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This is to certify that the

dissertation entitled

Single-Crystal X—Ray Diffraction and Alkali Metal
NMR Studies of Alkalides, Electrides
and Model Compounds

presented by

Songzhan Huang

has been accepted towards fulfillment
of the requirements for

Ph.D.

 

degree in Chemi sir):—

 
   

Major professor

Date 17 August 1994

MS U is an Affirmatiw Action/Equal Opportunity Institution 0-12771

 

 

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MSU IoAn Minnow. ActionlEqud 0mm Initiation

SINGLE-CRYSTAL X-RAY DIFFRACT ION AND ALKALI METAL NMR
STUDIES OF ALKALIDES, ELECTRIDES AND MODEL COMPOUNDS

By

Songzhan Huang

A DISSERTATION

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

DOCI‘ OR OF PHILOSOPHY
Department of Chemistry

1994

ABSTRACT

SINGLE-CRYSTAL X—RAY DIFFRACT ION AND ALKALI METAL NMR
STUDIES OF ALKALIDES, ELECTRIDES AND MODEL COMPOUNDS

By

Songzhan Huang

Three new alkalides that contain 21-crown-7 or dicyclohexano-
24-crown-8 were synthesized and their unusual crystal structures
were determined. (Cs+)2(21C7)2(Na’)2 has twin cation-anion ion
pairs in which the Cs+-Na' distances are only 4.44(2)A and 4.52(3)A
respectively, although optical absorption spectroscopy and 23Na NMR
show no charge transfer between Na' and Cs+. In
(K+)2(21C7)3(MeNH2)(Na')2, a third 21-crown-7 serves as a bridge
connecting the two K+ cations, while MeNHz forms a bond to one of
them. In K+(dicyclohexano-24C8)Na', the complexant twists around
the K+ cation so that all eight oxygen atoms are coordinated to the
cation. These alkalides are relatively stable, which is attributed to
their unusual structural features in which the cations can be fully
coordinated in different ways. The structures of two mixed sandwich
complexes, Rb+(l8C6)(12C4)Na‘ and Rb+(18C6)(12C4)Rb', were also
determined. These two compounds show multiple optical peaks in

contrast to the single peak of other alkalides.

The 133Cs chemical shifts in nitromethane, versus the [L]/[Cs+]
mole ratio (L = crown ether) were determined and showed the
formation of the stable 2:1 sandwich complexes, Cs+(18C6)2,
Cs+(15C5)2, and Cs+(HMHCY)2. The formation of an intermediate,
(Cs+)2(18C6)3, in nitromethane was indicated. By contrast, Cs+-12C4
showed only a single step complexation. The formation of the mixed
sandwich complexes, Cs+(l8C6)(15C5), Cs+(18C6)(12C4),
Cs+(HMHCY)(15C5), and Cs+(HMHCY)(12C4) in nitromethane was also
demonstrated.

The first single-crystal 133Cs NMR study of an electride,
Cs+(18C6)2e', was carried out and the quadrupole coupling constants
and asymmetry parameters were obtained for the two Cs+ ion sites.
The original crystalline orientation was preserved rather than the
formation of a random powder, even though a transition from a low-

temperature phase to a high-temperature phase had occurred.

To My Parents

iv

ACKNOWLEDGMENTS

I wish to express my sincere gratitude to Professor James L.
Dye for his guidance and support throughout this work.

I would like to thank Dr. John McCracken, Dr. Kim Dunbar and
Dr. William Reusch for their helpful advice.

I would also like to thank Dr. Rui Huang, Dr. Jineun Kim, and Dr.
Evy Jackson for their help and suggestions.

Thank also extended to all of the members of Dr. Dye research
with whom I have worked, in particular Kerry Reidy-Cedergren, Kuo-
Lih Tsai, Mike Wagner, Erik Hendrickson, and Ching-Tung Kou.

I would like to thank Dr. Long Le and Kermit Johnson for their
help with the NMR instruments. 1 would also like to thank the
glassblowers Scott Bancroft, Manfred Langer and Keki mistry and
instrument makers Russ Geyer and Dick Menke for their excellent
service.

I am grateful for financial support from the Chemistry
Department, Michigan State University, the National Science
foundation(Grant DMR 90-17292, Grant DMR 84-08088, and Grant
DMR 84-03823) and the Michigan state University Center for
Fundamental Materials Research.

Special thanks go to my family and my friends for their

constant encouragement and assistance.

TABLE OF CONTENTS

PAGE
LIST OF TABLES .......................................... viii
LIST OF FIGURES ......................................... xi
CHAPTER 1. INTRODUCTION ........................... 1
CHAPTER 2. SYNTHESIS, STRUCTURE DETERMINATION AND
CHARACTERIZATION OF ALKALIDES ........ 7
I. Introduction ................................... 7
11. Experimental .................................. 10
III. Results and Discussion .......................... l3
III.A. (Cs+)2(21 C7 )2(Na')2 ....................... 13
111.8. (K+)2(21C7)3(MeNH2)(Na')2 ................. 27
III.C. K+(dicyclohexano-24C8)Na' ................ 37
III.D. Rb+(21C7)Na‘ and Five Other Sodides ........ 45

III.E. Rb+(18C6)(12C4)Na‘ and Rb+(18C6)(12C4)Rb' 50
CHAPTER 3. SOLUTION NMR STUDIES OF COMPLEXED Cs+

IONS WITH MIXED CROWN ETI-IERS ........ 71
I. Introduction ................................... 71
11. Experimental .................................. 72
III. Results and Discussion .......................... 74

III.A. The Ion-Pairing Formation Constants of Cs+

Ion in Nitromethane Solvent ............... 74

vi

1113. Formation Constants of Cesium Thiocynate

Complexes with Crown Ethers

in Nitromethane .......................... 84
III.C. Formation Constants of Mixed Sandwich

Complexes ............................... 94

CHAPTER 4. SINGLE-CRYSTAL 133Cs NMR STUDY
OF Cs+(18C6)2e' .......................... 103
I . Introduction ................................... 103
11. Experimental .................................. 112
, III. Results and Discussion .......................... 113
CHAPTER 5. CONCLUSIONS ............................ 122

APPENDIX A. Crystal Structure Data of (Cs+)2(21C7)2(Na')2,
(K+)2(21C7)3(MCNH2)(N8')2.
K+(dicyclohexano-24C8)Na', Rb+(18C6(12C4)Na'

and Rb+(18C6(12C4)Rb' ................... 125
APPENDIX B. The Subroutine Program for the Multiple

Data Set Fitting ........................... 159
APPENDIX C. The Subroutine Program for the KINFIT

Fitting ................................... 160
REFERENCES ............................................. 162

vii

fa.)

A.)

L’.)
A . s

o
(.5)

TABLE
2-1.

2-2.

2-3.

2-5.

2-6.

2-7.

3-1.

3-2.

3-3.

LIST OF TABLES

PAGE
Summary of Crystallographic Data for
(Cs+)2(21C7)2(Na')2 ............................. 15
selected bond distances and bond angles for
(Cs+)2(21C7)2(Na')2 ............................. 18
Summary of Crystallographic Data for
(K+)2(21C7)3(MeNH2)(Na')2 ...................... 29
Summary of Crystallographic Data for
K+(dicyclohexano-24C8)Na‘ ..................... 38
Summary of thermal processes that occur in the
DSC traces with a heating rate of SOC/min. in 0C. . . . 48
l33Cs NMR chemical shifts of the complexed
cations in three sodides ......................... 48
Summary of Crystallographic Data for
Rb+(18C6)(12C4)Na'(I) and
Rb+(18C6)(12C4)Rb'(II) ........................ 55
133Cs Chemical Shifts of Cesium Salt Solution of
MeNOz at 25°C ................................. 75
Ion Pair and Complexation Formation Constants of
Cesium Compounds in Nitromethane at 25°C ....... 84

Mole Ratio Studies of Crown Ether Complexes

viii

3-4.

3-5.

3-6.

3-7.

A-2.

A-3.
A-4.

A-S.

A-6.

A-7.

with CsSCN in MeN02 Solvent by 133Cs NMR

at 25°C. [CsSCN]T=0.005M ....................... 87
Formation Constants for Cs+-Crown Ether

Complexes in Nitromethane Solvent at 25°C ....... 94
Mole Ratio Studies of Mixed Sandwich Complexes

with CsSCN in MeNOz Solvent by 133Cs NMR at 25°C.
[CsSCN]T=0.005M ............................... 95
Formation Constants for Cs+ Ion Complexes with Mixed
Crown Ethers in Nitromethane Solvent at 25°C ..... 97
Mole Ratio Studies of Mixed Sandwich Complexes

with CsSCN in MeNOz Solvent by 133Cs NMR at 25°C.

[CSSCN]T=0.005M ............................... 98
Results Obtained from Single-Crystal 133Cs NMR
Study of Cs+(18C6)2e' at -50°C .......... . ......... 120

Positional Parameters and Their Estimated

Standard Deviations for (Cs+)2(21C7)2(Na')2 ....... 127
Bond Distances (in Angstroms) for

(Cs+)2(21C7)2(Na')z ............................. 129
Bond Angles (in Degrees) for (Cs+)2(21C7)2(Na‘)2. . . 131
Positional Parameters and Their Estimated Standard
Deviations for (K+)2(21C7)3(MeNH2)(Na')2 ......... 136
Bond Distances (in Angstroms) for
(K+)2(21C7)3(MeNH2)(Na')2 ...................... 139
Bond Angles (in Degrees) for

(K+)2(21C7)3(MeNH2)(Na')2 ...................... 142
Positional Parameters and Their Estimated Standard

Deviations for K+(dicyclohexano-24C8)Na' ......... 147

ix

 

A-8.

A-9.

A-lO.

A-ll.

A-12.

A-13.

Bond Distances (in Angstroms) for

K+(dicyclohexano-24C8)Na' ..................... 149
Bond Angles (in Degrees) for

K+(dicyclohexano-24C8)Na‘ ..................... 151
Positional Parameters and Their Estimated Standard
Deviations for Rb+(18C6)(12C4)Na' ............... 154
Bond Distances (in Angstroms) for Rb+(18C6(12C4)Na'
(I) and Rb+(18C6(12C4)Rb'(II) .................. 155
Bond Angles (in Degrees) for Rb+(18C6(12C4)Na'(I)

and Rb+(18C6(12C4)Rb'(II) ..................... 156

Positional Parameters and Their Estimated Standard

Deviations for Rb+(18C6)(12C4)Rb‘ ............... 158

FIGURE

2-1.

2-2.

2-3.

2-4.
2-5.

2-6.

2-8.

2-9.

LIST OF FIGURES

Representative complexants for alkali metal

canons .......................................

Vacuum apparatus for the synthesis of alkalides

and electrides [3-chamber K-Cell] ...............

Large crown ethers used for the synthesis

of alkalides ...................................

The molecular structure and the numbering of

atoms in (Cs+)2(21C7)2(Na')2 ....................
Stereo packing diagram of (Cs+)2(21C7)2(Na')2. . ..

ORTEP plot of selected atoms in

(Cs+)2(21C7)2(Na’)2 ............................

133Cs static and MAS NMR spectra of
(Cs+)2(21C7)2(Na')2 at -60°C; A) Static; B) MAS,

f=3.6kHz; and C) MAS, f=5.0kHZ .................

Optical absorption spectrum of a thin film of

(Cs+)2(21C7)2(Na')2 at -60°C, prepared by rapid

evaporation of the methylamine solvent .........

23Na static NMR spectrum of (Cs+)2(21C7)2(Na')2

at -60°C .....................................

Differential Scanning Calorimetry trace of

xi

PAGE

11

16
17

19

22

24

25

2-10.

2-11.

2-12.

2-13.

2-14.

2-15.

2-16.

2-17.

2-18.

2-19.

2-20.
2-21 .

(Cs+)2(21C7)2(Na')2 at a ramping rate of SOC/min. .
The molecular structure and the numbering of
atoms in (K+)2(21C7)3(MeNH2)(Na')2 .............

Stereo packing diagram of

(K+)2(21C7)3(MeNH2)(Na‘)2 ......................

Optical absorption spectrum of a thin film of
(K+)2(21C7)3(MeNH2)(Na')2 at -60°C, prepared by

rapid evaporation of the methylamine solvent .....

23Na static NMR spectrum of

(K+)2(21C7)3(MeNH2)(Na')2 at -60°C ..............

Differential Scanning Calorimetry trace of

(K+)2(21C7)3(MeNH2)(Na')2 at a ramping

rate of SOC/min ................................

The molecular structure and the numbering of

atoms in K+(dicyclohexano-24C8)Na' .............

Stereo packing diagram of
K+(dicyclohexano-24C8)Na‘ .....................
Optical absorption spectrum of a thin film of
K+(dicyclohexano-24C8)Na‘ at -60°C, prepared by

rapid evaporation of the methylamine solvent .....

23Na static NMR spectrum of

K+(dicyclohexano-24C8)Na' at -60°C ..............

