11+Qz+Ui+pa0TiPzUthIVIIIPtzUIvaW
+ Qr+t+WIv+Qt2+Wm+Qt1+U11+PI+TPPaOUIQquQt 1WIIIQt2VIVPI+tM

- Px+1+Viv+Qtz+Wm+Qq+Wn+Qz+Ui+DQOTIPTUIIQIIWIIIQQWinli

212

+ QI+t+WIV+Qt2+WIIl+Qt1+UII+PI+VI+DBOWIQIWIIQI1WIIIQtQVIVpI+tM
- Pt+t+vlV+Qtz+vvlll+Qt1“NIl+QI+\Nl+pBOVIPIUIIQI1\NIIIQQ‘NIVQTHM+
+ QI+I+UIV+PI2+VIH+Qt1+UII+PI+VI+9BOWIQIWIIQHVIIIPtzTIVPI+tM

- Pt+t+TIV+Pt2+VIII+Qt1+WII+QI+WI+9BOVIPIUIIQI1VlIlPt2UIVQI+tM+

+ Qt+t+WIV+Qt2+UIll+Pt1+TII+PI+VI+PBOWIQIVIIPHUIIIQtZVIVPHtM

- P1+t+VIV+Qt2+UIII+pt1+VII+QI+WI+9BOVIPITIIPHUIIIQtzwIVQI+tM+
+ Qt+t+UlV+Pt2+Tlll+Pt1+TII+PI+VI+9BOWIQIVIIPHTIIIPtzTIVPt+tM

- Pt+t+TIV+Pt2+Tlll+Pt1+VII+QI+Wl+pBOVIPTTIIPt1TIIIPIQUWQI+tM+

: [111 - 23]

The above equation represents the general expression for envelope modulation with four-
pulse echoes. The initial Boltzmann populations of all nuclear sublevels belonging to a
particular electron spin manifold can be considered equal to a good approximation, i. e.,
paO E (1], p90 E b], where I is a 3x3 unit matrix, and a and b are proportionality

constants.
With the assumption of complete excitation (H1 >> H0) the rotation operator for

nutation, Equation III-l9, can be expanded as in Equation 1-92 to yield the submatrices T,
U, V, and W in the form of Equations 1-93. After substitution ofthe submatrices for the
initial density and the nutation with the corresponding expressions the unnormalized four-

pulse echo modulation fimction becomes

213

E = (1/16) sin(wN tpl) sin(mN tp“) sin(wN tpr) (a - b) ><

Tr{ sin2[(o)N tpm)/2] [Q1+t+Qt2+M+Pt1+PT+MQTM+PtlMQQMJFPHIM
+ PT+I+MQIZ+M+PtI+MQT+M+PTPHMQQQIHM+
+ QT+I+M+P12+MQt 1+M+PT+MQIQHM+PQPT+IM
+ PT+t+PQ+MQt1+QT+M+PIMQHM+Pt2MQT+tM+1

- cosz[(wN twp/2] [QT+I+M+PI2+P[1+PT+MQTM+PI lPtzpmM

+ Pfifiptzmt 1+MQT+M+PTPt1Pt2MQT+tM+
+ Q1+I+Qt2+Qt1+M+PI+MQIQt10t2M+PT+tM
+ PT+I+MQQ+QII+QI+M+PTMQIIQQQMM+1 }

[III-24]

The normalization factor for the envelope modulation function is given by the echo
amplitude when all times are set to zero, T—)O, t]——>O, t2——>O, while the free precession

matrices P and Q are set to 1. It is equal to

- (1/4) sin(coN tp1) sin(coN 1p") sin(wN thV) (a - b) COS((DN tp111) Tr{I}.

[111-25]

The normalized echo modulation envelope function is then given by

E(T,t],12)=(1/12)Tr{

- sin2[(wN tp11])/2]/COS(OJN tp111) ><

[Qz+t+Qtz+M+Ptl+PI+MQTM+PtIMQQM‘LPIHM

214

+ PmrMQQflWPt 1+MQT+M+PTPHMQI2QTHM+
+ QT+1+M+PQ+MQII+M+PT+MQIQHM+PIZPT+tM
+ PT+I+PQ+MQI1+QI+M+PTMQHM+Pt2MQI+tM+]
+ cosz[(wN tp11])/2]/cos(wN thII) x

[QT+I+M+PQ+P[]+P1+MQTM+PUPI2PI+IM

+ PT+I+P12+Pt1+MQT+M+PIPt1PtzMQT+tM+

+ QT+I+QIQ+QI1+M+PI+MQTQI1QIZM+PI+IM

+ Pt+t+MQt2+Qtl+QI+M+PIMQtlQLZQ1+tM+1

}. [III-26]

In a HYSCORE pulse sequence the turning angle for the third pulse is chosen to

be (0N tp111 = 7r. With this selection ofthe turning angle,

cos(coN tp111) = -1,
COSZ[((DN tp11])/2] = 0,
Sin2[((t)N tp11])/2] = l,

and

E(r, t1, t2) = (1/12) Tr{ QT+1+QI2+M+PH+PT+MQTM+PUMQQM+PTHM
+ PT+I+MQt2+M+Pt1+MQT+M+PTPIIMQIZQT+IM+
+ QT+t+M+Pt2+MQtl+M+PT+MQTQHM+Pt2PT+tM
+ PT+I+Pt2+MQt1+QT+M+PTMQHM+Pt2MQT+tM+ }.

