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Part I) AN NMR ANALYSIS OF CRYPTAND 111. CONFORMATIONS AND
RATES OF PROTON BINDING. Part II) AN NMR STUDY OF ALKALI

Date

METAL ANIONS IN SOLUTION

presented by
Patrick Bernard Smith

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PART I) AN NMR ANALYSIS OF CRYPTAND 111:
CONFORMATIONS AND RATES OF PROTON BINDING
PART II) AN NMR STUDY OF ALKALI METAL ANIONS
IN SOLUTION
By

Patrick Bernard Smith

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1978

I‘\
‘ \ f l\\ \ "J
\ J \

ABSTRACT
PART I) AN NMR ANALYSIS OF CRYPTAND 111:
CONFORMATIONS AND RATES OF PROTON BINDING
PART II) AN NMR STUDY OF ALKALI METAL ANIONS
IN SOLUTION
By

Patrick Bernard Smith

The conformations and sites of proton binding by
cryptand 111 (C111) have been characterized in great detail.
The free ligand exists in a conformation which has both ni-
trogen lone pairs pointing inside its cavity (endo-endo),
although external protonation studies indicate a degree of
flexibility toward nitrogen inversion. The endo-endo form
of the ligand in the absence of acid is preferred over the
exo-endo form (one nitrogen lone pair pointing inside the
cavity and the other outside) by a factor of about 50 in
water at 298 K.

External proton binding by 0111 occurs primarily at
the lone pairs of the nitrogen atoms with no apparent par-
ticipation in the binding by the oxygen atoms. C111 will
protonate externally at a nitrogen lone pair (exo-endo
form). The pKa value for external protonation in water
at 298 K is 7.1 1 0.1. The pKa value for the second exter—
nal protonation, which occurs at the other nitrogen atom

(exo-exo form), is between 0.0 and 1.5 in water at 298 K.

Patrick Bernard Smith
The exo-endo form of Clll-H+ is preferred over the exo-exo
form by a factor of 107 or greater.

One or two protons may also be bound internally by
C111. The first internal protonation is irreversible since
the complex cannot be deprotonated unless the cryptand is
decomposed. Internal proton binding also occurs primarily
at the nitrogen atoms. The internal proton rapidly ex-
changes between the nitrogen ione pairs, this motion being
more rapid than the NMR time-scale even at 170 K. The
internally monOprotonated complex exists predominantly in
the endo-endo form, which is favored over the exo-endo con-
figuration by a factor of about 108. The internally mono-
protonated complex will externally protonate at a nitrogen
atom (exo-endo form). The pKa value for this process in
water at 298 K is roughly O.u.

The internally diprotonated ligand, Clll-2H+,i-i
exists in the endo-endo form. The internal protons of
Clll-2H+,i-i either exchange very slowly or not at all.

The temperature dependence of the NMR spectra of C111
and its internally protonated complexes indicate that as the
temperature is lowered, one or more molecular motions are
slowed down considerably. One such motion, which has been
assigned to a vicinal carbon wagging motion, possesses

1 deg'1 for

AH+ = 9.0 1 0.5 kcal mol-1 and AS+ = -6 cal mol-
the internally monOprotonated species. A second type of
molecular motion, which is only observed in the case of the

internally monOprotonated ligand, is also slowed down at

Patrick Bernard Smith
temperatures below 190 K. This motion has AHI 8 16 t 2

kcal mol'"1 and AS4‘ = +39 cal mol"l deg"l and has been as-
signed to a concerted torsional motion of the ligand.

The rates of internal protonation and deprotonation
processes of Clll are very slow, due to large activation
barriers which are about 25 kcal mol'1 for each of the proc-
esses. The rate of the first internal protonation exhibits
a definite pH dependence which has been correlated with the
pH dependence of the equilibria involving the externally
protonated forms of Clll. It appears that two forms of the
ligand are able to go to products with different rate con-
stants, the first constant being 3.8 t 0.6x10'3 sec"1 and
the second being 2.3 t 0.3x10'u sec-1.

The rates for the second internal protonation and the
removal of the second internal proton are also expected to
exhibit a pH dependence although the rates of the second in-
ternal protonation have not been studied as a function of
pH. The rate of deprotonation of Clll-2H+,i-i by base has
been shown to depend on the base strength.

The rate data provide a means by which to estimate the
thermodynamic stability of the various complexes. The pKa
value for the first internal protonation of Clll in water at
298 K is 217.8 and AG° 5-5 kcal mOl-l. For the second in-
ternal protonation, pKa 28.3 and AG° 2+8 kcal mol-l.

NMR provides an excellent way to identify and charac-
terize alkali metal anion solutions. NMR data reveal that
the trend in thermodynamic stability of the alkali metal

anions, relative to the solid metals is Na'>Cs'>>K',Rb'.

to Karole

ii

ACKNOWLEDGEMENTS

The author wishes to express special gratitude to
Professor James L. Dye for his continual guidance and en—
couragement. Professors A. I. Popov, J. F. Harrison, D. G.
Farnum, and L. R. Sousa are also acknowledged for their
many helpful discussions and insights.

Appreciation is also extended to Mr. M. Yemen, Mr.
M. DaGue, Dr. E. Kauffmann, Mr. B. Van Eck, and Dr. Harlan
Lewis for their many hours of assistance. Mr. F. Bennis
and Mr. W. Burkhardt must also be recognized for their
assistance and support concerning the operation and main—
tenance of the NMR spectrometers.

Financial support from the Dow Chemical Company, the
United States Energy Research and Development Association,
and the General Electric Company is also acknowledged.

Finally, my sincere thanks to my wife, Karole, and
our families for their unending love, confidence, and sup-

port.

111

LIST OF TABLES

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

LIST OF COMMONLY USED TERMS . . . . . . . . .
PART I) AN NMR ANALYSIS OF CRYPTAND 111:
CONFORMATIONS AND RATES OF PROTON BINDING

Chapter

1. HISTORICAL . . . . . . . . . . . . . .

I) INTRODUCTION . . . . . . . . . .

II) GENERAL FEATURES OF NMR . . . .

TABLE OF CONTENTS

A) The Chemical Shift . . .
B) Spin-Spin Coupling . . .
C) NMR Relaxation . . . . .

2. EXPERIMENTAL

I)
II)
III)

IV)

v)
VI)
VII)
VIII)
IX)

GLASSWARE CLEANING . . . .
SOLVENT PURIFICATION
LIGAND PURIFICATION . . .

SAMPLE PREPARATION . . . .

A) Preparation of Anhydrous NMR

Samples . . . . .

B) Alkali Metal Anion Solution

Preparation . . . . .
Clll SYNTHESIS AND PURIFICATION
METAL PURIFICATION
VACUUM PROCEDURES . .
NMR SPECTROMETER . . . .
SAFETY . . . . . . . . . . . .

iv

vii
ix
xiii

a: r4 t4

19
29
29
29
3O
31

31
33
35
37
MO
“2
H3

3. CONFORMATIONAL ANALYSIS OF CRYPTAND 111 . . .

I)

II)

III)

INTRODUCTION . . . . . . . . . . . . .

A)

Clll Symmetry Considerations .

NMR SPECTRA AT AMBIENT TEMPERATURES

A) Clll in ’dQ-Acetone o o o o o o o
B) Clll H+ ' in d -Acetone . .
0) 0111 2H+, 1- 1 201’ In du MeOH . .
D) Musher's Theory of the Chemical
Shift 0 O O O O O O I O O O O
E) 011L H+,o in d6~Acetone . . . .
F) C1110 0H+ ,o in Water . . . . . .
G) The External Protonation of
0111 H+, 1 . . . . . . . . . .
H) General Conclusions . . . . . .
TEMPERATURE DEPENDENCE OF THE NMR
SPECTRA O O O O O O O O O O O O O O O
A) C111 in d6-Acetone . . . . . . .
8) C111 H+ 4i- oBr in d -Acetone . .
C) Clll 2H ,1- i 2C1 In du-MeOH . .
D) 0111- 2H+, i-o 1n du-MeOH . . . .
E) Clllo H+ ,o in d6-Acetone . . . .
F) summary 0 O O O O O O O O O O O

A. THE KINETICS OF INTERNAL PROTONATION OF C111

I)
II)
III)

IV)

v)
VI)

VII)

VIII)

INTRODUCTION . . . . . . . . . . . . .

THE FIRST INTERNAL PROTONATION OF Clll

THE KINETICS OF THE SECOND INTERNAL
PROTONATION OF C111 IN WATER . . . . .

THE KINETICS OF DEPROTONATION OF

Clll'2H+’1-i o o o o o o o o o o o o 0
METHOD OF ANALYSIS . . . . . . . . . .
SUMMARY 0 o o o o o o o o o o o o o 0

THE REACTION OF Clll H+ ,1 WITH
Na+ C222. Na- 0 I O O C O O O O O O O C

THE REACTION BETWEEN C111-2H+,i-i AND

es 0 O O O I O O O O O O O O O O O O O

5. DISCUSSION

“5
A5
53
56
59
60
62
65
66
78
82
83
84
85
105
108
117
121
125
125

126

138

1A2
1A5
1“?

152

153
156

I)
II)

III)

PART II) AN NMR STUDY OF ALKALI METAL
ANIONS IN SOLUTION

INTRODUCTION 0 O C O O O O O C O C O O O O O O O 16“

THERMODYNAMIC STABILITY OF THE ALKALI METAL
ANIONS O O O O O O O O O O O . O O O O O O O O O O 172

IDENTIFICATION OF NEW SPECIES . . . . . . . . . 178

vi

TABLE

1.

10.

11.

12.

LIST OF TABLES

Page
Summary of relaxation mechanisms . . . . . . 27
The solubility of C111 and its complexes in
various solvents . . . . . . . . . . . . . . 38
The chemical shifts of C111 and its complex-
es at ambient temperature . . . . . . . . . 58

The dependence of the chemical shifts of Clll
in d -acetone upon addition of trifluoro-
acetIc acid (TFAA) . . . . . . . . . . . . . 72

The dependence of the chemical shifts of C111
in d -acetone upon addition of dichloro-
acetIc acid (DCAA) . . . . . . . . . . . . . 75

The pH dependence of the chemical shift of
the CH2N protons of C111 in water at 299°K . 80

The pH dependence of the chemical shifts of
C111.H+ ’1 in water 0 O O O O O O O O O O O O 83

The temperature dependence of the NMR param-
eters for a 0.02 M solution of Clll in d6-
acetone 0 O O O O O O O O O O O O O O O O O 89

The temperature dependence of the NMR spec-
tra of a 0. 0“ M solution Of C111-H+,i Br in
d6-aCEt0ne o o o o o o o o o o o o o o o o o 91

The temperature dependence of the NMR+param-
eters for a 0.0M M solution of Clll-H ,i-Br’
in du-MGOH o o o o o o o o o o o o o o o o o 10“

The temperature dependence of the NMR param-
eters for a 0.04 M solution of
0111-2H+,1-1-201' in du-MeOH . . . . . . . . 107

The temperature dependence of the NMR param-
eters for a 0.0u M solution of
Clll-H+,i in du-MeOH, acidified with HCl . . 110

vii

TABLE

13.

1A.

15.

16.

17.

18.

19.

20.

21.

22.

23.

2A.

25.

Page

The temperature dependence of the equilib-
rium constant for the conversion of N
Clll-H ,1 to 0111-2H+,i-o inidu-MeOH: K
from the CH2-N protons and K from the in-

ternal proton . . . . . . . . . . . . . . . . 112

The temperature dependence of the equilib-

rium constant for the formation of

0111-2N+,o-o 1n d6-acetone with the addition

of TFAA . . . . . . . . . . . . . . . . . . . 121

The dependence of the equilibrium constant
for the conversion of Clll-H+,o to
C111'2H+,0-0 on the concentration of TFAA . . 122

Buffer compositions and their ionic strengths
in D20 I O O I O 0 O O O O O O O O O O O O O 127
The dependence of the rate of internal mono-
protonation of C111 upon pH and temperature . 128

The dependence of the rate of the second in-
ternal protonation of C111-H+,i upon tempera-
ture in l M HCl . . . . . . . . . . . . . . . 142

The dependence of the rate of deprotonation
of 0111-2H+,i-1 upon temperature in 5 M KOH . 1A5

The activation and thermodynamic parameters
for internal protonation processes at 298 K . 1A8

A selected list of chemical shifts and line-
widths in alkali metal NMR . . . . . . . . . 171

The products of some alkali metal solution
preparations . . . . . . . . . . . . . . . . 173

The products of the reaction of Na and Cs
metals and C222 in THF . . . . . . . . . . . 176

The temperature dependence of the chemical
shift of Cs+0222 in EA . . . . . . . . . . . 179

The temperature dependence+of the EPR signal
of a 0.08 M solution of Na l8-C-6-Na‘ in MA . 187

viii

FIGURE

1.

10.

11.

12.
13.

1“.

LIST OF FIGURES

Structures of cryptand 222, 18-crown-6 and
cryptand 111 O O O O C O O O C O O O O O C O

The dependence of the formation constant on
the ratio of the size of the ion to the
ligand's cavity size . . . . . . . . . . . .

The protonation scheme of C111 . . . . . . .

Diagram showing the components of the Musher
theory of proton chemical shifts . . . . . .

The effect of unpaired electrons on the NMR
spectrum 0 O O O O O O O O O I O O O O O O O

The effect Of bond angle on scalar coupling,
for A) vicinal protons and B) geminal pro-
tons O O O O O O O O O C O O O O O O O O O 0

Apparatus used in the preparation of anhy-
drous samples for NMR analysis . . . . . .

Apparatus used in the synthesis of alkali
metal anion solutions . . . . . . . . . .

Steps in the synthesis of Clll . . . . . .

"Trombone" apparatus for the storage Of
alkali metals . . . . . . . . . . . . . . .

Vacuum line arrangement used in sample prep-
aration O O O O O O O O O O O O O O O O O O

The conformations of 0222 . . . . . . . . .

Space filling models of C111, A) D h sym-
metry (large cavity) and B) compacé cavity

The possible binding sites and conformations
of C111, A) unprotonated, B) external pro-
tonation, C) internal protonation, D) exter-
nal protonation of the internally

ix

Page

1“

16

20

32

3A
36

39

141
AS

“9

FIGURE

15.
16.

17.

18.

19.

20.

21.

22.

230

2A.

25.

26.

27.

28.

Page
monOprotonated complex and E) internal dipro-
tonation O O O O I I O O O O O O O O O I O I 50
Model showing the torsional angle of C222 . 53

Model showing the symmetry elements of C111
in the D3h configuration . . . . . . . . . . 55

The NMR spectra of C111 and its protonated
complexes at ambient temperature . . . . . . 57

The dependence of the NMR spectrum of C111
in d -acetone upon the addition of trifluoro-
acetéc aCid (TFAA) O I O O O O I O O O O O O 69

The dependence of the NMR spectrum of C111
in d -acetone upon the addition of dichloro-
acetIc acid (DCAA) . . . . . . . . . . . . . 73

The dependence of the chemical shift of the
CH O protons of C111 in d6-acetone upon ad-
diéion of DCAA . . . . . . . . . . . . . . . 7A

The NMR spectra of Clll in water at various
pH values 0 O O O O O O O O O O O O O O O 0 77

The pH dependence of the chemical shift of
the CH2N protons of C111 in D20 . . . . . . 79

The spectrum of C111 in CHF2Cl at 163 K at
250 MHz 0 O O O O O O C O O O I O O C O O O 86

The temperature dependence of the NMR spec-
tra Of C11]. in d6-acetone o o o o o o o o o 88

The temperatu e dependence of the NMR spec-
tra of Clll-H ,i in d6-acetone . . . . . . . 90

Computer-simulation of the temperature depen-
dence of the spectra of the CHZO protons of
C111’H ’1 in d6'acetone o o o o o o o o o o 93

The dependence of 1n(k) on 1/T for the tor-
sional motion from the spectra of the CH2O
protons of 0111-H+,1 . . . . . . . . . . . . 95

The temperature dependence of the internal
proton resonance of Clll-H ,i in d6-
acetone 0 O O I O I O O O O O O O O O O O O 97

FIGURE
29.

30.

31.

32.

33.

3M.

35.

36.

37.

38.

39.

“0.

A1.

Computer-simulation of the temperature de-
pendence of the internal proton resonance of
0111’ 11+, 1 in d6-acetone o o o o o o o o o o o

The dependence of ln(k) on 1/T for the skele-
tal locking process from the spectra of the
internal proton of 01110 H+ ,i . . . . . . . .

The temperature dependence of the NMR spectra
Of C111. 11+ ,1 in du-MEOH o o o o o o o o o o o

The temperature dependence of the NMR spectra
Of C111. .2H+ ”1 1 in du-MGOH o o o o o o o o o

The temperature dependence of the NMR spectra
of C111-H,i in du-MeOH, acidified with HCl .

The dependence of ln(K) on l/T for the equi-
librium between Clll- H ,i and Clll 2H+, i-o in
du-MGOH o o o o o o e o o o o o o o o o

The variation in the NMR spectrum of the in-
ternal proton of Clll H+, i in du-MeOH with
the addition of HCl at 200 K . . . . . . . .

The temperature dependence of the NMR spec-
trum of the internal proton of Clll-H+,i in
du-MeOH with about 50 mole % HCl added . . .

The temperature dependence of the NMR spec—
tra of Clll H ,o in d6-acetone, acidified
"1 th TFAA O 0 O O O I C O O O I O O O O O 0 I

The variation of ln(K2 ) with 1/T for the for-
mation of Clll 2H+ ,o-o in d6-acetone upon the
addition or TFAA O O O O O O O I O O O O I O

The dependence of the equilibrium constant
for the +conversion of 0111- H ,o to

0111- 2H+ ,o-o in d6-acetone on TFAA concentra-
tion 0 O O O O O I O O O O O O 0 0 O O O O O

A typical rate analysis for internal protona-
tion of 0111 in water . . . . . . . . . . . .

The dependence of ln(k) on 1/T for the inter-
nal protonation of Clll in water at two dif-
ferent pH values: squares; pH 8 7.5 and cir-
cles; pH = “.9 . . . . . . . . . . . . . .

xi

Page

98

99

103

106

109

113

115

116

118

120

123

129

130

FIGURE
A2.

A3.

A“.

“5.

A6.

“7.

A8.

“9.

50.

51.

52.

53.

5A.

The pH titration of Clll with H01 in water
(only external protonation occurs) . . . . .

The variation of the relative concentrations
of the various forms of Clll in water with

pH. 0 O O O O 0,. O O O O O O O O O O O I O

The dependence of the rate of internal mono-
protonation of 0111 on pH: dashed line; pK
a 7.1 and solid line; pKa . 7.5 . . . . . 2

A typical rate analysis for the second in-
ternal protonation of Clll H ,i in l M HCl .

The dependence of ln(k) on l/T for+the sec-
ond internal protonation of Clll-H ,i in l M

HCl 0 O O O O O I O O O O O O O O O O C O O

A typical rate analysis for the deprotona-
tion of Clll 2H+ ,i- in 5 M KOH . . . . . .

The dependence of ln(k) on l/T for the de—
protonation of Clll 2H+ ,i- -i in 5 M KOH
(crosses) and l M KOH (circle) . . . . . . .

The potential energy diagram for the inter-
nal protonation processes . . . . . . . . .

The dependence of the total energy of the
complex on the location of the H proton
along the C3 axis for Clll H+ ,i in D3h sym-
metry . . . . . . . . . . . . . . .

The electronic spectra of the alkali metals
in tetrahydrofuran (THF) . . . . . . . . . .

The temperature dependence of the NMR spec-
trum of Cs+ 0222 Cs” in MA . . . . . . . . .

The temperature dependence of the NMR spec-
trum of Cs +0222 Cs in THF . . . . . . . . .

The temperature dependence of the NMR spec-
trum Of Na+18-C-6.-.Na in MA 0 o o o o o o o

xii

Page

133

135

136

1A0

181

1u3

11m

151

159
165
180
183

186

0222
0111
18-C—6
Clll-H+,o
Clll-H+,i
Hi

[.1

LIST OF COMMONLY USED TERMS

cryptand 2-2-2

cryptand l-l-l

18-crown-6

externally complexed Clll
internally complexed Clll
inclusively bound proton

magnetic moment

magnetic field strength

nuclear spin or moment of inertia
magnetogyric ratio

local magnetic field at the nucleus

screening constant

paramagnetic contribution to O
diamagnetic contribution to 0
average excitation energy
coupling constant

spin-lattice relaxation

spin-spin relaxation

relaxation rate

full linewidth at half height in Hz
correlation time or exchange time
Viscosity

Boltzmann's constant

xiii

EA
IPA
DEE
Na-K
THF

(DI
U)

KNEE

Planck's constant divided by 2w
temperature in °K
nuclear spin

Larmor frequency
chemical shift
methylamine

ethylamine
isopropylamine
diethylether
sodium-potassium alloy
tetrahydrofuran
solvated electron
alkali metal anion
alkali metal cation
equilibrium constant

rate constant

xiv

PART I

AN NMR ANALYSIS OF CRYPTAND III:

CONFORMATIONS AND RATES OF PROTON BINDING

CHAPTER 1

HISTORICAL

I) INTRODUCTION

 

The complexation of metal cations in solution is of
particular interest to chemists and biologists partly because
of the mystery surrounding ion transport in biological sys-
tems(l). Most attention has been given to transition metal
complexes with ligands such as ammonia, carbon monoxide,
EDTA, etc.(2), since these elements tend to form rather
stable and long-lived adducts. This is true because the
transition metal ions, in general, have valence deficiencies,
and thus coordinate to electron donating ligands in order to
satisfy the valence condition. In sharp contrast to the
transition metals is another group of biologically signifi-
cant ions, the alkali and alkaline earth elements which do
not have this valence deficiency. Instead, they tend to be
rather inert and very labile in solution. These ions com-
plex with conventional ligands so inefficiently that they
have often been used to maintain constant ionic strength in
solutions where the complexation of other metal ions was be—
ing studied.

Alkali metal complexation has been shown to be impor-
tant in the phenomenon of active ion transport across mem-
branes. Biologically significant molecules have been observed

(1’3). These molecules include

to facilitate this process
porphyrin and corrin ring complexes, phthalocyanines and

l

2

valinomycin, each of which is a macrocycle that possesses
a hydrophilic cavity and an organic backbone. The macro-
cycle is thought to bind the ion in the cavity, while main-
taining its organic nature, thereby dissolving the ionic
species in the membrane. This process allows the complexing
agent to "carry" the ion across an otherwise inaccessible
membrane barrier with the expenditure of little energy.

Synthetic macrocycles whose function mimics their
naturally occurring analogues were introduced by Pedersen
in 1967(8). These monocyclic polyethers were named "crown
ethers" because Pedersen envisioned them as sitting atop the
complexed ion in a fashion resembling a crown. Since the
introduction of crown ethers, many more macrocyclic complex-
ing agents have been synthesized, the designers of which em-
ployed freedom of imagination and prowess in the field of
synthesis to achieve very specific ends. Cryptands, bi-
cyclic polyethers developed by J.-M. Lehn and co-workers, are
the most famous Of these, since they combine extremely strong
binding characteristics with a well-defined, three dimen-
sional cavity. Thus, they possess selectivity in their bind-
ing characteristics with various ions, based on the ratio of
cavity to ionic size(5). Typical crown ethers and cryptands
are shown in Figure l. The demonstrated ability to synthe-
size these macrocycles, coupled with the unlimited freedom
of their design has provided for great utility of these
ligands in the aforementioned biological applications as

well as in several other significant applications(6'12).

KONG/W O 0 fl 0"‘\
N’VO’VO’VN [O O] N ’\,§’\,N
L‘vx%__JSA,/j K\¢JD\’/J \\__/ \__J/

CRYPTAND 222 IB'CROWN'G CRYPTAND lll

Figure 1. Structures of cryptand 222, 18-crown-6 and
cryptand 111.
It is not within the scope of this work to present a de-
tailed review of their applications. Instead, let it suf-
fice to say that macrocyclic polyethers hold potential in
all areas of ionic separations and have, indeed, proven
useful in many(l3'2u).
As mentioned previously, cryptands differentiate
between ionic species by binding most strongly those ions
which are compatible with their cavity dimensions. This
is portrayed in Figure 2 for several cryptands in which the
binding constant of a particular ligand is plotted versus
the ratio of the sizes of ion and ligand cavity. These
plots peak as the ionic size equals that of the cavity of
the ligand, and fall off considerably on either side of
this value. The smallest cryptand, C111, is not shown
because its cavity is too small to bind alkali metal ions
efficiently<2u). Cryptand 111 does bind Li+ slightly with a
pK of approximately 2.2 in water, but comparison with C211,

which has a pK of 5.5, demonstrates that C111 is too small for

.oufim huw>do m.ccmeH 029 On
20H on» no mean on» no oapmh on» so pcmpmcoo coaumsuom on» no mococcoqov 029 .m madman

>260 mo 350..
:2 .206 B «:69.

o.~ o... o

 

u 030..

 

 

5

efficient binding to occur. (From molecular models, the
cavity radius of 0111 has been estimated to be about 1.0
A.) This size dilemma would render Clll rather mundane in
the realm of ionic complexation except that it binds protons
and does so with such efficiency that it is the strongest
proton complexing agent yet reported. Clll binds one or
two protons in a number of binding sites and conformations,
thus qualifying it as a model Of the binding characteristics
of the larger cryptands as well as biological systems<25).