Differential Scanning Calorimetry trace of

K+(dicyclohexano-24C8)Na‘ at a ramping

rate of SOC/min ................................

133le static NMR spectra of three alkalides ........

The molecular structure and the numbering of

xii

26

30

31

34

35

36

40

41

42

43

49

2-22.
2-23.

2-24.
2-25.

2-26.

2-27.

2-28.

2-29.

2-30.

2-31.

atoms in Rb+(18C6)(12C4)Na' ....................
Stereo packing diagram of Rb+(18C6)(12C4)Na'. . ..

The molecular structure and the numbering of

atoms in Rb+(18C6)(12C4)Rb' ....................
Stereo packing diagram of Rb+(18C6)(12C4)Rb'. . ..

23Na static NMR spectrum of Rb+(18C6)(12C4)Na’
at 60°C ......................................
87Rb NMR spectra of A) Rb+(18C6)(12C4)Rb' and
B) Rb+(18C6)(12C4)Na', obtained with a solid state
Spin-echo pulse sequence. Note that NMR peaks
for both Rb+ and Rb' in Rb+(18C6)(12C4)Rb' were

observed ......................................

Temperature dependence of the NMR line shapes
of the Rb+ ions in Rb+(18C6)(12C4)Na'. A) -100°C;
B) -80°C; C) -60°C; D) -40°C; and E) -20°C .........
Temperature dependence of the NMR line shapes
of theRb+ ions in Rb+(]8C6)(12C4)Rb'. A) 4000C;
B) -80°C; C) -600C; D) -400C; and E) -20°C .........
Computer simulated static second order
quadrupolar line shapes for the central
transition of a quadrupolar nucleus ..............
Optical absorption spectrum of a thin film of
Rb+(18C6)(12C4)Na' at -60°C, prepared by rapid
evaporation of the methylamine solvent ..........
Optical absorption spectrum of a thin film of
Rb+(18C6)(12C4)Rb' at -60°C, prepared by rapid

evaporation of the methylamine solvent ..........

xiii

53
54

58
59

62

63

65

66

67

68

69

3-1.

3-3.

3-4.

Concentration dependence of the 133C3 chemical
shifts of cesium compounds in nitromethane at
25°C. The solid lines are least-squares plots,
obtained by simultaneous multiple data set fitting
of all three data sets with the KINFIT program .....
133Cs chemical shifts gs. [L]/[Cs+] mole ratio in
nitromethane at 250C. L=18-crown-6, 15-crown-5,
or 12-crown-4. The solid lines are least-squares
plots .........................................
Nonlinear least-squares curve fitting of the
chemical shift 3. [l8C6]/[Cs+] mole ratio without
the model of the intermediate (Cs+)2(18C6)3 .......
Nonlinear least-squares curve fitting of the
chemical shift ys. [l8C6]/[Cs+] mole ratio with

the model of the intermediate (Cs+)2(18C6)3 .......
133Cs chemical shifts y_s. [L]/[Cs+] mole ratio in
nitromethane at 25°C. L = HMHCY, 15-crown-5,

or lZ-crown-4. The solid lines are least-squares
plots .........................................
The series of transformations requireu to determine
the chemical shielding or quadrupolar tensor in the
PAS frame from the experimental data obtained

in the laboratory frame .........................
Crystal structure of Cs+(l8C6)2e'. A) Single
molecule diagram; B) ORTEP stereo packing

diagram. The anionic hole centers are indicated
by the symbol 6) ...............................

xiv

76

88

89

90

99

109

110

4-3.

4-4.

4-5.

4-6.

Single-crystal 133Cs NMR spectra of the high-
temperature phase of Cs+(18C6)2e' at two different
orientations at VL = 52.468MHz and at -50°C ......
Angular dependence of half the splitting of the
two first satellite transitions of Cs+ in site 1 from
the high-temperature phase of single crystal
Cs+(l 8C6)2e‘ ..................................
Angular dependence of half the splitting of the
two first satellite transitions of Cs+ in site 2 from
the high-temperature phase of single crystal
Cs+(18C6)2e' ..................................
Angular dependence of the chemical shift of

the central transition of Cs+ in site 1 from the
high-temperature phase of single crystal
Cs+(18C6)2e‘ ..................................
Angular dependence of the chemical shift of

the central transition of Cs+ in site 2 from the

high-temperature phase of single crystal

Cs+(18C6)2e‘ ..................................

XV

115

116

117

118

119

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CHAPTER 1. INTRODUCTION

The discovery of alkali metal-ammonia solutions by Weyl in
1863 has resulted in much research on this type of solution[1]. Two
new types of compounds, alkalides and electrides, were discovered in
Professor Dye's laboratory, while studying metal-amine solutions in
the presence of complexants[2-5]. Alkalides and electrides are ionic
compounds in which a metal cation is complexed by a cyclic or
bicyclic polyether or polyamine. The anions in an alkalide are alkali
metal anions, while those in an electride are electrons. A few
representative complexants used in the synthesis of alkalides and
electrides are shown in Figure 1-1.

In order to advance the understanding of these unique ionic
compounds, synthesis, structure determination and characterization
of new alkalides and electrides are of great importance. Over the
years, more than thirty alkalides and electrides have been
synthesized and most of the crystal structures of these compounds
have been solved since a new technique for the growth and handling
of single crystals was established by S. Dawes and O. Fussa[6-8]. NMR,
EPR, x-ray crystallography, powder conductivity, photoelectron
emission, magnetic susceptibility and other techniques were also
used to study the properties of these compounds[9-30]. But crown
ethers larger than 18-crown-6 have never been used successfully as
complexants for the synthesis of crystalline alkalides or electrides
because of their flexible nature and their large cavity sizes

compared to the radii of the alkali metal cations. The alkalides made

O O
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LI
l8-Crown-6 (18C6)
”Or—‘0’»
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Cryptand 222 (C222)

Hexamethyl Hexacyclen (HMHCY)

Figure 1-1. Representative complexants for alkali metal cations.

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with large crown ethers are often so 'soft' that it always presents the
difficulties of growing single crystals and the problems of disorder in
the crystal structures. But the hope of putting two cations into one
crown ether and the interest in knowing their crystal structures led
us to synthesize these compounds and to further determine their
crystal structures. Among other topics, this thesis presents the
details of the syntheses and crystal structure determinations of
alkalides with large crown ethers as complexants.

While large crown ethers were used intentionally as
complexants to synthesize alkalides, the first mixed sandwich
compound, Cs+(18C6)(15C5)e’, was made accidentally during an
experiment in which Cs+(18C6)2e' and Cs+(15C5)2e' were mixed as a
temperature reference in 133Cs NMR measurements[7,31]. In this
experiment, a new 133Cs NMR peak was observed at a position which
is different from that of either Cs+(l8C6)2e‘ or Cs+(15C5)2e'. This
indicated the formation of a new compound, the mixed sandwich
electride, Cs+(18C6)(15C5)e'. After the discovery of this compound,
another mixed sandwich compound, K+(18C6)(12C4)Na'- was made
by mistake when samples of K+(18C6)Na' and K+(12C4)2Na‘ were put
together in an attempt to grow single crystals of K+(18C6)Na'[32]. To
better understand the nature of these mixed sandwich compounds
syntheses of additional mixed sandwich complexes were carried out.
Two of them, Rb+(l8C6)(12C4)Na‘ and Rb+(18C6)(12C4)Rb', were
synthesized and their crystal structures were determined in this
work. The discovery of the mixed sandwich alkalides and electrides
also led to the successful synthesis and structure determination of a

model salt, the mixed sandwich complex of Rb+(l8C6)(12C4)I',

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indicating that mixed sandwich model salts indeed exist. The
characterization of the mixed sandwich compounds showed that they
are not only thermally stable but also have interesting properties.

It was the discovery of the mixed sandwich complexes and
their thermal stability that prompted us to study the kinetics and
thermodynamics of the complexation of these compounds in solution
by using NMR techniques. The solution NMR studies mainly focused
on the mixed sandwich complexes of the Cs+ cation with 18C6-15C5
or 18C6-12C4 although complexed Rb+(18C6)(12C4) and
K+(18C6)(12C4) exist and are thermally stable. Both Rb and K nuclei
have relatively low NMR sensitivities and large electrical quadrupole
moments which give very broad NMR lines even in solutions due to
the second order quadrupolar coupling. These characteristics present
difficulties in the NMR studies of K or Rb nuclei. In contrast, Cs+ is a
very good candidate for solution NMR studies. Its NMR sensitivity is
relatively high. It has a very small electrical quadrupole moment and
line broadening by quadrupolar interaction is not a factor. The
solution NMR studies showed that complexed Cs+(18C6)(15C5) and
Cs+(18C6)(12C4) indeed exist in solution as well as in solids. In
addition, complexed Cs+(18C6)2, Cs+(HMHCY)2, Cs+(HMHCY)(15C5),
and Cs+(HMHCY)(12C4) were also studied by solution NMR.

NMR studies of half-integer Spin quadrupolar nuclei in solids
are becoming increasingly important since this technique can give
convenient information about the structure and dynamics in many
different chemical systems[33-37]. In general, the NMR spectra of
half-integer spin quadrupolar nuclei depend on the local magnetic

fields induced by nuclear quadrupolar coupling, chemical shift

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anisotropy, and spin-spin coupling to the surrounding nuclei. In the
past, NMR studies of quadrupolar nuclei were carried out in
relatively low applied magnetic fields so that the field-dependent
chemical shift anisotropy is small and both direct and indirect spin-
spin couplings are usually negligible compared to the quadrupolar
interaction. Consequently, most early studies of these nuclei focused
on the investigation of the nuclear quadrupolar interaction. The
improvements of NMR instrumentation in recent years have shown
that measuring the influence of chemical shift anisotropy and spin-
spin coupling is possible. These improvements include the application
of superconducting magnets and the development of high resolution
solid state techniques for quadrupolar nuclei. These techniques are
2-D NMR, dynamic angle spinning, double rotation, and zero field
NMR[38-43]. '

Solid state NMR is one of most important techniques used for
the studies of crystalline alkalides and electrides. Na' was first
identified in solution by using 23Na NMR[44-45]. Magic angle sample
spinning NMR was also used to identify Li‘l', Na'l', Cs+, Na', K', Rb‘, and
CS' in powdered alkalides and electrides. In addition, other NMR
techniques were used to study solid alkalides, electrides, and their
model salts[9,11]. These techniques include solid state spin-echo,
NMR relaxation measurements, and line-shape analysis of powder
NMR spectra. Information about chemical shift anisotropy and
quadrupole coupling constants can be obtained from line-shape
analysis of static and magic angle spinning NMR spectra.

133C8 is an ideal nucleus for solid state NMR studies because it

is 100% naturally abundant and has a relatively small quadrupole

moment. A number of Cs+ alkalides and their model salts have been
studied by using static powder and magic angle sample spinning
NMR. The line-shape analysis of the NMR spectra of these compounds
gave some information about the quadrupolar interactions and
chemical shift anisotropy of the Cs+ cations in these compounds. In
spite of the success of Cs+ powder NMR studies, there are limitations
that can only be eliminated by single-crystal NMR studies. Single-
crystal NMR studies can give accurate quadrupolar coupling constant
values, asymmetry parameters, and the orientations of the principal
axes. The separation of the effects of chemical shift anisotropy and
quadrupolar interaction also requires single-crystal NMR studies. The
first and only single-crystal NMR study carried out in our laboratory
is the single-crystal NMR investigation of Na+(C222)Na' by J. Kim[46].
This successful single-crystal NMR study showed that it is possible to
carry out this type of study for alkalides and electrides, although
they are temperature- and air-sensitive.

Cs+(18C6)2e' was the first electride synthesized and is the most
stable one of the five electrides whose structures have been
determined. After its synthesis, Cs+(18C6)2e‘ was intensively studied
by using numerous techniques including powder NMR, EPR,
conductivity, magnetic susceptibility and others because of its unique
physical properties. All of these led us to carried out the first single-

crystal 133CS NMR study of Cs+(18C6)2e'.

im]

0116

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CHAPTER 2. SYNTHESIS, STRUCTURE DETERMINATION
AND CHARACTERIZATION OF ALKALIDES

I. Introduction

The synthesis of new alkalides and electrides is one of the most
important goals in the studies of these compounds. For this purpose,
one has to have suitable complexants. It appears that the synthesis
of electrides requires encapsulation of the cation in a cage structure
or, for crown ethers, by sandwich formation in which a 2:1 ratio of
complexants to alkali metal cations is used. So far, electrides only
have a 1:1 ratio of complexants to cations when cryptands are used
as ligands. The size of the complexants also plays an important role
in the formation of electrides. By contrast, alkalides can have 2:1, 1:1,
and other ratios. They can also have solvent molecules bound to the
cations or have free complexant molecules in the crystal
structure[32, 47-48]. These different molecular structures and the
crystal packing of alkalides depend greatly on the sizes of the
complexants and the cations. Control of the temperature is also very
important for the synthesis of alkalides and electrides since these
compounds are temperature-sensitive and some compounds
decompose, decomplex or undergo phase changes at temperatures as
low as -50°C. For example, (Cs+)2(21C7)2(Na')2 in solution starts to
decomplex at a temperature of about -49°C. With the same
complexant, 21-crown-7, (K+)2(21C7)3(MeNH2)(Na’)2 is still stable in

solution at a temperature as high as -32°C.