[111-27]

215

Note that since the sum contains both product terms and their Hermitian conjugates, the
corresponding terms can be combined to simplify the expression: In addition. the variable
time, t, must be set to zero to ensure exact cancellation of the phase factors associated

with inhomogeneous broadening. Equation Ill-27 can thus be rewritten in the form

Eu, t 1. t2) = (1/6) Tr{ QT+Qt2+M+Ptl+PT+MQIM+PIIMQI2M+PIM
+ QT+M+PQ+MQH+M+PI+MQTQth+Pt2PTM }.

[III-28]

For an S = 1/2, 1 = 1 spin system, the 3x3 diagonal matrices P and Q for the free

precession period 1 have non-zero elements

(ij){31 = exp(i (Dog t1), [III-29a]

(ijltJ = eXpU ij ti). [III-29b]

where oq and Bj refer to the nuclear spin states |a>, |b>, |c>, and |d>, |e>, |f>, respectively.
Evaluation of Equation III-28 (carried out by the algebraic computer program
Mathematica) with definitions of P and Q according to Equation III-29, and M according
to Equation III-15 leads to an explicit form of the HYSCORE echo modulation formula
for S = 1/2, 1 = 1 spin system. The expression is given in Appendix B and consists ofa
lengthy sum of cosine terms, each multiplied by a modulation depth related factor.
Examination of the expression shows that it includes (a) constant terms that do not

contribute to the echo modulation (numeric constants or cosine terms that depend only on

216

 

I). (b) terms containing the modulation frequencies wab, (”be mac, (ode, (Def, (Ddfln either

It or t2 time domain, which produce peaks along either 0)] or (02 axes in the frequency
domain, and (0) terms that contain cosine functions with both time variables
simultaneously in the argument giving rise to cross peaks. Unfortunately, due to the size of
the expression, simplification ofthe formula is not feasible by symbolic manipulations even
when utilizing heavy computing resources. However, the derived echo modulation
function can be readily encoded as a C or FORTRAN function and used for numerical

simulations of experimental HYSCORE spectra.

111.4. Application of HYSCORE t0 the Study ofa Tyrosyl Radical Model System

111.4. 1. Introduction

 

Tyrosyl radicals belong to the class of amino acid radicals, which are known as
essential participants in the reactions of a variety of enzymes.29-30) The first catalytically
important amino acid radical, the tyrosyl radical in the Ribonucleotide Reductase (RNR)
from E. coli , was only discovered in the 19705.31) Tyrosyl radicals have been found in
other enzymes such as RNR,32) Photosystem 11 (PS II),33) Prostaglandin H Synthase
(PGHS),34) Galactose Oxidase (GOase),35) and in amine oxidases36) Ofthe twenty
biologically essential aminoacids, tyrosine is the easiest to oxidize. 1n aqueous solution at
pH 7 it has a redox potential of+930 mV relative to normal hydrogen electrode37) This
fact may account for its widespread occurrence in enzyme catalysis.

Radical enzymeszg) generally contain metal centers such as Fe, Cu. Co or Mn,38)

or a redox active cofactors such as S-adenosyl methionine whose function is similar to that

217

ofthe metal. The metal center acts to generate the amino-acid radical, which in turn
initiate catalysis by abstracting a hydrogen atom from the substrate. This general
functional scheme is related to a general structural frame of the metalo-radical enzymes.
The metal, the redox-active side chain and the substrate—binding channel are all physically
close in the enzyme structure. The aminoacid radicals typically occur as transient species
during the enzyme catalytic cycle. There are exceptions, such as the Y122 in RNR or YD
in PS 11, both of which are stable radicals.

The transient nature of the radicals necessitates the use of more sophisticated
spectroscopic and trapping methods to detect and characterize them, which accounts for

the delayed discovery of the metalo-enzyme aminoacid radicals.