Lehn and cO-workers published two preliminary papers
about 0111(26'27), in which they described the synthesis and
unusual proton binding ability Of Clll. They also discussed
the possibility of several different protonated complexes
which might be formed as illustrated in Figure 3. In protic
solvents or acidic media, Clll was shown to complex a proton
externally, presumably at the nitrogen with its lone pair
pointing outside the cavity. This complex behaved as a typ-
ical protonated amine, the proton being readily exchangeable
with protons in solution. Evidence for such complex forma-
tion came from a rise in pH upon addition to aqueous solu-
tions and from line broadening in the NMR spectra. Lehn
estimated that the pKa for external protonation would be
about 7.5-8.0 based on triethanolamine or N-ethylmorpholine
if the ligand were present with one nitrogen lone pair point-
ing outside the cavity and available for binding (exO-endo
configuration). The actual pKa was found to be somewhat

A

lower (6.3) based on the pH of a 2x10' M solution of Clll

7
and therefore, an equilibrium between exo-endo and endo-
endo forms was suspected. A second external protonation
(at the other nitrogen) was thought to induce too severe a
strain to be possible because both nitrogens would be
forced into the exo conformation. This conclusion was based
on molecular models and the fact that the reduction of the
dilactam of C111 by diborane results in the monoborane ad-
duct rather than the diborane adduct obtained in the case
of larger cryptands (see Experimental section for details).

Simultaneous with the rapid external protonation, a
second, much slower process was observed by which a proton
was very tightly bound. This process proceeded with a half-
life of several days at room temperature and presumably cor-
responded to inside protonation. The resulting complex was
so stable that heating it to 60°C in 5 M KOH for days did not
significantly deprotonate it! Even with excess sodium in
liquid ammonia, the proton could not be removed without de-
stroying the ligand.

The internally monOprotonated ligand, Clll-H+,i, could
be protonated a second time externally. The degree of exter-
nal protonation was pH dependent, leading to the conclusion
that there was again an equilibrium between the endo-endo
and exo-endo configurations, the former being more favorable.
As the pH was decreased, the ligand was forced into the exo-
endo form but the exchange was always very rapid.

A second proton could also be taken inside the cavity

(endo-endo), but only under rigorous conditions (1 M HCl at

8
100°C for one hour). Again, this inclusive proton was
found to be bound tightly and was very difficult to remove
from the cavity, the complex being stable for days in
5 M KOH at room temperature. Above 60°C, however, one of
the two protons could be removed slowly. Treatment with
sodium in liquid ammonia caused reduction to the free amine
in about 10% yield with about 90% decomposition. No mono-
protonated ligand was ever obtained and thus an intermediate
of the sort, Clll-H +, 1—1 was postulated, the reaction pro-
ceeding via reduction rather than proton abstraction by
base.

In general it was thought that proton binding occurred
mainly at the nitrogens and that external protonation was
weak and rapidly exchangeable whereas internal protonation
was difficult to achieve but very strong. Subsequent sec-
tions of this discussion will deal with binding character-

istics and rates of encapsulation of protons by 0111.

II) GENERAL FEATURES OF NMR

Nuclear magnetic resonance provides a direct probe of
the electronic environment of the nucleus since the resonance
frequency, or Larmor frequency, of that nucleus is greatly
dependent on electronic shielding. The symmetry of the
electron cloud and the electron density in the vicinity of
a nucleus contribute to local magnetic fields which influence
its chemical shift. These contributions will be discussed

qualitatively in order to give significance to the Clll

9
spectra in the latter portions Of this work. For a more

detailed discussion, see references 28-33.

A) The Chemical Shift

 

When a nucleus is placed in a magnetic field, Ho,
its nuclear spin states are no longer degenerate but are
separated by an energy difference given by:

pH

0
AE I _I_'= YHOh (Hz) (1)
where:
u - Magnetic moment of the nucleus
Ho - Magnetic field (gauss)
I — Nuclear spin
7 - Magnetogyric ratio
h - Plank's constant divided by 2

Transitions are induced between the levels by irradiation

at the Larmor frequency, equal to the energy separation of
the nuclear spin states (in the radio frequency region).

The electronic distribution becomes important when deter-
mining the true magnetic field at the nucleus, Hloc’ because
the electrons produce magnetic fields of their own as they
interact with Ho and may therefore cause considerable shift—
ing in the resonant frequency from that given by equation
(1). The electrons perturb the field at the nucleus in a
number of ways. First, as was mentioned before, when an
atom is placed in a magnetic field the nuclear spin states
separate but the field also induces a precession of the elec-
tron cloud about the field, Ho. The electronic precession

in turn generates a magnetic field, which opposes HO so that

10
the nucleus is "screened" by these electrons according to
the equation:

H .. Ho(l-O) (2)

100
where:

H10c - the field at the nucleus
0 - the screening constant

This type of screening, which results in an upfield shift,

is called diamagnetic screening and may be a sum of several
contributions. Other effects, which cause downfield shifts
due to the mixing of excited state molecular wave functions,
are referred to as paramagnetic terms after the development

of Ramsey<28), and hence:

0 = 0d + Up (3)

Ramsey expressed these terms theoretically from

perturbation theory as follows:

AAA

 

e2 rkzl-rkrk

O = ‘—‘ <XOI£ 3 |X0> +
2M02 k rk

-1 A I
MEG-EM) <xol>21nxm><xmlz 4W (A)
M k k Pk
where:
e - electronic charge
M - mass of the electron

C - velocity of light

1k — angular momentum of the

rk - radial distance of the k
at the nucleus

th

h electron

electron from the origin ‘

The first term depends only on ground state electronic wave
functions and is a function of the symmetry of the elec-

tronic distribution and the density of electrons in the

ll
vicinity of the nucleus. The second term is much more dif-
ficult to determine because it involves mixing of ground
and excited State wave functions, the latter, in general,
not being known. Simplistically, 0d may be thought of in
terms of s-type (spherically symmetrical) orbitals and the
screening they produce as a result of precession about Ho'
Paramagnetic screening, on the other hand, results from
excitation of electrons to p, d, and higher states which
in turn hinders the precession of the s-type electrons
about HD by introducing directionally dependent electric

fields. It follows that the magnitude of 0 is greatly

D
influenced by the accessibility of the excited states.

Since the calculation of Up is impossible due to the lack

of proper wave functions, an average excitation energy
approximation has been made in order to simplify it so that:
2 A A '
"'e 1klk’

OP 8 AMzcz oI

 

 

I xo> (5)

kk’ r;
where:

A - average excitation energy
When A is large, as in proton NMR, Op contributes little
to the chemical shift. When A is small, excitation occurs
readily and Up, which potentially can be very large, usually
dominates. More specifically, 0d dominates in proton NMR
even though it is only about 18 ppm, since op is negligible.

In carbon and fluorine NMR, 0 is much larger, (about 260

d
and 338 ppm respectively), but op may get as large as 1,000

ppm and is therefore the more dominant of the two. In some

12
heavy metal systems, the value of 0p may get as large as
10,000 ppm because of a high density of excited states and

their ease of accessibility. The a term is also relatively

d
constant for a particular nucleus even though it may be
large and its range of shifts is usually only about 20 ppm

at most. The magnitude of O , on the other hand, varies

p
greatly from nucleus to nucleus, but more importantly, may
change by several hundred ppm for the same nucleus in dif-
ferent environments. For example, Cs+ in the gas phase and
Cs+ inclusively complexed by the cryptand, 0222, are
shifted about 500 ppm from one another<3u).
Ramsey's equations provide a good theoretical start-
ing point, but in practice are of little value in the pre-
diction of chemical shifts due to the unavailability of
molecular wave functions. More empirical approaches have
found greater utility in this area and will be discussed.
In order to be consistant with the literature, downfield
shifts will be referred to as paramagnetic and upfield
shifts as diamagnetic, but this terminology should not be
confused with the two terms in the Ramsey equation. There

are contributions to a which lead to paramagnetic shifts,

d
as we shall see, but which do not involve the mixing of ex-
cited and ground electronic states. For example, the para-
magnetic term in the Ramsey equation is extremely small for

proton NMR and yet large downfield shifts from TMS are ob-

served. These shifts are due to reduction of ad by the

13
decrease in electron density, etc., rather than to contri-
butions from the 0d term.

In general, the contributions to the chemical shift
may be classified as either diamagnetic or paramagnetic,
but there are several factors which may influence these
terms. Four of the more important contributions in proton
NMR include:

a) anisotropic screening

b) electric field effects

0) unpaired electrons

d) solvent effects
a) through d) contribute to °d whereas only d) may signifi-
cantly contribute to O for nuclei with available excited

P
state orbitals.

a) Anisotropic Screening

 

Anisotropic effects are caused by an asymetrical elec-
tronic distribution of neighboring substituents which does
not average to zero with molecular tumbling. This asym-
metry causes time-independent local fields at the nucleus
which result in the shift. Perhaps the most familiar exam-
ple of these effects is in relation to ring currents produced
by aromatic systems, but all n electron systems have the po-
tential to produce anisotropic screening. These shifts are
normally only about l-A ppm, significant in proton NMR, but

much less so in carbon NMR.

b) Electric Field Effects

 

A charged species or highly polar group may induce

polarization of a bond and alter the electronic distribution

1A
about a nucleus. This causes a two-fold change in the local
field at the nucleus by altering the electron density around
the nucleus and by initiating an anisotropic electronic en-
vironment. The shift produced may be represented in the

following way(30):

qicosei Q1
0 = -l3.3 Z _______ -l7.0 Z __ (ppm) (6)
e i r2 1r2
1 i
where:
q1 - the total charge of the polar group in units
of one electron
gisei - defined in Figure A
This equation reduces to:
o - -ll.2q - 12.0q2 (7)

for axial symmetry assuming r = 1.09A, the typical hydrogen-
carbon bond length. The former equation, called the Musher
equation, provides the means by which to predict the shift
expected from a change in the charge distribution at or near

a nucleus. It should therefore prove amenable to the study

of the protonation of Clll, since the dominant cause of change
in the chemical shift of the backbone protons upon protonation

is a result of this electric field effect.

 

 

Figure 4. Diagram showing the components of the Musher
theory of proton chemical shifts.

15

c) Unpaired Electrons

 

The magnetic moment of an electron is 860 times as
large as that of a proton and therefore, scalar coupling
of nuclei with unpaired spins produces enormous local fields,
as large as hundreds of thousands of ppm. Dipole - dipole
relaxation via electrons is also very efficient and in many
cases broadens lines to obscurity. This phenomenon is rep-
resented in Figure 5 in which a) shows a line in the absence
of scalar coupling. The normal chemical shift range in pro-
ton NMR is about 18 ppm, so that scalar coupling to elec-
trons with a magnitude of 100,000 ppm may put the resonance
well out of the tunable range of the spectrometer. Figure
5b) shows the spectrum when electron relaxation is slow,
and 50) when the relaxation is comparable to the hyperfine
coupling, A. In the latter case the line is broadened over
several kilohertz and in most instances it is not observable.
When the relaxation is very fast compared to A, a narrow
line occurs as shown in 5d) whose shift is the population
average of the two lines as shown in 5b), when electron re-
laxation is slow. This average position does not lie at the
frequency average of those in 5b) because there is a large
population difference between the levels as a result of the
Boltzmann distribution and in fact, the line is usually
shifted many kilohertz from the average frequency. (This
shift also occurs in proton NMR with the collapse of multi-
plets resulting from J coupling, but is not seen because the

energy separation between spin states is three orders of

16

NMR Spectrum Electron
' Roloxotm

0) A00

I
I
l
a) Ao-ZOMHz I I T,'>A
I
I
A .
c) Ao-mMHZ I 71"
I
l
I
l
a) Ao-2OMH1 I T:<A

31“

Figure 5. The effect of unpaired electrons on the NMR
spectrum.
magnitude less than with electrons and the population dif-

ference is therefore negligible.)

d) Solvent Effects

The solvent may have a very great influence on the
chemical shift of solute particles by means of the following
effects:

1) the magnetic susceptibility of the solvent which
is due to time-independent magnetic anisotropics. This is
usually less than 1 ppm and easily measured;

2) orientation Of a polar solvent about a polar solute
in such a way as to enhance its electronic shielding;

3) interaction of a solvent with the solute. The
characteristics of the solvent such as polarity, dielectric

constant and donating ability greatly determine the extent

17
of ion-pairing, solvation, hydrogen bonding, etc., in solu-
tion. For many alkali ion systems, the major contribution
to the chemical shift is the donation of electrons from the
solvent into their p and d orbitals. The role of solvent

is often overlooked, but may produce large and subtle shifts.

e) Summary
Electric field and anisotropic shieldings are most

important in proton NMR and other nuclei of small chemical
shift range (ap small) because their magnitude is usually
less than 10 ppm. For nuclei in which Op dominates, however,
the chemical shift range is much larger and these two sources
of shielding are often not as important. The role of solvent
is subtle, but must be considered, because it may have large

effects on the chemical shift.

B) Spin-Spin Coupling

 

Nuclei which have magnetic moments couple with one
another in a magnetic field and perturb the energy of the
nuclear states involved. This scalar or spin-spin coupling
is observed in splitting of the NMR signal into 2 n I + 1
lines, where n is the number of equivalent nuclei causing
the splitting and I is the spin of those nuclei. This cou—
pling will average to zero unless the effect is anisotropic,
and it is therefore observed only for bonded partners in
solution, since the lifetime of the coupling interaction
must be longer than the reciprocal of the coupling in Hz to

be observed. Spin-spin coupling may arise from three sources:

18
the interaction Of nuclear and electron magnetic currents
arising from’their motion in the magnetic field, dipole-
dipole interaction Of the nuclei and electrons, and the so-
called Fermi contact term, which is a function of the elec-
tron density at the nucleus. The contact term is always
dominant, being about 100 times larger than the others.
This interaction is transmitted through the chemical bond
as electrons and nuclei spin pair via the contact term, the
bonding electrons also spin pair and thereby transmit the
spin characteristics of the first nucleus to the other as
it spin pairs with its bonding electron. The contact inter-
action depends on s-electrons, since only they have a finite
probability density at the nucleus, but the interaction is
transmitted in some cases by excited state electrons. The
magnitude of the contact term depends only on the accessibil-
ity Of excited states, bond angle and distance, and is there-
fore Ho independent. The theory also predicts that the size
Of the contact term is proportional to the product of the

magnetogyric ratios of the nuclei involved:

J

 

hy.v 321'
AB = 28 (T) 82(Snl5(I’N)ISN)(SN’|6(I'N’)ISN’)P (8)

where:

Y - magnetogyric ratio of nucleus 1
average excitation energy
(SN|5(PN)ISN). magnitude of valence
at nucleus N
P - charge density matrix

This equation predicts, for example, that the coupling between

two protons is (YH/YD) or 7 times as large as the coupling

19
between a proton and a deuteron, all other factors being
constant.

Scalar coupling depends greatly on bond angle as
shown in Figures 6a) and b) for vicinal (three bond) and
geminal (two bond) coupling. Vicinal coupling reaches a
maximum of 8 to 10 Hz at 0 and 180° bond angle with a mini-

mum at about 85°, but geminal coupling may be much greater.

C) NMR Relaxation

 

Relaxation in the broad sense of the term concerns
itself with the exchange of energy from one system to another.
Three conditions must be satisfied in order to achieve suc-
cessful relaxation:

1) there must be a system in an excited state with
energy to donate;

2) there must be another system which can accept this
energy;

3) there must be a pathway by which the two systems
may couple in order to transfer this energy.

In NMR, the energy to be transferred is always at the
Larmor frequency, since it involves the relaxation of a
nucleus from a high energy spin state to a lower energy state.
Thus, the acceptor system must be able to accept energy at
the Larmor frequency. There are at least five mechanisms by
which relaxation may occur and they depend, in part, on the
characteristics of the nucleus, but some general statements

may be made about relaxation phenomena.

20

 

12 T I T 1 I I I I T I I T I I I I l

 

 

 

l

0 20 40 60 80 100 120 140 160 180

 

 

4° 1\ l I I

3. \

 

 

JHH (cps)
N
o
W

 

 

 

 

 

 

 

90 100 110 120 130
Degrees

Figure 6. The effect of bond angle on scalar coupling, for
A) vicinal protons and B) geminal protons.

21

The dissipation of energy from a nucleus in an excited
nuclear spin state to its surroundings (lattice) is referred
to as spin-lattice or T1 relaxation. The relaxation pathway
is generated by alternating local fields due to random rota-
tions and translations (Brownian motion) of neighboring
molecules and anisotropics of bonded substituents, which
occur at the Larmor frequency. Another type of relaxation

called spin-spin or T relaxation, is produced by the in-

2
teraction of the magnetic moments of like nuclei which in-
duces the relaxation of the one nucleus, while at the same
time promoting the other to the excited state. Energy is
transferred between the nuclei, but no net change in the
energy of the system results.

These two relaxation times may be described in terms
of the magnetic moment Of the system, Mo’ which precesses
about Ho. T1 is related to the component along Ho, which
determines the magnitude of Mo, whereas T2 is related to those
components perpendicular to H0’ or the phase characteristics
of Mo‘ This can be shown mathematically by expressing the
relaxation rate, R = T%:§3 in terms of the local field, b,
and the magnetic moment, M, for Ho along the z-axis:

R :- (Bxfi) = 1(1),,1'1z - szy)

+ “szx - bez) + 14bey - bny) (9)

T1 processes are, by definition, dependent on the k terms
whereas T2 processes depend on the i and J terms. T1 processes
are not dependent on local fields in the z-direction, but T2

processes are, and since bz is identical in both laboratory

22
and rotating frame, a static local field may induce T2 but
not T1 relaxation. This is especially important when field
inhomogeneity is on the order of ;;. The spin-spin relaxa-
tion time, T2, is always larger than or equal to T1 and is
related to the line width by:

1
2 g nAvl

 

T (10)
where: 2

AViis the full linewidth at half height in Hz.
2

a) Dipole-Dipole Relaxation

The dominant source of relaxation for spin --}nuclei
is dipole-dipole relaxation, which results from the interac-
tion of the magnetic dipoles of two nuclei and produces

local fields at the nucleus which may be represented by:

D-D W a

Hloc - ins (300826-1) rES (11)

“s is the magnetic moment of S, 9 is the angle between Ho
and the axis Joining nuclei S and I and r13 is the distance
between I and S. These fields can be very large, but as a
rule, molecular motions average them to zero. In the case
of solids or liquid crystals, this is not true, and dipolar
splitting may often be observed. For most liquids, however,
molecular reorientation is rapid and in the "extreme narrow-
ing" limit for nuclei of spin %, dipolar relaxation may be

represented by:

1 1 2 -5
T1 ' T2 3 (“YIYS) firISTc (12)

23
The correlation time, Tc, can be defined as the average
time between collisions for translational motion, or the
average time for a molecule to rotate by one radian for

reorientation motions and may be represented as follows for

a sphere in a viscous f1uid<35):
Unna’
T = 3kT (13)

c
where:

n - the solution viscosity
a - the radius of the sphere

The correlation time is dependent on the shape of the molecule
because a branched molecule will tend to be more highly re-
strictive to reorientation than a molecule with spherical shape
as assumed in the derivation of equation (13). For solutions

10

of normal viscosity, Tc lies between 10- and 10"13 seconds

and T is equal to T As the correlation time increases

1 2'
due to large molecular size, increased solution viscosity,
etc., equation (12) is no longer valid and T1 may be greater

than T2.

b) Spin-Rotation Relaxation

 

The motion of electrons in a molecule also produces
local magnetic fields, which when modulated by molecular
collisions, provide another pathway for relaxation, called
spin-rotation relaxation. For molecules with moment of
inertia, I, undergoing isotropic reorientation in a liquid

medium, the relaxation time may be given by:

 

= 2 2 2
T1,2 (2IkT/3h )(2c_L+ c//)TJ (1n)

2H
where C is the appropriate spin—rotation coupling constant,
‘3 is the angular momentum correlation time defined below
the normal boiling point of the liquid by:
o 8 1

TJ Tc /6kT (15)
1‘J
spin-rotation relaxation becomes less efficient as the

is inversely proportional to temperature and therefore

temperature increases in contrast to other relaxation path-

ways.

c) Scalar Relaxation

When a nucleus is spin coupled to another nucleus,
time dependent local magnetic fields may be produced as a
result of fluctuations in the coupling constant by either
chemical exchange or by rapid relaxation of the spin state
of one of the nuclei. As an example of the second mechanism,
consider a spin-} nucleus (a proton) coupled to a quadru-
polar nucleus (a nitrogen). Fast quadrupolar relaxation of
the nitrogen modulates the coupling constant and produces the

relaxation mechanism. This relaxation rate may be represented

as follows:

T
('I'i°)'1 = g. n2J23(s+1) |:

 

e
l+unz(vI-vs)zTez:] (16)

 

‘l'
sc--1a 22 e
(T2 ) “/3fl J S(S+1) [ie + 1+"fi2(VI'VS)2Te2:I (l7)

25

where:
J - the coupling constant
S - the spin of the coupled nucleus, S
v1 and vs - the Larmor frequencies of the nuclei

1 - the exchange time or the lifetime of the
spin state of 8, depending on the mechanism
of relaxation.

The local fields produced by scalar coupling are much smaller
than those produced by dipole-dipole interactions, but this
mechanism may be dominant under the proper conditions, namely
when (vI -vs)m%é, or when reml/A. In the latter case, TZSC
may be very different from Tlsc, since it contains a fre-
quency independent term. In the case of very rapid exchange
times or relaxation of the coupled nucleus, (heteronuclear
decoupling), TlscszSC and dipole-dipole relaxation is domi-

nant.

d) Chemical Shift Anisotropy

Anisotropies in the shielding constant, a, may produce
alternating local fields, as they are modulated with respect
to Ho by molecular tumbling. Bound substituents with w-
electrons are the most common, but in most of these molecules,
dipolar relaxation is still dominant. For the case of axial

symmetry, the relaxation times may be represented:

CA -1 2 2 2 _ Tc
(Tl ) 'fg Y Ho (07/ 9L) [é+(2"vo)2162] (l8)

 

 

(T CA)-l l__ 2H 2( ) u + are
7 o -o T
2 A5 0 // -‘- |: c 1+(2nv0)2rcz] (l9)

26

e) Quadrupolar Relaxation

 

A quadrupole moment is associated with nuclei of spin
greater than %, and therefore the charge distribution of the
nucleus is not spherical as with spin fi'nuclei. A fluctuat-
ing electric field may be produced as the quadrupolar nucleus
tumbles in solution, which in turn gives rise to a relaxation

pathway. In the "extreme narrowing" limit, 2nvorc<<l this

relaxation is given by:

Q -l _ Q -l _ 3 21+3
(T1 ) " (T2 ) " Etna-1)]x

2 2
e 9Q
(1+n2/3) ( .fi’ Tc (20)
where:
Q - the quadrupole moment
q - the electric field gradient at the nucleus
n — the asymmetry of the electronic environment of
the nucleus
For quadrupolar nuclei, this relaxation pathway dominates
unless the nucleus possesses high symmetry or the quadrupole

moment is very small.

f) Summary of Relaxation Mechanisms

 

The observed relaxation rate is a sum of the contribu-

tions:
CA -1

Q -1 SR -1
+ (T1 ) + (T1 ) + ... .(21)

Table 1 illustrates the time ranges and coupling modes of the
(32)

previously mentioned mechanisms

27

m a Hm u Hexa+ .oom

o
s—IOH a 9 non:

 

:mo .-«momm
.mmo2 .mmOHo

mama .msmmo.u

a) $74.8

«\amfia + mvmuAm\~<mv

0mm OOH.w a v «uoa

0mm OOH v E v H.o

:oaumuopncaom

wzfiansoo awamom

 

I. I. maoauomficm
mooonlmmo A4.u swvom> 0mm OOH v as v OH poanm Hmofismno
omo .maozo .
.mmmm .mmz Asxauumv 0mm «OH v He v .-oa mdoassomsa
sfioovoom
.+:mz .uNmomm I_ I
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28

Because T1 may not necessarily be equal to T2, a
quantitative analysis using the pulsed-fourier transform
(P - FT) method of data acquisition may be Jeopardized.
Care must be taken in order to insure complete relaxation
before pulse repetition or else standardization may be

necessary. A detailed discussion of these problems will

be presented in subsequent sections of this work.

CHAPTER 2

EXPERIMENTAL

I) GLASSWARE CLEANING

 

All glassware used in alkali metal anion synthesis,
solvent purification, or alkali metal storage was cleaned by
first rinsing with an RF cleaner composed of 33% HNO3, 5% HF,
2% acid soluble detergent, and 60% water by volume. This
rinsing was followed by several washings with distilled water
and a 12 hour minimum soaking period in aqua regia. The ves-
sels were then rinsed a minimum of five times with distilled
water and five times with conductance water and dried at
110°C for at least eight hours. This procedure insured a

fresh glass surface free of reactive species.

II) SOLVENT PURIFICATION

 

Tetrahydrofuran (THF) was dried over calcium hydride
for at least 24 hours and then vacuum distilled over a sodi-
um-potassium (Na-K) alloy. The resulting light blue color
served as an indicator of solvent dryness. If this color
faded, the solvent was transferred over a new metal alloy,
but in most cases the solution was stable for several weeks.
The Na-K alloy slowly attacked the THF to give a polymer, so
the THF was transferred away from it for storage.