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Alkalides and electrides can be prepared in a K-cell or a glass
apparatus called a three-chamber cell which has a third chamber
attached to the K-cell as shown in Figure 2-1. Synthesis methods that
use a K-cell have been described elsewhere[4-5]. The three-chamber
cell is used especially for the synthesis of Li or Ba compounds.
Because Li and Ba have relatively high melting points and react with
glass, neither can be distilled by the usual methods used to distill
alkali metals. Li or Ba was dropped into chamber C directly and
washed with ammonia to chamber B through the frit between
Chamber B and C. Once the metal ammonia solution was in chamber
B, ammonia was removed by vacuum distillation and clean metal
could be obtained in chamber B. Chamber C with its impurities could
then be sealed off. After this procedure, the synthesis of Li or Ba
compounds is similar to the others.

There are many ways of growing single crystals, but the two
methods used most often in our laboratory are slow solvent
evaporation and temperature scanning. Although these two methods
are still being used, the strategy of crystal growth had been changed
over the years. Nowadays, crystal growth can be carried out directly
in the same K-cell in which the sample had just been synthesized
without removing solvent and reloading the sample into another
apparatus. Crystals can also be grown and harvested several times
with the same sample and apparatus as long as the sample has not
decomposed. In this case, a portion of the crystals could be collected
in one or even half of one of the sample fingers so that some sample
could be left to grow crystals at another time; the remaining sample

fingers could then be used to collect crystals that were grown later.

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This can be repeated several times until no sample is left or the
sample fingers are all used.

To determine the identity and stoichiometry of a compound
and to help in understanding its physical properties, single crystal X-
ray diffraction is the most direct and reliable method. This has been
proved in our laboratory before. For example, the only mixed
sandwich electride, first synthesized by S. B. Dawes and J. L. Eglin,
was thought to be Cs+(l8C6)(15C5)e’ even after this electride had
been studied with NMR, magnetic susceptibility, conductivity and
other techniques by J. L. Eglin[48]. But the crystal structure
determined by Rui Huang shows that its molecular formula is
actually [Cs+(18C6)(15C5)e']6(18C6) in which a free 18-crown-6 sits
in the center of six Cs+(18C6)(15C5)e' members[50].

11. Experimental

Syntheses and crystal growth of alkalides in this work were
carried out with two different crystal growing methods and different
solvent combinations in order to find out the best way to grow good
single crystals. The large crown ethers used for the synthesis of
alkalides are shown in Figure 2-2. All large crown ethers, 21-crown-
7, dicyclohexano-24-crown-8, and dicyclohexano-30-crown-10, were
obtained from Parish Chemical Co. These large crown ethers are very
viscous liquids. Before being used, the complexants were purified by
vacuum distillation at 190°C under 2x10'5 torr to yield a clear
liquid. The methods of synthesis of alkalides and electrides can be

found elsewhere[4-5]. The temperature scanning method for crystal

ll

(5 23
c. .5

LJ

21-Crown-7 (21C7)

(“7,
Ct. .10
LUJ

Dicyclohexano-24-Crown-8 (Dicyclohexano-24C8)

 

Dicyclohexano-30-Crown-10 (Dicyclohexano-30C10)

Figure 2-2. Large crown ethers used for the synthesis of alkalides.

12

growth with a programmable NESLAB LT-9 bath has been described
in detail by Rui Huang[51]. When the slow solvent evaporation
method was used, the mixed solvents of dimethyl ether or methyl
amine with either diethyl ether or trimethyl amine were slowly
evaporated into a liquid nitrogen trap through a series of frits under
dynamic vacuum(10'5 torr) for 3-4 days after the samples had been
synthesized. Each frit has a bypass so that the speed of the solvent
evaporation could be controlled.

A complete description of the techniques for the examination
and mounting of single crystals for the X-ray diffraction is given by
S. B. Dawes and O. Fussa[6-8].

X-ray data collection was carried out in a Nicolet P3F
diffractometer with a LT-l low temperature device. Cold nitrogen gas
was used to keep the crystals under an inert atmosphere at low
temperature throughout the entire data collection. The temperature
of the crystals was kept at -70°C or -80°C.

7Li, 23Na, 87Rb, and 133C5 NMR spectra of the samples were
obtained on a Varian VXR-400 superconducting NMR spectrometer
equipped with a variable temperature controller. Various NMR
techniques were used including static powder, solid state spin echo,
and magic angle sample spinning. Static and solid state spin echo
NMR measurements were carried oat with a 45 to 165 MHz broad-
band probe, while the magic angle sample spinning measurements
were made with a Varian 7-mm VT CP/MAS probe. The sample
holder was a Zirconia rotor designed to allow sample loading and
NMR measurements at low temperatures. After the samples were

loaded into the NMR rotor under a nitrogen gas atmosphere and at or

13

near liquid nitrogen temperature, the rotor containing the sample
was transferred to a precooled NMR probe. Cold nitrogen gas was
used to control the temperature and to keep the samples under an
inert gas atmosphere during the NMR measurement.

A Model 260 Guided Wave Spectrophotometer was used to
measure the optical absorption spectra. After the samples were
reloaded into an optical apparatus at low temperature in a nitrogen-
filled glove bag, the optical cell was pumped on a vacuum line, while
being kept cold at -78°C. Solutions of the compounds were made by
the addition of methylamine or dimethyl ether. The thin films were
then prepared by pouring the solution over the quartz cell window
and rapidly distilling the solvent to another side-arm of the
apparatus.

Differential Scanning Calorimetry(DSC) was performed on a
DuPont 910 Differential Scanning Calorimeter. Samples were sealed
in aluminum pans under nitrogen gas atmosphere at liquid nitrogen

temperature.

111. Results and Discussion

III.A. (Cs+)2(21C7)2(Na')2

Single crystals of (Cs+)2(21C7)2(Na')2 were grown by the
temperature-scanning technique. Since this compound decomplexed
at about -49°C, the temperature scan range was set from -50°C to
-70°C. Methylamine or dimethyl ether with either trimethylamine or

diethyl ether were tried as first and second solvents to form

14

different solvent combinations for the synthesis and crystal growth.
But only the combination of methylamine and diethyl ether was
suitable for crystal growth. The crystals obtained were very small.
Attempts to grow bigger crystals were not successful, probably
because of the small temperature scan range. The crystals were
purple in color.

The single crystal used for the X-ray study had the
approximate dimensions of 0.1x0.2x0.4 mm3. The unit cell
parameters and orientation matrix were determined by least squares
from the setting angles of 16 reflections in the range of 15°<29<20°.
The space group of the crystal is triclinic P1 with 2:1 and the cell
parameters are a=10.469(4), b=10.032(6), c=12.708(6),
a=90.919(42)°, B=73.385(30)°, and y=107.453(38)°. These yield a
calculated cell volume of 1216.5(2.1)A3. The crystal was kept at
-70°C throughout the entire data collection. Intensity data were
collected by using the 9-26 scan method at 3°/min.(in 29) with
minimum 26:3.50 and maximum 26:450. A linear decay correction
was based on the intensities of three standard reflections measured
for every 150 reflections. The number of reflections measured was
3485 and the number of reflections used in refinement was 2296
with a data cut-off of I>3 sigma(o). The crystal structure was solved
by using direct methods with the Texsan Program. Hydrogen atoms
were constrained to ride on their bonded C-atoms with fixed
isotropic thermal parameters. The R factors were R=0.063 and
Rw=0.051 with R defined as (leFol-IFCIIVEIFOI. Peak heights in the
final difference map ranged from -0.91 to 0.67 e/A3. The molecular

structure and numbering of the atoms are shown in Figure 2-3 and

the
para

A-Z.

Tabl

Cell

V0111]

R fa:

15

the stereo packing diagram is shown in Figure 2-4. The positional
parameters, bond distances, and bond angles are given in Tables A-l,

A-2, and A-3 in Appendix A.

Table 2-1. Summary of Crystallographic Data for (Cs+)2(21C7)2(Na')2

 

Space Group Triclinic P1

Cell Parameters a=10.469(4)A, b=l0.032(6)A, c=12.708(6)A,
a=90.919(42)°, B=73.385(30)0, y=lO7.453(38)°

Volume 1216.5(2.1)A3

z 1

R factors R=0.063, Rw=0.0Sl

d 1.267g/cm3

 

(Cs+)2(21C7)2(Na')2 was the first alkalide synthesized with a
large crown ether as complexant. The X-ray crystal structure data
show that its crystal structure is completely different from the
structures known for other alkalides. There are two Cs+ cations, two
crown ethers, and two Na' anions in one molecule although their
molar ratio is 1:12]. Each Cs+ cation in the molecule is bonded to all
seven oxygen atoms in one 21-crown-7 and surprisingly to one of
the seven oxygen atoms from another 21-crown-7. This gave the Cs+
cations a coordination number of eight and connected the two
Cs+(21C7)Na‘ units together to form (Cs+)2(21C7)2(Na')2 as shown in
Figure 2-3. Even more surprisingly, the distance between the two Cs+

cations is only 5.283(4)A and the Na' anions and Cs+ cations form

Figure

l6

 

 

 

 

Figure 2-3. The molecular structure and the numbering of atoms

in (Cs+)2(21C7)2(Na‘)2.

17

 

 

 

 

 

 

Figure 2-4. Stereo packing diagram of (Cs+)2(21C7)2(Na’)2.

18

Table 2-2. selected bond distances and bond angles

for (Cs+)2(21C7)2(Na')2

 

 

 

 

Bond Length(A)
Csl-O7 3.25(3)
Csl-Oll6 3.47(3)
CsZ-O7 3.45(3)
CsZ-Oll6 3.13(3)

Bond angle Angle(degree)
O7-Csl-Oll6 73.9(7)
O7-CsZ-Ol 16 75.7(6)
Csl-O7-C52 104.1(8)

Csl-Oll6-C82 106.2(7)

 

19

IA.
\7/

u-

011“ “

Figure 2-5. ORTEP plot of selected atoms in (Cs+)2(2lC7)2(Na')2.

20

two cation-anion ion pairs on both sides of the molecule. The
distances from the Na' anions to the Cs+ cations are almost the same,
4.44(2)A and 4.52(3)A respectively. This is the only alkalide that has
two cation-anion ion pairs in one molecule with two closely
separated cations. Aside from these short Cs-Cs and Cs-Na distances
in the molecule, the shortest Cs-Cs, Cs-Na, and Na-Na distances in the
crystal structure are 8.904(4), 7.67(2), and 7.18(1)A respectively.
The bond distances of Csl-O7, Csl-Oll6, CsZ-O7, and CsZ-Oll6 are
325(3), 3.47(3), 3.45(3), and 3.13(3)A respectively and the bond
angles of O7-Csl-Oll6, O7-CsZ-Oll6, Csl-O7-CsZ, and Csl-Oll6-C52
are 73.9(7)°, 75.7(6)°, 104.2(8)°, and 106.2(7)° respectively. These
data are summarized in Table 2-2 and show that the four atoms
. formed a nearly symmetric parallelogram as shown in Figure 2-5.
The two cation-anion ion pairs are on both sides of the Cs+ cations to
give rather interesting twin ion pairs in the molecule.

This crystal belongs to the space group triclinic P1 and there is
only one molecule in the unit cell. This is the first alkalide without
any symmetry elements although most of the more than thirty
alkalides and electrides belong to low symmetry space groups. The
Csl-O distances range from 3.18(2) to 3.55(2)A with an average
distance of 3.34A and the CsZ-O distances range from 3.10(2) to
3.48(3)A with an average distance of 3.30A. The average distances of
3.34A for Csl-O and 3.30A for CsZ-O are very close to those in
Cs+(18C6)2Na'(3.36A)[7,52] and Cs+(18C6)2CS'(3.31A)[51], and
Cs+(l8C6)2e'(3.35A)[6]. The two Cs+ cations in the unit cell are
expected to be inequivalent because of their nonsymmetric positions

in the crystal structure, regardless of the difference between their

21

average Cs-O distances. In fact, static powder and magic angle sample
spinning NMR spectra in Figure 2-6 showed that there are two
distinct 133Cs peaks, at chemical shift values of +60ppm and
-28ppm, separated by 88ppm. The two 133Cs peaks are
temperature independent. The large separation between the two
peaks not only indicated the two Cs+ cations are asymmetric in the
molecule, but also confirmed that they are chemically inequivalent
because of differences in the Cs-O distances.