111.4.2. EPR smectroscmgic studies oftyrogzl radicals

Determination of the electronic and nuclear structures of tyrosyl radicals is
necessary to gain insight into the molecular mechanisms of participation of protein-
attached tyrosine-based radicals in enzyme catalyses39'4l). EPR has proven to be the most
informative spectroscopy to study the tyrosyl radicals in both biological and model
systems. However, since the radical is effectively immobilized in the protein structure at
random orientations, powder EPR spectra are generated. These spectra lack resolution
due to inhomogeneous EPR line broadening. To obtain information on various hyperfine
couplings, ENDOR and pulsed EPR spectroscopies have been utilized in combination with
specific isotopic labeling. B-CHZ proton, Figure III-8, is characterized by an axial

hyperfine tensor, which reports on the unpaired electron spin density on Carbon-1 as well

218

as on the dihedral angle ofthe CB-ll bonds with respect to the 2pZ orbital of Carbon-1, in

accordance with the relation (cf. Chapter 1),

Also = [0% + 092 cosztenpn‘ia, [Ill-30]

where Also is the isotropic hyperfine coupling for the B-proton, pnCOL is the unpaired
electron density at Carbon-l, QBO :‘Z— 8 MHz, 0132 = 164 lVsz, 8 is the dihedral angle of
the C-H bond ofthe B-proton relative to the 2pZ orbital of Carbon—l (cf. Chapters 1,
10.42) B-ZHC- labeled tyrosyl radicals have been found to exhibit unexpected 2H -ESEEM

lineshapes as well as anomalous EPR and ENDOR linewidths43'45) This phenomenon has

COO'

 

 

Figure III-8: Spin-density distribution in the tyrosine neutral radical.

 

 

219

 

been attributed to the rotation mobility ofthe phenol head group about the C1-C5 bond.
As the rotation barrier decreases, the heterogeneity in the dihedral angles increases,
leading to increased dispersion ofthe magnitude ofthe isotropic coupling, Aiso- Analysis
onH-ESEEM spectra has yielded values ofthe rotational barrier and relative populations
ofthe rotamers.44‘46)

The or-protons at the 2,6 and 3,5 ring positions, Figure III-8, are characterized by
rhombic hyperfine tensors. 1n general, the coupling to the 2,6 protons is relatively weak,
reflecting low unpaired spin density at these positions. The 3,5 as well as the methylene
protons are more strongly coupled. The hyperfine tensors for tyrosyl radicals in various
enzymes and in two model systems are summarized in Table Ill-1.21) The results of
various studies lead to the same basic spin density pattern displayed in Figure III-8, which
appears to be common for all tyrosyl radicals studied so far. ENDOR and high-field EPR
experiments45~47-48) have led to the conclusion that possible hydrogen bonding
interactions perturb the basic spin-density pattern only slightly and that the striking
variation of lineshapes observed in the CW-EPR spectra of tyrosyl radical enzymes and
models is due to variations in the dihedral angles ofthe B-CH2 bonds, rather than
variations in the spin-density distribution.

In the present study, the hyperfine coupling of 3,5-proton nuclei in tyrosyl neutral
radical in frozen, aqueous NaOH glass is addressed to illustrate the applicability ofthe
HYSCORE analysis with the 2D ESEEM modulation function derived in the previous
section, and to determine the corresponding nuclear quadrupole and anisotropic hyperfine
parameters. The 3,5-proton hyperfine tensor components have been estimated indirectly

from simulation of EPR spectra,39) and the 3,5—1H coupling in tyrosyl radical in

220

Table Ill-l: Hyperfine tensors oftyrosyl radicals. Values are in MHz. (From Ref. 21)

Radical Source

Atom/ RNR GO YD YZ PGHS Aqueous
Position (PS-11) (PS-11) Glass
H 3.5 x -26.7 -26.4 -26.8 -25.7 -25.4
H 3.5 y -8.4 -8.4 -7.9 -8.4 -7.2
H 3,5 2 -19.6 -21.6 -l9.5 -19.5 -l9.5 -l9.5
H 2.6 x 5.0 4.8 4.2 5.0 4.9

H 2.6 y 7.6 6.8 7.1 7.5 7.1 6.5
H 2.6 2 2.1 2.4 1.3

H CH2 H 61.2 43.4 31.5 35.4 69 3.0
H CH2 1 53.7 39.8 27.2 29 58.2 2.3
H CH2 H 2.1 11.4 9.8 7.9

H CH2 1 -4.5 4,4 1.4

H bond u N. A.

Hbondi NA. 3.1 3.0

011(2) -125 -111

Ref. 4755 5e 39.43.57. 45 a) 44,46,49.
58 55

a) Shi, W.; Hoganson, C. W.; Espe, M.;Bender, C. 1.; Babcock, G. T}, Kulmacz, R. 1.;

Palmer. (3.; Tsai, A.-L. unpublished results.

221

ribonucleotide reductase has been determined at liquid helium temperatures under near-
optimum conditions for ENDOR.47) These studies indicate that the hydrogen nuclei at
ring positions 3 and 5 are essentially magnetically equivalent. Utilizing the advantages of
the 2H ESEEM over lH-ESEEM Warncke and McCracken have characterized the
coupling ofthe 3,5 (it-protons, using tyrosine specifically 2H labeled at these positions49)
Their 2H ESEEM results have demonstrated that, by rational manipulation of the
microwave pulse time interval, 1, in the stimulated echo ESEEM experiment, the
magnitude of the principal components of the rhombic hyperfine tensor and the relative

sign ofthe isotropic coupling can be determined.