Methylamine (MA), ethylamine (EA), and isopropylamine
(IPA) were also initially dried over calcium hydride and

then vacuum distilled over the Na-K alloy. If a blue

29

30

solution did not result, the amine was redistilled over a
fresh metal film until the blue color was stable for two
days. The solvent was then distilled into Pyrex storage
bottles since the Na-K alloy also slowly decomposed the
amines to yield ammonia and other decomposition products.

Diethyl ether (DEE) was dried over calcium hydride and
then vacuum distilled into a vessel containing benzophenone
and excess Na-K alloy. A purple color developed with the
formation of the benzophenone ketyl radical. If the purple
color faded, the ether was redistilled onto a new mixture
until the color became permanent. This solvent was stored
over the metal since decomposition was negligible.

Deuterated solvents were refluxed at least eight hours
with barium oxide and then vacuum distilled onto freshly
dried type AA molecular sieves (Linde, Union Carbide). The
sieves were dried by passing dry nitrogen over them while
baking at approximately 250°C. Final drying was accomplished
by heating under vacuum. The solvent was stored over molecu-
lar sieves to insure dryness and samples were made up by
vacuum distilling into an NMR tube with dry solute already
in place. This procedure provided samples with less than
100 ppm water. (usually about 50 ppm) with no noticeable-

contamination or decomposition.
III) LIGAND PURIFICATION

C222 (E.M. Laboratories, Inc.) was recrystallized

twice from hexanes and vacuum sublimed at approximately

31

110°C in the dark using a cold finger filled with a dry
ice-isopropanol mixture. C111 was purified by filtering
through a type F—2O basic alumina column with anhydrous
ether.

The liquid cryptands, C211 and C221 (both obtained
from E.M. Laboratories) and C322 (synthesized in our labo-
ratory at Michigan State University), were vacuum distilled.

The purification of l8-C-6 (PCR, Inc.) was accomplished
by following the procedure established by E. Mei(36). All

ligands were stored under vacuum and in the dark.

IV) SAMPLE PREPARATION

 

A) Preparation of Anhydrous NMR Samples

Figure 7 shows the apparatus used in the preparation
of anhydrous samples for NMR analysis. The solvents were
dried by using the previously mentioned methods and stored
via vacuum distillation in Pyrex bottles equipped with high
vacuum valves and Fischer-Porter Joints. The solvent was
introduced into the NMR tube by distilling through a tee,
the bottle being attached to one end and a valve, fitted
with a ground glass Joint attached to the other end. An NMR
tube, also equipped with a compatible ground glass Joint was
affixed to the valve (using a minimum of high vacuum grease)
and the entire system evacuated. Thus, any volatiles could
be pumped from salts, ligands, etc. before distilling in the
solvent. The solvent could then be distilled, the sample re-

moved from the tee, and capped by a layer of argon using a

32

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33

"Schlenk" line procedure(87)

and the valve quickly replaced
by a sealed ground glass top. This procedure allowed water
content in the final sample to be kept well below 100 ppm

(usually about SOppm) with no contamination.

B) Alkali Metal Anion Solution Preparation

The apparatus used in alkali metal anion synthesis for
observation via NMR or EPR is depicted in Figure 8. The
ligand was introduced from the top and evacuated to about
1 x 10-5 torr. Metal was introduced through a side-arm and
distilled several times so as to obtain a pure metal mirror
in the compartment before the frit. The side-arm was then
removed by a flame seal-off at the constriction and discarded.
The solvent was introduced as described earlier, by vacuum
distillation through a tee and the apparatus transferred to
a dry ice-isopropanol bath. The solution of ligand was trans-
ferred over the metal as many times and at as high a tempera-
ture as could be withstood without decomposition. When an
equilibrium was achieved, the dark blue solution was poured
into the NMR tube and flame sealed at the constriction. The
prepared sample was stored at dry ice temperature until NMR
analysis was conducted, usually within an hour after sample
preparation was complete.

The apparatus employed in the synthesis of solid powders
and crystals of alkali metal anion salts was very similar to
that previously described, except that the NMR tube was not
incorporated in this process. The sample was initially made

in an identical fashion by distilling metal and solvent,

3A

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35

then washing over the metal several times. The deep blue
solution was next poured away from the metal and cooled in
a dry ice-isopropanol bath for about an hour and observed
periodically for signs of precipitate formation. The cold
solution was then decanted back over the metal and warmed
as much as possible without inducing decomposition. This
procedure was continued until either all the ligand was
complexed or decomposition had begun. At this point, the
cold solution was decanted back over the metal, leaving
the powder behind, and the solvent distilled out of the
vessel. The precipitate was either sealed under vacuum and
stored in dry ice or washed with a nonpolar solvent, such

as diethyl ether (if stable), and stored in a similar manner.
v) 0111 SYNTHESIS AND PURIFICATION

The synthesis of Clll follows the scheme depicted in
Figure 9 and involves the condensation of the acid chloride,
1, with the monocyclic diamine, II, to give the bicyclic
diamide, 111(26). This is reduced with diborane to give
the unusual monoborane adduct, IV, rather than a diborane
adduct, presumably because the ligand cannot extend both
nitrogen lone pairs outside the ligand (exo) except with
much difficulty. The borane adduct is then reduced with
KOH in methanol to give the free diamine.

Approximately 200 mg of C111 was received from
Professor J.-M. Lehn and was purified by passing through

an alumina column with anhydrous ether.

36

NH "* N’\’0 N
L: OLEIV<0
Cl 0 Ci
0V.L‘o I

Figure 9. Steps in the synthesis of Clll.

Residues (8-10 grams) containing the bicyclic diamide
of C111 and polymer by-products were also obtained from
Lehn's laboratory. The residues were dissolved in CHCl3
and precipitated with diethyl ether. The polymer precipi-
tated first and the diamide was left behind (about l.A grams
of the impure diamide was obtained). The diamide was re—
duced by suspending it in dry tetrahydrofuran (1A0 m1) and
about 35 ml of diborane solution (1 M in THF, Alfa Divi-
sion, Ventron Corporation) was added dropwise with cooling.
The mixture was refluxed for two hours and cooled to room
temperature upon which 7 ml of conductance water was added.
This addition caused much effervescence as the diborane was
decomposed. The solution was evaporated to dryness and ex-
tracted with ether using a soxlet procedure. This procedure
gave no monoborane product, but instead, about 0.7 grams of

the monOprotonated, Clll-HX,i was obtained. The means by

37
which the borane adduct was reduced and the monoprotonated
ligand formed is not known.

The internally monoprotonated ligand with its un-
identified anion was converted to the bromide by an ion
exchange procedure using a Dowex l x 2 column. The resin
was converted from the chloride to the bromide form by
using an aqueous NaBr solution and testing the effluent
with AgN03.

3 form by using

precipitation followed by filtration through a small

Clll-HBr,i was converted to the NO
A N0
5 3
alumina column.

Table 2 gives an indication of the solubility of

several Clll complexes in many solvents.

VI) METAL PURIFICATION

 

Alkali metals were purchased as follows:
Na: Alpha Division, Ventron Corporation (99.95%)
K: Alpha Division, Ventron Corporation (99.95%)
Rb: Fairmont Chemical Company
Cs: Donated by The Dow Chemical Company

All metals were stored under vacuum in pre-measured
tubes using the "trombone" apparatus shown in Figure 10.
The trombone consists of three Pyrex chambers separated by
constrictions for sealing off, which allow the metal to be
divided into three portions. These chambers also contain
long glass tubes of premeasured inner dimensions into which

the metals can be distributed. The volume of these tubes

38

Table 2. The solubility of C111 and its complexes in
various solvents.

 

 

Species Solvent Solubility
Clll Water, MeOH, Acetone, Ether, Benzene v
Clll°HCl,o Water v
Clll-HCl,o Acetone i
Clll°HBr,i Water, Acetone, MeOH v
Clll-HBr,i Ether i
Clll-HNO3,1 MeOH, EtOH s
Clll-HNO3,i Acetone i
Clll°2HCl,i-o Water, MeOH v
C111°2HC1,i-o Ether, Acetone i
Clll-2HCl,i-i Water, MeOH v
Clll°2HCl,i-i Ether, Acetone i

 

v - very soluble s - soluble i - insoluble

is two to three times greater than that of the metal to be
distributed.

The metals were received in three to five gram am-
poules under argon with a break seal for access. The am-
poule was first flame sealed to the trombone into which a
break bar had previously been placed. The entire system
was then pumped to less than 1 x 10"5 torr, the break seal
broken and the argon pumped out of the system. The metal
was then distributed equally among the chambers which could
be flamed sealed from each other to yield three separate

systems. The metal was forced down the tubes by heating

39

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and gently shaking, then each tube was sealed off. In
order to facilitate distribution of the metal into the
tubes, it was imperative that the system had been pumped to
high vacuum since any residual gas pressure would have
blocked this transfer.

Known volumes of metals were easily obtained from
these tubes since their inside diameters had been measured.
The proper amount of metal could then be isolated and sealed
from the rest of the tube and introduced into the sample
preparation vessel using heat-shrink tubing as shown in
Figure 8. The tube was scratched with a glass knife and
placed into a side-arm of the apparatus. The side-arm was
then capped with a glass end made vacuum tight with flexible
heat-Shrink tubing. The system could then be pumped to high
vacuum (10-5 torr) and the metal tube broken by bending the
heat-shrink tubing. The metal was then distilled into the

vessel and the side-arm flame—sealed away.

VII) VACUUM PROCEDURES

 

Vacuum distillation provides a convenient method by
which to purify and transfer air sensitive materials.
Standard high vacuum procedures were employed throughout
this work. Figure 11 Shows the type of vacuum line arrange-
ment used. It was composed of two Pyrex chambers, one for
high vacuum work and the other used exclusively for work
which did not require high vacuum. These compartments were

separated by a valve which permitted two preparations to be

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done simultaneously. Greaseless Teflon valves of the
Kontes and Fischer-Porter type were utilized to eliminate
the possibility of contamination by vacuum grease. Pres-
sures of 10.6 torr were easily attained. The diffusion
pump was separated from the manifold by a liquid nitrogen
trap to prevent its contamination. All distillations were
done through tees and not through the manifold in order to

insure a clean and efficient system.

VIII) NMR SPECTROMETER

 

Two NMR spectrometers were utilized for the maJority
of the analyses presented in this dissertation. Proton
and carbon-13 NMR studies have been performed using a
Bruker WH-180 super-conducting NMR spectrometer operating
at a field strength of A.228 Tesla. The WH-180 operates
only in the pulse-fourier transform (P-FT) mode and is
equipped with quadrature detection which provides a A0%
signal to noise enhancement. The spectrometer is completely
computer controlled via a Nicolet 1180 computer package
which provides versatile pulse and decoupling Options.
Homo and hetero nuclear and gated proton decoupling, inter-
nal deuterium lock, temperature control and multinuclear
options are also capable with the instrument. The large
field strength provides exceptional resolution and sensitiv-
ity such that samples of less than 1 mg may be utilized for

analysis.

A3

The temperature meter of the WH-180 was calibrated
on several occasions by placing an NMR tube of methanol
with a thermocouple in the probe and allowing it to equili-
brate. The temperature in the probe was measured by a
calibrated Doric digital thermocouple and compared with the
setting of the temperature meter on the spectrometer. A
calibration chart was thus developed and periodically moni-
tered for accuracy. The temperatures could be reliably
measured to 13K with this procedure.

Nuclei other than 13C and 1H have been analyzed on a
greatly modified Varian DA-60 spectrometer which also oper-
ates in the P—FT mode. It is equipped with external lock,
a Nicolet 1080 computer system, a versatile multinuclear
package patterned after the development of Traficante<37),
and operates at a field strength of l.A09 Tesla. The tem-
perature of the sample in the probe may be monitored to t2K
by using a calibrated Doric digital thermocouple with the
thermocouple affixed less than 20 mm from the sample tube.
For further details of the design and operation of the
DA-60 spectrometer see the Ph.D. dissertation of Joseph M.
(38)

Ceraso
IX) SAFETY

Many of the crown ethers have been reported to be
highly toxic<39). l2-crown-A is absorbed through the skin
and its vapors may be inhaled in sufficient quantity to

cause severe inJury and death. Testicular atrophy,

AA

sterility, lack of coordination, convulsions and death

have been observed in rats exposed to l to 6A ppm in a

6 hour day for one week. The toxicological studies of some
higher crown ethers indicate that this entire class of mol-
ecules should be treated with care. Caution should also

be utilized when handling the cryptands although their
toxicity has not been reported.

The Chemistry Department safety guidelines should be
consulted and understood before attempting laboratory work.
These guidelines may be obtained from the Chemistry Business
office. It should also be emphasized that safety glasses
are a mandatory protection for work involving vacuum tech-

niques.

CHAPTER 3

CONFORMATIONAL ANALYSIS OF CRYPTAND lll

I) INTRODUCTION

The fact that cryptands bind ionic species is easy to
demonstrate, but distinguishing how and where the interac-
tion occurs is a much more subtle problem. Cryptands, for
instance, may exist in a number of conformations and possess
several potential binding sites. As shown in Figure 12, the
free ligands are thought to exist as a mixture of rapidly
interconverting isomers in solution<uO-ul). The nitrogen

atoms are free to invert their lone pairs from inside the

cavity (endo) to the outside (exo) with relative ease.

 

exo-exo exo-endo

endo-endo

Figure 12. The conformations of C222.

It has not been established that these conformations contrib-
ute to ion binding or that they exist at all, except that
the following model compounds seem to support the likelihood.

These model compounds, synthesized by Park and Simmons(u2'

AA), are macrobicyclic diamines similar to the cryptands,
except that the strands consist of hydrocarbons rather than
polyethers. Upon acidification, these protonated diamines

undertake a new conformation which has been shown to be an

“5

A6
interconversion of the bridge-head nitrogens from the exo-
exo form to the endo-endo form, with the protons bound
internally. The interconversions are very slow and proceed
with equilibrium constants which are greatly dependent on
the sizes of the hydrocarbon strands.

It has been demonstrated from their crystal structures
that the cryptands exist in the endo-endo conformation when
binding ions in the solid state and this form would be ex-
pected to be most thermodynamically stable, because the nitro-
gens could also participate in binding(u5). In solution, one
may only speculate as to the conformations of the ligand, be-
cause if the interconversion is taking place, it is too rapid
to be observed.

Several experiments support the idea that the structure
of the ligand is at least somewhat flexible in solution.
Protonation studies of C222, C221, and C211 and its metal ion
complexes reveal that the free diamines can protonate at both

14..
nitrogen atoms( 6 “8). The pKa values for C222 are 1.53 x

10"10 and 6.3 x 10'8 (25)

. The pH titration of sodium-cryptate
complexes indicates that protons and sodium are not compatible
in the same cavity, the metal ion being forced out of the
ligand at pH values where the cryptand is significantly pro-
tonated. This process is acid catalized in many instances<25).
A mechanism has been suggested by which the proton would bind
to the exo-endo conformation of the ligand (although it is
thought to be unfavorable) and thereby initiate the removal

of the metal ion. Many other mechanisms could also be

A7

envisioned which would show acid catalysis and, therefore,
these data do not substantiate the exo-endo conversion
process.

In order for the cryptands to bind cations, the
ligands must greatly distort one face so as to expose the
cavity. This is evident in the slow rates of formation and
dissociation of cryptate complexes in comparison with crown
ether complexes, and other monocyclic ligands<u9-52). Once
the ion is located inside the cavity, the cryptand has the
ability to conform to the size of the ion so as to provide
the most stable binding<53). As previously mentioned, X-ray
studies indicate that the nitrogen atoms and the oxygen atoms
participate in ion binding. These studies substantiate the
fact that the cavity size of the ligand may contract or ex-
pand to accommodate ions of various size.

Another illustrative example of this flexibility may
be drawn from the complexation of Cs+ ion by C222. Cesium
ion is too large to easily fit inside the ligand, as the ion's
radius is 1.8A A while the cavity radius is about l.A A.
Depending on the conditions, cesium seems to bind either in
an exclusive fashion, sitting on one face of the ligand in a
crown type complex, or it will go inside, even though the
nominal cavity Size is much too small to accommodate it. In-
deed, crystal structures of cesium complexes with C222 reveal
an inclusive complex, but cesium NMR data provide strong evi-

dence for the presence of both inclusive and exclusive com-

plexes in solution which rapidly interconvert at room

A8

temperature and favor the inclusive form at lower tempera-
tures(5u_55). Recent crystallographic studies show that the
KSCN:C221 complex has the exclusive configuration in the
solid state<56).

Proton binding to C111 is similar to the metal ion
binding in the larger cryptands, because Clll may also be
envisioned as undertaking several topologies which could con-
tribute to the binding. The maJor difference rests in the
fact that a bare proton has negligible size and should be free
to bind at any of the nitrogen atoms and oxygen atoms indivi-
dually rather than interacting concurrently with all the donors,
as is the case with metal ions. Another important distinction
is that Clll is a very "tight" molecule, in that movement of
the strands or nitrogen inversion seems to be much more dif-
ficult than in the larger cryptands, as shown in Figure 13.
Synthetically, Clll also reflects this strain by the diffi-
culty of ring closure, producing low yields, the bulk of the
product being the dimer and polymers. Also, as mentioned
earlier, the exo-exo diborane adduct is not obtained in the
diborane reduction of the dilactam as with larger cryptands,
instead the exo-endo monoborane adduct is produced. Since
with Clll there appears to be a large activation barrier to
nitrogen inversion as well as other molecular interconversions,
it may serve as a good candidate for the observation of indi-
vidual conformations.

In view of the previous discussion, it would be of

value to define the sites which might be expected to

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The possible binding sites and conformations of

Clll, A) unprotonated, B) external protonation,

C) internal protonation, D) external protonation
of the internally monoprotonated complex and

E) internal diprotonation.

51

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Figure 1A (cont'd.)

52
participate in proton binding. Figure 1A shows the more
logical structures, although the exo-exo conformations may
be too strained to exist. Protons probably bind externally
at the nitrogens, since in solution the latter are much
stronger bases than are the ether oxygens. The latter, how-
ever, should not be reJected as viable sites, especially
after one nitrogen has been externally protonated. Inside
the cavity, the situation changes very drastically, because
the ligand shields the inclusively bound proton from the sol-
vent and the donicities of the polar groups would be expected
to be very similar to those in the gas phase. Taft and co-
worders have tabulated gas phase bacisities of several amines
and ethers<57'58), which demonstrate the similarity in base
strength of these groups in the gas phase. Therefore, both
the nitrogen atoms and the oxygen atoms might be expected to
contribute to the binding inside the cavity of Clll.

Finally, torsional motions may also contribute to the
strength of proton binding. The larger cryptands, for instance,
conform to small ions bound inside, in order to optimize the
interaction with the donor atoms. This optimization involves
a concerted rotation of the nitrogens so that the angle, a,
shown in Figure 15, can be large for small ions or small for
the larger ions to provide conditions more conducive to bind-
ing. Figure 13 depicts models of Clll in both configurations.
The one in which a is large, B), might be expected to be most

stable because in this conformation, the nitrogens are closer

53

 

Figure 15. Model showing the torsional angle of C222.

to the Hi' This conformation would also be expected to

greatly shield the inclusive proton from the solvent.

A) Clll Symmetry Considerations

 

Nuclear magnetic resonance spectroscopy is admirably
suited for the identification of the nonequivalence of nuclei
which develops due to the asymmetric configurations. This
nonequivalence is observed in both the proton chemical shift
and in spin-spin coupling constant. For example, geminal
protons (those on the same carbon) have identical chemical
shifts and do not couple with one another if they are chemi-
cally equivalent, but if for some reason they become non-
equivalent, they do couple to one another and their chemical
shifts are no longer identical. A very frequent cause of
geminal nonequivalence, and one which occurs often with the
cryptands, is the slowing of molecular vibrations at low
temperatures, which "locks" the geminal protons into slight-
ly different chemical environments (on the NMR time-scale).

Nuclear magnetic resonance also provides characteris-
tic information about the electronic environment of the bind-

ing site from the chemical shift and thereby facilitates the

5A
identification of the functionality of that site. The
relative stabilities of various sites may be obtained from
the populations in those sites and the dynamics of exchange
between sites may be obtained from line broadening. The
theory of line broadening in NMR has been thoroughly devel-
oped by Bloch<59'60), so that the NMR spectra may be math-
ematically simulated in order to define the exchange rates
associated with spectra at various temperatures (see the
Appendix for a complete derivation). The temperature depen-
dence of the exchange rates which, in principle, should ad-
here to the Arrhenius theory, provides activation parameters
for exchange.

The interpretation of the NMR spectra of Clll and its
complexes is greatly simplified if the symmetry of the mole-
cule is understood. As can be seen in Figure 16, Clll is a
highly symmetric molecule and belongs to the D3h point group.
The most useful symmetry elements for interpretation purposes
are the C3 rotational axis through the nitrogens, the Oh
plane through the oxygens, and the three ov planes which in-
clude the C3 axis, a polyether strand, and bisect the other
two strands. It is simplistic to assume that the av symmetry
exists, because gauch conformations are more energetically
favored than are the eclipsed conformations which are neces-

sary for 0 symmetry. When rapid methylene wagging motions

v
occur, so that the interconversion between the two gauche
forms is rapid, the 0V symmetry will be presented if the

"average" conformation preserves this symmetry. This

55

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56

interconversion must proceed in milliseconds or faster in
order to present an exchange averaged picture in the NMR
spectrum, since the maximum exchange rate observable is on
the order of the chemical shift difference of the two sites.
This difference rarely exceeds 1,000 Hz. Therefore, if an
exchange occurs, whether it be a proton Jump or interconver-
sion of two conformations of the ligand, and is more rapid
than milliseconds, the NMR spectrum will present a single
line (or a multiplet if scalar coupling is present) which is
the population average of those sites involved. The chemical
shift of this exchange averaged line is defined by:

6obs = i xi 61 (22)
where:

5obs - the observed chemical shift

61 the shift in site 1
x1 the mole fraction (the population) in site i

The room temperature spectra of the Clll complexes Show that
the av symmetry element is preserved because interconversion
rates are faster than the NMR time-scale and the exchange

averaged conformation preserves this symmetry.

II) NMR SPECTRA AT AMBIENT TEMPERATURES

 

At room temperature, molecular motions are rapid and
the NMR spectrum of a given species usually reflects an ex-
change average of several different conformations. This is
true of the spectra of Clll and its complexes shown in Figure

17 and the chemical shifts which are given in Table 3. The

57

 

 

 

 

 

 

A
B
o
b
C
o
b
“SOLVENT
LkH D
4.00 3.50 3.00 2.50
6 ppm

Figure 17. The NMR spectra of C111 and its protonated com-
plexes at ambient temperature.

58

 

 

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.onsumnmanu unmanem pm mmxoaasoo mum ond HHHU mo mpuficm awedscno one

.m mHQMB

59
most striking feature of these spectra is the dependence of
the chemical shift of the backbone protons on protonation.
The CH20 proton lines shift downfield by about 0.3 ppm per

proton added and the CH N proton lines shift by about 0.7

2

ppm per proton, more than double the CH O proton shift. This

2
downfield shift is caused by the delocalization of the positive
charge of the bound proton throughout the backbone of the mol-
ecule, which is an electric field contribution to the chemical
shift. The fact that the CH2N protons show a greater shift

is indicative of greater interaction of the internal proton
with the nitrogens than with the oxygens.

Assignment of the binding interactions should be done
with care because these spectra represent the average of many
rapidly interchanging molecular conformations. Nevertheless,
some qualitative assignments may be made from them. Three of
the four structures, Clll, Clll°H+,i and Clll-2H+,i-i, preserve
the D symmetry since the spectra show equivalence of the

3h

CH20 protons as well as of the CH N protons. The fourth struc-

2
ture, Clll-H+,o, has lost at least some molecular symmetry,
because these two sets of protons are no longer equivalent.
A discussion of the three symmetric complexes will be presented

first, focusing on each structure individually, and the exter—

nally protonated ligand will be discussed thereafter.

A) Clll in d6-Acetone

 

The NMR spectrum of Clll contains two sets of triplets,
one set at 3.AA ppm (CH20 protons) and the other at 2.52 ppm

(CH2N protons). The two sets of protons split each other

60

with a coupling of 5 Hz. Figure 1AA shows three possible
conformations of the ligand. From the room temperature
spectrum, one is not able to conclusively establish their
presence except that, if exo-endo nitrogen inversion or any
other conformational change is occurring, it is doing so
rapidly on the NMR time-scale, and its average preserves D3h
symmetry. Based on an examination of molecular models, the
exo-exo form is not expected to exist, but a rapid exchange
between the endO-endo and exo-endo forms would preserve the
D3h symmetry. Rapid vicinal carbon wagging vibrations must
also be occurring in order to retain the av plane through the
polyether strand, which is necessary for the geminal CH2 pro-
ton equivalence. This vibration entails exchange of the vic-

inal carbons between the gauche conformations whose average

is the eclipsed conformation.