Perhaps the most interesting feature of this molecular
structure is the twin cation-anion ion pairs. Taking the effective
radius of Cs+ to be 1.69A[53] and that of Na' to be between 2.50 and
2.70A determined from the anionic cavity size in other sodides[7, 8,
51, 54], the separation between the Van der Waals surfaces of the
cation and anion is between 0.00 and 0.20A. It is remarkable that
the 23Na NMR and the optical absorption spectra of Na' show no
evidence of appreciable charge transfer to the cations in spite of the
close contact of the anions and the cations; that is, the optical and
NMR properties of Na' are the same as those for other sodides in
which Na“ is well isolated from the cations. The optical absorption
spectrum of Na' in (Cs+)2(21C7)2(Na')2 is shown in Figure 2-7. The
single absorption peak at approximately 650nm in the spectrum of
the thin film produced by solvent evaporation is attributed to the
electronic transition of Na' from the ground state, 3s2, to the excited
state, 3s3p. The two Na' anions in the molecule show no differences
in their optical properties and the absorption spectrum is very
similar to those of the typical Na' anions. The transition was

temperature independent from -120°C to -200C.

22

 

”W

 

YTI’VYVVIYY'YIY7YYIYTrYjY—YYYTVrfWIYYrYTTYYY'YYYIIYUIYTYYYTTVYY—YIVYYTT
600 500 400 300 200 100 0 -100 -300 -500 Dom

Figure 2-6. ‘33Cs static and MAS NMR spectra of (Cs+)2(21C7)2(Na')2
at -60°C; A) Static; B) MAS, f=3.6KHz; and C) MAS. f=5.0KI-IZ.

23

Figure 2-8 shows the 23Na static powder NMR spectrum of
(Cs+)2(21C7)2(Na')2. The spectrum has a single 23Na NMR peak at a
chemical shift value of -56.3ppm and shows no evidence of
difference between the two Na' cations. The chemical shift of
-56.3ppm is well within the range of typical Na' NMR spectra about
-60ppm in other sodides considering the rather broad half height
line width of 40ppm. Again, the chemical shift is temperature
independent. Both the optical and NMR properties of Na' in
(Cs+)2(21C7)2(Na')2 indeed show no evidence of charge transfer
from the anion to the cation, similar to the results obtained with
M+(HMHCY)Na', which also contains ion pairs for M=K, Rb, and Cs[55].

The stability of this compound is of interest because of the
large size of the complexant. According to Pedersen and Izatt[56-58],
the cation radius and cavity size of the complexant are the most
important factors which determine the stability of the complex. The
difficulties encountered while trying to grow good quality crystals
and to refine the crystal structure indicated that there is some kind
of disorder in the crystal structure that was probably caused by
thermal motion or packing disorder of the crown ethers during the
crystallization. These effects are probably caused by the flexible
nature of the crown ether and its large cavity size compared to the
Cs+ cation radius. All crown ether atoms had to be refined
isotropically because of this kind of disorder. This does not
necessarily mean that this complex is unstable, but rather that a
variety of crown ether conformations can be accommodated. DSC
studies indicated that, at a ramping rate of SOC/min, this compound

decomposes at about 120°C with a AH value of -l68kJ/mole.

24

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Tcnpernture(°C)

Figure 2-9. Differential Scanning Calorimetry trace of

(Cs+)2(21C7)3(Na')3 at a ramping rate of SOC/min.

200

27

(Cs+)2(21C7)2(Na')2 also undergoes an irreversible endothermic
transition with a AH value of about 5kJ/mole at about 68°C before
decomposition. The cause of the transition is not known, although it
could be due to decomplexation. The DSC trace of (Cs+)2(21C7)2(Na'
)2 is shown in Figure 2-9. The absence of low tempareture peaks due
to decomplexation and the high decomposition temperature show
that (Cs+)2(21C7)2(Na')2 is rather stable in the solid state, although
it decomplexes even at -490C in solution.

The stability of this compound may be attributed to the
extensive coordination of the Cs+ cations to the complexants and to
the presence of cation-anion contact ion pairs. These unusual
features show that the Cs+ cations are well coordinated, leaving no
open space around the Cs+ cations, which in turn stabilizes the
complex. In solution, the Cs-O bond formed between a Cs+ cation and
the oxygen atom from the second 21-crown-7 might be easily
dissociated to form two Cs+(21C7)Na' molecules. Another possibility
is that the cation-anion ion pairs might not be as stable as in the
solid state.

EPR studies of this compound, being carried out by K. Reidy-
Cedergren and Dr. J. McCracken of Michigan State University, are
being used to determine the interactions of defect electrons trapped

at the Na' positions with nearby Cs+ cations and other nuclei[59].

III.B. (K+)2(21C7)3(MeNH2)(Na')2

In contrast to Cs+(2lC7)Na’, this compound is much more

stable in solution. Single crystals of (K+)2(21C7)3(MeNH2)(Na')2

28

were grown by using the temperature-scanning technique. The
temperature scan range was set from -45°C to -700C at a scan rate of
1°C/hour. Methylamine and diethyl ether were used as first and
second solvents. The crystals were shiny brown in color.

The single crystal used for the X-ray study had the
approximate dimensions of 0.25x0.4x0.7 mm3. The unit cell
parameters and orientation matrix were determined by least squares
from the setting angles of 46 reflections in the range of 4°<20<20°.
The space group of the crystal is monoclinic P21/n with 2:4 and the
cell parameters are a=9.140(3), b=36.574(8), c=l9.475(5), and
B=94.630(23)°. These yield a calculated cell volume of
6489.0(5.4)A3. The crystal was kept at -80°C throughout the entire
data collection. Intensity data were collected by using the 6-20 scan
method at 4°/min.(in 26) with minimum 26-1350 and maximum
29:450. A linear decay correction was based on the intensities of
three standard reflections measured for every 100 reflections. The
number of reflections measured was 9634 and the number of
reflections used in refinement was 3443 with a data cut-off of I>3
sigma(o). The crystal structure was solved by using direct methods
with the Texsan Program. Hydrogen atoms were constrained to ride
on their bonded C-atoms with fixed isotropic thermal parameters.
The R factors were R=0.102 and Rw=0.052 with R defined as (ZIIFOI-
ch||)/2|Fol. Peak heights in the final difference map ranged from
-0.46 to 0.86 e/A3. The molecular structure and numbering of the
atoms are shown in Figure 2-10 and the stereo packing diagram is
shown in Figure 2-11. The positional parameters, bond distances, and

bond angles are given in Tables A-4, A-5, and A-6 in Appendix A.

29

Table 2-3. Summary of Crystallographic Data for
(K+)2(21C7)3(M6NH2)(Na')2

 

Space Group Monoclinic P21/n

Cell Parameters a=9.140(3)A, b=36.574(8)A, c=l9.475(5)A,
B=94.630(23)°

Volume 6489.0(5.4)A3

z 4

R factors R=0.102, Rw=0.052

d 1.131g/em3

 

This is another unusual crystal structure. In this compound,
there is a third 21-crown-7 that serves as a bridge that connects the
two K+ ions in the molecule, while a solvent molecule, MeNHz, forms
a bond to one of the two K+ cations. The two K+ cations in the
molecule have completely different coordination features. One is
coordinated by all seven oxygen atoms from a 21-crown-7 and an
eighth oxygen atom from the third 21-crown-7, giving it a
coordination number of eight. By contrast, the other K+ ion is
coordinated by only five of the seven oxygen atoms from a second
21-crown-7 and one from the third 21-crown-7. It is also bonded to
a solvent molecule, MeNHz. This gives the second K+ ion a total
coordination number of seven. These two K+ cations, therefore, are
clearly chemically inequivalent. The K1-K2 distance within the

molecule is 9.985(7)A, while the shortest K-K, K-Na, and Na-Na

30

.NA-aZXm:ZoEVm:U_Nvmfbc E

2:35 .3 wctoczsc 2: ES 222:; 3:522: 2:. .c_-~ Eswi

 

31

 

 

 

 

 

Figure 2-11. Stereo packing diagram of (K+)2(21C7)3(MeNH2)(Na')2.

32

distances in the crystal structure are 8.819(7), 6.41(1), and 8.21(1)A
respectively. The Kl-O bond distances range from 2.84(1) to
3.12(1)A with an average bond distance of 2.93A. The K2-O bond
distances range from 2.92(2) to 3.05(4)A with an average bond
distance of 2.98A. These average K+-O distances are very close to
those in K+(l8C6)(12C4)Na'(2.98A), K+(18C6)(12C4)K’(2.99A), and
K+(18C6)(l2C4)K'(18C6)(3.02A)[32], but are slightly longer that
those in K+(C222)Na'(2.82A) and K+(C222)e'(2.83A)[51]. The K-N
bond distance is 2.94(2)A. The distances between K2 and 0213 and
0216 are 3.45(4)A and 3.64(3)A respectively, indicating that these
two oxygen atoms are too far away from the K+ cation to form bonds
between them. This type of crystal structure is very unusual because
the second K+ cation does not have the same surroundings and
coordination number as does the first K+ cation on the other side of
the molecule, even though there could be similar conditions for the
K+ ion to do so. In the first structure determination, the results for a
crystal that was grown by the temperature-scanning technique with
a scan range from -32°C to -70°C showed that all atoms except those
in the second 21-crown-7 could be well refined. The second set of
crystals was grown with a temperature scan range from -45°C to
-70°C, and the temperature for the entire X-ray diffraction data
collection was also lowered to -80°C, in the hope that this would
reduce the disorder due to thermal motion. However, the results
were exactly the same as those obtained the first time. This indicated
that the temperatures for crystal growth and data collection were not
the cause of the disorder problem. It might be attributed to

disordered packing of the second 21-crown-7 because the

ull

CI“

We

11.

33

coordination number between the K+ ion and 21-crown-7 is only
five, leaving part of the crown ether free and more flexible.

The optical absorption spectrum of this compound is shown in
Figure 2-12. The single absorption peak at approximately 690nm is
typical for Na' anions. The NMR spectrum in Figure 2-13 has a single
23Na NMR peak at -60.80ppm. Both optical and NMR spectra
indicated that this compound is a typical sodide and there is no

observable difference between the two Na' anions in

(K+)2(21C7)3(MeNH2)(Na')2. The 39K solid state NMR peaks of
(K+)2(21C7)3(MeNH2)(Na‘)2. could not be observed because of the
expected large second order quadrupolar coupling. This would
broaden the NMR lines greatly and bury them into the base line. This
large second order quadrupolar coupling can be attributed to the
large quadrupole moment of potassium and the very asymmetric
interaction between the K+ cations and their surroundings.

The DSC trace of (K'*')2(21C7)3(MeNH2)(Na')2 in Figure 2-14
shows that this compound decomposed at about 65°C with AH:-
233kJ/mole at a ramping rate of SOC/min. There was no sign of K-N
bond dissociation between the solvent molecule, MeNH2 and the K+
cation even when temperature reached the decomposition point. This
indicated that the K-N bond is rather strong.

The disorder problem was believed to be caused by the
unusual stereo-coordination nature of the second K+ cation and 21-
crown-7 and the presence of a coordinated solvent molecule.
Therefore, attempts to synthesize and to crystallize K-(21C7) sodide
were carried out with dimethyl ether as a first solvent instead of

MeNHz, in the hope that the second K‘l' and 21-crown-7 would be

34

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Temperature ('C)

Figure 2-14. Differential Scanning Calorimetry trace of

(.K+)2(21C7)3(MeNH2)(Na')2 at a ramping rate of SOC/min.

37

forced to coordinate to each other in a similar fashion to that of the
first K+ and 21-crown-7, because the K-N bond would no longer be
available for coordination. Unfortunately, only powder samples were

obtained when dimethyl ether was used as the first solvent.

III.C. K+(dicyclohexano-24C8)Na'

K+(dicyclohexano-24C8)Na' is the only alkalide complexed by a
crown ether as large as 24-crown-8 that could be crystallized.
Crystals were obtained by using the temperature-scanning
technique. The temperature scan range was set from -40°C to -70°C
at a scan rate of 1°C/hour. Methylamine and diethyl ether were the
solvents for synthesis and crystal growth. The crystals were golden
in color.

The single crystal used for the X-ray study had the
approximate dimensions of 0.2x0.4x0.8 mm3. The unit cell
parameters and orientation matrix were determined by least squares
from the setting angles of 32 reflections in the range of 4°<20<20°.
The space group of the crystal is orthorhombic P21212 with 2:4 and
the cell parameters are a=10.439(5), b=10.954(7), and c=27.773(13).
These yield a calculated cell volume of 3175.8(5.0)A3. The crystal
was kept at -70°C throughout the entire data collection. Intensity
data were collected by using the 0-26 scan method at 2°/min.(in 29)
with minimum 29:3.50 and maximum 29:450. A linear decay
correction was based on the intensities of three standard reflections
measured for every 100 reflections. The number of reflections

measured was 1285 and the number of reflections used in

38

Table 2-4. Summary of Crystallographic Data for

K+(dicyclohexano-24C8)Na'

 

Space Group

Cell Parameters

Volume
Z

R factors

(1

Orthorhombic P21212
a=10.439(5)A, b=10.954(7)A,
c=27.773(13)A,
3175.8(5.0)A3

4
R=0.147, Rw=0.067
1.093g/cm3

 

39

refinement was 272 with a data cut-off of I>3 sigma(o). The crystal
structure was solved by using direct methods with the Texsan
Program. Hydrogen atoms were constrained to ride on their bonded
C-atoms with fixed isotropic thermal parameters. The R factors were
R=0.147 and Rw=0.067 with R defined as (XIIFol-IFCIWXIFOI. Peak
heights in the final difference map ranged-from -0.73 to 0.79 e/A3.
The molecular structure and numbering of the atoms are shown in
Figure 2-15 and the stereo packing diagram is shown in Figure 2-16.
The positional parameters, bond distances, and bond angles are given
in Tables A-7, A-8, and A-9 in Appendix A.