111.4.3. HYSCORE of 3, 5 2H-labeled tyrosyl radical model system

Recently, Filep2 1) has carried out HYSCORE experiments a 3, 5 2H-labeled
tyrosyl radical model system. The neutral tyrosyl radical (Figure III-8) has been generated
by UV irradiation of 5 mM specifically labeled tyrosine in frozen, aqueous NaOH glass
containing 5 mM Gd3+ ions and approximately 12 M LiCl. The metal salts have been
added to form a glass matrix as well as to enhance the relaxation of tyrosyl radical at liquid
helium temperatures. Without increasing the relaxation rate of the tyrosyl radical, low
sampling rates (below 10 Hz) in the pulsed EPR experiments would have to be used,
which would make impractical collecting experimental data points in two time dimensions.
An HYSCORE time-domain data set (128x128 data points) and a contour plot ofthe
corresponding frequency-domain spectrum are shown in Figure III-9. The contour pattern
is clearly different from the one generated by an axial hyperfine interaction (cf. Section

111.2.). As rhombic hyperfine tensors are expected to give rise to horn-shaped contour

222

 

—4000
\Iw I ...J . “'"‘ v 4
I 1' ~.
V V ~2500

i

(9)

,,_"'
Mme—o» (- 2000 a,

 

 

 

 

 

 

 

 

 

:5
c-j ’M
:3; ”WWW"- ‘—_— __ —: #1500
3 200- M,’ _ If __
a W!“ ’_.._A—~ ' 1“ '°°°
o 0_ is?” - , fie ~5oo
'5
”3 '100 t l T t l r t 0
0 500 1000 1500 2000 2500 3000 3500 4000
t2(US)
b .

 

 

 

 

#7

A e . €2\ A
5

2.0 2.5 3.0 3. 4.0

0.5 1.0

 

 

Figure Ill-9: (a) Time-domain HYSCORE data (128x 128 data points) from 3,5 2H-
tyrosyl, with T = 200 ns; (b) the corresponding HYSCORE frequency-domain

contour plot. B0 = 3129 G, v = 8.910 GHz. f] = 001/271, f2 = (Dz/27L (From Ref. 21)

 

223

 

 

lines, the two clearly resolved arcs (designated by 1 and 2) are identified as the two
limiting arcs, which form the boundary ofthe horn. They correspond to (p = 0° and (p = 90
°, where (p is the azimuthal angle specifying the position of B0 in the principal axis system
of the hyperfine tensor (Figure III-10). In a randomly oriented sample B0 spans with equal
probability all possible positions determined by pairs of values OM) and 9 between 0° and

90°. At a particular value of (p, sweeping B0 from 9 = 0° to 0 = 90° results in a pair of

 

vy

 

 

 

Figure III-10: Definition ofthe position ofthe external magnetic field vector, B0,

in the principal axis system of a hyperfine tensor with rhombic symmetry.

 

 

 

 

arcs as for an axial hyperfine tensor. There is one such pair for each (p and the ensemble of
these arcs creates the horn. When tp = 0°, the two principal values of the hyperfine tensor
are A 1 = Axx and All = AZZ. When (9 = 90° the hyperfine parameters are A i = Ay'V and A“
= A22- The evaluation of these boundary arcs can, in principle, yield all three principal
values of the rhombic hyperfine tensor. (One should be cautious, however, since the
observed arcs might not represent the actual boundary arcs because the modulation depth
at the turning points and the singularity points becomes zero. In addition, it is not clear
how the I suppression comes into effect for an S = 1/2, 1 = 1 spin system.)

The hyperfine tensor components can be obtained by analyzing the boundary arcs l
and 2, following the method of Dikanov and Bowmanzz) and combining the two resultant
axial hyperfine matrices into a rhombic one?” The principal values for the 3,5 2H
hyperfine tensor obtained through this analysis are Axx = -0.8 MHz, A”. = -3.1 MHz, and
A22 = -3.6 MHz2 1), while the values determined by Warncke and McCracken by
theoretical simulations of stimulated ESEEM data for a tyrosyl model trapped in 40%
NaOH glass matrix are Am. = -3.0 MHz, A“. = -3.9 MHz, and A22 = -1.1 MHz, i0]
MHz.4-9)

Numerical simulations ofthe HYSCORE contour mapZI) have shown poor
agreement with the experimental spectra, Figure III-1 l. The simulated spectrum in Figure
Ill-l l (b) has been generated using hyperfine parameter values considerably different from
those determined according to the method of Dikanov and Bowmanzz) There is also
significant discrepancy in the intensities at certain parts ofthe contour lines (e. g., the tail
of are 1). This can be understood considering that the intensities have been calculated

using the formulae of Gemperle et al.”) derived for S=l/2, I=l/2 spin systems. While the