B) Clll-H+,i-Br- in d6-Acetone

 

The internally monOprotonated ligand shows D3h symmetry
at room temperature for the same reason as does Clll; namely,

rapid interconversion between the conformers. The CH20 pro-

tons are equivalent at 3.76 ppm as are the CH2N protons at
3.2A ppm. These two sets of protons again split each other

into triplets of 5 Hz, and the inclusive proton, H , also

1

couples to the CH2N protons with a coupling constant of 2.5
Hz, resulting in a six line pattern. The H1 resonance is
located at 9.07 ppm with a linewidth of about 15 Hz. No

coupling is observed to the nitrogens or oxygens by any of

61
the protons or carbons, presumably because of very fast
quadrupolar relaxation, but the breadth of the H1 signal
(approximately 15 Hz) and the backbone proton lines (approxi-
mately 1.5 Hz) probably originates from efficient scalar re-
laxation by the nitrogens<62). No coupling of the R1 to the
carbons is observed in the C13 NMR spectrum, but it would be
expected to be about one fifth that Of the CH2O proton split-
ting and would not be observable(61).

The fact that coupling of the H1 proton is observed to
the CHZN protons and not the CH20 protons is good evidence
that the H1 proton interacts most strongly with the nitrogens
and not the oxygens. Coupling is transmitted through a chemi-
cal bond via Fermi contact interactions<62), and the magnitude
of the coupling interaction is similar through the protonated
ether oxygens and the protonated amines. Three bond coupling
constants of about 5 Hz have been documented for ethers pro-
tonated with super acids and for protonated amines(63'5u).
Therefore, if the ether oxygens did interact appreciably with
the Hi, we would expect to observe coupling to the CH20 pro-
tons, although attenuated slightly since there are three oxy-
gens, rather than only two nitrogens. The 2.5 Hz coupling of
the H1 to the CH2N protons agrees with literature values for
protonated amines. The observed coupling is half the litera-
ture value since the H1 is shared equally between the nitro-
gens.

A structure which would be consistant with the nitrogen

protonation as well as the preservation of D symmetry is

3h

62
shown in "a" of Figure lAC. The proton Jump between the
nitrogen atoms is always rapid. The exo-endo inversion is
probably hindered by coulombic interactions between the Hi
and the nitrogen lone pair, and therefore occurs very infre-
quently. The internal proton exchange phenomenon is very
unusual, since it occurs much more rapidly than the NMR
time-scale (since it preserves symmetry), and yet coupling
to the CH2N protons by the H1 is not lost. Normally, when
proton exchange is more rapid than the NMR time-scale,
coupling between the exchanging protons and those attached
near the binding site is lost. This loss occurs because
protons of either spin state have an equal probability of
binding at the site and the NMR spectrum presents a single
line which is an exchange average of the two. With
Clll-H+,i, the spin character of the exchanging proton is
preserved between Jumps (ignoring Tl relaxation which is slow
by comparison), because the same proton exchanges back and
forth between the two nitrogens. The H1 is not able to ex-

change with protons in solution, but is restricted to move

only within the confines of the cavity of Clll.

C) Clll-2H+,i-i-2Cl- in d“ MeOH

 

The internally diprotonated ligand must exist in the

endo-endo form as a prerequisite for D symmetry, due to

3h
the size restrictions of the cavity. The H1 protons must

be located on the C3 axis, each equidistant from the center

of the cavity. Their distance from the nitrogens is probably

63
less than in the monoprotonated ligand, because of the
coulombic repulsion of the two protons. As'a result of
the symmetry, the spectrum, as seen in Figure 17D, presents
the equivalence of all CH20 protons at 3.96 ppm and CH2N
protons at 3.7A ppm, the two sets splitting each other into
triplets with a coupling constant of 5 Hz. The H protons,

1

whose resonance is located at 7.33 ppm, couple to the CH2N

protons (but not to the CH O protons) with a coupling of

2
5 Hz, producing two sets Of overlapping triplets which re-
sult in a four line multiplet. Coupling, which originates
from the Fermi contact interaction, is a function of the
ability of the nitrogens to donate electron density to the
H1. The introduction of a second proton into the cavity of
Clll-H+,i would be expected to double the coupling through
the nitrogen, because each nitrogen binds to one full proton
rather than sharing one between them. Thus, the contribution
of electron density from each nitrogen doubles. This is
exactly what is observed, since the coupling to the CH2N
protons increases from 2.5 Hz to 5.0 Hz with the addition
of the second internal proton.

When one Of the two internal protons is replaced by a
deuteron which has a coupling constant one sixth Of that of
a proton (less than 1 Hz for three bond coupling), the NMR
spectrum of the CH2N protons indicates two overlapping pat-
terns which may be distinguished by decoupling experiments.
One pattern shows coupling of 5 Hz to the H1, whereas the

other does not, a result of negligible exchange of the proton

6A
and deuteron between the nitrogens inside the cavity. This
complex probably exists in the configuration displayed in
Figure 13A with the cavity as large as possible in order to
allow maximum separation for the H1 protons.

The upfield shift of the H protons in going from the

i
mono to the di internally protonated ligand is a consequence
of two opposite contributions. The size limitations of the
cavity of Clll tend to restrict the donation of electrons
from the nitrogens to the internal protons because, as they
gain electron density, they also increase in size. This
contribution induces a downfield shift. The increase in
charge density inside the cavity greatly overshadows the for-
mer contribution, and induces a large electronic shielding,
which in turn produces the Observed upfield shift.

The linewidth of the H1 is dominated by scalar relaxa-
tion to the nitrogen, and on the basis of a twofold increase
in coupling constant from the mono to the di internally pro-
tonated ligand, the linewidth of the Hi would be predicted
to increase by a factor of four between the two complexes
on the basis of the Fermi contact term. The observed line—
width of the H1 in Clll-2H+,i-i is about 50 Hz, which is in
the range of the predicted values (A8 to 60 Hz). The line-
width decreases with decreasing temperature because the re-
laxation rate of the nitrogen increases and thereby causes
the scalar interaction to be less efficient<62). All assign-

ments have been verified by decoupling experiments wherever

possible.

65
The room temperature spectra indicate that the H1
protons interact at the nitrogens, and that the shifts pro-
duced for both the skeletal protons and the inclusive pro-
tons upon protonation are a result of the electric field
contribution to the chemical shift. For this reason, Musher's
equations, which predict the shifts resulting from changes

in charge distribution, should prove valuable in understand-

ing the observed shifts.

D) Musher's Theory of the Chemical Shift<30>

 

Musher's equations describe the chemical shift induced
by the electric fields associated with charged or polar
groups. The magnitude of the field is proportional to the
charge density and the distance of the bond from the charge,
as described in the Historical section. In order to calcu-
late the shift expected upon protonation of 0111, a geometry
for the ligand must be assumed. The nuclear coordinates have

been calculated utilizing D symmetry, and the assumption

3h
was made that the center of positive charge was at the nitro—
gen. The theory predicts a downfield chemical shift of A.l

ppm and 1.0 ppm respectively for the CH N and CH20 protons

2
upon the introduction of two protons into the cavity of Clll.
The observed downfield shifts are l.A and 0.6 ppm, which are

in the right direction and relative magnitude, but much smaller
than the theory predicts. The theory predicts an upfield

Shift of about 2.6 ppm for the H1 in going from Clll'H+,i to
Clll°2H+,i-i, and again it is in the correct direction but

too large (the real shift is 1.A ppm). The theory applies

66
to gas phase interactions, so that solvent interactions with
the ligand may cause the discrepency between the theory and
the observed shifts, but it lends credence to the belief
that protonation occurs at the nitrogens, and is also able

to account for the entire shift.

E) Clll-H+,o in d6-Acetone

The NMR spectrum of Clll-H+,o in d6-acetone acidified
with trifluoracetic acid (TFAA) (Figure 178), reflects the
loss of molecular symmetry, because four lines of equal area
are present rather than two. (The multiplet at about 2.5 ppm

is a C13

satellite of acetone.) There are two plausible
sites for external protonation, shown in Figure lAB, one at
an exo nitrogen and the other at an oxygen. Only nitrogen
protonation, with the loss of Oh symmetry, could give rise
to four lines of equal intensity. Protonation of the oxygen
atoms would not give lines of equal intensity. Therefore,

the resonances a and b correspond to CHZO and CH N protons

2
on the protonated side of the molecule and a' and b' to the

unprotonated side.

Assuming these assignments are correct, the chemical
shifts of the skeletal protons are informative in determin-
ing the contribution of exo-endo conformational changes to
the chemical shifts of the Clll complexes. The Clll'2H+,i-i
complex and C111 probably exist in the endo-endo form. Those
resonances from the protonated side of Clll-H+,o, namely a
and b, are very similar in their chemical shift to those of

Clll-2H+,i-i, whereas those on the unprotonated side, a' and

67
b', are very similar to those of Clll. Therefore, even in
the presence of a greatly different conformation, the chemi-
cal shift of the backbone protons is dominated by nitrogen
protonation and the contribution from the conformational
change is less than 0.2 ppm.

Perhaps the most striking feature in relation to exter-
nal protonation of C111 by TFAA is the lifetime of the com-
plex, being greater than milliseconds. The spectrum of this
complex demonstrates that the exo-endo form of Clll exists
in solution.

The theory of Eigen concerning general proton-transfer
processes predicts that when the strength of an acid is much
different than that of the conJugate acid of the base used
in proton-transfer reactions, the rate of transfer is fast.
The transfer also is complete, favoring the formation of
the species with greater pKa(65) and the reverse reaction is
slow. If the relative strengths are similar, however, the
proton is rapidly exchanged between the two, but the transfer
is incomplete. Eigen has shown that a proton-transfer reac-

tion may be written as follows:

K1 K2 K3
AH+B:AH--~B:A~~HB:A+HB (23)

where AH-ooB and A-ooHB are encounter complexes. When the
reaction favors one set of products, say A + BH, as is the
case involving protonation of Clll with TFAA, the proton is
rapidly transferred and the resulting complex is long-lived.

This can give a long enough value of the exchange time, T, to

68

permit observation of both HB and B when less than a
stoichiometric amount of HA has been used. However, if the
values of pKa and pr are similar, fast proton exchange and
an incomplete transfer occurs. I

The external protonation of Clll has been studied by
NMR as a function of acid strength in d6-acetone and dA-
methanol. Three acids were utilized; namely, HCl, trifluoro-
acetic acid (TFAA), and dichloroacetic acid (DCAA), each of
which appeared to interact differently with Clll. HCl was
generated by addition of about 0.1 m1 acetyl chloride to
about 10 ml of du-methanol and allowing time enough for the
reaction to proceed to methyl acetate and HCl. This method
provided an internal standard for a quantitative determina-
tion of acid content. When one drop of this solution was
added to a solution of Clll in du-methanol, a white powder
immediately precipitated, and the NMR signal of Clll was no
longer observed. Presumably the acid formed the monohydro-
chloride salt of Clll, the proton being bound externally and
the resulting complex was insoluble in du-methanol. This
sample was immediately cooled to -70°C, after which some yel-
lowing of the solution was noted. Addition of KOH cleared
the solution and caused the precipitate to quickly redissolve.

Addition of TFAA to a solution Of Clll in d6-acetone
at 270 K caused no precipitation, but a dramatic change in
the NMR spectrum was observed compared to that Of the free
amine, as shown in Figure 18. Addition of less than one

equivalent of acid caused immediate production of a

69

 

b+ b“

 

1 1 1
oppm 4.00 3.50 3.00

 

 

Figure 18. The dependence of the NMR spectrum of Clll in
d6-acetone upon the addition of trifluoroacetic
acid (TFAA).

70
monOprotonated form of the ligand. This externally pro-
tonated form exchanges only slowly with the free amine (as
evidenced by slight line broadening) via the following

scheme:
4. ..
Clll + HTFAA:;::::Clll-H ,O + TFAA (2A)

but the proton transfer greatly favors the C111. As TFAA
is added, lines a', b', a", and b" grow as a and b (those of
the free ligand), disappear (an impurity peak overlaps the
signal, a'). The new lines are consistant with the structure

"b" of Figure lAB. As mentioned previously, the a symmetry

h
is removed, thus the exchange scheme (2A) must be slower
than the NMR time-scale and highly favor the monoprotonated
form.

As more than one equivalent of acid is added, the
downfield CH2N line shifts farther downfield and eventually
coalesces with the CH 0 line at A.00 ppm. Continued addition

2
of acid causes the upfield resonances to disappear and that
at A.00 ppm to grow. At a mole ratio of about 50/1 acid to
Clll, the sample is almost completely converted to this new
form, since the resonance at A.00 ppm accounts for nearly the
entire area of the resonances. This new form is probably a
diprotonated species, which has protons bound externally at

both nitrogens, the ligand being in the exo-exo form. A

logical reaction scheme is shown below:

+
0111 + H+-—.: Clll-H ,o (25)

Clll-H+,o + I1+;_=-__ Clll-2H+,o-O (26)

71
Reaction (25) goes to products quickly and completely as
mentioned earlier, but with excess acid, reaction (26) be-
comes important. The first external protonation is stable
and the transfer is fast and complete, whereas the second
exo protonation is much more difficult to achieve. Therefore,
the proton is exchanged rapidly and the equilibrium needs to
be forced to the right by a large excess of acid. External
oxygen protonation is ruled out as a maJor contributor to

the second external protonation, because the CH O protons

2

would show a much larger downfield shift than the CH N pro-

2

tons. The fact that the CH20 and CH2N proton lines coalesce

at A.0 ppm with excess acid indicates that the interaction
involves exo-exo nitrogen protonation. External nitrogen
protonation is also necessary to account for the very large

shift in the CH2N proton resonances as acid is added. The

identical chemical shifts of the CHZO and CH2

this externally diprotonated species seems to be accidental.

N protons in

The acid concentration was determined by the comparison
of the exchangeable proton line of TFAA (the —OH signal) with
those Of the ligand. Considerable error is inherent in this
method, since at least two acid proton signals are present,
that bound to the ligand and that bound to the TFAA anion.

The latter line is very broad and the bound proton line often
overlaps the ligand signals. Water also interferes. This
makes the measurement Of the acid concentration very difficult,
but general trends have been established. Table A lists the

chemical shifts of the resonances as a function of TFAA present.

72

Table A. The dependence of the chemical shifts of Clll in
dé-acetone upon addition of trifluoroacetic acid
(

 

 

FAA).

MR %§%%.(tuoz) ogggo 633 N

A 0.0 3.u7 2.56

B 0.7 3.99, 3.65 3.76, 2.63
p 1.u u.01, 3.65 3.88, 2.63
E 1.7 u.o3, 3.66 3.96, 2.6A
F 7.6 u.o2, 3.66 n.02, 2.6A
6 8.A u.01, 3.70 u.01, 2.67
H 29 3.98, 3.73 3.98, 2.77
I 50 3.91 3.91, 2.78

 

Dichloroacetic acid, DCAA, has been utilized to better
determine the amount of acid added, since it has one non-
exchangeable proton. As shown in Figure 19, the addition of
DCAA gives very different NMR spectra than does the addition
of TFAA. Proton exchange between the free and the monopro-
tonated amine at 270 K is much more rapid. As DCAA is added,
the lines broaden and shift downfield, the CH2N protons show-

ing a more dramatic effect than the CH O protons. A plot of

2
the chemical shift of the CH O protons as a function of total

2
acid added, as shown in Figure 20 and Table 5, gives a break
in the slope at a mole ratio Of 1:1 acid to Clll indicating
efficient formation of the monoprotonated form ( as with TFAA)
and a difficult second protonation. The break occurs at a

chemical shift of 3.79 ppm, which is midway between the values

73

 

M.

U13 M
01 M‘

a
1
6ppm 500 4100 3.00 4100 300

 

 

 

 

 

Figure 19. The dependence of the NMR spectrum of Clll in d6-
acetone upon the addition of dichloroacetic
acid (DCAA).

7n

.<<om mo coauaoom cons ocouoomumo
ad HHHo mo mCOpono o~mo on» no awash Hecasono on» no cocoocomoo one .om madman

 

 

Eon m
oN me
one om.» co.»
1 % .N. w
\.\ m
. w
F u
I .o.~ O
=
V
D
o.» O
[I
D
6.?
o
6.0

 

 

75

Table 5. The dependence of the chemical shifts of 0111 in
d5-acetone upon addition of dichloroacetic acid

 

 

(DCAA).
Mole ratio %%%% (120%) 601120 6OHZN
PPm ppm
A 0.0 3.“? 2.56
B 0.18 3.50 2.58
C 0.25 3.55 2.57
D 0.52 3.65 2.85
E 0.8 3.71 2.96
0.9 3.76 2.97
1.A 3.79 too broad
1.7 3.80 to define
F A.3 3.83 .....

 

of A.00 and 3.6A ppm observed for the CHZO proton lines of
Clll-H+,o with TFAA. This implies that the same two confor-
mations of the ligand are present upon protonation with either
DCAA or TFAA, but with DCAA, they are rapidly interconverting
and an exchange averaged signal is observed. Thus proton ex-

change is rapid with DCAA so that the time-average o sym-

h
metry element is retained. As with TFAA, the reaction (25)
goes to completion, since the CH20 chemical shift at the

break point is midway between those observed with TFAA. Reac-
tion (26) is fast and incomplete as before. (The same corre-

lation could probably be made utilizing the CH2N proton lines,

except that they are too broad to locate accurately.)

76

Eigen's formulation concerning proton exchange proc-
esses indicates that in order to achieve proton exchange
times of 10'3 seconds or longer between an acid and a base,
the difference in their pKa values must be at least 6.5 to
7.0(65). The pKa values of TFAA, DCAA and C111 are known
in water but they are not known in acetone. Therefore, we
must assume that their relative strengths in acetone are
similar to those in water. The pKa values of TFAA, DCAA and
C111 in water are 0.23, 1.25 and 7.08 respectively<66). The
difference between the pKa values of C111 and TFAA (6.85) is
large enough to yield proton exchange times in the millisec-
ond region, whereas the difference between the pKa values of
Clll and DCAA (5.83) would be predicted to give rates of
about 10’“ seconds according to Eigen's theory. These find-
ings are consistent with external protonation.

The mole ratio of DCAA present was measured by compar-
ing the resonances of the acid (both the backbone proton and
the exchangeable proton of DCAA being coincidentally located
at 6.6 to 6.0 ppm) to the CH2O proton lines of the ligand.

A delay of 20 seconds between pulses was utilized to insure
complete relaxation. Delays of 10 seconds and longer caused
no measurable change in the values obtained. The temperature
of the samples was kept below 275 K to preclude inside pro-
tonation. The acidified samples were stored in a freezer at

about -30°C for months with no apparent inside protonation.

77
...
F) Clll-H ,o in Water

 

The NMR spectra of Clll have been determined for a
number of pH values utilizing buffers in D20. These data
were Obtained in conJunction with the rate studies of inside
protonation presented in the following section. The chemi—
cal shift and lineshape of each spectrum shows a pH depen-
dence in D20, which is similar to that observed in acetone.
The spectra at several pH values are shown in Figure 21.
These spectra reveal that external protonation in water is
fast, since neither the CH2N lines nor the CH2O lines give
evidence of nonequivalence. The variation of the chemical
shift of these lines with pH is given in Table 6, and plotted
for the CH2N protons in Figure 22. The plot shows a break
at a pH of about 6, above which the lines are very narrow
due to rapid proton exchange between C111 and Clll'H+,o.
Using the values of 2.53 ppm and 3.10 ppm for the chemical

shifts of the CH N protons Of C111 and Clll-H+,o in the

2
absence of exchange, and equation (22) from the Introduction,

a value for the pKa of the first protonation of about 8 t 2

is obtained from the break in the curve.

Below a pH value of 6, the lines begin to broaden greatly
and continue to shift downfield, indicating conversion to the
externally diprotonated species. At a pH value of about 2.6
they begin to sharpen again. This behavior indicates that
the rate of formation of the externally diprotonated species

from the externally monoprotonated species is not extremely

fast. The plot in Figure 22 indicates that the conversion to

78

 

 

 

 

 

 

 

 

 

8.7
2.6
40 3.'O 20 4'0 3'5 32>
6.5 L4
40 is 3'0 4'0 35 30
1
J 1
A
4.0 H
40 3.5 32) 40 3'6 3b 25

Figure 21. The NMR spectra of Clll in water at various pH
values.

79

.O

N

a as ammo mo msoeoao z

m

so one mo smash Hoossoso on» mo oosoosoaoo ma one .mm osswam

 

ccoamw
00.0 on.” Z~IU 00m ond.
_ a 00
a /o( o
d
/
o/
d
o
/ H
\- mom
0

I.

 

80

Table 6. The pH dependence of the chemical shift of the

 

 

CH2N protons of Clll in water at 299°K.*

pH? CHQO CH2N

ppm ppm
9.0 ---- 2.53
8.7 ---- 2.69
7.5 3.78 3.05
6.5 3.85 3.21
A.9 3.82 3.13
A.0 3.81 3.19
3.2 ---- 3.23
2.6 ---- 3.27
1.8 ---- 3.A0
1.A 3.79 3.AA
1.1 3.81 3.A9

 

* Reference to DSS., those absent in the CH20 column are due
to overlap.

I Corrected for deuterium effects.

the diprotonated species is not complete, even at a pH
value of 1.0. Comparison with the shift in acetone indi-
cates only about 50% conversion. The average shift of the
CHZN protons of Clll-H+,o in acetone is very similar (10.1
ppm) to that in water (arrow "a" of Figure 22). Thus a
chemical shift for the CH2N protons of Clll-2H+,o-o of 3.9
ppm (arrow "b") may be assumed, from which a pKa value
lower than 2 is obtained for the second external protona-

tion. The pH values of all buffers were measured (and

81
corrected for deuterium influence)(67) with a calibrated
radiometer and microelectrode.

A pH titration of Clll was also performed in water.
Only one break was observed, yielding pKa = 7.1 i 0.1 for
the first external protonation. The titration went only to
a pH value of 1.0, which was probably still too high to per-
mit observation of the second break. From the pH dependence
of the NMR chemical shift, the second pKa is estimated to be
between 0 and 1.5 in water.

The pKa values Of C111 and its complexes reflect the
presence of the exo conformation, since only this form may
be externally protonated. 1,A diazabicyclo (2-2-2) octane,
or Dabco, is a carbon analogue of the cryptands, whose small
size requires both nitrogens to be in the exo conformation.
The pKa values of the cryptands would be expected to be very
similar to that of Dabco, 8.8 i 0.2 at 25°C, if the molecule
had no endo conformation present. Proton transfer reactions
of the cryptands actually involve a two step process:

+ Ka + K1
Clll-II ,0:H + Clll (endo-exo):

Clll (endo-endo) (27)
and the apparent Ka of C111 is equal to the following:

app _
Ka - (Ka)<K1> (28)

Assuming that the value of Ka for external protonation of

Clll in the exo form is equal to that Of Dabco, 1.6 x 10'9,

8

the observed value of Kaapp, 7.9 x 10 M, gives K1 8 50.

82

Therefore, the endo-endo form is favored over the endo-
exo form by about 2 kcal mol'"1 in the absence of acid and
the endo-endo form accounts for about 98% Of the ligand at
room temperature in the absence Of acid. For the second
external protonation, if we assume that Kaapp is 10"2 or

I

less, we obtain K > 10+7, establishing a difference of at

1
least 6 kcal mol'1 between the two forms. The value of K1
represents the analog of K in equation (27) for the mono-

1
protonated ligand.

0) The External Protonation of Clll-H+,i

 

In water and in methanol, the chemical shifts of the
CH2O and CH2N protons are strongly dependent on the strength
of the added acid and on the temperature, indicating that
the exo-endo diprotonated complex is present in equilibrium
with the internally monOprotonated form. The spectra in
du-MeOH will be discussed in detail in the next section, but
the results of this analysis show that the exo-endo inversion
and the proton exchange rates are very rapid. A pKa value
of 3 is obtained for external protonation in methanol.

The pH dependence of the NMR spectra of Clll-H+,i in
water indicates that an exchange similar to the one Observed
in methanol is occurring. A compilation of the pH dependence
of the chemical shifts Of the CH2O and CH2N proton lines of
Clll-H+,i in water is shown in Table 7. It we assume that
the chemical shift for the CH2N protons of C111°H+,i is 3.0
ppm and the shift of the same protons of Clll'2H+,i-O is

3.A5 ppm (from Table 7), a value Of 0.A i 0.5 is obtained for

83
the pKa of the process. This pKa value indicates that the
preference for the endo-endo form is higher in water than
in methanol by two orders of magnitude. Using the Ka of

8 in water

Dabco, an equilibrium constant, Kg, of about 10
and about 106 in methanol is Obtained for the ratio of the
endo-endo form to the endo-exo form. Thus the endo-endo
form is the only significant species in solution in the ab-
sence of added acid. The endo-exo form of Clll-H+,i seems
to be as difficult to attain as the exo-exo form of Clll.

Table 7. The pH dependence'og the chemical shifts of
Clll-H+,i in water 5 .

 

 

Acid Strength CH2N CHZO

ppm ppm
3N 3.A5 3.82
1N 3.3A 3.76
0.AN 3.20 3.72
0.1N 3.10 3.70
0.01N ‘ 3.03 3.66
0.0 3.02 3.66

 

H) General Conclusions

 

1) External protonation occurs at the nitrogens in
both C111 and Clll-H+,i.

2) Internal protonation would be expected to also in-
volve oxygen interaction, but the NMR evidence suggests other-

wise.

8A

3) The chemical shifts of the CH20 and CH2N protons
upon protonation are determined mainly by electric field
effects caused by the protonation at the nitrogen and not
by conformational changes.