It was thought that a dicyclohexano-24-crown-8 molecule
might be able to complex two K+ cations because this crown ether has
a large size compared to that of K+. But the single crystal X-ray
diffraction study showed that this compound has a 1:1 ratio of K+ to
dicyclohexano-24-crown-8. Because of the mismatch of sizes
between dicyclohexano-24-crown-8 and K+ cation, the crown ether
twists around the K+ in order to have all eight oxygen atoms form
bonds to the cation. Despite the twist of dicyclohexano-24-crown-8
around the potassium cation and the flexibility of its two six-carbon
member rings, which could let any possible symmetry within the
molecule disappear, only one half of the crown ether is
crystallographically unique and both the cations and the anions are
in special positions. It is also interesting to note that there are two
types of crystallographically non-equivalent molecules in the unit
cell while only one half of each of the two inequivalent molecules is
crystallographically unique. The Kl-O distances range from 2.71(3) to
2.83(2)A with an average distance of 2.79A and K2-O distances range

40

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42

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Temperature ('0

Figure 2-19. Differential Scanning Calorimetry trace of

K+(dicyclohexano-24C8)Na‘ at a ramping rate of SOC/min.

45

from 2.81(3) to 2.92(3)A with an average distance of 2.86A. These
average K+-O distances are close to those in K+(C222)I‘(2.79A)[60],
K+(c222)Na-(2.82A), and K+(C222)e'(2.83A)[51], but are shorter than
those in K+(l8C6)(12C4)Na'(2.98A), and K+(18C6)(12C4)K'
(2.99A)[32].

The optical absorption and 23Na solid state NMR spectra of
K+(dicyclohexano-24C8)Na' are given in Figure 2-17 and Figure 2-18.
The absorption peak is at about 700nm and the 23Na NMR peak is at
-6l.22ppm. These results indicated that K+(dicyclohexano-24C8)Na‘
is a typical sodide. The 39K solid state NMR spectrum could not be
obtained because of the large second order quadrupolar coupling as
was the case for (K+)2(21C7)3(MeNH2)(Na')2. The DSC studies of this
compound showed decomposition at about 55°C with AH=-72kJ/mole
at a ramping rate of 5°C/min. An irreversible endothermic transition
at about -5°C was also observed. The cause of this transition is
unclear, but it could be due to decomplexation or melting. The DSC

trace of this compound is shown in Figure 2-19.

III.D. Rb+(21C7)Na' and Five Other Sodides

It took several attempts to get single crystals of Rb+(21C7)Na"
for single crystal X-ray structure determination. Methylamine and
diethyl ether were used as the solvents. Crystals were grown by the
temperature-scanning technique with a scan range set from -45°C to
-70°C. The crystals are golden in color.

The single crystal used for X-ray study had the approximate

dimensions of 0.15x0.30x0.40 mm3. The unit cell parameters and

46

orientation matrix were determined by least squares from the
setting angles of 44 reflections in the range of 4°<29<20°. The space
group of the crystal is monoclinic C2/c and the cell parameters are
a=16.832(4), b=15.205(4), c=25.362(5), and B=91.262(16)° with cell
volume of 6489.2(2.6)A3. The crystal was kept at -80°C throughout
the entire data collection. Intensity data were collected by using the
9-20 scan method at 4°/min.(in 26) with minimum 29=3.5° and
maximum 20=45°. A linear decay correction was based on the
intensities of three standard reflections measured for every 150
reflections. The number of reflections measured was 9434 and the
number of reflections used in refinement was 2404 with a data cut-
off of I>3 sigma(o). Direct methods with the Texsan Program was
used in the attempt to solve the crystal structure. Unfortunately, the
complete crystal structure could not be solved in this case, probably
because of the disorder problem.

No crystalline sodide could be made with Cs+(dicyclohexano-
30C10). This compound appeared to be an amorphous material in the
solid state at temperatures below -30°C. At higher temperature, it
became a sticky blue-brown liquid and could even flow inside the K-
cell. When it was cooled to below -30°C, a brown solid was formed
again. After this attempt, four more sodides were made with Rb+ and
Cs+(dicyclohexano-24C4) and K+ and Rb+(dicyclohexano-30C10) in
order to obtain a more systematic idea about these large crown ether
complexes. Methylamine and diethyl ether were used as solvents for
synthesis. As with the sodide of Cs+(dicyclohexano-30C10), K+ and
Rb+(dicyclohexano-30C10) sodides are amorphous-like solid

compounds at low temperature and sticky liquids at higher

47

temperature. The two other sodides made with Rb+(dicyclohexano-
24C8) and Cs+(dicyclohexano-24C8) seem to be very 'soft' solids and
could become very sticky liquid-like compounds at higher
temperature, but DSC studies show that both of them undergo
irreversible transitions at -7°C and -9°C respectively, and no melting
processes were observed up to the decomposition temperature. The
DSC results of all six sodides are summarized in Table 2-5.

Attempts to crystallize these compounds failed, probably
because they are too 'soft' and disordered because of the flexible
nature of the large crown ethers. It seems that the larger the crown
ether, the more flexible it is. Consequently, the alkalide made with it
will be 'softer'.

Since no crystal structures were obtained for these six sodides,
methylamine tests were performed to determine if solvent molecules
were present in the complexes. The testing method has been
described in detail elsewhere[49]. The testing results indicated that
methylamine was not present in any one of the six complexes. 23Na
solid state NMR experiments showed that all six compounds are
sodides with 23Na NMR peaks at about -60ppm. 133Cs solid state
NMR spectra of the sodides of Cs+(dicyclohexano-24C8) and
Cs+(dicyclohexano-30C10) are shown in Figure 2-20. and their 133Cs
chemical shift values are summarized in Table 2—6. The wide range
of chemical shift values of these Cs+-large crown ether complexes is
indicative of differences in their Cs-O coordination numbers and

distances.

48

Table 2-5. Summary of thermal processes that occur in the DSC
traces with a heating rate of SOC/min. in 0C.

 

 

Compound M.P. or Decomposition
Phase Change Temperature
(K+)2(21C7)3(MeNH2)(Na')2 -- 65
Rb+(2 1C7)Na' -- 87
(Cs+)2(21C7)2(Na')2 68 120
K+(Di-24C8)Na' -5 55
Rb+(Di-24C8)Na" -7 S4
Cs+(Di-24C8)Na' -9 60
K+(Di-30C10)Na' -25 65
Rb+(Di-30C10)Na' -28 70
Cs+(Di-30C10)Na' -30 67

 

Table 2-6. 133Cs NMR chemical shifts of the complexed
cations in three sodides.

 

 

compound Chemical shift(ppm)
(Cs+)2(21C7)2(Na')2 +60, -28
Cs+(Di-24C8)Na' -83

Cs+(Di-3OC10)Na' -174

 

49

(Cs+)2(21C7)2(Na')2

Cs+(dicyclohexano-24C8)Na'

Cs+(dicyclohexano-30C10)Na‘

 

 

 

600 500 400 300 200 $00 0 -100 '300 '500 I“

Figure 2-20. 133Cs static NMR spectra of three alkalides.

50

III.E. Rb+(18C6)(12C4)Na' and Rb+(18C6)(12C4)Rb'

The synthesis of these two mixed sandwich complexes followed
the same procedures used for the synthesis of normal sandwich
compounds[4-5], but 18-crown-6 and lZ-crown-4 were used in a 1:1
molar ratio. The K-cell used for the synthesis had to be cooled during
evacuation to prevent loss of the more volatile 12-crown-4.

Rb+(18C6)(12C4)Na' can be synthesized with the solvent
combination of dimethyl ether or methylamine together with either
diethyl ether or trimethylamine. Beautiful prism-shaped crystals
were obtained with dimethyl ether and diethyl ether as solvents. The
temperature scan range was set from -35°C to -70°C to grow crystals
by using temperature-scanning method at a scan rate of 1°Clhour.
The crystals are bright green in color. A very difficult problem of
disorder was encountered during the refinement when crystals
grown with dimethyl ether as first solvent were used for the single
crystal X-ray diffraction studies. In order to obtain better quality
crystals, methylamine was used instead of dimethyl ether. Large size
crystals with approximate dimensions of 5x5 x5 mm3 or larger could
be obtained with methylamine and diethyl ether as solvents and by
using the temperature-scanning method with a scan range from
-35°C to ~70°C. The temperature scan range was set from -45°C to
-63°C to grow smaller size crystals for the single crystal X-ray
diffraction studies. The crystals appeared to be rod-shaped and
green in color when methylamine was used as first solvent. The

single crystal X-ray diffraction studies proved methylamine to be

51

indeed a better solvent for growing better quality crystals of
Rb+(18C6)(12C4)Na’.

The single crystal used for X-ray diffraction study of
Rb+(18C6)(12C4)Na' had the dimensions of 0.4x0.4x0.5 mm3. The
unit cell parameters and orientation matrix were determined by
least squares from the setting angles of 34 reflections in the range of
3.5°<26<22°. The space group of the crystal is orthorhombic ana
with 2:4 and the cell parameters are a=13.989(5), b=13.677(14), and
c=16.683(5). These yield a calculated cell volume of 3191.9(5.4)A3.
The crystal was kept at -90°C throughout the entire data collection.
Intensity data were collected by using the 9-20 scan method at
4°/min.(in 20) with minimum 26:3.5° and maximum 26:450. A
linear decay correction was based on the intensities of three
standard reflections measured for every 200 reflections. The number
of reflections measured was 9170 and the number of reflections used
in refinement was 2060 with a data cut-off of I>3 sigma(o). The
crystal structure was solved by using direct methods with the Texsan
Program. Hydrogen atoms were constrained to ride on their bonded
C-atoms with fixed isotropic thermal parameters. The R factors were
R=0.072 and Rw=0.050 with R defined as (leFol-IFCIIVZIFOI. Peak
heights in the final difference map ranged from -0.67 to 0.66 e/A3.
The molecular structure and numbering of the atoms are shown in
Figure 2-21 and the stereo packing diagram is shown in Figure 2-22.
A summary of crystallographic data for Rb+(18C6)(12C4)Na' is given
in Table 2-7. The positional parameters, bond distances, and bond

angles are given in Tables A-10, A-11, and A-12 in Appendix A.

52

The carbon atoms on 12-crown-4 were found to have large
temperature factors during the refinement. It was caused primarily
by the apparent mirror symmetry of the space group, ana. The 12-
crown-4 molecule does not usually possess mirror symmetry. The
oxygen atoms of the 12-crown-4 molecule were refined well with
normal temperature factors, indicating that they are well described
by the mirror symmetry. But the carbon atoms of the 12-crown-4
must be divided into two configurations which are mirror images of
each other. Therefore, these carbon atoms were refined isotropically
with disorder, resulting in much lower temperature factors. The Rb+
cation is 1.24A out of the least-squares plane of the six oxygen atoms
of l8-crown-6 and 2.30A out of the plane of the four oxygen atoms
of 12-crown-4. The Rb+-O distances range from 2.969(9) to
3.101(8)A with an average distance of 3.038A for the oxygen atoms
of the l8-crown-6 and are 2.988(6) and 3.128(7)A with an average
distance of 3.058A for the oxygen atoms of the 12-crown-4. The
shortest Na'-Na' and Na'-Rb+ distances in the crystal are 7.891(7)
and 7.960(7)A respectively, indicating that Na“ is well isolated from
other Na' anions and Rb+ cations. The bond distances and angles for
the atoms of 18-crown-6 are well within the normal values, but
those of 12-crown-4 deviate substantially from normal, probably
due to the disorder. In contrast to those of the 18-crown-6
configuration, in which the oxygen and carbon atoms alternate on
both sides of the least-squares plane of the six oxygen atoms, the
carbon atoms of 12-crown-4 are all on one side of the plane of the

four oxygen atoms, away from the Rb+.

53

 

 

Figure 2-21. The molecular structure and the numbering of atoms

in Rb+(18C6)(12C4)Na'.