225

 

-‘Jl

 

 

 

Figure Ill-ll: (a) HYSCORE contour plot of3,5 2H-tyrosyl (same as Figure 111-
9b); (b) the corresponding frequency-domain simulation using the following
parameters: nuclear Larmor frequency, v] = 2.1 MHz; Axx = - 3.82 MHz, Ayy =

- 2.98 W2, AZZ = -l .0 MHz; tau-value, T = 200 ns. f] = (91/27:, f2 = (02/21:. (From

Ref. 21)

 

 

22f)

 

(a)

 

 

 

 

 

 

 

(bi)

 

 

 

1r

P

 

P

0.5

4.0

3.5

3.0

2.5

 

 

2 c..~
:23: Ne.

w.—

c.—

We

c

1.5 2.0

1.0

Figure III-1]

227

frequencies can still be calculated with this formula to a good approximation (the small
nuclear quadrupole interaction of deuterium does not alter the hyperfine frequencies
substantially), the intensities of the cross peaks may be more significantly affected by the
quadrupole interaction?” The observed hyperfine correlation pattern, Figure Ill-11 (a), is
also strongly affected by the t-suppression effect, which is not apparent from the

presented simulation.

111.4.4. I-sugpression effect in HYSCORE

The "c-suppression effect in HYSCORE has been mentioned in Section III-2. There
is cross peaks intensity dependence on the separation ‘C of the first two pulses
superimposed on the amplitudes determined by the spin Hamiltonian. As a result, at
certain t-values the intensity of certain cross-peaks becomes zero (blind spots). 1n
randomly oriented samples this leads to a distortion of the lineshape, which makes the
lineshape analysis necessary in both 1D ESEEM and HYSCORE experiments. In
HYSCORE of S = 1/2, 1 = 1/2 spin systems, partially suppressed contour lines may still
provide sufficient information to deduce the hyperfine tensor parameters without spectral
simulationszz) As shown by Hofer.12) in this case, the I-suppression effect can be
predicted and possibly avoided by experimentally adjusting the value of T. For a limiting

case of a weak hyperfine anisotropy, AZZ < (1)], where the modulation frequencies can be

approximated by

(nag = lwl i All/2|, [111-31]

228

the suppression effect can be calculated from the cross peak amplitude, Equation Ill-3c. as
a function of A22 and colt, as shown in Figure Ill-12 for 0 < AZZ < 603] and 0 < (1)11 < 47:.
If one line ofa pair is at zero frequency, the corresponding cross peaks cannot be
observed. The frequency width of this blind spot decreases, however, with increasing I.
Line pairs arising from AZZ < 2w] fell within the frequency range 0 < to < 20)]. 1ft is
chosen according to (011 < it, a bell-shaped amplitude function attenuates cross peaks at
the wings of this spectral window (0, 200]), but no extra suppression holes are generated
inside the spectral window. At the expense of signal-to-noise, the frequency dependence

ofthe amplitude function is reduced for decreasing (1)11. For it < colt < 21:, two

 

suppression holes are generated which merge into one hole at (n == co] when (or: = 2n. A
further increase of (911 produces an increasing number of suppression holes across the
spectrum. By a proper choice of I, a spectral window can be selected to minimize
amplitude distortions for a given range of hyperfine coupling constants. It is clear that the
summation of suppression-effect functions for an infinite number oft values will result in a
frequency-independent amplitude function with two blind spots, at (D = 0 and w = 2a)]. For
AZZ > 2m], a general rule for the optimum (01‘! cannot be established other than an increase
of A22 should be compensated for by a decrease oft to maintain a certain amplitude

function.

Ifthere is appreciable hyperfine anisotropy, the modulation frequencies, ma and
(up, are described by

(50,13 = [Ax22/4 + 14,244 + (e), i AZZ/2)2] 1/2. [11192]

229

mn/n

s
‘ 3.5
. 3.0

2.5

 

 

-210 -1‘.o oio 1Z0 20 3.0

 

 

Figure Ill-12: Calculated suppression effect as a function of A22 (0 < Azz < 6m)
and 0311 assuming 0) = lw] i All/2|. Dark (light) shading corresponds to weak
(strong) suppression effect. The sum ofthe suppression function over (1)11 results in
an amplitude function with only two suppression holes at (n = 0 and u) = 2m] (top).