A) Exo-endo inversion is rapid at room temperature,
but favors the endo-endo form especially in Clll-H+,i.

5) Exo-endo inversion does not take place in
Clll-2H+,i-i.

6) The solvent and acid used, greatly influence the

extent of external proton binding and the exchange rate but

have no observable effect on inclusively bound protons.

III) TEMPERATURE DEPENDENCE OF THE NMR SPECTRA

 

The time-scale of proton NMR is relatively slow since
it is only able to distinguish between processes which occur
more slowly than milliseconds and, in fact, is limited in
the C111 systems to exchange times longer than about 0.01
seconds. Exchange phenomena which occur more rapidly than
this yield only a population average signal, and the charac-
ter of the individual site is lost. One of two things may
be done in order to identify individual sites when exchange
times are more rapid than 10'3 seconds. First, an analysis
method which employs a faster time-scale may be utilized,
such as IR, UV or EPR spectroscopy if applicable. The other
alternative is to continue using NMR methods, but at lower
temperatures. A change in temperature affects more factors

than Just the rates of exchange processes, however. It also

85

alters the populations Of the sites involved in the exchange
in accord with Boltzmann statistics, and changes such physi-
cal properties of the medium as the viscosity and the di-
electric constant. The enthalpy and entropy of a binding
site are temperature invariant if external influences of the
medium remain constant. Therefore, going to lower tempera-
tures does not cause stronger binding (unless the site is
perturbed externally) although the lifetimes at sites do
become longer, as governed by the Arrhenius or Eyring equa-
tions(68)-

The equations which describe chemical exchange are
well characterized for NMR. McConnell modified the Bloch
equations to describe chemical exchange processes and ob-
tained equations which are applicable to phenomena invOlving
single lines and first order multiplets(59-6O). These equa-
tions are developed in a simplified form in the Appendix, and
may be easily utilized in processes which involve fewer than
four or five sites. For systems of more sites, or second

order spectra, a density matrix approach would be more suit-

able(69).

A) Clll in d6-Acetone

 

The temperature dependence of the proton and carbon-l3
NMR spectra of Clll in CHF2Cl has been reported by Lehn and
(26)

co-workers at 250 MHz. The C13 NMR spectra were tempera-
ture-independent down to 178 K except for slight line shifts,
but the proton spectra at 163 K show a well resolved ABXY

pattern for the backbone CH2N and CHZO protons with chemical

86

Ammv

um: 0mm um x mmH um Ho

N

Emu :H HHHU ho Sahpomam 0:9

.mm enemas

 

87
shifts and coupling constants of 3.67 (A), 3.32 (B), 2.58

(X), and 2.A7 (Y); J = 10, JXY = 1A, J = 10,

AB BX

JAx = JBY AYmi 2 Hz as depicted in Figure 23. Since

the pattern was of the ABXY form, the conformation at low

2 J

temperatures did not involve exo-endo isomers, because the

Oh symmetry element was still intact. Instead, the process
was described as the slowing of a torsional motion, such as
vicinal carbon wagging motions, concerted twists of the
strands, etc. The rate of this torsional motion was obtained
at the coalexcence temperature of -65°C, which yielded a AGI
of 9.8 i 0.1 kcal molml (from the Eyring equation). The
torsional motion was assigned to a possible concerted process,
such as the passage of a strand through the intramolecular
cavity, since the activation barrier for the process was rel-
atively large. Typical vicinal carbon wagging motions possess

activation enthalpies of 3 to 6 kcal mol-1

, depending on sub-
stituents, whereas concerted processes normally yield an ac-
tivation barrier which is roughly the sum of the individual
components. Therefore, a concerted twist would be expected

to have an activation barrier of 10 to 18 kcal mol-l, and the
value reported by Lehn of 9.8 kcal mol”1 would put it in the
range of concerted processes. (The free energy of activation
has no direct physical meaning, since it is the sum of AH;

and -TAS¥, both of which can be given physical meaning. There-

fore, in order to equate the AG1 obtained form coalescence data

with the activation enthalpy, AS; must be assumed to be zero.)

88

 

 

 

.m:ouoomnoo :« Haao mo onuOOQn mzz on» no consummate waspmnmaEOp 029 .:m oaswfim
Edam MN om mm.” mm OM mm nm 0.4» mm
om. CON CNN

 

nNN : ))<fi 0.0

89

Figure 2A shows spectra for the same process in d6-
acetone at 180 MHz which have very similar features, except
that they are more poorly resolved, due to a lower field
strength, higher temperature and a more polar solvent. The
assignments are the same as those at 250 MHz (see Table 8),
but the separations due to nonequivalence are not as pro-
nounced in acetone as they are in CHF2C1. From the coales-
cence temperature of -58°C for the process in acetone, AG* =
10.7 1 0.3 kcal mol’l, in agreement with Lehn's results.

Table 8. The temperature dependence of the NMR parameters
for a 0.02 M solution of Clll in d6—acetone.

 

 

Temp (°K) 6C1120 6CH2N

ppm ppm
290°K 3.AA 2.52
190°K 3.A9, 3.39 2.52

 

B) Clll-H+,i°Br' in d6-Acetone

 

The temperature characteristics of Clll-H+,i (Figure 25
and Table 9) are more striking than for the free amine. As
the temperature is lowered, both CH20 and CH2N proton lines
broaden, the CH20 proton lines broaden more extensively be-
cause their chemical shifts in the two conformers are farther
apart than are the CHZN proton shifts. The CH20 lines split
at about 215 K, and the CH2N lines at about 207 K. A very
similar coupling pattern emerges with the spectrum at 195 K,
compared to that of Clll at 163 K from Lehn's publication.

This pattern is also an ABXY spectrum with lines and coupling

9O

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Eoomomn on ed on

_ . MW ndv 0m” _Mn 0d.
mm. \\\\1 \llMMKY\/\>fi/i\\\.
mm.

9 J 13

CON CNN

 

 

 

 

 

 

CNN ¢

 

 

91

 

 

 

Table 9’ 3h?.3fimfiefiii‘éiioffin‘éii‘fingfi1535-11343 323222303}
H +
Temp (°K) 6CH20* 5CH2N* 5H1* Av1/21 (hz)
ppm ppm ppm
290 3.76 3.2A 9.06 10
270 3.7A 3.22
250 3.72 3.21
230 3.71 3.19
220 3.71 3.19
215 3.83, 3.59 3.19
210 3.85, 3.50 3.21, 3.13
200 3.86, 3.A6 3.2A, 3.11 9.0 70
195 3.85, 3.A6 3.23, 3.08
190 3.83, 3.A3 --, 3.07 9.1 150
185 .___ ___
180 3.82, 3.36 -————, 3.09 8.3 150
175 8.0 110
170 A0
i

Dashes indicate disappearence of

no data available.

Chemical shifts are reported i 0.

Uncertainty in the linewidths is t

3 ppm-

a signal, blanks indicate

92
constants of 3.85 (A), 3.A6 (B), 3.2A (X), and 3.08 (Y);
JAB = 10 Hz, JXY BX = 10 Hz, JAX = JBY = JAY
i 2H2. The preferential vicinal coupling, (JBX>>J

= lO-lA Hz, J

AX’

J JBY)’ explains the unusual breadth of X. These assign-

AY’
ments demonstrate again that exo-endo isomerism does not
contribute to the observed spectra and that the nonequiva-
lence is caused by the slowing of torsional motions as the
temperature is decreased. The fact that the CH20 protons
broaden and split to a larger extent than do the CH2N protons

signals indicates that the CH O protons are more nonequiva-

2
lent in the gauche conformation.

The carbon-l3 NMR (CMR) spectra Of the same sample are
temperature invariant, except for line broadening below 200 K.
Carbon—13 NMR would be expected to be very sensitive to exo-
endo nitrogen processes. Since the carbons retain their
equivalence even at very low temperatures, the CMR spectra
provide evidence that this inversion process either does not
occur or remains very rapid.

The lineshapes of the CH O protons and the CH2N protons

2
have been simulated using the modified Bloch equations. The
simulation of the CH20 proton signals was done using line-
width values of 0.3 Hz for both sites and 5.0 Hz for both
sites in the absence of exchange. Either choice produced
nearly the same calculated lineshape. A chemical shift dif-
ference of 76 Hz between the two sites was utilized. The

lineshapes were simulated for several values of 1, the ex-

change time, which in this case, is the rate of the torsional

93

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on» no opuooam on» no oococcoaoo onspwpooEop on» no coauwfisefimIAOpsoEoo .mm oaswam

 

 

 

 

Edam on 0.... II .I. | o.» co can a: om...
fl _ fl _ q _ l
x mm. 0. com 58
x mm. xo- x OR

 

 

9A
motion. The simulated lineshapes are shown in Figure 26.
As this motion is slowed down, the lines go from a very
sharp triplet to a broad singlet, and then split again when
the exchange time is greater than 3 msec.

The linewidths and general appearance of the experi-
mental and calculated spectra were closely analysized in order
to best match the simulated spectra with the real spectra
shown in Figure 25. The rate of exchange, k, was then Ob-
tained at various temperatures and an Arrhenius plot made by
graphing 1n (k) versus l/T (Figure 27). This plot gives a
straight line which yields Ea = 9.A t 0.5 kcal 1001""1 down to
about 210 K. Then the slope deviates as another process be-
gins to interfere. This latter process causes line broaden-
ing in excess of that predicted for the slowing of a single
exchange process.

The exchange process which causes the line broadening
above 210 K is probably due to the sloWing of a torsional
motion. From the coalescence temperature (215 K and 207 K
for the CH20 and CH2N proton signals), rate constants of 169
sec’l and 60 sec"1 are obtained, with A07 = 10.3 t 0.3 kcal

-1 1

mol , AHI = 9.0 i 0.5 kcal mol' , and A87 = -6 cal mol-l

deg‘l. These values are somewhat large for typical vicinal
carbon wagging motions, but the bicyclic nature of Clll prob-
ably causes these vibrations to be coupled throughout the
rest of the molecule. The concerted exchange process which

Lehn suggested for the free Clll, namely, the passage of a

strand through the intramolecular cavity Of C111, could not

95

.H.+m.HHHo mo ecooosa cmmo one mo ‘
mnuooam on» anu coapoe HoseammOp on» non B\H co Axvca no cocoocoaoo one .nm shaman

To. xi.
00.0 Omé 00.? Oman

 

7.2: .68. 3.6va

1.9: .8 c. n. om M 1 2.

.. .106
A55

3

.1 0.0.

 

96
take place with the internally monoprotonated species.
Thus, vicinal carbon wagging motions probably give rise to
this phenomenon.

Below 200 K, another process begins to slow to the
millisecond time-scale as suggested by the temperature de-
pendence of the resonance of the internal proton. The motion
of the internal proton is very rapid at room temperature,
giving rise to a single narrow line at 9.0 ppm. As the tem-
perature is reduced, this line broadens greatly and splits
within a very narrow temperature range, as shown in Figure
28. The two resulting peaks are located at 10.8 and 8.0 ppm
with areas of roughly 1 to 3. The value of A01 at coales-
cence (187 K) is 8.A i 0.3 kcal mol'l.

These lineshapes were also simulated using linewidths
of 30 Hz for both sites as well as 10 Hz for both sites in
the absence Of exchange, the choice of which did not appre-
ciably change the calculated lineshape. The chemical shift
difference Of the two sites in the absence of exchange was
taken as 50A Hz (2.8 ppm). The simulated lineshapes are
given in Figure 29, and the plot of ln(k) versus 1/T is given
in Figure 30. The Arrhenius plot (Shown in Figure 30) has
two distinct slopes, a behavior similar to that of Figure 27
for the vicinal carbon wagging motion. Again, two processes
seem to be involved, one which is operative at high tempera-
tures, and one which is important below 190 K. Close compari-
son of the two plots reveals that in the intermediate region,

where the two plots overlap, the slope of the lines deviate

295°K

 

 

1

ZOO°K

 

 

 

 

 

97

L

 

Aw

 

U

|85°K

MN

I80°K

 

 

I 78°K

M

Figure 28. The temperature dependence of the internal proton
resonance of Clll-H+,i in d6-acetone.

98

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X05.

v.00.

cocoocogoo snapshanou on» no

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+:o«umassfimlh093asoo .mm whswfim

0.0 O“ 0.0. 0.. . 0,0 cm 0.0. 9 .
H

 

 

V. CON

 

 

xnm. xmmN

 

 

99

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can Bonn mmOOOHQ weaxooa ampoaoxm on» you B\H so Axvca no cocooconoo one .om shaman

muo— x ... \ .
0.0 0.0 8.? COM
QM

 

 
    

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0.0.

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.IBE .00! N I DU
$3....

 

l 0.0.

100
from that of the other temperature regions. In this inter-
mediate region, both plots indicate the presence of two
processes which causes line broadening or narrowing in ex-
cess of that predicted by the computer simulation analysis.
The high temperature process has already been assigned to
the slowing of the vicinal carbon wagging motion. The simu-
lation of the second process yields Ea = 16 t 2 kcal mol'l,
AH+ = 16 t 2 kcal mol'l, and AS4‘ = +39 cal mol-1 deg-1.
The large activation enthalpy necessitates a concerted proc-
cess, if it involves only conformational changes of the ligand.
The nature of the process is highly unusual, because any
process with such a large value of AH+ would be expected to
be slow even at room temperature. If the value of AH+ is
correct, then it is the large positive AS+ which is respon-
sible for the very rapid exchange rates at such low tempera-
tures, but its origin remains a mystery.

This exchange phenomenon might arise from one of three
processes. First, a phase transition might have occurred at
these temperatures. In order to rule out this trivial ex-
planation, the sample was pulled from the magnet gap and in-
spected. No abnormality of this sort was noted. In addition,
the spectra were duplicated in methanol, and the same kind of
splitting was also Observed.

A second process which could give rise to the spectra
would involve the exchange of the Hi between two sites inside
the ligand, namely, the nitrogens (8.0 ppm) and the oxygens

(10.8 ppm). The different pOpulations of these sites would

101
reflect their relative energies, the nitrogen site being
more stable. One discrepancy in this mechanism involves the
expected effect on the chemical shifts of the backbone pro-
tons when the exchange of the H1 is slow. We have shown
that the maJority of the shift of the backbone protons upon
protonation is due to the location of the added proton
rather than to a conformational change. Therefore, if the
motion of the internal proton was slow, the CH2N proton sig-
nals would be shifted about 250 Hz apart, corresponding to
protonated and unprotonated sides. If the exchange of the
Hi were slow enough (and simulation suggests that it indeed
would be), the CH2N resonances should be vastly broadened at
about 185 K and two or more lines shouId appear which are
centered at 3.11 ppm, but separated by 250 Hz at 180 K and
below. The spectra in Figure 25 indicate that this phenome-
non is not occurring. Therefore, we must conclude that the
exchange Of the H1 between the nitrogens is always rapid.

The third explanation involves two conformations of the
ligand, which possess different cavity sizes and donating
abilities to the internal proton. The environment of this
proton is determined by the topology of the ligand's cavity,
and if it changes, the chemical shift of the H1 would also
change. A process which involves an exchange between the two
conformations of the ligand, similar to those shown in Figure
13, might well explain our observations. The cavity size
would change by an Angstrom or more in going from one confor-

mation to the other and the conformation with the smallest

102

cavity would be expected to be more stable. The line at
8.0 ppm would result from the proton in the small cavity,
since this conformation would allow efficient electron
donation, whereas that at 10.8 ppm would correspond to the
conformation with the larger cavity. The populations of
the two sites, reflected by the areas of the respective
resonances, suggest that the former conformation is more
stable.

This exchange phenomenon could also reasonably explain
the unusual thermodynamic parameters, because in a concerted
process, the individual thermodynamic components of the

+

of 16 kcal mol"1

1 deg"1 is

processes are additive. Therefore, the AH
is unexpected, but the large 68* of 39 cal mol‘
still surprising. It may arise from several factors, such

as an increase in molecular volume between the products and
transition state, several pathways from transition state to
products, a greater mobility Of the Hi in the transition
state, etc. Proton tunneling might also effect the line-
shape in a way which is not described by this classical ap-
proach. Whatever its origin, the large value of A81 is the
dominant factor which allows rapid exchange of this high
energy process at such low temperatures. It must be stressed
however, that the apparent values of the activation para-
meters are fairly well determined experimentally. The large
values of AHI and AS:'1 are not the result of large experimen-
tal errors. The process which gives rise to these parameters

must therefore be unusual. Of course, since the two-site

103

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Edam con om.» 9...» can om.» 9...» can om.» 9...»

 

 

 

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mON OVN OmN

 

 

 

 

10A

 

 

Table 10. The temperature dependence of the NMR parameters
for a 0.0A M solution of Clll°H ,i°Br' in dA'
MeOH.
CH 0 CH N H H
Temp (°K) 6pp771 Gppg 6pém Avl/21(hz)

300 3.70 3.11 9.03

280 3.68 3.10 9.02 15

260 3.68 3.10 9.03 1A

2A0 3.67 3.09 9.0A 1A

220 3.67 3.10 9.10 20

210 3.79, 3.11 9.1A 30
3.56

205 3.82, 3.15, 9.16 30
3.50 3.0A

200 3.83, 3.18, 9.2 50
3.A8 3.01

190 3.82, 3.17, 9.1 130

- 3.A5 2.98

185 3.82, 3.16, -———— ————
3.A5 2.96

180 3.83, 3-16: '— _—
3.A5 2.96

175 3.83, 3.16 8.0 200
3.AA 2.9A

170 3.82, 3.16, 7.9 150
3.A2 2.97

165 3°79, —_ 709 70
3.A0 3.00

 

105

mechanism was used in the simulation, the analysis could be
in error if more than two conformations are involved.

Figure 31 and Table 10 describe the exchange in dA‘
MeOH, and illustrate that the process is very similar in
both solvents. The H1 splitting is also Observed in dA'
MeOH, but the populations of the two sites are somewhat dif-
ferent, probably as a result of different solvation of the

ligand.

C) Clll-2H+,i-i-2C1_ in du-MeOH

 

The internally diprotonated cryptand, Clll-2H+,i-i,
should have a very rigid structure in comparison to Clll or
Clll-H+,i, because of the crowded nature of the cavity. Pro-
ton-proton repulsion inside the cavity would force the ligand
to expand to as great an extent as possible, and its tempera-
ture characteristics should reflect this strain. Figure 32
shows that the temperature dependence of the NMR spectra of
Clll-2H+,i-i in du-MeOH shows behavior similar to those of
Clll and Clll-HI-Br‘. As the temperature is decreased, the
CHZO lines broaden most rapidly and split into two lines,
while the CH2N proton lines broaden, but neither shift nor
split. This pattern is again consistent with an ABXY assign-
ment, except that the breadth of the lines masks the coupling.
The chemical shifts are assigned as follows (Table 11):

A.15 ppm (A), 3.75 (B,X,Y). It should be noted that the

CHZN proton and one of the CH20 proton resonances overlap,

an assignment which is confirmed by the relative areas (1:3).

106

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Edam 2am on? 2..» owe can 02»

 

ON. ON ONN

OnN OVN OmN

107

 

 

Table 11. The temperature dependence of thi NMR parameters
for a 0.0A M solution of Clll-2H ,i-i-2Cl in dA’
MeOH.
CH O CH2N H H
Temp (°K) 6ppi7i ppm 6pém Avl/21(h2)
305 3.96 3.74 7.33 50
280 3.96 3.7A 7.33 50
260 7.31 37
2A5 3.96 3.76 7.30
2A0 3.96 3.7A 7.30 30
230 7.28 25
220 3.95 3.76 7.28 21
210 A.15, 3.75 7.2A 25
180 A.15, 3.75 7.21 30
170 A.15, 3.7A 7.20 30

 

The extreme breadth of the lines is probably caused by the

rigidity of the molecule, which leads to more efficient
dipole-dipole relaxation. The chemical shifts of the two

Hi resonances are independent of temperature, which suggests
that the topology of the cavity is also temperature indepen-
dent. The linewidth of the H1 protons, however, is very
temperature dependent, as mentioned in the section which
considered spectra at elevated temperatures. This tempera-
ture dependence results from efficient scalar relaxation via

the nitrogens. This Complex provides supportive evidence that

108
the skeletal locking process described for C111 and
Clll-H+,i is vicinal carbon locking rather than exo-endo
isomerization, because the diprotonated species is not able

to undergo nitrogen inversion.

D) Clll-2H+,i-o in du-MeOH

 

The inclusively monoprotonated ligand, Clll-H+,i has
an NMR spectrum which is very pH dependent in water, as pre-
viously attributed to the formation of the exo-endo dipro-
tonated species, Clll-2H+,i-o. This complex is also pro-
duced upon the addition of an acid to methanol and, upon the
acidification of a solution of Clll in methanol and, as in
water, external proton exchange is rapid on the NMR time-

scale and average D symmetry is preserved. As acid is

3h
added to the solution, the skeletal protons shift downfield,
and broaden slightly (Table 6) in conformity with the fol-
lowing rapid equilibrium:

K

+ + +
Clll-2H ,i-o —-‘___—-9—> Clll-H ,i + H (29)

The temperature dependence of the process also indicates an
equilibrium of this sort, with preference given to the di-
protonated form as the temperature is lowered. This is
shown in Table 12 and Figure 33 for a solution of 0.0A M

Clll-H+,i-Br' in d -MeOH acidified with excess hydrochloric

0
acid (HCl). As the temperature is lowered, the CH2N proton
resonance broadens more rapidly than that of the CHZO protons,
both sets shifting downfield. The H1 resonance also shifts

with temperature, but it moves upfield simultaneously with

109

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.3002: o :H H. m.HHHo no mpuomam mzz 0:» mo mocoocoooo opSpMMOQEou 0:9 .mm mpswfim
+

Eammr can on...» one can 0m.» 03. on.» em...” ope

iéj

 

 

110

Table 12. The temperature dependence of the NMR parameters
for a 0. 0A M solution of 0111' H+ ,i in du-MeOH,
acidified with HCl.

 

 

CH2O CH2N H1 H1
Temp (°K) 699m 6ppm 6ppm Av1/2 (hz)
295 3.72 3.18 8.98 16
280 3.73 3.19 8.96 15
260 3.73 3 21 8.95 15
2A0 3.7A 3.25 8.93 18
230 3.75 3 28 8.91 22
220 3.76 3.29 8.89 A0
210 3.85, 3.3A 8.8A 66
200 3.89, obscured by 8.66 50
3.97
190 3.89, CH2O proton 8.6A A5
3.51
180 3.87, " 8.58 30
3.50
170 3.88, " 8.59
3.51

 

111
the downfield skeletal proton shifts. Below 200 K the
CH2N proton resonances broaden extensively, and are ob-
scured by the CH20 proton lines. The extreme width of all
the lines and the shifts with temperature, which show a more
pronounced effect for the CHZN protons, are consistent with
external protonation at the nitrogen, which is fast at room
temperature, but slow below 230 K. Comparison of these spec-
tral features with those of the same sample prior to acidi-
fication, shown in Figure 31 and Table 10, indicates that the
two complexes are indeed different structures. Nitrogen
inversion must be slow in order to facilitate this slow pro-
ton transfer at low temperatures, thus the molecule is
"locked" into the exo-endo isomer. A pseudo-equilibrium

constant for protonation, defined by:

(Clll-H+,i)

K = (0111.2H+,i-O) ' (30)

may be obtained from the shift of the CH N proton line and

2
the H1 line, by using equation (22) to obtain the mole ratio
of the two species from the observed chemical shift. The
CH2N proton chemical shift in the absence of exchange for

the diprotonated (i-o) ligand was chosen as 3.7A ppm, the
same as Clll-2H+,i—i in du-MeOH, and Table 10 gives a value
of 3.10 ppm for the monoprotonated cryptand. The chemical
shift of the internal proton of the diprotonated ligand (i-o)
was taken as 8.58 ppm, that of Clll°H+,i was taken from Table
10 for each temperature because it shifted slightly with

temperature. The values of ln(K) which were obtained

112

Table 13. The temperature dependence of the equilibrium
constant for the conversion of Clll-H+,i to
Clll-2H ,1-0 in du-MeOH: KN from the CH-ZN
protons and K from the internal proton.

 

 

Temp.(°K) (l/T)x10"3 KN ln(KN) K1 ln(xi)
295 3.39 7.0 1.95 8.0 2.1
280 3.57 6.1 1.81 6.3 1.8
260 3.8A A.8 1.57 A.6 1.5
2A0 A.17 3.3 1.19 3.2 1.2
230 A.35 2.6 0.96 2.1 0.72
220 u.55 2.A 0.88 1.5 0.39
210 A.76 1.7 0.53 0.87 -0.lA
200 5.00 0.15 -1.9
190 5.26 0.13 -2.0

 

(Table 13) from the two sets of resonances are plotted in
Figure 3A versus the reciprocal of the temperature. Both
sets of data fall on the same straight line, except at very
low temperatures, where skeletal locking causes the H1
points to deviate. The slope of the line and the values
of K give AHO = 2.0 i 0.1 kcal mol'l, and an apparent ASO =
11 i 1 cal mol-l deg_1 is obtained. Since the study was
done only at one acidity, the true value of AS0 was not deter-
mined.

The two forms are very similar in energy, although the
diprotonated complex is slightly preferred, but the monopro-

tonated form has a more favorable entropy at this acidity.