54

 

 

 

 

T

 

 

 

 

 

 

 

 

 

 

Fi - ' '
gure 2 22. Stereo packing diagram of Rb+(18C6)(12C4)Na'

55

Table 2-7. Summary of Crystallographic Data for
Rb+(18C6)(12C4)Na’(I) and Rb+(18C6)(12C4)Rb'(II)

 

 

I 11
Space Group Orthorhombic ana Orthorhombic ana
Cell Parameters
a(A) 13.989(5) 14.06300)
b(A) 13.677(14) 14.16700)
c(A) 16.683(5) 17.03000)
Volume(A3) 3191.9(54) 3392.9(6.6)
z 4 4
R 0.072 0.059
Rw 0.050 0.031

d 1.142g/cm3 1.197g/cm3

 

56

Dimethyl ether and diethyl ether were used for the synthesis
and crystal growth of Rb+(l8C6)(12C4)Rb‘. Crystals were grown by
the temperature-scanning method with a scan range from ~35°C to
~70°C at a scan rate of 1°Clhour. The crystals appeared to be rod-
shaped and golden in color.

The single crystal used for the X-ray diffraction study of
Rb+(l8C6)(12C4)Rb' had the approximate dimensions of 0.3x0.4x0.5
mm3. The unit cell parameters and orientation matrix were
determined by least squares from the setting angles of 20 reflections
in the range of' 3.5°<26<22°. The space group of the crystal is
orthorhombic ana with Z=4 and the cell parameters are
a=l4.063(10), b=14.167(10), and c=l7.030(10). These yield a
calculated cell volume of 3392.9(6.6)A3. The crystal was kept at
-90°C throughout the entire data collection. Intensity data were
collected by using the 6-26 scan method at 4°/min.(in 26) with
minimum 26=3.5° and maximum 26:450. A linear decay correction
was based on the intensities of three standard reflections measured
for every 150 reflections. The number of reflections measured was
3471 and the number of reflections used in refinement was 1135
with a data cut-off of I>3 sigma(o). The crystal structure was solved
by using direct methods with the Texsan Program. Hydrogen atoms
were constrained to ride on their bonded C-atoms with fixed
isotropic thermal parameters. The R factors were R=0.059 and
Rw=0.031 with R defined as (ZIIFOI-IFcll)/2|Fol. Peak heights in the
final difference map ranged from -0.47 to 0.47 e/A3. The molecular
structure and numbering of the atoms are shown in Figure 2-23 and

the stereo packing diagram is shown in Figure 2-24. The positional

57

parameters, bond distances, and bond angles are given in Tables A-
13, A—11, and A-12 in Appendix A.

This mixed sandwich compound, Rb+(l8C6)(12C4)Rb', is
isostructural with Rb+(l8C6)(12C4)Na‘. Again the refinement was
performed with disorder of the carbon atoms of 12-crown-4 and
they were refined isotropically. The location and coordination of the
complexed Rb+ cation in this compound is very similar to that in
Rb+(18C6)(12C4)Na'. The Rb+ cation is 1.2021 out of the 18-crown-6
oxygen plane and 2.30A out of the plane of the 12-crown-4 oxygen
atoms, with oxygen and carbon atoms of the l8-crown-6 ring
alternately above and below the plane. All carbons of 12-crown-4
are on one side of the plane of the four oxygen atoms, staying away
from the Rb+ cation. The Rb+-O distances range from 2.98(2) to
3.08(1)A with an average distance of 3.03A for the oxygen atoms of
the l8-crown-6 and are 2.964(7) and 3.155(9)A with an average
distance of 3.060A for the oxygen atoms of the 12-crown-4. The
shortest Rb'-Rb' and Rb'-Rb+ distances in the crystal are 7.843(5)
and 8.166(5)A respectively, indicating that Rb' is well isolated from
other Rb“ anions and Rb+ cations. The bond distances and angles for
atoms of 18-crown-6 are well within the normal values, but those of
12-crown-4 deviate substantially from normal.

These two compounds were synthesized and characterized
following the synthesis of the Cs-18C6-15C5 and K-l8C6-12C4
systems. Rb+(l8C6)(12C4)Na' is thermodynamically more stable than
its 'parent' compounds, Rb+(12C4)2Na’ and Rb+(18C6)Na'(MeNH2).
Rb+(12C4)2Na' hardly exists in solid state and easily decomplexes in

solution at higher temperature. In fact, several attempts to

58

 

Figure 2-23. The molecular structure and the numbering of atoms

in Rb+(l8C6)(12C4)Rb‘.

59

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2-24. Stereo packing diagram of Rb+(18C6)(12C4)Rb'.

60

crystallize Rb+(12C4)2Na' failed, simply because it is very unstable
when the solvent is removed. Another 'parent' compound,
Rb+(18C6)Na'(MeNH2), crystallizes with a solvent molecule, MeNHz,
on one side of the 18-crown-6, while the Rb+ cation sits in the cavity
of the 18-crown-6. Na' anion also forms cation-anion ion pairs with
Rb+ on the same side as the solvent molecule is. Apparently, the
solvent molecule and cation-anion ion pair formation are necessary
in the crystal in order to stabilize the complexed Rb+(18C6) cation.
Examples of the sandwich complexed ion Rb+(l8C6)2 are not known.
By contrast, the mixed sandwich complex Rb+(18C6)(12C4)Na‘ is well
coordinated by the 18-crown-6 and 12-crown-4 molecules. The Rb+
ion resides in the cavity formed between the 18-crown-6 and 12-
crown-4. No solvent molecule or cation-anion ion pair is needed for
coordination.

Rb+(18C6)(12C4)Rb' is isostructural with Rb+(l8C6)(12C4)Na‘.
One of its 'parent' compounds, Rb+(18C6)Rb' has cation-anion ion
pairs to better coordinate the Rb+ while the other 'parent' compound,
Rb+(12C4)2Rb', has not been synthesized.

Two features of these two mixed sandwich complexes increase
the interest in their study. First, is the pronounced green color of
Rb+(l8C6)(12C4)Na‘ which prompted the study of its optical
spectrum. Second, solid state 37Rb NMR spectra of the two
compounds showed that the NMR line shapes of the Rb+ cations in
both compounds are very similar and their line widths are very
narrow compared to those of other Rb‘l‘ alkalides. The 23Na NMR
spectrum of Rb+(18C6)(12C4)Na' is shown in Figure 2-25. This
spectrum has a single 23Na NMR peak at -61.24ppm, indicating that

v

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61

it is indeed a sodide although this compound appeared to be green in
color. Figure 226 shows the 87Rb NMR spectra obtained by the solid
state spin-echo technique for both compounds. The half-height line
width is less than 200ppm for Rb+ in both mixed sandwich
compounds in contrast to values of about 1000ppm for Rb+ cations in
Rb+(18C6)Na'(MeNH2) and Rb+(18C6)Rb'[49]. The chemical shift
value of Rb' in Rb+(l8C6)(12C4)Rb' is -203ppm, a typical value for
an isolated Rb' in alkalides, while that of Rb' in Rb+(18C6)Rb‘ is
paramagneticly shifted about 70ppm. It was suggested that Rb+
cations in Rb+(l8C6)Rb' or Rb+(18C6)Na‘(MeNH2) are in a very non-
symmetric environment, and are strongly coupled to Rb‘ or Na' due
to the cation-anion ion pairs. In addition, the paramagnetic shift of
Rb' in Rb+(18C6)Rb' was suggested to be caused by some degree of
overlap of the p and d orbitals on the anion with its
surroundings[49]. By contrast to these compounds, Rb+ cations in
both mixed sandwich compounds sit in a more symmetric
environment and cations and anions are well isolated from each
other so that the dominant second order quadrupolar broadened
NMR lines of Rb+ are quite narrow and NMR peaks of the anions are
in the typical chemical shift value ranges for the Rb' and Na' in
alkalides. It is interesting to see that the NMR line shapes, shown in
Figure 2-27 and Figure 2-28, of Rb+ in both compounds show a
pattern of decreasing asymmetry parameter, 1], with increasing
temperature, indicating an approach to axial symmetry. This pattern
can be compared to the computer simulated static second order
quadrupolar line shapes for the central transition of a quadrupolar

nucleus in Figure 2-29[9]. The line shape change with temperature

62

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63

 

 

 

 

 

Rb'
Rb+
A
Rb+
B
“m -i‘i‘t‘. ............. -
f; 000 ‘00 £0 20'!) 100 0 -100 -200 -300 «00 -500 -600 no.

Figure 2-26. 87Rb NMR spectra of A) Rb+(l8C6)(12C4)Rb‘ and
B) Rb+(l8C6)(12C4)Na', obtained with a solid'state spin-echo
pulse sequence. Note that NMR peaks for both Rb+ and Rb' in
Rb+(l8C6)(12C4)Rb’ were observed.

64

suggests that as the temperature increases, thermal motion of
vibration or even hopping[61] of the crown ethers which are locked
in position at low temperature in the crystal also increases. The
thermal motion is eventually so fast at higher temperature that the
asymmetry parameter is reduced greatly, indicating that the Rb+
cations are approaching a thermally-averaged axially-symmetric
environment.

The optical absorption spectra of solvent—evaporated films of
Rb+(18C6)(12C4)Na' and Rb+(18C6)(12C4)Rb‘ are shown in Figure 2-
30 and Figure 2-31. In general, Na' in sodides has a single absorption
peak at 640nm which is attributed to the electron transition of Na'
from 3s2 to 353p. By contrast, the absorption spectrum of
Rb+(18C6)(12C4)Na’ shows two peaks, at 550nm and 780nm
respectively, one red-shifted by about 140nm and the other blue
shifted by 90nm from the usual position. These spectra explain why
Rb+(l8C6)(12C4)Na' has a beautiful green color while other sodides
generally are shiny brown, golden or reddish in color. The origin of
these shifts is not known. It should be noted that the similar
compound, K+(18C6)(12C4)Na', which is isostructural with
Rb+(l8C6)(12C4)Na’, is also green in color and has a similar optical
absorption spectrum[62]. Another compound, Cs+(18C6)(12C4)Na'
which can be synthesized in MeNHz» solvent with exact 1:1 molar
ratio of 18-crown-6 to 12-crown-4, also appears to be green in color
as a 'wet' film, but it decomplexes when the solvent is removed.
Nevertheless, sodides made with M-18C6-12C4(M=Cs+, Rb+, and K+)
seem to be green in color, while their 'parent' compounds,
Cs+(l8C6)2Na', Rb+(18C6)Na’(MeNH2), and K+(18C6)Na'(MeNH2)2 or

65

v—v vvvvvvvvvvvvvvvvvvvvv
'V‘V' ' vvvvv T vvvv 77" 7" vavvvv—v va vvv‘vy—v 'vr vvvv

Figure 2-27. Temperature dependence of the NMR line shapes of
the Rb+ ions in Rb+(l8C6)(12C4)Na'. A) -100°C; B) -80°C; C) -60°C;
D) 40°C; and E) -20°C.

66

 

 

 

 

A LJL

/

l
l

.111 . ’

v v v v V v " v
. - -.

 

 

 

 

Figure 2-28. Temperature dependence of the NMR line shapes of
the Rb‘l’ ions in Rb+(18C6)(12C4)Rb‘. A) 400°C; B) -80°C; C) -60°C;
D) 40°C; and E) -20°C.

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Figure 2-29. Computer simulated static second order quadrupolar

line shapes for the central transition of a quadrupolar nucleus.

68

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70

another mixed sandwich compound Cs+(18C6)(15C5)Na' are reddish
or golden in color. The optical absorption spectrum of
Rb+(18C6)(12C4)Rb’ has three absorption peaks at 660, 750, and
1150nm respectively. It is, however, unclear what causes these

absorption peaks.

CHAPTER 3. SOLUTION NMR STUDIES OF COMPLEXED Cs+
IONS WITH MIXED CROWN ETHERS

I. Introduction

Since the macrocyclic crown ethers are capable of forming
stable and selective complexes with alkali and alkaline earth metal
ions[56], the studies of these complexants and their complexes have
become an important research area in science. During the past two
decades, one of the most exciting results from the studies of crown
ethers is the discovery of two new classes of compounds, the
alkalides and electrides. In addition, intensive efforts have been
undertaken to understand the factors that control the
thermodynamic and kinetic stability and the selectivity of these
complexes[63-66].

One of the interesting features of crown ethers, as two
dimensional macrocyclic complexants, is their ability to form
2:1(complexant to metal) sandwich complexes. Evidence for the
formation of such sandwich complexes both in solution[67-69] and in
the solid state[70-7l] has been reported. Recently, five alkalides, one
electride, and one model salt with mixed crown ethers as
complexants have been synthesized, and their crystal structures
have been determined[32]. After the discovery of these mixed
sandwich compounds, it was of interest to study the possibility of the
formation of such mixed sandwich complexes with alkali metal ions

in solution. It was also of interest to study the stability of the mixed

71

fl

61.

72

sandwich complexes and their 'parent' compounds in solution.
Information on the relative stabilities of these complexes may be
useful as a guideline for the synthesis of other mixed sandwich
alkalides and electrides.