(From Ref. 21)

 

230

 

The presence of sz and A}.Z components in the expressions for ma and (DB destroys the
symmetry ofthe ESEEM lines with respect to (1)] (or All/2), and the correlation ridges in
a HYSCORE spectrum are no longer perpendicular (or parallel) to the frequency diagonal.
However, for those paramagnetic species which have one ofthe hyperfine tensor principal
axes parallel to the external magnetic field, the simple equation for ma and 033. Equation
111-31, is valid. Therefore, the corresponding cross peaks will be located at (031 - Aii/Z» 0)]
+ Ail/2) and ((o] + Ail/2» (.01 - Ali/2) and the distance between the peaks, measured parallel
to either one ofthe two axes ofthe 2D spectrum, gives directly the principal values ofthe
hyperfine tensor. Although these cross peaks have zero intensity (k = 0), their expected
location can still be found by following the ridges to the points where they intersect the
line crossing the diagonal at ((01, (9]). Hofer has shown that, in general, when no simple
picture ofthe suppression effect can be developed. the amplitude distortions can be
eliminated completely if 2D spectra are collected for a series ofI values and then added
together, i. e., by a 3D experiment. 12) Obviously, improving the spectrum authenticity in
this manner requires collection ofa large amount of experimental data.

For an S = 1/2, 1 = 1 spin system, the analysis and prediction ofthe I-suppression
effect becomes more difficult because it is also influenced by the quadrupole coupling. The
I-dependence ofthe 1D ESEEM lineshape for the 3, 5 2H-labeled tyrosyl radical has been
described in Ref. 49. Figure Ill-13 shows a series of experimental HYSCORE contour
plots obtained with different T-ValUCSZI). Suppression of various parts ofthe lineshape
depending on I can be observed. These spectra demonstrate that the shortest I-value (200

ns) yields the least suppressed features, in agreement with Hofer’s analysiszl)

231

 

 

Figure Ill-l3: HYSCORE experimental contour plots of3,5 2H-tyrosyl radical taken
at various values of I: (a) 200 ns; (b) 300 ns; (c) 400 ns; (d) 500 ns; (e) 600 ns. f] =

col/27:, f2 = (02/211. (From Ref. 21)

 

232

 

(a)

(b)

 

 

 

  

 

 

 

 

 

0v oé Wm

3 2. 3 2 o._ no we

 

3.5

3.0

2.0 2.5
f, (MHz)

1.5

1.0

 

0.5

3. ,2 3 mm 3 m. 3 2
3:23

Figure III-l3 (a, b)

233

3.0

f2 (MHZ)
2.5

1.5 2.0

1.0

0.5

4.5

4.0

f2 (MHZ)
1.5 2.0 3.0 3.5

1.0

 

(C)

3.5

 

 

 

 

 

 

2.5

0.5

 

 

 

 

. J
l 4
l- 4
1
0.5 1.0 1.5 2.0 2.5 4.5
f] (MHZ)
Y j T j j T v (d)
f
.9 J
t \
'l
‘1
i l
0 5 1:0 1 5 4.5
fl (MHZ) Figure III-13 (c, d)

234

 

 

(8)

 

 

we

nu .mwwuv.
10. WE

o.e tm.m on em -q~
nzzvo

010

 

 

 

m.—

o._

md

3.5

3.0

2.5

f] (MHZ)

1.5 2.0

1.0

0.5

Figure III-l3 (e)

235

111.4.5. Simulations ofthe HYSCORE exyerimental data for 3, 5 2H-labeledtyrtggl
radical

The HYSCORE experimental spectra obtained for the 3, 5 2H-labeled tyrosyl
radical from Ref. 21 have been simulated using the C-language program "mims4".59) The

program evaluates the HYSCORE modulation function, encoded as the module

 

"EnvE4.c", for given spin Hamiltonian parameters and values of I, t], and t2. The P:
modulation function is multiplied by an exponential dumping factor (exp[ - Mt] + t2)], i
where 7» is an adjustable parameter determining the linewidths in the frequency-domain

spectrum) to simulate the decay of the echo envelope. By incrementing t1 and t2 the '

simulated two-dimensional spectrum is built for a particular orientation defined in terms of
the angles 0 and (p (Figure III-10). The orientation dependency is contained in the zero-

order hyperfine frequencies, ma and (DB, expressed a549=50)

ma = [(0)] - Axx/2)2 sin2(0)cos7-(tp) + (0)] - A3372)2 sin2(0)sin2(tp)
+(w1 - AZZ/Z)Z e052((p)]i/2 [III-33a]
(Up = [too] + Axx/2)2 sin2(e)c052(tp)+ (001+ 4,372)2 sin2(9)sin2(q))

+(m1+ AZZ/Z)2 C052(tp)]l/2. [111-3315]

where 1x = sin(0)cos((p), l}. = sin(0)sin((p), and 12 = COS(([)) are the direction cosines for the
direction of the laboratory field B0 in the hyperfine principal axis system. These
frequencies are modified by the quadrupole corrections as in Equation III-17. Averaging

of the 2D time domain data is performed over all orientations of the paramagnetic species.