The increase in entrOpy might be attributed to greater

113

.moozuso cm oua.+mm.HHHo
ocs .+:.HHH0 coozpon Edapnaaasco on» you B\H so AxvcH no occopsoaoo 039 .:m mpswfim

n10_ X .—. \_
0.0 0.? 0.?

0.»

 

_ _ _

zmzo 68. _u
_I Eat G

 

Av: S

 

11A

vibrational freedom for the endo-endo complex, both for the
internal proton and the strands of the ligand. Much Of this
vibrational freedom is lost in the exo-endo complex, as indi-
cated by the very broad lines at low temperatures. This loss
of vibrational freedom is also indicated by the H1 resonance,
which does not split at low temperatures, in contrast to the
monoprotonated ligand.

8 A pH titration of Clll-H+,i was performed in du-MeOH,
using NMR techniques to measure the amount of diprotonated
species formed. HCl was generated by preparing a solution
of ~10% acetyl chloride in du-MeOH, which reacted with water
to give HCl and acetic acid, or with methanol to give HCl
and methyl acetate. This solution was added dropwise to a

solution of Clll-H+,1'Br- (0.02M) in d -MeOH, and the acetyl

u
moiety served as an internal standard for acid determination
(This titration was also attempted with TFAA, but it was not
a strong enough acid to externally protonate the internally
monoprotonated ligand.) Figure 35 depicts the behavior Of
the H1 resonance at 200 K as acid is added. It goes from a
single line in the absence of acid to two lines, when less
than one equivalent of acid is added. These lines correspond
to Clll-H+,i (9.2 ppm) and Clll-2H+,i-o (8.6 ppm). Figure 36
shows the temperature dependence of the system when the mole
ratio of acid to ligand is about 0.5. It shows the same
skeletal locking process which causes splitting of the H1

resonance in Clll-H+,i, while the H1 resonance of C111'H+,1-0

remains unchanged. These data confirm the conclusion reached

115

 

 

 

. +1CI
mole r0110 0|er
()3)
réflv-dfluflvflrJ/j/\\M/ <14£3
A
JV I. 2
WA

 

 

 

 

J W

10.0 9.0 so 80pm

Figure 35. The variation in the NMR spectrum of the internal
proton of 0111-H+,i in du-MeOH with the addition
of HCl at 200 K.

116
128k
l80
I

l I 1
9.5 9.0 8.5 Sppm

Figure 36. The temperature dependence of thg NMR spectrum
of the internal proton of Clll-H ,i in du-MeOH
with about 50 mole 2 H01 added.

117
previously, that the exchange between the mono and dipro-
tonated ligand is fast at elevated temperatures, but slows
greatly as the temperature is lowered and shifts toward the
diprotonated form. The relative areas of the H1 resonances
at 200 K provide an estimate of the equilibrium constant

for the process:
+ Kg , + +
Clll-2H ,i-o ‘____. Clll-H ,i + H (31)

yielding xa - 7.0 s 1.0 x 10‘3 M. Using AH° = 2.0, the
equilibrium constant may be extrapolated to 298 K, giving

a value of about 0.06 M. The true AS° may also be calculated
since the acid concentration is known, thus AS° = l cal mol"1
deg-1.

The monoprotonated ligand, Clll-H+,i, may be recovered
from Clll-2H+,i-o by evaporating the solvent and evacuating
the ligand in a vacuum desiccator with the aid of a roughing
pump, provided the acid is volatile and the concentration

process does not cause cleavage of the ligand (as with

HNO3).

E) Clll-H+,O in d6-Acetone

 

The temperature dependence of Clll-H+,o protonated with
TFAA in d6-acetone gives rise to very complex patterns, due
to the presence of two or more species in solution. As the
temperature is lowered, the equilibrium tends to favor the
mono and di externally protonated Clll, as shown in Figure
37, for a mole ratio of acid to Clll equal to 1.7. With

increasing acid concentration, the equilibrium is also

118

0
M

 

__J

«1' b
b
27
27.0"K

 

,J

' 240°K
c

260°K

2 50°K

 

2|O°K
d

 

4.0

3.5 3.0 2.5

Figure 37. The tempegature dependence of the NMR spectra
of Clll°H ,o in d6-acetone, acidified with TFAA.

119
forced toward the diprotonated form in accordance with the
following scheme:

K + K
C111 + 2H+--l-* Clll-H ,o + H+'—* 2

? _—

Clll°2H+,O-O
(32)

The first external protonation is very efficient and K1 is
large, whereas K2 is small and the rate of deprotonation of
C111'2H+,O-O is very rapid. Therefore, as the temperature
is decreased, the line corresponding to the diprotonated
species at 3.8-A.0 ppm grows in intensity. The other lines
of Figure 37 correspond to the externally monoprotonated
species. A rough calculation from the relative areas of
the resonances provides the temperature dependence of the
pseudo-equilibrium constant, K2([H+]), which is shown in
Table 1A for mole ratios of 1.A and 1.7 acid/Clll. A plot
of 1n K2 with l/T is presented in Figure 38, which gives a

1 1

value of AH° . -5 s l kcal mol‘ , AS° = -16 cal mol‘ 1

deg" .

AG°298 = -0.2 kcal mol'l, K s 1.0 at 298 K and :20 at 220 K.

2
The same process may be followed at a single tempera-
ture by addition of acid. For example, at 220 K the line at
3.8-A.0 ppm shifts from about 3.82 to 3.91 ppm upon addition
of acid (Table 15). From this shift, the ratio of
Clll-2H+,o-o to Clll-H+,o may be obtained, assuming that
their chemical shifts in the absence of exchange are 3.99
and 3.82 ppm respectively. The plot of this ratio versus
acid strength (Figure 39) gives a straight line of Slope =

_l__ , where C
K2Ct

t is 0.005 M, the total concentration of Clll.

120

ueo ea ouo.+mm.HHHo mo sofiosssom one pom exa some A

.<¢m9 mo COHWHUUm on» com: ocoumom
mVCH mo cofipmfiaw> 0:9 .mm ogsmfim

MIC—XF\_
nae nxum

 

. o..

 

121
Table 1A. The temperature dependence of the equilibrium
constant for the formation of Clllo2H+,o-o in
d6-acetone with the addition of TFAA.

 

3

 

Mole ratio %§%% Temp (°K) l/Txlo' K2[H+] K2 1n K2
1.A 220 A.55 0.16 23 3.1
1.A 230 u.35 0.10 1A 2.7
1.A 290 u.17 0.06 9 2.1
1.A 250 A.00 0.0u 6 1.7
1.7 210 A.76 0.30 35 3.6
1.7 2A0 A.17 0.08 9 2.2
1.7 250 . A.00 0.06 7 2.0

 

This yields a value of K2 8 5.0 at 220 K compared to 20 by
the first method. The discrepency between the values Of K2
obtained by the two methods is probably due to large system-
atic errors in both methods, especially the first, since the
lines of the monoprotonated ligand are too broad to measure
accurately. Therefore, the agreement is satisfactory and

supportive of the previous assignments.

F) Summary
1) C111 exists in the endo-endo configuration which is
preferred by a factor of 50 over the exo-endo form in
water at 298 K.
2) C111 protonates externally (exo-endo form) with a pKa
Protonation occurs at the nitro-

at 298 K in water of 7.1.

gen.

 

122

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m.= H>.o mm.m mm

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m.m Hm.o mw.m p.m

m.m see.e ms.m m.s

H.m smo.o mm.m s.H
m+muo.+m.aaao u ms o.+m.HHHo u mxm+xu . seam flwwwmm oases omoz

 

 

+mm.HHHo ouo.+m~.HHHo +mm <<me

 

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123

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no commum>coo on» now ucmumcoo Esfinnaaasoo MS» MO cocoocomoo 029 .mm madman

 

 

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12A
3) C111 will protonate a second time externally at
the unprotonated nitrogen (exo-exo) with a pKa (in water)
of between 0 and 1.5.
A) Internal protons bind most strongly to the nitrogens
and the proton exchanges rapidly between them.

5) The barrier (AHI) to vicinal carbon wagging motions

1

is about 9 i 0.5 kcal mol' with AS+ = -6 cal mol-l

deg-1 for the internally monoprotonated species.
6) Another motion freezes out at temperatures below those

which freeze out the vicinal carbon wagging. This process

1

has 60+ = 8.A kcal mol' at coalescence and apparent

1

values of AH+ of 16 i 2 kcal mol' and A81 of -39 cal

-1 -1

mol deg . It probably originates from a concerted

torsional motion of the skeleton of the cryptand.

7) The structure, Clll-H+,i, protonates externally at

the nitrogen with a pKa value at 298 K in water of roughly
0.A. This low pKa value indicates that the endo-endo

form of Clll-H+,i is favored by a factor of about 108

over the exo-endo form.

8) Clll-2H+,i-i exists in the endo-endo form with very

slow or no exchange Of the H protons.

i
9) For the external protonation of Clll-H+,i in du-MeOH,

AH° = 2 i 0.1 kcal mol"1 and AS° = l. cal mol-1 deg-1.

10) For the second external protonation of Clll-H+,o in

d -acetone, AH° = 5 i l kcal mol-1 and AS° = —16 cal mol"1

6
deg-1.

CHAPTER A

THE KINETICS OF INTERNAL PROTONATION OF Clll

I) INTRODUCTION

Cryptand 111 has the remarkable ability to irrevers-
ibly bind protons. It does so by encapsulating them inside
its cavity so as to exclude solvent interactions and to
provide a very thermodynamically favored environment for
the proton. The internally monoprotonated complex, for
example, is not significantly deprotonated even upon heat-
ing for days at 60°C in 5 M KOH! Neither do sodium in liquid
ammonia or ion exchange methods accomplish deprotonation,
except when the ligand is destroyed. The second internally
protonated complex is also very stable to base at room tem-
perature. At elevated temperatures, however, one of the
two protons may be removed, but only at a slow pace.

In light of the apparent stability of the internally
protonated complexes, it is unusual that their rates of
formation are slow. It was shown earlier that proton trans-
fers between donors of quite different pKa values proceed
very rapidly and favor the one of largest pKa. Yet the rate
of formation of the internally monoprotonated complex pro-
ceeds with a half-life of several hours at room temperature
at a pH of 7 indicating that the mechanism is more complex
than for normal proton transfers. This is confirmed by the
disclosure that internal protonation occurs with an enormous
1

activation energy of 25 to 27 kcal mol' This large

125

126
activation energy causes the rates of proton transfer to
be slow. Therefore, the long life-time of the complex is
not completely thermodynamic in origin, but is also strong-
ly affected by this kinetic phenomenon.

The rates of internal protonation provide estimates
of the thermodynamic stability of the internally protonated
complexes. Their pH dependence also sheds light on the
mechanism of proton transfer. These and other topics will
be discussed in the ensuing sections upon presentation of

the kinetic data.
II) THE FIRST INTERNAL PROTONATION OF Clll

The rate of the first internal protonation of Clll

was studied as a function of pH and temperature in D O,

2
using buffers to obtain the desired pH. The pD value of
the buffers was measured using a calibrated radiometer with
a type GK2321C electrode, the values being shifted upward
by 0.A pH units to give a correct pH reading<67). About 1
mg. of Clll was utilized for each sample, this amount being
5% or less of the buffer content and insignificant to the
final pH. Table 16 presents the buffers utilized to achieve
various pH values and their ionic strengths.

The rates of internal protonation, which were measured
at constant temperature (checked periodically) and pH pro-
ceeded with first order dependences on the ligand in all

cases and also depended heavily on both pH and temperature

as shown in Table 17. A typical rate analysis is shown in

127

Table 16. Buffer compositions and their ionic strengths

 

 

in D20.
pH Composition Ionic Strength
8.65 KH2POu-NaOH 0.29
7.A7 KHZPOu-NaOH 0.37
6.A6 KHZPOh-NaOH 0.33
A.93 KHP-NaOH 0.3A
A.0A KHTartrate 0.22
A.00 KHP-HCl 0.29
3.19 KHP-HCI 0.29
2.60 KCl-HCl 0.30
1.78 KCl-HCl 0.36
1.AA KCl-HCl 0.Al
1.25 KCl-HCl 0.38
1.11 KCl-HCl 0.55

 

Figure A0 in which the natural log of the reactant concen-
tration is plotted versus time. It should be emphasized
that these rates were extremely slow, each reaction requir-
ing several hours to go to completion.

The temperature dependence of the rate Of internal
protonation has been studied at pH values Of 7.5 and A.9,
both of which provide similar Arrhenius activation plots
which are depicted in Figure Al. The temperature dependence
of the rates at the pH values provide straight line plots
of nearly equal slope, giving values for the activation

parameters at 299 K of Ba = 26 i 2 kcal mol-l,

128

Table 17. The dependence of the rate of internal monopro-
tonation of Clll upon pH and temperature.

 

Temp. +

 

pH (buffer)* (°K) k(sec"1) 0 1n k loglo k
unbuffered (=9) 299 A.27x10’6 2.7::10"7 -12.36 -5.37
8.7 299 1.57x10“5 3.0::10"7 -ll.06 -A.8l
7.5 299 8.70x10'5 3.03:10'6 -9.35 -A.06
7.5 310 3.65x10'” 8.3x10‘6 -7.92 -3.AA
7.5 320 1.25x10‘3 5.0x10“5 -6.69 -2.90
6.5 299 1.1ux10’“ 8.0x10'6 -9.08 -3.95
A.9 299 1.70x10'” 1.2x10'5 -8.68 -3.77
A.9 320 2.08x10'3 2.0x10’“ l-6.l7 -2.68
A.0 (tartrate) 299 2.02x10'u 1.9x10'5 48.59 -3.73.
u.o (HCl-KCl) 299 1.95x10'“ 1.2x10'5 -8.A8 -3.68i
3.2 299 2.25x10’“ l.0x10"5 -8.33 -3.62
2.6 299 A.22x10‘“ 7.3::10'5 -7.A7 -3.2u
1.8 299 6.A0x10'” 1.7x10"5 -7.35 -3.19
1.5 299 8.53x10‘" 1.3x10"5 -6.67 -2.90
1.3 299 9.u2x10‘“ 1.8x10'5 -6.65 -2.89
1.1 299 1.03x10"3 1.1x10‘5 -6.A9 -2.82

 

* pH values measured by calibrated radiometer and corrected
up 0.A pH units for deuterium isotope effect.

I Some values corrected to 299 K using Ea = 26.A kcal/mole.

Linear estimate of the standard deviation on k.

129

 

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65F; mit.
00 OM o N o. o
. . AWN
/O/
O
O r O.”
O
////// Amwbrh
O
/O/
0 .0d.
///0
/O
///,

 

130

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Ca HHHO mo COHuHCOpopQ assumpca on» pom B\H so Axvca no cocoocmaoo one

MLU3§F\_
cum mm «Mn 3
AHN

2?...

AH?

 

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.H: mpswfim

131
A61 = 23 kcal mol"1 and AH+ s 25 kcal mol'1 and AS1’ - +7 cal
deg"l mole-1(73). The large free energy of activation
originates mainly from the enthalpy term. This is pre-
sumably the energy required to distort the face of the
ligand, which allows the proton access to the cavity. This
topic will be discussed further when the activation param-
eters of the other internal protonation processes have been
documented. It is clear, however, that the slow rates of
internal protonation are dominated by a large enthalpy bar-
rier which results from ligand deformation.

The large activation barrier is somewhat unexpected,
since a proton possesses negligible size and should easily
fit into the holes of the ligand's faces. However, in
solution (as H3O+) the proton possesses electron density
obtained from its hydrogen bonded counterpart and has a
finite size. As the proton interacts with the nitrogen and
the oxygen atoms of Clll, it accumulates considerable elec-
tron density from this source which also imparts significant
size to the proton. Therefore, the same interaction which
induces proton binding also restricts the proton from enter-
ing into the cavity of the ligand. Once inside, it accumu-
lates even more electron density as it interacts with the
nitrogen and oxygen lone pairs and its effective size be-
comes larger. This phenomenon probably contributes most to
the resistance of the complex to deprotonation.

The conformation of C111 is very much influenced by

the pH of the medium, since it may bind either one or two

132
protons externally. Such changes in conformation also
seem to correlate with the pH dependence of the rate of
internal protonation. Table 6 (Chapter 3) lists the chem-

ical shifts of Clll as a function of pH in water, the CH N

2
proton shifts being plotted in Figure 22 (also in Chapter
3). A break is observed in this curve at a pH value of
about 6, above which C111 and Clll-H+,o are the predominant
forms of the ligand in solution. Below a pH value of 6,

the ligand is fully monoprotonated externally and begins

to add a second proton (also externally). However, even

at a pH value of 1, only about half of the ligand is dipro-
tonated externally, if it is assumed that the chemical
shifts of these species in D20 are similar to those in d6-
acetone (as they appear to be). The reversal of the CH2N
proton shifts after complete formation of the externally
monoprotonated form (at a pH value between 5 and 6) is also
observed in d6-acetone upon the formation of the externally
diprotonated complex. This reversal is probably a result

of less effecient proton binding as the ligand must accomo-
date a second positive ion.

This NMR titration agrees qualitatively with a pH
titration done in a conventional way with a calibrated
radiometer, as shown in Figure A2. This titration gives
an endpoint at a pH value of about 5 and a value of pKa =
7.1 i 0.3 at 299 K for the first external protonation. A

second break has not been observed, even at pH values as low

as 1.2, but the second pKa may be estimated at :_l.5.

133

 

 

901K
00 - '\
.
..\.
7o -1 \l
O
0
pH \9,

EK)‘ ‘\

.

\fEND POINT
5,04

.

1 \o
4.0 \
C.
. .\
.\.\.
310 . \.\o
2.0 . . , C
O O I 0 2 0 3 0.4 0 5 O 6 07
Ml HCI

Figure A2. The pH titration of Clll with HCl in water

(only external protonation occurs).

13A
(The NMR data indicate a pKa value of between 0 and 1.5.)
The relative concentrations of the various forms of the
ligand in solution may be calculated as a function of pH by
using pKa values of 7.1 and l. for the two external protona-
tions (Figure A3). The externally monoprotonated complex
is the predominant structure over a very wide pH range, 2
to 7, above and below which the other forms are important.

The rate of internal protonation correlates well with
the form of the ligand in solution. Figure AA depicts the
dependence of this rate upon pH. It shows a nearly linear
curve between pH values of 3 and 7 where the monoprotonated
species is predominant and in fairly constant concentration.
Below a pH value of 3, the rate increases and approaches a
first-order dependence on the hydrogen ion concentration
simultaneous with the build-up of the externally diproton-
ated complex. Above a pH value of 7, the rates are very
slow, decreasing markedly as the mole ratio of Clll°H+,O
decreases.

The correlation Of the rates of internal protonation
with the form of the ligand suggests that it is easiest to
internally protonate the externally diprotonated ligand.
The externally monoprotonated form, C111°H+,0 will inter—
nally protonate, but with difficulty and the free ligand is
even more difficult, if not impossible to internally pro-
tonate. This observation is represented schematically as

follows:

135

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.m: shaman

 

 

 

 

NOIiDVHd 310W

136

 

 

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Ia
cm 0.0 05 0.0 0.0 Q? on ON 0.. Dad
..on
.0... .
m.
.0
no
for.
-00

 

 

137

 

0111
k
+ _1 1
Ii 1L Kal k
Clll-H+,o 2 s: Clll-H+,i
+ -1
H H, K82
+ k3
Clll-2H ,o-o (33)

in which kl<<k2<k3.

If we assume that this is a valid mechanism for in-
ternal protonation, we can write a rate expression as fol-
lows:

rate = kl [Clll][H+] + k2 [Clll-H+,o] +

k3 [Clll-2H+,o—o] (34)

The rate observed from the NMR analysis is equal to some

rate constant multiplied by the total Clll concentration,

Ct’ or:
rate = kobs ct (35)
Solving for Kobs , one obtains for the expression of equa-

tion (3N):

k3(Ka1) + k2 + Ka2k1(H+)
kobs = + (36)
n /Ka1 + 1 + Kaz/(H+)

 

This equation has been used to computer fit the pH depend-
ence of the rate of internal protonation of Clll. The values

8 and 0.1. The rate of

of Kal and Ka2 were taken as 7.9x10'
internal protonation of the free Clll, kl, was taken to be

zero and the other two rate constants were the variables.

138
A computer fit (using KINFIT) of the data is shown in
Figure NM (dashed line) and gives values for the rate con-

stants, k and R2, of 3.8 : O.6xlO"3 sec'1 and 2.3 t

3
0.3x10'u sec-1. Thus the experimental points are fit rather

well by this rate expression. If Kal is given a value of

8

3.1x10‘ , the fit is even better (solid line). The values

of k3 and k2 do not change appreciably when the latter value
of Kal is used, however.
It should bepointed out that several rate eXpressions

would yield the same form of kobs as given in equation (36).

These flnclude:

rate = k; [Clll-H+,o][H+] + k2 [Clll-H+,o] (37)
' + + ' +
rate = k1 [Clll-H ,o][H ] + k2 [ClllJEH J (38)
rate = k; [Clll] + k2 [Clll-H+,o] +
k3 [Clll-2H+,o-o] ~- (39)

Therefore, a mechanism for internal protonation may not be

determined from the rate expressions.

III) THE KINETICS OF THE SECOND INTERNAL PROTONATION
OF Clll IN WATER

 

 

The species Clll-H+,i may be internally protonated a
second time, but only under more rigorous conditions than
those used for the first internal protonation. For example,
the free ligand at a pH of l and room temperature converts
to the internally monoprotonated ligand in minutes, but forms

no internally diprotonated complex for days. In 1 M HCl, the

139
second internal protonation proceeds with a time-scale of
several weeks at room temperature and is accompanied by
considerable decomposition of the ligand. At elevated
temperatures, the rates are much faster and decomposition
is minimized.

The internal protonation of Clll-H+,i has been studied
as a function of temperature in l M HCl in D20. The data
obtained for a typical rate study are shown in Figure “5.
Just as for the first internal protonation, the rates show
a first order dependence on the ligand concentration but
are slower than the former under similar conditions. Table
18 gives the rates as a function of temperature in l M HCl
and an Arrhenius plot of these data is shown in Figure #6.
The plot shows a linear dependence of ln(k) on l/T and gives
Ea = 26.h : 2 kcal mol-l, AGI at 298 K = 26.5 kcal mol-l,
AH+ = 25.8 kcal mol-l, and AS+ = -2.H cal deg"1 mol'l.

These values are strikingly similar to those for the
first internal protonation and lend credence to the theory
that ligand deformation is responsible for the majority of
the energy barrier, since AH+ is as large as for the first
internal protonation. This rate analysis was performed at
only one pH, but a pH dependence of the rate similar to that

of the first internal protonation is also expected for the

process.

1140

.Hom 2 H ca
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+

 

e :5 9::
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_ _ e _

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c... $2:

0.?

0.?

 

 

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mAZx.F2
on aw ma hm

P

AH?

35:

AVw

 

142

Table 18. The dependence of the rate of the second internal
protonation of Clll°H ,1 upon temperature in

 

 

1 M HCl.

Temp.(°K) l/TxlO-3 k(sec'l) 0* ln(k)
333 3.00 2.27::10"5 1.6x10'6 —1o.69
343 2.92 8.00xlO-5 1.1x10'6 -9.u3
359 2.79 3.65x10-u 1.2x10'5 -7.92
361 2.77 5.28x10'” 1.6x10’5 -7.53

 

* Linear estimate of the standard deviation.

IV) THE KINETICS OF DEPROTONATION OF Clll'2H+,1-1

 

The rate of proton extraction from Clll-2H+,i-i has
been studied as a function of temperature in 5 M KOH in D20.
The rates were again first order in ligand as shown in Fig-
ure H7 and were very slow. For example, at room temperature
the complex was stable for weeks in 5 M KOH, while at ele-
vated temperatures, the reaction proceeded with the extrac—
tion of only one of the two internal protons. At very high
temperatures (386 K), the reaction was accompanied by con-
siderable decomposition of the ligand.

The temperature dependence of the rates of deprotona-
tion are shown in Table 19. Figure 48 presents an Arrhenius
plot of the of the three data points which give a linear
dependence of ln(k) versus l/T, resulting in values of Ba =

l l

2U.8 i 2 kcal mol- , AG+ = 27.“ kcal mol- , AMI 8 2u.1 kcal

-1

mol , and AS* = -11 cal mol-l deg-1. Again, the similarity

of these activation parameters with those for internal

1&3

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1A5
protonation is striking, but it may only be coincidental,
since deprotonation may proceed by a very different pathway
than the protonation.

Table 19. The dependence of the rate of deprotonation of
Clll-2H ,i-i upon temperature in 5 M KOH.

 

 

Temp. l/TxlO"3 k(sec-l) 0* ln(k) Stgzzgth
3H9 2.87 2.55x10‘5 3.9x10"7 -10.57 5 M
363 2.75 1.1302(10"4 6.7x10"6 - 8.87 5 M
386 2.59 1.0ux10‘3 8.2x10‘5 - 6.87 5 M
372 2.69 14.33x10‘S A.5x10'7 -1o.05 5 M

 

* Linear estimate of the standard deviation.

This process would be expected to depend upon base
concentration Just as the internal protonation depends on
acid strength. In order to check this, the deprotonation
rate was determined in l M KOH at 372 K. This rate, in com-
parison with those obtained in 5 M KOH (Figure “8), gives a

0.7 order dependence on base strength.