The use of nuclear magnetic resonance has long been popular
in the studies of complexation in electrolyte solutions because of the
presence of extremely rapid and generally random molecular
motions. These molecular motions can result in narrow resonance
lines, even for nuclei with quadrupole moments. Moreover, the
resonance frequencies of metal ions are very sensitive to their
chemical environment. Therefore, ion-ion, ion-complexant, and ion-

solvent interactions can be easily studied by NMR techniques.

II. Experimental

The solution NMR studies were done in collaboration with
Professor Mojtaba Shamsipur during his sabbatical leave from Shiraz
University, Iran.

12-crown-4, 15-crown-5, 18-crown-6, and HMHCY were
obtained from Aldrich and all complexants were purified and stored
in a He filled dry-box for use in the synthesis of alkalides and
electrides. These complexants were removed from the dry-box and
used for solution NMR studies without further purification. CsSCN
was obtained from Pfaltz and Bauer and nitromethane was obtained
from EM Science. They were purified and dried as described

elsewhere[72-74].

73

133CS NMR measurements were carried out on a Varian VXR-
300 NMR spectrometer equipped with a variable temperature
controller.

All chemical shifts were measured at 25.0i0.l°C and were
calibrated with 0.5M CsBr in D20 as an external reference during
measurement. However, all data reported in this thesis are
ultimately referenced to the infinitely dilute Cs+ ion in water at 25°C.
The chemical shift of the Cs+ ion at infinite dilution was obtained by
extrapolation of plots of the chemical shift vs. concentration. All data
are also corrected for differences in bulk diamagnetic susceptibility
between sample and reference according to the following

equation[75]

4
8cm: = 80b; + Tn (Xref ' Xsample)
(3 - 1)

where Xref and xsample are the volumetric susceptibility of the
reference and sample solvents, respectively and 801,3 and 8cm, are
the observed and corrected chemical shifts, respectively.

The formation constants of ion pairs and complexes were
obtained by computer fitting of the experimental data using the
appropriate equations and the nonlinear least-squares KINFIT
program[76]. Some of the related equations and computer

subroutines have been described in detail elsewhere[71, 77-78].

74

III. Results and Discussion

III.A. The Ion-Pairing Formation Constants of Cs+ Ion in

Nitromethane Solvent

It should be noted that cesium salts may form ion pairs in
solvents with low dielectric constants or low donor ability in
concentrated solutions. The nitromethane solvent used in this study
has an intermediate value of the dielectric constant(36.87) and a low
value of the donor number(2.7)[79]. Naturally, it was important to
determine the extent of ionic association of CsSCN in nitromethane in
order to evaluate the complexation reactions of Cs+ ion with crown
ethers. For this purpose, the concentration dependence of the l33Cs
chemical shift as a function of the salt concentration was studied for
Cs+SCN’, Cs+(18C6)SCN', and Cs+(l8C6)2SCN'. The results are given in
Table 3-1 and shown in Figure 3-1.

The ion-pairing constants of these compounds in nitromethane
were calculated based on the idea that the exchange between the
free solvated cesium ion and the ion pair is fast on the NMR time
scale; consequently, only one resonance signal is observed.

For CsSCN, the ion-pairing reaction which takes place in

nitromethane may be represented by:

Kip

 

Cs+ + SCN’ Cs+SCN'

 

where Kip is the ion pair formation constant of Cs+SCN'. The observed

chemical shift is given by the expression[80],

75

 

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5 e ct+(lSC6)sc1~l-
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M

n

F 4

I

a

o
.501
’60 V r v T V r ' r r
0.00 0.01 0.02 0.03 0.04 0.05

Concentration(M)

Figure 3-1. Concentration dependence of the 133Cs chemical shifts
of cesium compounds in nitromethane at 25°C. The solid lines are
least-squares plots, obtained by simultaneous multiple data set

fitting of all three data sets with the KINFIT program.

77

8obs = Xf°f + Xip°ip = Xf°f + (1 ' XI) 51p (3‘2)

where 81 and 51p are the chemical shifts of the free and ion-paired
Cs+ ion respectively and Xf and Xip are the corresponding relative
mole fractions of the two cesium species. Let CfM be the
concentration of the free Cs+ ion and CM be the total concentration of
CsSCN. Obviously,

Xf = CfM/CtM (3'3)

Combining Equations (3-2) and (3-3), Equation (3-4) can be obtained
as
566s = (CfM/CtM)(5f - 81p) + 51p (3-4)
The ion pair formation constant is
Kip = Kc/Yiz =[Cs+SCN‘]/[Cs+][SCN']Y:t2

= (CIM'CfM)/(CfM)2 7:2 (3 -5)

where Kc is the concentration equilibrium constant. Substituting

Equation (3—5) into Equation (3-2) gives
°obs = ['1 + (1 + 4Kip7i2CtM)1/zl(5f - 51p)/2KipYizctM + 5ip (3‘6)

This equation relates the observed chemical shifts to the total

concentration of CsSCN salt(C-M ), the chemical shift of the free Cs+

78

ion(5f), the chemical shift of the ion-paired Cs+(81p), the mean activity
coefficient 7: and the ion pair formation constant Kip. The values of
C11“ and 61 are known and the value of Y: can be calculated using the
Debye-Huckel Equation. The values of 81p and Kip can be obtained
with the help of the non-linear least-squares curve-fitting program
KINFIT. In fact, 81 can also be obtained by KINFIT fitting.

For Cs+(18C6)SCN’, the reactions may be represented by:

K1

 

 

 

 

 

Cs+ + 18C6 Cs+(18C6)
Ki
Cs+ + SCN' Cs+SCN‘
+ - Kip. + -
Cs (18C6) + SCN Cs (18C6)SCN

 

where K1 is the formation constant of complexed Cs+(18C6) and Kip' is
the ion pair formation constant of Cs+( 18C6)SCN '. K1, Kip, and Kip' can

be expressed as

K1 = [Cs+(18C6)]/[Cs+][l8C6] (3 -7)
Kip 7:2 = Kc = [Cs+SCN'l/[Cs+l[SCN'l (3 -8)
Kip' 712 = Kc' = [Cs+(l8C6)SCN']/[Cs+(l8C6)][SCN‘] (3 -9)

Since the total concentration of the Cs+ ion, SCN" ion, and 18-crown-6
molecule in the solution are the same, let Ct represent the total

concentration,

79

C1 = [Cs+] + [Cs+SCN'] + [Cs+(18C6)] + [Cs+( 18C6)SCN'] (3-10)
C- = [SCN‘] + [Cs+SCN'] + [Cs+(1 8C6)SCN'] (3-1 1)
C1 = [18C6] + [Cs+(18C6)] + [Cs+(18C6)SCN'] (3-12)

From Equation (3-7) to (3-12), there are six independent equations.
There are also six independent variables of [Cs+], [Cs+SCN'],
[Cs+(l8C6)], [Cs+(18C6)SCN'], [SCN'], and [18C6]. Therefore, any of
these variables can be expressed as a function of K1, Kc, Kc', and C1.
For example, [Cs+(l8C6)] can be expressed as

Kc'2[Cs+( 18C6)]4 + (Kch' + Kc'2 + KCKC'Z) [Cs+(18C6)]3

+ (K1 - K1KC'C1 - 2KCKC' - Kc'Ct) [Cs‘*'(18C6)]2

- (2K1Ct + KC) [Cs+(18C6)] + K1C12 = 0 (3-13)
Since the observed chemical shift is

Solis = XCs+ 5Cs+ + XCs+sc1~r 5Cs+SCN- + XCs+08C6) 5Cs+08C6)

+ XCs+(18C6)SCN' °Cs+(18C6)SCN' (3-14)

where XCs+ = [Cs+]/Ct- XCs+SCN’
[Cs+(18C6)]/Ct. and XCs+08C6)SCN'

[Cs+SCN'l/Ct. XCs+(18C6) =
[Cs+(18C6)SCN']/Ct, to fit the

80

calculated results with the experimental data, an expression for the
relative mole fractions of all four species in terms of K1, Kc, Kc', and
C1 is demanded. However, Equation (3-13) is a fourth order one for
[Cs+(l8C6)]. In order to avoid the difficulty of solving this high order
equation, reasonable simplification must be made. Obviously,
complexed Cs+(l8C6) is a strong complex, and its formation constant,
K1, is much larger than Kc and Kc'. Therefore, the relation between
[Cs+(18C6)] and [18C6] and [Cs+] can be expressed as

[Cs+(l8C6)] >> [18C6] 2 [Cs+] (3-15)
From Equations (3-10) and (3-11),

[SCN‘]=[Cs+]+[Cs+(18C6)] (3-16)
So that with (3-15)

[SCN'] = [Cs+( l 8C6)] (3-17)

Using (3-15) and (3-17) and combining (3-9) and (3-12), equation

(3-18) can be obtained as

C1 = [Cs+(18C6)] + [Cs+(18C6)SCN']

= [Cs+(18C6)] + Kc'[Cs+(l8C6)][SCN']

= [Cs+(18C6)] + Kc'[Cs‘*’(18C6)]2 (3-18)

81

or K<;'[Cs"”(18C6)]2 + [Cs+(18C6)] - C1 = 0 (3-19)

Equation (3-19) is a quadratic equation for [Cs+(18C6)]. Solving this
equation for [Cs+(18C6)] gives

[Cs+(l8C6)] = { -1 i (1+4Cth‘)”2 }/2Kc' (3-20)

Since physically [Cs+(18C6)] cannot be negative, only the positive root

is chosen. Therefore,

[Cs+(18C6)] = { -1 + (1+4C-Kc')1/2 }/2Kc' (3-21)
Then,

Cs+(18C6)SCN'] = Kc'[Cs+(18C6)]2 (3-22)

[Cs+] = { [Cs+(18C6)]/K1(1 + Kc[Cs+(l8C6)] ) }1/2 (3-23)

[Cs+SCN'] = Kc[Cs+(18C6)][Cs+] (3 -24)

Now all four species are expressed in terms of K1, Kc, Kc', and C1.
Note, however, that Kc and Kc' are not independent of concentration
because of the concentration dependence of 71. This effect' was
accounted for at each concentration by using Kip and Kip' as
concentration independent parameters and the mean activity
coefficient ‘Yi. Therefore, Kc and Kc' can be replaced with Kip, Kip',

and 71. The computer fit of the data with Equation (3-14) can give
the values of K1, Kip, and Kip'.

82

The concentration dependence of 133Cs chemical shift for
Cs+(18C6)2SCN’ can be obtained in a similar way. For Cs+(18C6)2SCN',
Cs+(18C6) can be considered as a very strong complexed ion and no
free Cs+ ion exists in the solution. Therefore, the reactions may be

expressed as

K
Cs+(18C6)+18C6 ——2- Cs+0806)2

 

9
Kip

 

Cs+(18C6) + S CN’ Cs+(18C6)SCN'

 

Kip

 

Cs+(lliC6)2 + SCN'

 

Cs+(18C6)ZSCN‘

where K2 is the second formation constant of complexed Cs+(18C6)2
and Kip" is the ion pair formation constant of Cs+(18C6)2SCN'. The
expression of Kip' can be found from Equation (3-9). K2 and Kip" can

be expressed as

K2 = [Cs+(l8C6)2]/[18C6][Cs+(18C6)] (3-25)

Kip"in = Kc" = [Cs+(18C6)2SCN']/[SCN'][CS+(18C6)2] (3-26)

Material balance gives

C1' = [Cs+(18C6)] + [Cs+(l8C6)SCN’] + [Cs+(l8C6)2]

+ [Cs+( 1 8C6)2SCN'] (3-27)

83

2C1' = [18C6] + [Cs+(18C6)] + [Cs+(18C6)SCN']
+ 2[Cs+(18C6)2] + 2[Cs+(18C6)2SCN‘] (3-28)
CI' = [SCN'] + [Cs+(18C6)SCN'] + [Cs+(18C6)2SCN'] (3-29)

where C-' is the total concentration of the Cs+ or SCN‘ ion in the
solution. Similarly, all four species, [Cs+(18C6)], [Cs+(l8C6)SCN'],

[Cs+(18C6)2], and [Cs+(18C6)2SCN'], can be expressed in terms of K2,
Kip', Kip", 7i, and Ct'. The observed chemical shift is

-8obs = XCs+08co) 5Cs+(lsco) + XCs+(l8C6)SCN' 5Cs+(18C6)sc1~r
+ XCs+08C6)2 5Cs+08co)2
+ XCs+(18co)zscu' °Cs+(18C6)28CN' (3-30)

where XCs+08C6)=[Cs+(18C6)l/Ct'- XCs+03C6)SCN' =[Cs+(l8C6)SCN'l/Ct'.
XCs+(lSC6)2 =[Cs+(18C6)2l/Ct'. and Xcs+03co)2SCN' =[Cs+(18C6)2SCN']/Ct'-
The computer fit of the data with Equation (3-30) gives the values of
K2, Kip', and Kip". Because Kip and Kip' are common parameters for
Cs+SCN', Cs+(l8C6)SCN', and Cs+(18C6)2SCN', multiple data set fitting
of the data of the three compounds with Equations (3-6), (3-14), and
(3-30) were carried out by using the KINFIT program. The
subroutine program for the multiple data set fitting is given in

Appendix B. The resulting ion pair formation constants for all three

84

compounds are listed in Table 3-2 along with their complexation
formation constants.