236

0 < 0 < 90°, 0 < (p < 90°, via Simpson numerical integration over 9 and (p with the usual
solid-angle probability distribution weighting for the random molecular orientations. A
small 8 region (a = |sin(o.) - of < 104. where 0t denotes 9 or (p) around the boundary
values for the angles is excluded from the computation, as the modulation depth becomes
zero or a very large number there. The final result is a HYSCORE time-domain data file
for the disordered paramagnetic system. The time-domain data are then analyzed by 2D

Fourier transformation in the same manner as the experimental HYSCORE data, using a

set ofMATLAB scripts. 51259)

A 2D time-domain data set and its corresponding frequency-domain contour map
are shown in Figure Ill-l4. The agreement with the respective experimental HYSCORE
contour plot, Figure 111-1 1, is satisfactory. Each cross peaks appears split as a result ofthe
I-suppression effect. The major discrepancies are observed in the relative intensity of the
two portions of a cross peak as well as the orientation of the peak lineshapes in the f lfz
coordinate system. A series of contour maps for different I values is shown in Figure 111-
15. It is apparent that the I-suppression effect creates blind spots in the spectra and
modifies the appearance of the contributions of the hyperfine frequency components. The
demonstrated I-suppression efi°ect is consistent with the experimental HYSCORE data in
that larger I values create more suppression holes. Although there is no complete
correspondence between simulated (Figure 111-15) and experimental (Figure III-13)
contour maps for all values of I, the simulated and experimental cross—peak patterns
follow the same trend. Detailed simulations carried out upon incrementing I by 20 ns have
shown that there is a smooth development of cross-peaks lineshapes between the patterns

of Figure Ill-15. The lack of complete agreement between the HYSCORE experimental

237

 

 

 

Figure Ill-l4: Simulated HYSCORE spectra of 3,5 2H-tyrosyl radical. (a) A 3D plot
ofthe time-domain simulated data (128x 128 points). (b) The corresponding 3D
frequency-domain magnitude spectrum obtained by 2D Fourier transformation ofthe
time-domain data in (a). (c) Contour plot ofthe frequency spectrum. Parameters:
nuclear Larmor frequency, v] = 2.1 MHz; Axx = - 2.3 MHZ, Ayy = — 3.1 MHz, AZZ = -
0.9 MHz; 1] = 0.1; e2qO = 0.22 MHz; 2t = 0.7 usec’l; tau-value, I = 200 ns; number of
0 increments over the interval 0-90°, 30; maximum number ofq) increments over the

interval 0-90°, 30. f] = col/2n, f2 = (02/27:.

 

238

 

 

Echo Amplitude (an)

 

(a)

\\ \\ \ s .
“\‘lt it“ tit
'\‘

l

iljltl, 'i” ”

ll 11 1111' '

'llii‘illllhl "
“.7131,”

t (“filllli
l

 

Figure Ill-l4 (a)

239

(b)

  
   

    
   

    
    
   

 
   

   
 
  

 

   

 

250W
MW
‘1" (115.111 11
E 100‘ \ "V”! _ , >. 1.11"
50‘ ’hu, "“3“ ”Austlfl‘ I.” //:I.\..'I0i"‘1“\m\“l
o ‘ i‘t 1111i M””11””!Illflilliiii.‘ "é“...

     
 

  
 

Figure Ill-l4 (b)

240

 

 

 

 

 

Figure Ill-l4 (c)

24]

and simulated spectra may be due, in part, to a possible offset between the I values fi‘om
the experiment relative to those from the simulations. Time offset of 30 ns can influence
the cross-peak morphology substantially. Another reason for the observed discrepancies
may, of course, come from lack of perfect adjustment ofthe spin Hamiltonian parameters
used in the simulations.

Figure 111-16 represents a HYSCORE contour map generated with no quadrupole
coupling. (a), and with a relatively large value ofthe deuteron quadrupole coupling
parameter, eZqQ = 300 kHz, (b). It is evident that the quadrupole coupling does affect the
lineshape ofthe cross peaks by modifying the I-suppression effect. This is to be expected
since the quadrupole coupling is included in the wij (i,j = a, b, c, d, e, f) hyperfine
frequencies. which appear in the HYSCORE modulation function as arguments of cosines
ofthe type cos(wij I).