V) METHOD OF ANALYSIS

 

The samples utilized in the analysis were prepared by
weighing the ligand into an NMR tube and adding about 2 ml
of D20 at the appropriate pH. The samples were then brought
to temperature in the probe of the NMR and analyzed by taking
several scans in the pulse-FT (PFT) mode. The spectra were

then stored on a magnetic disk and plotted if time permitted

1&6
and subsequent spectra taken. These spectra provided an
accurate time profile of the reaction. The relative areas
of the resonances of the products and reactants were ob-
tained by tracing the spectra onto tracing paper, the
images being cut and weighed.

Nuclear magnetic resonance, as a method of analysis,
has several inherent shortcomings which could cause attenu-
ation of one or all resonances, and thereby undermine its
accuracy. Delay time attenuation, filtering and imcomplete
relaxation could each contribute to instrumental errors and
overlapping resonances could further complicate the analysis.
Care was taken to insure full relaxation and in many cases
a calibration chart was deve10ped for pulse repetition rates
near the saturation limit, to be certain that attenuation
from this source was not occurring. Delay times and filter-
ing did not present a problem because the lines utilized for
the analysis were narrow and of similar width, and were cen-
tered in the middle of the spectrum. The largest errors
originated with overlapping lines which were often of slight-
ly different linewidth. The poorest of these analyses, how-
ever, provided rate constants with standard deviations of
20% or less, and usually less than 10%. Linear estimates of
the standard deviation, obtained from KINFIT data analy-

sis(72), have been given with all rate constants.

VI) SUMMARY

The ultimate goal in this analysis is to develop a
mechanism for internal protonation and deprotonation of
Clll. It is not possible to determine a mechanism from the
rate expression for the internal protonation of Clll since
the form of this expression can be produced by several mech-
anisms. However, the rates of the internal protonation-
deprotonation processes do provide an estimate of the thermo-
dynamic stability of the complexes when some assumptions are
made. The activation parameters for the internal protonation
processes are summarized in Table 20. Using these values
and the rates obtained for internal protonation, one can

+
estimate the thermodynamic stability of Clll-H ,i in the

 

following way.

For the reaction:

k
l ,+ -
H20 + 0111 ‘_--_—___—*~ 0111-11 ,1 + OH (I40)
k
-1
k1 has been measured in pure D20, giving a value of “.3 x
10'6 at 299 K. kl may also be calculated by the following
scheme:
x 1 + _
1120 + 0111 # Clll-H ,o + OH (141)
is
Clll-H+,i

k2 was calculated by computer fitting the pH dependence
of the rate of internal protonation and its value is

l“?

1148

o N I, m
o o m++m4|+o m
. m
3+ umo++m4§1ulr m
.m+ umo+fiufi.+mm.aflao
“nun".omm+a. m.HHHo
mpg +
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”HIM: o 5.33
x
0mm o~m+HHHo

+nmo+fi.+m.HHHo

 

mm nmo+fi.+m. Hao
+o m+HHHo
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ou< +m< +0< +m< m

 

.x mam pm mommooopo
coauMCOpopo chnopcfi pom mummempma oHEmczooEponu can coaum>fluom one .om manna

1U9

2.3xlO'u. k1 is the overall rate constant for the process

given by:

 

k1[Clll] = k2K [0111] (A2)
[OH

at a pH value of 9, where only Clll and the externally mono-

protonated complex are present:

a (2.3x10'“)(1o'7’1)
(10‘5)

= 1.8x10"6 (#3)

 

k1

This value of k1 is very similar to that calculated by the
other method.
k_1 is too slow to be observed, but upper limits can

be estimated from:

+ - k-2 +
Clll-2H ,i-i + OH-—————a Clll-H ,i + H20

k_2 equals A.3x10'5 at 372 K for l M KOH, which may be

extrapolated to 299 K using Ea = 24.8 kcal mol"1 to give

k_2 = 1.Ax10'8. The formation of the free ligand must be

slower than 5% of this rate or else it would be detected,

so k_ may be estimated at less than 5% (k_2), giving

1
k_l:7.0xlO-lo. Therefore:

 

Kb = -—— i _ z_6.lx10‘3 (8“)

pr £_-3.8 and pKa 1 17.8. For reaction (43) as written
above, AG° 5 -5. kcal mol"1 which indicates that because

of encapsulation, the first internal protonation is

150
thermodynamically stable as opposed to possessing only
kinetic stability; that is, C111 is a very good base
thermodynamically but a poor one kinetically. For the

second internal protonation,

k
Clll°H+,i +11 0 :32 Clll-2H+,i-i + on‘ (115)
k-2

k2 . 3.1x10'7 at 300 K and [H+] = 1 M. Assuming a first
order dependence on [H+], the rate may be extrapolated to

pH . 7, giving k2 - 3.1x10‘1”. k - 1.!4x10‘8 at 300 K,

-2
and [OH'] = l M as before. Therefore:

-14
k 3.1xlO -
sz : .3. a = 2.2x10 6

8 (46)
k_2 1.14X10-

 

pr2 = 5.7, pKa2 = 8.3, and AG° z +8.0 kcal mol-l. The

stability of the second internal protonation is similar

to that of Dabco, thus not as thermodynamically favored as
the first. Its apparent stability, as indicated by the
slow rates of proton transfer from the cavity, does not
originate from a thermodynamic source. Rather, the slow
proton transfer processes are due solely to the large acti-
vation barrier which must be surmounted in order for the
proton to escape from the cavity.

A fairly complete potential energy diagram may be
constructed from the kinetic and thermodynamic parameters
which have been accumulated. This diagram, presented in
Figure 49, utilizes free energies for consistency, since

the AH values of some processes are not known. The

151

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IIO+_I_.+IN.=_U

qu++r+ 2.2.6 \

on» non Ewhwwfio mmpocm

o~:+_pz.=_o

\l/

e x
22010.. 51...},

  

Hmfiucmuoq was .m: mpsmfim

ll. oml

l ON...

o~z+=.o

lo_+
ION+

.I On...
20:503. 0Q

152

direction of the plot, indicated by a solid line, has been
determined experimentally, whereas the dashed line merely
Joins the transition state with the products, and has not
been measured experimentally. The diagram may be somewhat
misleading because the pathway between reactants and transi-
tion state is represented by a smooth curve, and is probably
in error. The route more likely goes via a series of inter-
mediates, but the one(s) of highest energy determines the
rate of the reaction. The shape of the dashed line profile
is also not known. It has been assumed that the reverse
reaction follows the same profile as that of forward reac-
tion in order to Join the reactants and products.

The value of AGI has no physical interpretation since
it is the difference of AH+ and TASI which do possess a
physical interpretation. Rather, the value of AGI is only
a measure of the reaction rate at a given temperature.
Therefore, the difference in the values of AG+ for the first
internal protonation of Clll by acid and by water merely
reflects the pH dependence of the rates and does not sug-
gest a different reaction profile for the two processes.
The mechanism for this protonation has not been established
but a definate pH dependence for the rate of internal pro-

tonation has been observed.

VII) THE REACTION OF 0111-H*,i WITH Na+C222 Na‘
The reaction between the internally monoprotonated

0111 (with a hydroxide counter-ion) and Na+C222-Na- was

153
studied by mixing approximately stoichiometric amounts
(2.x10'5 moles) of Na+c222-Ma‘ and Clll-H+,i in methylamine.
The sample was prepared by using the technique described
in the Experimental section in a vessel similar to that
shown in Figure 8. The vessel had two side-arms, one for
the Na metal and one for the cryptand. The solution of
Na+C222oNa- was prepared first and then was poured over the
Clll-H+,i. The temperature was held at about 0°C. As the
Clll-H+,i dissolved, the solution went from deep blue to
clear, an evidence of decomposition. An NMR spectrum of
the products of the reaction revealed complete decomposi-
tion, except for some starting material which did not dis-

solve. No free Clll was obtained.

VIII) THE REACTION BETWEEN C111°2H+,1-1 AND ES

 

The reaction between Clll-2H+,i-i and ES was studied

by the addition of Na metal in liquid NH3 to a solution of

=3.x10-5 moles of Clll-2H+,i-i in liquid NH The sample

30
was prepared in a vessel equipped with an EPR tube. The

solution of Na+ and ES in liquid NH was prepared first (an

3
excess of about 3 to 1 metal was present) and the entire
vessel cooled in a dry ice, isopropanol bath. The dark

blue solution was then poured over the ligand upon which
considerable effervescence was observed. The dark blue sam-
ple was quickly transferred into a 3mm EPR cell, frozen in

liquid nitrogen and its EPR spectrum taken. Only the signal

of precipitated sodium metal with a linewidth of about

15A
20 gauss was observed. The sample was transferred back and
forth over the undissolved ligand (probably decomposed),
frozen and analysed several more times in like manner.
Again, only the precipitated sodium metal line was observed.

The NMR spectrum of the chloroform soluble portion
of the resulting sample showed mostly decomposition, but
some free 0111 (210%) was present. The reaction between
58 and the internally diprotonated ligand must have occurred
very rapidly and the effervescence observed upon mixing was
probably hydrogen gas being evolved. A rapid EPR mixing
cell would be valuable for this experiment since electron
transfer into the cavity of the ligand appears to be facile
and very rapid.

The speed of these deprotonation reactions indicates
that a very different mechanism is operative than in the
case of proton abstraction by base. The reaction products
substantiate this belief since the free amine cannot be
prepared from either of the internally protonated complexes
by base in water. Therefore, the deprotonation probably
proceeds via the production of a hydrogen atom inside the
cavity of the ligand, which in the case of the diprotonated
complex, may unite with the other proton to form H2+. The
transfer of a second electron produces molecular hydrogen
and the free ligand is generated. In the case of Clll-H+,i,
the H' has nothing to react with except the ligand, which
is therefore completely destroyed. In either case, H' is a

very reactive species and causes considerable decomposition.

155

These experiments verify the findings of Lehn and Cheney
(27)

who conducted very similar reactions

CHAPTER 5

DISCUSSION

156

Cryptand 111 has been shown to be unique in its
ability to bind protons. It irreversibly binds protons
by encapsulating them and isolating them from solution.

The pKa for the first internal protonation is greater than
18, which illustrates the tremendous thermodynamic stability
for a proton inside the cavity of Clll. The complex derives
most of its stability, however, from a kinetic source, be-
cause the activation barrier to internal protonation-
deprotonation processes is at least 25 to 28 kcal mol. The
activation barrier results from the difficulty in opening
the face of the ligand so as to expose its cavity to the
proton-donor. Thus, internal protonation proceeds slowly,
with a half-life at 26°C of roughly 800 sec at a pH of 1.
However, the half-life for deprotonation in 5 M KOH at 26°C
is greater than six years.

The internally monoprotonated complex, as mentioned,
gains the bulk of its stability from two sources. First,
the interaction of the donor atoms of the cavity of Clll
with the H1 provide stability of a thermodynamic nature.
Second, as the proton approaches the cryptand from a proton-
donor in solution, it interacts with the nitrogen and oxy—
gen atoms, thus accumulating electron density. Therefore
its size increases as the interaction becomes stronger and
the proton becomes sterically restricted from entering the
cavity of the cryptand. Once inside, the proton attracts
almost an entire electron from the donor atoms, and its size

increases to about an Angstrom. This large increase in size

157
makes proton abstraction nearly impossible, because the
ligand is physically unable to distort itself enough to
allow the proton to exit. Proton acceptors are also ster-
ically restricted from approaching the encapsulated proton.
Therefore, it is likely that physical encapsulation provides
the majority of the kinetic stability for internal complex-
ation.

Quantum calculations have been utilized to gain in-
sight into these characteristics of proton binding by C111.
0111 is an excellent candidate for a theoretical analysis
because it possesses properties which are similar to the
larger cryptands, thus making the study of ion binding by
this class of ligands possible. It is also a relatively
small molecule whose topology and conformations are well
characterized. C111 is a huge molecule for INDO and espe-
cially ab initio calculations, but it fortunately possesses
only atoms whose atomic wave functions are relatively well
known.

The calculations are based on the linear combination
of atomic orbitals (LCAO) technique to construct the basis
set. The energies of the ensuing molecular orbitals are
determined by the self-consistent molecular orbital theory
using some semiempiracal approximations which decrease the
number of matrix elements to be evaluated. The INDO<8u)
(intermediate neglect of differential overlap) method has
been utilized for these calculations. This technique ignores

interactions except between neighboring atoms and those two

158
bonds away. Clll possesses 93 atomic orbitals which are
important to the calculation (only valence electrons are
considered). The large number of matrix elements to be
evaluated would render the calculation nearly impossible
if these approximations were not made but in doing so, the
accuracy of the energy values of the molecular orbitals is
sacrificed. The INDO calculations are most valuable as
models to guide our intuition and are only to be interpreted
in light of experimental results.

The calculations reveal that the inclusive proton's
lowest energy position along the C3 axis is about 1.12 from
the nitrogen (Figure 50). The charge on the proton is
given beside each point. (Typical N-H bond distances are
about 13.) The barrier to proton Jump from one nitrogen
to the other, along the C

3
mol-l, but a known weakness of the INDO calculations is

axis is indicated to be 31 kcal

that it gives energy values which are much too large. The
barrier may also be much lower if the proton leaves the C3
axis, because the oxygens may also participate.

The sites of lowest energy seem to be nearest to the
nitrogens and the INDO calculation shows that the proton
in this position has accumulated 0.7 electrons. Therefore,
its size is between 0.6 and 13, which is very large for the
cavity. Its large size not only makes it impossible to re-
move the proton from Clll, but it may also restrict partic-
ipation of the H1 with the oxygens. The topology of the

inside of the cryptand is such that there are two large

159

.znpoEEmm nmn :H fi.+m.HHHo Lou maxm mo on» mcoam sonopn
m an» no coaumooa on» no meQEoo can ho mwhmcm Hmuou on» no mocoocmqmo one .om mpswfim
N Illa?

thO o\/ \/0 Ia
0_oc..\_Oux _m

Enos/f. \ I I f-

novd

fl

 

 

2295..
6525 cc

865 228d

V4.89. \ 4

_ 88

catacoaom 2...... n “O... o: o
cozoeooom z: Z. dean o L
0 +1

 

 

——-°'——'

 

 

160
chambers between the nitrogens and oxygens, which are large
enough to contain this ion. The cavity is restricted at
.its center by the oxygens, and in order for the proton to
exchange between the nitrogens, it must squeeze through this
orifice at the center. The resulting steric barrier may
explain why the Hi does not interact appreciably with the
ether oxygens inside the cavity.

If the energy barrier to proton exchange is substan-
tial due to steric restriction by the ether oxygens, the
exchange would be expected to be easily slowed to the NMR
time—scale at low temperatures. Since this does not occur,
a tunnelling mechanism is suggested for proton exchange.
The expected tunnelling frequency may be calculated using
the mass of the proton, a barrier height of about 30 kcal
mol"1 and a proton Jump distance of 1.583 (3.0au). This

frequency, which is typically 10’8

seconds or less for sym-
metric potentials, is much faster than the NMR time-scale
and is theoretically independent of temperature<86). If the
cavity were smaller due to the concerted twistabout the
nitrogens, the tunnelling rate would be expected to be even
faster.

The fact that C111 is small and rigid, and has a well
defined cavity topology makes it a favorable model for test-
ing several NMR theories. Its ability to shield solvent
from its internally complexed protons magnifies this utili-

(30)

ty. iusher's theory , for example, was shown to predict

shifts which were in the right direction and relative

161
magnitude although they were too large. However, if the
correct charge density on the nitrogen is utilized for the
calculation, 0.? (as obtained in the INDO calculations),
rather than 1.0, the values are much closer to the observed
shifts, -2.5 ppm for the CHZN protons, -0.9 ppm for the

CHZO protons, and +1.6 ppm for the H The observed shifts

1.
are -l.u, -0.6, and +1.A ppm respectively. The two former
moieties are greatly influenced by solvation, whereas the
H1 is not. Therefore it is interesting that the H1 shift
is much closer to the predicted value.

The theory of nuclear coupling via the Fermi contact
interaction is supported by the behavior of the C111 com-
plexes as is that of scalar relaxation between the H1 and
the nitrogens. Both the increase in magnitude of the
scalar coupling between the complexes, Clll-H+,i and
Clll-2H+,i-i, and its temperature dependence are in close
agreement with theory.

Clll answers several questions concerning metal ion
binding by the larger cryptands. The conformational analy-
sis of Clll indicates that the free diamine exists substan-
.tially in the endo-endo configuration, but has the flexi-
bility of nitrogen inversion. Even when binding a proton,
it may still invert a nitrogen lone pair to the exo config-
uration, although this process occurs quite infrequently.
The larger cryptands are much more flexible than C111 and

would therefore be expected to more easily undergo exo-

endo nitrogen inversion, even when complexed to a metal

162
cation. The acid catalyzed removal of metal cations com-
plexes by the cryptands, observed by Cox and Schneider<25),
probably does proceed by the mechanism which they suggest.
Inference from the C111 binding conformations supports
their belief that the exo conformation of the nitrogen
should be fairly substantial and available for proton bind-
ing.

The binding characteristics of Clll also support the
findings of Pizer, et. a1.(“7-“8), who attributed the slow
rates of complex formation and dissociation of the cryptands
to a steric phenomenon arising from the rigidity of the
ligand. However, they also attributed part of the slowness
to a very low percentage of the "reactive" endo-endo con-
formation. The preference for this conformation with 0111
and the ease of nitrogen inversion (when unprotonated),

suggest that this latter argument is not valid.

Future Projects

 

The most significant experiment left unfinished is

the preparation and identification of H + inside the cavity

2

. of 0111 by adding es to Clll-2H+,i-i in liquid NH This

3.

reaction was attempted once and although H + may have been

2
formed, the solution decomposed too rapidly to obtain its
EPR spectrum. A different experimental design is necessary
to accomplish this goal.

The quantum calculations dealing with proton binding
by C111 will also be very useful in identifying the most

favorable conformation of the ligand, both when bound to a

163

proton and when free. This theoretical analysis may also
help to determine the energy barrier to proton exchange
inside the cavity of the ligand, the most favorable en-
trance for a proton into the cavity from solution and many
other important questions.

The binding characteristics of C111 and Clll-H+,i
with other ions would also be interesting. For example,

+2 2 ions able to coexist in-

are both protons and Be or Mg+
side the cavity of C111. If not, do any metal cations bind
either internally or externally to the internally monopro-
tonated complex? The kinetics of decomplexation of L1... or
Mg+2 ions from C111 by protons may also prove interesting,
since the kinetics of external protonation of Clll are now
known. This would help to answer the question of whether
acid catalyzed decomplexation of metal ions by other cryp-
tands occurs by external or internal protonation at the
nitrogen. Finally, the crystal structures of the protonated
complexes of Clll would be of interest, especially

C111°H+,i, Clll-H+,o and C111°2H+,i-o.

PART II

AN NMR STUDY OF ALKALI METAL ANIONS

IN SOLUTION

I) INTRODUCTION

The properties of solutions of alkali metals in liq-
uid ammonia (NH3) have intrigued investigators for well
over one hundred years since the discovery of Weyl in
1863(7u) that sodium and potassium metals could be dissolved
in liquid ammonia to give deep blue colored solutions. The
solubility of alkali metals was later shown to be as high
as 15 to 20 mole per cent in some cases, the resulting blue
to bronze solutions being stable for days at room tempera-
ture. Electronic and EPR spectra and electrical conduc-

(75’78) indicate that the solutions contain a

tance studies
variety of chemical species, those of maJor importance being
the metal cation (M+), the solvated electron (ES) and the
neutral ion pair, M+-§S or "monomer". Other more exotic
species such as e2 -, alkali metal anions (M') and higher
order ionic aggregates have also been postulated to be pres-
.ent(78).

The study of alkali metal solutions has been limited
almost entirely to liquid ammonia, since the alkali metals
are quite insoluble and highly reactive toward most sol-
vents. Exceptions to this rule include hexamethylphosphor-
ic triamide (HMPA), ethylenediamine (EDA), and methylamine
(MA), which dissolve at least some of the alkali metals to

concentrations higher than 0.01 M. In most solvents,

16A

165
however, the alkali metals are quite insoluble or only
slightly soluble without decomposition. The chemistry of
solutions of the alkali metals in amines and ethers is
superficially similar to that in ammonia, since deep blue,
highly reducing solutions result<75’78). The maJor dif-
ferences between metal ammonia and metal amine solutions
are solubility and stability toward decomposition, both
of which decrease in the amines, and the appearance of metal
dependent bands in the electronic spectra of the metal amine
solutions. Metal ammonia solutions show only one broad
electronic band, regardless of the alkali metal, assigned
to ES and aggregates containing this species. The elec-
tronic spectra of metal amine and ether solutions are char-
acterized by a band whose frequency maximum is greatly de-
pendent on the metal as shown in Figure 51. These bands

have been assigned to the alkali metal anions.

 

|.O "’

1 1 4 1 1 L L i 1
4 6 a lo I2 I4 I6 la 20

waveuwaen (car'aIO’3)

 

 

 

Figure 51. The electronic spectra of the alkali metals in
tetrahydrofuran (THF).

166
Electron paramagnetic resonance spectra of metal
ammonia solutions in fairly dilute solutions (<10.1 M)

show only the 8 line with a g-value near that of the free

S
electron. Metal amine solutions often show this line and

an overlapping multiplet attributed to the solvated mono-
mer. Thus, the solvent plays a maJor role in the character
of species produced in solutions containing the alkali
metals.

The solubility of a particular metal is also greatly
influenced by the prOperties of the solvent. Solubility
seems to correlate well with solvent dielectric constant,
which decreases in the progression NH3, HMPA, MA, EDA,
ethylamine (EA), isopropylamine (IPA), tetrahydrofuran (THF),
and dimethylether (DME). For example, the solubility of
sodium in NH3 is about 15 mole per cent (=5 M), but in THF

6 M.

it is less than 10-
Solvent polarity may also be related to the following

equilibrium:

M ———-—-s-M+ + 258 (A7)

The more polar solvents favor the formation of E , whereas,

S
those which are less polar tend to shift the equilibrium to

M-. The character of the metal itself also influences the

ratio of metal anion to 5 in solution. For example, sodium

S
has a strong preference to form the anion even in MA, but

potassium seems to favor the formation of the metal cation

and ES. kl is so large for lithium, that Li‘ has not yet

167

been observed in solution. In order of increasing k the

1,
progression seems to follow Na, Cs, Rb, K, L1.

The advent of crown ethers and cryptands has greatly
extended the number of solvents in which alkali metal solu-
tions may be studied<76). They provide a great increase in
the solubility of the alkali metals for the previously men-
tioned solvents, as well as for many other nonpolar sol-
vents such as benzene and toluene<77). Cryptands, in par-
ticular, fulfill another role in alkali metal solutions.
They tend to isolate the cation from the anion, and thereby
increase the stability of the anionic species by preventing
recombination to form metal. The exchange rates from these
ligands are slow, on the order of milliseconds and greater.
The cations are therefore encapsulated and insulated from
the alkali metal anion by the backbone of the ligand. This
can lead to either thermodynamic or kinetic stabilization
of M” (or both).

The cavity dimensions of the ligand may also be impor-
tant in determining the products of metal amine reactions
and their stability. Since cryptands discriminate between
ions by orders of magnitude in their binding constants, the
products of mixed metal reactions may be perturbed by the
proper choice of cryptand. For example, the reaction with

excess metal produces one product via the following scheme:

EA + _
2Ha(s) + C222 —->Ha C222°Na (‘48)
whereas:
EA

HaK(o) + 0222 —> K 0222-Na— (II9)
L)

168
produces a different product<23). The replacement of the
Na+ by K+ in the ligand occurs because C222 binds K+ more
strongly than Na+ by a factor of about 100 in water and
presumably also in ethylamine.

The ligand may also influence the products in a dif-
ferent way, namely by stoichiometry. If an equivalent
amount of metal and ligand are introduced, the principal
anionic species will be ES, whereas if a twofold or greater
excess metal is utilized, the reaction will tend further
toward the production of M’.

For a more detailed discussion of the properties of
these solutions, the reader is referred to the Ph.D. dis-
sertation of J. M. Ceraso and the references listed in
this chapter.

The most definitive methods for characterizing alkali
metal solutions in amines and ethers include EPR, NMR, opti-
cal spectra, X-ray crystallography (if crystals can be ob-
tained), and magnetic susceptibility. All the alkali metal
anions, with the exception of lithium and francium, have
been produced in solution or in films(23:75), and have been
identified by their optical spectra. The optical spectra
of the films produced by rapid evaporation of solvent (MA)
from solutions of M+C222-M- or 3 give bands which are very
similar to those in solution (Figure 51). The absorbance
maxima for Na", K', Rb', Cs-, and 5 occur at 15,A00, 11,900,
11,600, 10,500, and 3,000 to 7,000 cm"1 respectively, in the

film spectra.

169
Crystals of Na+C222 Na“ have been successfully grown

and an X-ray structure performed<21'22).

The crystal struc-
ture indicates that Na- is a large anion, about the size of
1-, and that Na+ is trapped inside the ligand. The struc-
ture is essentially a hexagonal closest-packed type with a
closest (Na+) to (Na-) distance of 7.063 and (Na') to (Na’)
distance of 8.83;. The films and crystals of Na+C222oNa-
are diamagnetic, whereas those of K+C222-E produced by evap-
oration of MA from a solution of K+C222 + E are strongly
paramagnetic<76).