The values of the simulation parameters for the hyperfine and quadrupole
interactions, Axx = -23 MHz, A}, = -3.1 MHz, AZZ = -09 MHz, eZqQ/h = 220 kHz,
asymmetry parameter I] = 0.1, fall in the range ofthe 3,5 OL-proton values (cf. Table III-1)
after appropriate scaling by the factor of 6.5 l, and agree well with the range of 2H
quadrupole coupling constants for a wide variety of organic compound352'54).
respectively. HYSCORE cannot provide direct information on the sign ofthe hyperfine
coupling; however, it reports on the relative sign ofthe isotropic and the dipolar part of
the hyperfine interaction. Furthermore, it is known that Also < 0 for or-protons, which is
expressed in the negative value ofthe McConnell constant (Qa(2HC) = -lO.7 MHz).42)

The discrepancies in the exact hyperfine constant values can be attributed to the

effect ofthe matrix. Gadolinium (111) salt has been added to the sample to enhance the

242

 

 

Figure Ill-15: Frequency-domain contour plots for the 3,5 2H-tyrosyl radical
HYSCORE time-domain simulations performed with the C program "mims4" using
the following parameters: nuclear Larmor frequency, v] = 2.1 MHz; Axx = - 2.3
MHz, Ayy = - 3.1 MHz, AZZ = —0.9 MHz; n = 0.1; e2qo = 0.22 MHz; w = 0.7 usec'
1; number oftime-domain data points, 128x128; number of0 increments over the
interval 0-90°, 30; maximum number of (9 increments over the interval 0-90°, 30; tau-
value, I = 150 ns (3), 200 ns (b), 300 ns (c), 400 ns ((1), 500 ns (e), 600 ns (f). f] =

(0 1/271, f2 = (DQ/ZTE.

 

 

243

“can. '.:. -Ak‘“fl“fcfi'

f2 (MHZ)

Figure II]-15 (a)

244

I , .5 I
(VlaZJ MHZ O

( =-2.3 MHz
Ayy=~3.1 MHz’
AZZ=~O.9 MHZ

 

 

(b)

         
  

 

V l

V1821 MHZ
mar-2.3 MHZ

Ayy:-3.1 M ‘
$57.42
I

 

Figure 1]]-15 (b)

245

f2 (M1121

 

 

Figure III-15 (c)

246

 

 

liz (MHZ)

 

(d)

 

   
 
   

 

r I 7

V1=2.1 M‘HZ
Now-2.? MHz
Aw=.31.1 MHZ

 

 

Figure Ill-15 (d)

247

 

 

(e)

 

 

  
 

imbaoj
nThatq=31
"Phl830(

ntpts;1 23

 

Figure Ill-15 (e)

248

 

 

 

 

 

  
     
 
 

 

Figure Ill-15 (f)

249

(0
r v' } jI \ 1
Vial] MHZ
Agra-2.3 MHZ
Ayyé;3.1‘M1.-lz
Az;=,-O.9 MHz ~
ta 0.1\\

 

4 4.5

-.( '.I‘ "JR-um

 

 

 

Figure Ill-l6: Frequency-domain contour plots for the 3,5 2H-tyrosyl radical
HYSCORE time-domain simulations performed with the C program "mims4"

using the following parameters: nuclear Larmor frequency, v] = 2.1 MHz; Axx = -
2.3 MHz, Ayy = - 3.1 MHz, AZZ = -0.9 MHz; number of time-domain data points,
128x128; number ofB increments over the interval 0-90°, 30; maximum number of
(p increments over the interval 0-90°, 30; it = 0.7 usec‘l; tau-value, I = 200 ns; T]

= 0.1; e2qo = 0. (a), equ = 0.3 MHz, (b). f] = tin/2n, f2 = egg/zit.

 

250

 

 

 

3

z
3:): NA

 

f] (MHZ)

Figure Ill-l6 (a)

251

(b)

 

 
 
 
  
 

vl=2.1 MHZ
Azy‘zrz-ois MHz J
eta=0.1

   

N

     

 

\:\“\ “i .

“ 7 r“; ‘1

\\ XE V 1;;

\“L \\_ '

. n C's-.2": ': 351‘ \ 5. .
5 4 4

3. .5

Figure Ill-16 (b)

252

very slow relaxation of tyrosyl radicals at low temperatures, thus making possible
collection ofa large number of 2D HYSCORE data points in a reasonable amount oftime.
Gd3+ is a strongly paramagnetic ion, containing seven unpaired electrons (S = 7/2). It
gives rise to a very broad EPR signal, which is hardly observable in derivative EPR
spectra. This signal is superimposed on the tyrosyl radical signal. As a consequence, the
spin densities on Carbon 3 and Carbon 5 may be altered changing the values ofthe

hyperfine coupling parameters.

111.5. Conclusion

2H-ESEEM is an alternative method to proton ENDOR to obtain detailed
structural information on organic radicals. The potential of HYSCORE technique has still
not been exploited to its full extent. The HYSCORE echo modulation function for an S =
1/2, 1 = 1 spin system has been derived using the density matrix formalism. lts applicability
to the interpretation of the HYSCORE data for 2H—labeled tyrosyl radical has been
demonstrated through simulations. The simulations show that the 2D ESEEM function
adequately describes the experimental correlation patterns. In particular, it reproduces to a

good approximation the I-suppression-effect modulated lineshapes of the observed

HYSCORE cross peaks.

253

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