Perhaps the strongest evidence that the alkali metal
anions are indeed anions with electrons in the outer s-
orbitals, rather than contact ion pairs between the cation
and electrons, comes from the NMR spectra of these species
in solution<20). The spectra present very narrow lines for
the anions (except for potassium which has not been ob-
served), which are diamagnetically shifted very near to the
position of the gaseous neutral atom. This observation de-
mands that the solvent be excluded from contact with inner
p-electrons by filled outer s—orbitals. The extreme nar-
rowness of the lines also indicates a very symmetrical elec-
tron distribution, since the relaxation of alkali metals is
governed by quadrupolar effects. Quadrupolar relaxation is
very sensitive to the symmetry of the electronic environ-
ment of the nucleus, thus the NMR spectra of the alkali

metal anions provide strong evidence that they are indeed

anions, with a symmetrical electron distribution, rather

170
than contact ion pairs between the cation and electrons
which would produce large anisotropies in the electronic
distribution.

This chapter is devoted to the characterization of
alkali metal amine and ether solutions with special empha-
sis on the relative thermodynamic stability of the alkali
anions and the preparation of new structures. The data
which will be presented have been obtained from alkali
metal NMR spectra using the DA-60 spectrometer described
in the Experimental section. The NMR spectra provide a
definitive method by which to characterize the species in
these solutions. Table 21 gives the chemical shifts of
several alkali metal cations and anions in solution, with
each chemical shift value referenced to the free metal atom

in the gas phase<79).

Of particular interest is the fact
that the Cs0222 chemical shift may vary from -590 ppm to
-400 ppm depending on the temperature and solvent<55).
This phenomenon has been ascribed to a rapid exchange be-
tween inclusive and exclusive complexes (as described in the
Introduction to Chapter 3), the shift of the inclusive com-
plex being -590 ppm, and that of the exclusive crown-type
complex being about -400 ppm.

The samples have been synthesized by the procedure
described in the Experimental section, except that metal
alloys have been utilized sometimes rather than single metal

films. Common characteristics of all samples are their blue

to black colors, an evidence of the presence of M- and e

3;“

171

 

 

 

882w 882I <2 mmI I88 .8+88 mo.o 8+88

882w oamI 222 omI I88. 8 88 888.8 8+M8

o2 m.mmI 228 28I :m 2.8 I 88

mv 8. memI 882 mm 288 2.8 I88

m2 8. 82 I 228 88I I82.o+sm 2.8 I82

omm 8.88 I <8 88I I82 .8+om 2.8 I82

8882 oomI 28m28 mm I2. 8+om 8.8 8+8m

oom2 memI 882 mm I2 8 82 2.8 8+82

mm2 8.82NI 0mm mm 82 2.8 +82

mv m.m + 228 2 I I82.8+82 m2.8 I82

mIm 8.2 + <2 2+ o8 82I I82.8+82 m2.o I82

22 2.2 + <2 m2I I82.8+82 m2.o I82

2882888 8.m + 888 I82

2m 2.8m I 2mg 8 I I82.8 82 m2.o 8+82

882Iom2 8.8m I <8 2+ o8 82I I82.8+M2 82.8 8+82

8.8m 8.82 I <2 m2I I82. 8 m2.o 8+82

8.mm m.mm I 288 mm 822M82 8.8 +82

8.82 8.88 I <2 mm 282 mm.o +82

8.8 «.88 I <2 m2I 282 m.o +82

8.8 8.28 I 8mm mm 2882 888. +82

No.8 m.m w m.88mI 882 mm 2283 +88

8.2 8 8.22mI ow: mm 2283 +82

82.8 2 8 8.88 I o 2 mm 2283 +82
8 Sam

32 .238 Km: .m> >Homzvo acme/How Do .9289 E ..ocoo COH

.822 28882 228228 :2 8888238822 888 888288 28822888 8o 8822 88888288 < .28 82888

172
solution, and considerable bronze to gold colored films

upon solvent evaporation. M' and E absorb in the red,

S
therefore their solutions appear blue. Films of these spe-
cies are gold and metallic-looking because they absorb
strongly in the near-infrared and have a sharp cut-off in

the visible, similar to the absorption spectra of metals.

II) THERMODYNAMIC STABILITY OF THE ALKALI METAL ANIONS

The measurement of the relative thermodynamic stabil-
ity of the alkali metal anions involves several complex
factors. It is very difficult to determine whether the
products of these reactions are the most thermodynamically
stable, or whether they possess kinetic stability, e.g.,
the kinetics of the reaction may favor one product which is
much less thermodynamically stable than another. The lat-
tice energy of the metal, alloying effects, the formation
constant of the cation and ligand, the desire of the anion
to dissociate to cation and electrons, etc., may each in-
fluence the thermodynamic stability of the anion in solu-
tion.

The measurement of the relative thermodynamic stabil-
ity of the alkali anions has been attempted in spite of the
many pitfalls, by using mixed metal alloys. The metals
were always in at least a twofold excess to C222. The prod-
ucts of these reactions are given in Table 22. Tetrahydro-
furan has been utilized because it tends not to support ES,
and yet provides good solubility for the alkali metals in

the presence of C222.

Table 22.

preparations.

The products of some alkali metal solution

 

 

Sample Conc. Identification by NMR
NaK alloy (x8) 20.05 M Na- at+2 ppm
0222 inHtNH2 no NaC
NaK alloy (xS) 20.07 M Ha’ at+2 ppm
C222 in EtNH2 no NaC
NaK alloy (xS) 20.07 M Na” at+fl ppm
C222 in THF no NaC
NaK alloy (xS) =0.05 M x0222+ at -7 ppm
C222 in MeNH2 no K“, very broad
K metal (xs) 20.08 M nothing observed
0222 in THF
...
K, 0222 in THF 20.12 M K 0222 at 2-20 ppm
very broad, no K‘
03, 0222 in EtNH2 0.05 M 030+ at =-u33 ppm
no Cs"
Cs, 0222 in MeNH 0.06 M 030+ at -598 ppm, temp. dep.
2 no Cs , decomp. at -u30
0s, 0222 in THF 0.08 M 030+ at -58A and
Cs’ at ~N3 ppm
, +
NaCs alloy 0.06 M CsC at -A18 ppm,
C222 in EtNH2 no Cs or Na-
NaCs alloy alloying effect to be
C222 in THF discussed later
KCs alloy 0.06 M Cs" at 2&7 ppm,
C222 in THF ' no CsC222
Cst alloy 0.06 M Cs' at -u§ ppm,
C222 in THF no CsC222
RbNa alloy 0.05 M Na' at =3 ppm,
0222 in THF no Mac222+
Na metal

15-0-5, MeNH2

Na 18-C-6
THF

decomp., nothing observed

very slow dissolution

17“

Table 22 (cont'd.)

 

Sample Conc. Identification by NMR

 

Na 18-0-6 Mac+ at -70 ppm, Na‘ at
MeNH2 +1 ppm

EPR gives temp. dep. elec-
tron signal; g - 2.002A,
linewidth - 0.2 gauss

Na 18-C-6 dissolution or solubility
EtNH2 problems; powder (metal
+ crown) observed

Na C221 EtNH2 very slow dissolutiog,
Na" at 3 ppm, no NaC

Na C221 THF very slow dissolution,
nothing observed

NaCs 0221 THF Na“ at 2 ppm, 030* at -56A
ppm; Cs' at -A3 ppm.
Very slow dissolution of Na

metal.
Cs in EA nothing in NMR
Cs in THF nothing in NMR
Cs 18-0-6 in THF 0.11 M ? CsC+ at -322 ppm

very broad at -100, disap-
pears at higher temps.

Na 0222+-Na’ solid Na metal observed
Na metal film, Distilled over meta1--gave a blue solid.

4. ..
Cs C322-Cs in THF Cs+C322 at -u39 ppm,
Cs- at —50

 

175

An equimolar alloy of Na and K metals with C222 in
THF gives complete conversion to Na“, but no Na+ is observed
in the Na23 NMR spectrum of this solution. The K39 NMR
spectrum has been taken of the sample in MA, which gives
only one broad resonance, at -6.5 1 0.5 ppm (referenced to
sat. KNO2 in H20), corresponding to K+C222. These findings
suggest that the maJor product of the reaction is K+0222oNa'.
Optical spectra of films from solutions prepared in the same

(23). Rb-Na alloys give a

manner support this conclusion
similar product, Rb+C222oNa'. These two findings are entire-
ly expected, since both K+ and Rb+ have a greater affinity
for C222 than does Na+<8l). Also, Na“ has been shown to be
more thermodynamically stable than the other anions, since

Na+ is converted to Na” in the presence of K', Rb”, Cs", or

83(79)°

The products of Cs-K and Cs-Rb alloys with 0222 in
THF yield the production of Cs- as evidenced by their C8133
NMR spectra, but the NMR signal of 03+ is never observed in
these solutions. This fact leads to the conclusion that the
maJor products are K+C222-Cs" and Rb+C222oCs- respectively,
again in line with expectation. The NMR spectra of K39 and
both isotopes of Rb are difficult to obtain due to broad
lines and low sensitivity. Thus, the measurement of their
relative stability is not possible by this technique.

An unusual dilemma is presented in the solutions from
the alloys of Na and Cs, C222 in THF (Table 23). The compo-

sition of the alloy tends to have a pronounced effect on

176

Table 23. The products of the reaction of Na and Cs metals
and 0222 in THF.

 

 

Sample in THF Products

NaCs (excess metal) CsC+, 20% Cs-, 80% Na-
NaCs (excess metal) CsC+, 20% 03', 80% Na-
over Na metal first, + _ _

then over Cs metal CsC -Cs , slight Na
over Cs metal first, + _

then over Na metal CsC -Na only
over Na metal (gold powder), + _ _

then over Cs metal CsC °Cs , slight Na
NaC+-Na' powder over Cs metal NaC+oNa-, slight Cs+C

 

whether the maJor anion produced is C3" or Na”. This occurs
because Cs and Na metals form a nonideal alloy, with the
production of the compound, Na2Cs(80). The solution in THF
is further complicated by the fact that the dissolution of
Na is very slow, although it is enhanced by the presence of
Cs. Several attempts have been made to overcome this alloy-
ing effect, including the formation of Cs+C222-Cs- over Cs
metal first and then taken over Na metal, and the use of
Na+C222oNa' powder dissolved in THF and taken over Cs metal.
The former experiment gives Cs+C222oNa- and the latter, most-
ly Na+0222-Na', although some Cs+C222 is also produced.

When these solutions are made up over the alloy, which is

in great excess to C222, the products of the process usually

are Cs+C222 and a mixture of 03' (lo-20%) and Na‘ (80-90%).

The equilibria which control this process are:

177

Kl + _

2 31(3): M + M (50)
- + K2 - +

C8 + Na :Na + CS (51)
+ K3 +

M + C M C (52)

The constant, K1, is not known because of the alloying
effect and K2 is the one of interest, since it is deter-
mined by the anion's relative stability. It appears that
the equilibrium is not shifted too far to the right, but
definite conclusions are difficult because of the slow dis-
solution of Na in THF and by the alloying effect.

Another very unusual consequence of this process is
that the equilibrium constant, K3 (which is also influenced
greatly by K1), tends almost exclusively toward the forma-
tion of Cs+C222 rather than the Na+ complex. This is highly
irregular because in water, the formation constant of 0222
with Na+ is more than 100 times greater than that of
Cs+(81). This may be entirely a function of the alloying
effect or possibly even a kinetic phenomenon. The formation
constants of the complexes have not been measured in THF or
the amines but that of Na+ would still be expected to be
much greater than that of Cs+. This competitive complexa-
tion should be explored in more detail in THF. The trend of
thermodynamic stability relative to the solid metals from

these NMR data indicate Na’>Cs’>>K',Hb'.

178
III) IDENTIFICATION OF NEW SPECIES

Attempts to observe K“ by_NMR. The potassium anion
has never been observed by NMR for two reasons, low sensi-
tivity of the potassium nucleus and considerable affinity
to dissociate to and interact with ES. Even a slight inter-
action with electrons in solution tends to broaden the sig— '
nal out of existence (see Historical section). Four at-
tempts have been made to observe K-, three in THF with ex-
cess metal at concentrations varying from 0.01 M to 0.1 M.
The samples were prepared at or near room temperature.
very dark films were observed, but the NMR spectra showed
only the complexed cation at about -20 ppm from saturated
KNO2 in water, the line being 300 to 600 Hz broad, depend-
ing on the temperature.

The final attempt to obtain a K- signal in the NMR
utilized IPA as solvent with ligand concentration at about
0.02 M. The sample was again made up at -10 to 0°C with no
apparent decomposition. A black powder precipitate was ob-
served which seemed to be somewhat crystalline (black nee-
dles), as previously reported by Dye and co-workers(76).

The NMR spectrum showed no peaks, an indication of either low
solubility or the presence of solvated electrons which
broaden both cation and anion peaks. Otherwise, the concen-
trations should have been high enough to permit observation
of the NMR spectra.

Cs, 0222 in EA and MA. When Cs is dissolved in EA or

 

MA in the presence of C222, only the complexed cation is

179

observed in the NMR spectrum at -A18 to -A33 ppm (depending
on sample conditions and temperature) and -591 ppm respec-
tively. The chemical shifts indicate that the complex in
EA is an exclusive complex, whereas that in MA is inclusive.
Both solutions are somewhat unstable, and decomposition
peaks, presumably corresponding to Cs+ complexed by the de-
composed ligand, occur at -384 and -A1A ppm in EA and MA.

The linewidth of the complexed cation is somewhat
peculiar in both solvents, since it broadens as the tempera-
ture is raised in MA, while the opposite is observed in EA.
Figure 52 shows this temperature dependence in MA. The
chemical shift of this species is rather temperature in-
variant in MA, but in BA the line shifts slightly downfield
with decreasing temperature. When the ethylamine solution
is frozen, the complexed cation resonance shifts to -580 t
30 ppm, corresponding to an inclusive complex (Table 2A).

Table 2A. The temperature dependence of the chemical shift
of Cs+0222 in BA.

 

 

 

Temperature (°C) GPPm+ AV1/2*
-9A -580 81000 Hz
-69 -N33 108
-62 -u32 83
-52 -A28 3A
-38 —A27 16

+ i A ppm.

* Full width at half height.

180

 

 

 

)\_jk-~ "HDB '

_]

T I
Sppm '800-600-400

 

Figure 52. The temperature dependence of the NMR spectrum
of Cs+0222-Cs' in MA.

181

The EPR spectrum of a sample prepared in a similar
way in EA gives a single, narrow, intense line with g =
2.002“ t 0.0002 between a temperature range of -32 to -70°C.
This spectrum indicates that electrons are present, but
that they do not interact to a large extent with the Cs
nucleus.

The electronic spectra of films from solutions in
MA prepared in a similar way(23), show nearly complete con-

version to Cs- with only slight presence of § The con-

8'
centration of these samples was much lower than those for
NMR analysis, however.

All indications suggest that Cs- should be observed
in the NMR spectrum in MA and EA, but it is possible that
exchange between a paramagnetic species in minute concen-
trations could account for its disappearance. This paramag-
netic species could also be the source of the instability of
these solutions.

The strange Cs+C222 broadening with temperature is
probably due to the rapid exchange between inclusive and ex-
clusive complexes, the former being preferred at lower tem-
peratures. In EA the exclusive crown-type complex is fa-
vored, whereas in MA the opposite is true. The spectra in
EA are especially supportive of this conclusion, because as
the temperature is lowered, the Cs+C222 line broadens and
shifts downfield. When the sample is frozen, the chemical
shift of the complexed Cs+ is nearly identical to that of

the inclusive complex. In methylamine, the equilibrium

182
seems to highly favor the inclusive complex, but above
-90°C the exclusive complex is present in high enough con-
centration to cause considerable exchange broadening of the
Cs+C line.

An interesting sidelight to these observations con-
cerns the dissolution of Na metal and 0222 in EA which gives
Na+C222oNa-. However, the solution prepared from the alloy
of Na and Cs metals in BA with C222 gives a Cs+0222 signal
at about -A18 ppm, but no anion or Na+ species is observed.
Cs metal is soluble in EA to 10’3 or 10'” M(76), and gives
rise to solvated Cs monomers. Since these species are para-
magnetic, they would cause tremendous broadening and shift-
ing the resonances of those ions with which they exchange
or interact strongly. Only minute levels of these species
would be necessary to induce the Cs- disappearance, because
their chemical shifts are normally tens of thousands of ppm
downfield.

Cs and C222 in THF. Samples of Cs metal and C222 in

 

THF seem to be much more stable than in MA and EA. An esti-
mated half-life for decomposition in THF is approximately 12
hours. The NMR spectrum of these samples shows both Cs+C222
at -583 to -587 ppm and Cs— at -A6 to -Al ppm. The Cs+C222
line is about 100 Hz broad at -110°C, and broadens greatly
as the temperature is raised (Figure 53). Meanwhile, the
Cs- line remains very narrow (<10 Hz), and indicates no ex-
change broadening, except at -A1°C, where slight broadening

occurs. These spectra are reproducible upon raising and

183

THF
C222
+ Cesium

 

 

 

 

 

 

 

 

 

 

/\ -74
4‘ - L I
CsIC+ C5-
.1. L 11 1 L. l L 11
-600 -590 -580 -570 -60 -50 -4O -30
ppm ppm
Figure 53. The tgmperature dependence of the NMR spectrum

of Cs 0222-Cs" in THF.

18A

lowering the temperature, and are not symptons of decompo-
sition. Above -A1°C, however, decomposition occurs rapidly.

This exchange phenomenon is peculiar for two reasons.
First, the chemical shift of the complexed Cs+ does not
change appreciably throughout the temperature range. Sec-
ondly, the exchange does not significantly involve the Cs'
because it would be expected to broaden by exchange to the
same extent as the cation resonance.

The chemical shift of the Cs+C222 resonance demon-
strates that it is an inclusive complex, and its temperature
characteristics are similar to those of its counterpart in
MA, which is also an inclusive complex. By inference from
the exchange in MA, the line broadening of the Cs+C222
resonance in THF might be assigned to the rapid interconver-
sion of inclusive and exclusive complexes with the latter
present at lower concentrations which increase with increas-
ing temperature. Above -A1°C, the Cs+C222 resonance is very
broad indicating that the exclusive complex is appreciable.
Since this complex allows more efficient interaction between
Cs+ and Cs', the anion peak also begins to show evidence of
the exchange phenomenon.

In order to verify that the exchange process involving
the complexed cation was the result of two rapidly intercon-
verting conformations of the ligand, rather than an electron
transfer reaction or related process, the temperature Char-
acteristics of a simple salt, cesium octanoate, were studied.

(Most cesium salts are insoluble in THF, and only cesium

185

octanoate has been found to be soluble enough for C8133

NMR analyses.) The chemical shift of the cesium cation in
solution of cesium octanoate, C222 in THF comes at -403 to
-A33 ppm, and indicates no complex formation. This obser-
vation further demonstrates that complexation of Cs by C222
in THF is easily perturbed by solvent, temperature, and
anion.

Another possible explanation for the exchange broaden-
ing of the Cs+C222 line would involve its interaction with
ES or cesium monomers, both of which are paramagnetic. Ex-
changes of this sort would also be expected to involve Cs-
as in MA and EA, and since this is not observed, interac-

tions of this kind are doubtful.

Na and 18-0-6 in MA. Andrews, Ceraso, and Dye(3“)

 

described a peculiar two electron exchange process between
Na+ complexed by 18-crown-6(l8-C-6) and Na- in MA. The ex-
change was followed by line broadening in the NMR, as shown
in Figure 58. This process did not seem to originate from
a simple two-site exchange, but a more complex reaction was
indicated. In order to ascertain whether a paramagnetic
species could give rise to a third site, an EPR analysis
has been performed. A sample prepared from 0.08 M C222 in
MA taken over excess Na metal showed a single narrow line
with g = 2.002“. The intensity of the line was very temper-
ature dependent (Table 25), indicating a process:

Na-: Na+ + 2E8 or 52:28' (53)

186

 

Figure 5A. The t$mperature-dependence of the NMR spectrum
of Na 18-C-6-Na in MA.

187

Table 25. The temperature dependence of the_EPR signal of
a 0.08 M solution of Na 18-C-6-Na in MA.

 

 

Temp, °K Intensity
269 18.1
259 16.2
246 10.5
237 5.1
227 $0.2

 

In either case, the presence of ES could greatly perturb
the NMR spectra.

The synthesis of crystals of Cs+C222-Cs-. Gold col-

 

ored crystals, very similar in appearance to those of
Na+C222oNa' were synthesized from a 20.1 M solution of 0222
in IPA, taken over excess metal at 0. to -20°C. As the
solution was cooled to -78°C, the small crystals precipi-
tated, and seemed to be quite stable if kept at ~78°C. The
solution phase was less stable, and turned from deep blue
to clear upon decomposition, but the crystals remained gold
for several days at dry ice temperature. The crystals were
never isolated from the solution phase because decomposi-
tion occurred too rapidly.

Attempts to grow crystals of other alkali metals and
ligands were also made, but without success. They include
Cs with 18-C-6 in MA and K+C222-E (1:1 stoichiometry of C222

and metal) from MA, with the addition of DEE. A black

188
powder precipitated from the latter when the MA was removed
and DEE was added.

Complexes With Cryptands Other Than C222. C221 has
also been utilized to dissolve Na metal in EA and THF as
well as Na-Cs alloy in EA. The rate of dissolution of Na
metal by C221 is extremely slow in EA and THF and therefore,
the products of these reactions may be greatly dependent on
the kinetics of dissolution. The products of the reaction
of Na-Cs alloy and C221 in EA are reflective of the slow
dissolution of the Na metal since mostly Cs+C221 and Cs'
are formed. The resonance assigned to the Cs+C22l complex
at -56A ppm was very broad and may not have been real.

A sample has also been prepared by distilling 0221
over a fresh film of Na metal. Upon contact with the metal,
the C221 forms a dark blue crust which lasts for weeks at
-78°C.

The NMR spectrum of a solution from Cs metal and C322
in THF showed two resonances, one at -A39 ppm (1000 Hz
broad) and the other at -50 ppm corresponding to Cs+C322
and 08' respectively. The chemical shift of the cation is
normal since it is in the range of inclusive complexes of

simple salts of Cs+ with C322<85).

APPENDIX

THE THEORY OF CHEMICAL EXCHANGE IN NMR

APPENDIX

The equations which describe the NMR lineshape of a

system undergoing chemical exchange of the sort:

kr
A + L.¢——>.AL
kb

(A1)

are those of Bloch, modified by McConnell to include chemi-

cal exchange.

These equations describe the X and Y compo-

nents of the magnetization in the rotating frame of refer-

ence as follows:

dG
A _ -1 -1
Et— + GAGA - -1YH1M0A 4' TB GB - TA GB (A2)
d6
__5. - -1 -1

These equations are solved using the slow passage condition

in which:
dGA dGB
—z—=O
dt dt
thus:
-1 -l
-(uA - TA )GA + TB GB

(AA)

= 17H (A5)

lMOA

189

 

190

1

 

 

-(ab - ‘61)Gb + 1; Ca = -iYH1Mob (A6)
The expressions are further simplified by:

M0A = pAMo (A7)

MOB 2 pBMO (A8)
and by arranging in a matrix form:

alch + 31203 2 CDA (A9)

a21GA + a220B a CpB (A10)
Using Cramer's rule (see any matrix algebra text):

GA -.% :2 ::: 8 g-IEpAa22 - pBalz] (All)

GB 3'% ::: E: ' % [pBall ' pAa21] (A12)

D = :ll :12 (A13)

21 22

 

 

The total complex moment, 0, is the sum of the two:
C
The absorbtion lineshape function is given by the imaginary

portion of 0, but for lines which are imperfectly phased:

g(v) 2 (real G) sine + (imaginary G) cose (A15)

191
where 6 is the angle of zero order phase correction.

These equations may be easily expanded to include
three or more sites and are equivalent in both P-FT and CW
modes‘7o’71’83) in most cases. They may be used to simulate
or fit NMR lineshapes using KINFIT. (The structure of the
input deck, subroutine EQN, may be obtained from my first
notebook on pages 18A and 185, the entry dated August 25,
1977.)

The mean lifetimes at sites A and B, TA and TB, are
defined in the following way:

the rate of removal of a nucleus from
site i by exchange (A16)

l/‘t1 =
the total number of nuclei in site i

and is related to the rate constant of reaction A1 in the

following way:

 

1/rA = kaAJEL] (A17)
1/rB = kbEAL] (A18)
TA and TB are not unique, but are coupled by the expression:
TATB
T ' ¥XI?§ (A19)
and since:
PA = I :fi (A20)

192

we have:

t a p T a p 1 (A21)

A B B A

and only T is unique.
The temperature dependence of the rate constant, k,
may then be utilized to calculate an activation energy for

the process, using the Arrhenius equation:

k - Ae‘Ea/RT (A22)

AH* is related to the activation energy for reactions in

solution by:
AH+ . Ea—RT (A23)

The Eyring equation may be utilized to calculate AGIr and
AS+:

k a K[:%1] e'AG‘lI/RT (A2")

where K is assumed equal to 1.0, and

AS* a AH+ ; AG+ (A25)

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