These results show that the formation constants of the
complexes are much larger than the ion-pairing constants, indicating
that complexation is the major cause of the variation of the chemical
shift when l8-crown-6 molecule is involved in the complexation

reactions.

Table 3-2. Ion Pair and Complexation Formation Constants of

Cesium Compounds in Nitromethane at 25°C.

 

Compound K ip* K1 K2

 

CsSCN (2.2il.5)x10 -- --
Cs+(18C6)SCN° (4.5:0.1)><l 0 (1.7:0.2)x105 - -
Cs+(l8C6)ZSCN' (1.9:0.5)x10 (l.7i0.2)><105 (1.010.3)><103

 

* Kip represents Kip, Kip', or Kip".

III.B. Formation Constants of Cesium Thiocynate

Complexes with Crown Ethers in Nitromethane

It is well known that the Cs+ ion is the least solvated among the
alkali metal ions because of its large size and low charge density and
that nitromethane is a very poor solvating solvent for ions since it
has a low donor number(2.7) in spite of the rather large dielectric
constant(36.87). Consequently, ion pairing and complexation

reactions are important competitors for solvation in this solvent.

85

In a solution of CsSCN and crown ethers, there may exist crown
ether molecules, free Cs+ and SCN’ ions, ion—paired Cs+ and SCN‘ ions,
and complexed Cs+ ions. When exchange between the free and
complexed Cs+ ions is fast on the NMR time scale, only a population

averaged chemical shift is observed.

501,5 = Xf 8f + Xip 51p + Xc 5c (3-31)

In the above equation, 5obs is the observed chemical shift. Xf, Xip,
and Xc are the relative mole fractions, and 8f, 51p, and 8c are the
chemical shifts for free Cs+, ion-paired Cs+ and complexed Cs+ ions,
respectively.

Complexed Cs+(12C4) was treated as a one step complexation
reaction and ion-pairing formation was also considered because of
the mismatch of sizes between Cs+ ion and l2-crown-4 molecule and
the weak complexation ability of lZ-crown-4. The equilibrium

equations may be represented by

K1'

 

Cs+ + 12C4 Cs+(12C4)

Kip

 

Cs+ + SCN' Cs+SCN'

 

where K1' is the formation constant of complexed Cs+(l2C4).
For complexed Cs+(15C5)2, a two step complexation reaction
treatment was adopted and the ion pairing reaction was also

considered. The reaction equilibria can be expressed as

86

 

Cs+ + 15C5 Cs+(15C5)

 

K 2”
~——— Cs+(15C5)2

 

Cs+(15C5) + 15C5

k.
Cs+(15C5)+SCN- & Cs+05C5)SCN-

In the above equations, K1" and K2" are the first and second
formation constants of Cs+(15C5)2, respectively, and kip is the ion
pair formation constant of Cs+(15C5)SCN'.

Complexed Cs+(18C6)2 was also considered as a two step

complexation reaction with a possible ion pairing reaction,

 

 

 

 

 

K
Cs+ + 18C6 1 Cs+(18C6)
K2
Cs+(18C6) + 18C6 Cs+(18C6)2
Kip' + _
Cs+08C6) + SCN' Cs (18C6)SCN

 

Since the results given in Table 3-2 shows that the first-step
complexation is very strong, it was assumed that the second-step
complexation takes place only after the first-step complexation has
been completed. Therefore, this two step complexation reaction was
treated as two single step complexation reactions.

From the data list in Table 3-3 and plotted in Figure 3-2, it is

clear that the subsequent reaction of Cs+ ion with 18-crown-6

87

Table 3-3. Mole Ratio Studies of Crown Ether Complexes with CsSCN
in MeNOz Solvent by 133Cs NMR at 25°C. [CsSCN]T=0.005M.

 

 

[1.8m 1.1.5951 MAI
[Cs+] 51mm [Cs+] 50pm [Cs+] 5mm
0.0 -56.88 0.0 -56.88 0.0 -56.88
0.2 -50.50 0.4 -51 .05 0.4 -55.94
0.4 -45.19 0.6 -48.68 0.6 —55.84
0.6 -37.11 0.8 -45 .43 0.8 -55.47
0.8 -31.49 1.0 -42.86 1.0 -55.12
1.0 -26.09 1.2 -40.83 1.2 -54.83
1.2 -23.51 1.6 -37 .73 1.6 -54.26
1.4 -21.61 1.8 -36.22 1.8 -53.98
1.6 -20.61 2.0 -35 .75 2.0 -53.77
1.8 -20.09 2.4 -3 3 .7 5 2.4 -53.33
2.0 -19.88 3.0 -31 .69 3.0 -52.85
2.4 -19.71 4.0 -28 .52 4.0 -51.92
3.0 -l9.56 5.0 -26.07 5.0 -51.25
4.0 -19.22 6.0 -24.37 6.0 -50.70
5.0 -19.23 8.0 -21 .00 8.0 -49.74
6.0 -19.12 0.0 - l 8.51 10.0 -48.95
8.0 -19.03 12.0 -16.79
10.0 -18.72 15.0 -14.53
18.0 -13.03

20.0 -12.28

 

88

 

 

 

 

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Male Ratio([L]/[Cs+])

Figure 3-2. 133Cs chemical shifts Li. [IA/[Cs+] mole ratio in
nitromethane at 25°C. L = 18-crown-6, lS-crown-S, or

lZ-crown-4. The solid lines are least-squares plots.

89

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91

molecule forms a sandwich complex of Cs+(18C6)2. But the plot also
shows that there is a sharp slope between mole ratio [18C6]/[Cs+]=l
and 2, and the KINFIT fitting gives a rather different curve from the
experimental data in this region, as shown in Figure 3-3. This
indicates that it may form a club sandwich complex(18C6:Cs+=3z2) in
this region. In order to discriminate a sandwich complex(2:1) from a
club sandwich complex, a substitute reaction equilibrium model was
used to fit the data with the KINFIT program for the possible
formation of club sandwich complex in [18C6]/[Cs+] mole ratio range

from 1 to 2. The model is presented as follows:

K3

 

2Cs+(l8C6) + 18C6 (Cs+)2(18C6)3

 

K
(Cs+)2(18C6)3+18C6 V————“—* 2Cs+(18<:6)2

where K3 = [(Cs+)2(l8C6)3]/[18C6][Cs+(18C6)]2 (3-32)

K4 = [Cs+(18C6)2]2/[18C6][(CS+)2(18C6)3] (3-33)

In the above reaction equilibrium model, complexed Cs+(18C6) was

treated as starting material. Therefore, material balance gives

CMt = [Cs+(18C6)] + [Cs+(18C6)2] + 2[(Cs+)2(18C6)3] (3-34)

C1} = [18C6] + [Cs+(18C6)2] + [(Cs+)2(l8C6)3] (3-35)

92

where CM1 and C1,I are the total concentration of the Cs+ ion and 18-
crown-6 molecule in the solution. The observed chemical shift can be

represented by

aobs = sz+(18C6) 5Cs+(18C6) + XCs+(18C6)2 5Cs+(18C6)2

+ X(Cs+)2(18C6)3 5(Cs+)2(18C6)3 (3-36)

with XCs+(18C6) = [Cs+(18C6)1/CM‘. XCs+(18C6)2 = [Cs+( 18C6)21/CM‘. and
X(Cs+)2(18C6)3 = [(Cs+)2(18C6)3]/CM1. An expression for the relative
mole fractions of all three species in terms of CM‘, C1}, K3, and K4 is
required in order to carry out the computer fit with the experimental
data. From Equation (3-32) to (3-35), equation (3-37) can be

obtained as

K3[Cs+(18C6)]3 + {2K3CLI - K3CM1+ (K3K4)1/2] [Cs"’(18C6)]2

+ {1 + CI.‘(K3K4)V2 - CM‘(K3K4)1/2} [Cs+(18C6)] - CM‘IK3 = 0

(3-37)

Cubic Equation (3-37) can be solved for [Cs+(18C6)] in terms of CM‘,
C1}, K3, and K4. [Cs+(18C6)2] and [(Cs+)2(18C6)3] can then be obtained
in terms of CM‘, C1}, K3, K4 and [Cs+(18C6)]. Therefore, a computer fit
of the data with Equation (3-36) can give the values of K3 and K4.
Combining Equations (3-32) and (3-33), Equation (3-25) can also be

obtained as

93

(K3K4)1/2 = K2 = [Cs+(18C6)2]/[18C6][Cs+(18C6)]

The subroutine program used to solve Equation (3-37) and to fit the
calculated results with the experimental data is given in Appendix C.
The KINFIT fitting of the data based on the formation of the club
sandwich complex gives a much smaller standard deviation and the
fit is much better as shown in Figure 3-4. The formation constants
obtained from the fitting are K2 = (9.3:1.2)><102, K3 = (7.11:0.2)X103,
and K4 =(1.2i0.3)><102. From the fitting results, it may be suggested
that after complete formation of a 1:1 complex of Cs+(18C6), the
intermediate club sandwich complex is favored between mole ratio
[l8C6]/[Cs+] = 1 and 2 because nitromethane is a poor solvating
solvent and ion pair formation of Cs+(18C6)SCN' is weak. When the
mole ratio of [18C6]/[Cs+] increases, the 2:1 sandwich complex,
Cs+(l8C6)2, is formed.

The formation constants for complexed Cs+(12C4), Cs+(15C5)2,
and Cs+(18C6)2 are listed in Table 3-4. These results clearly show
that K] for the complexation of Cs+ with 18C6 is much larger than K2,
but that K2 is also large, indicating that complexed Cs+(18C6)2 is very
stable in nitromethane. In addition, both K1 and K2 of complexed
Cs+(l8C6)2 ion are much larger than those of complexed Cs+(15C5)2,
presumably because the cavity size of the 18-crown-6 molecule
provides a much better fit for the Cs+ ion.

It is interesting to note that the K1 and K2 values of complexed
Cs+(li8C6)2 in Table 3-4 are close to those in Table 3-2, although

those values from Table 3-2 were obtained by the computer fitting

cc

C0

fez

94

of the data of 133Cs chemical shift vs. concentration of the complex
while the values from Table 3-4 were obtained from the data for the
133Cs chemical shift vs. [18C6]/[Cs+] mole ratio. This indicates that the
equilibrium equations of complexation reactions used for the

computer fitting are at least internally consistant.

Table 3-4. Formation Constants for Cs+-Crown Ether Complexes
in Nitromethane Solvent at 250C.

 

 

Complexed Ions K 1* K2"
Cs+(12C4) (3.6i0.1)><10 - -
Cs+(15C5)2 (2.2i1.2)><103 (3.01:0.2)Xl 0
Cs+(l8C6)2 (l.6i0.2)><105 (9.33:1:l.2)><102

 

* K1 represents Kl', K1", or K].

** K2 represents K2" or K2.

III.C. Formation Constants of Mixed Sandwich Complexes

In order to examine the possibility of formation of mixed
sandwich complexes of the Cs+ ion, either lS-crown-S or 12-crown-4
was added to the solution in which the [18C6]/[Cs+] mole ratio was
already maintained at a value of one. The two resulting complexation

reactions and the ion pair formation reaction may be represented by

162'

 

 

Cs+(18C6) + 15C5 Cs+(18C6)(15C5)

95

Table 3-5. Mole Ratio Studies of Mixed Sandwich Complexes with
CsSCN in MeN02 Solvent by 133Cs NMR at 250C. [CsSCN]T=0.005M.

 

[18C6]=0.005M [18C6]=0.01M [18C6]=0.005M

 

 

LUSH L15_95_1 [1194.1

[Cs+] Sppm [Cs+] Sppm [Cs+] 8ppm
0.0 -26.09 0.0 -19.69 0.0 -26.09
0.2 -24.22 0.4 -1 8 .86 0.2 -25.74
0.4 -23.71 0.8 -1 8 .54 0.4 -25.31
0.6 -23.08 1.0 -1 8 .43 0.6 -24.97
0.8 -22.68 1.4 - l 8 .08 0.8 -24.70
1.0 -22.47 2.0 - 1 7 .46 1.0 -24.57
1.4 -21.77 3.0 - l 6 .66 1.4 -24.45
2.0 -21.08 4.0 - l 5.7 8 2.0 -24.03
3.0 -l9.87 6.0 - 14.42 3.0 -23.33
4.0 -l 8.66 8.0 — 1 3 .26 4.0 —22.92
5.0 -l7.64 10.0 -12.52 5.0 -21.94
7.0 -15.95 13.0 -12.21 7.0 -21.07
9.0 -l4.77 16.0 - 1 2 .09 9.0 -20.22
10.0 ~14.25 20.0 -11.90
13.0 -l3.72 25.0 -1l.75
16.0 -13.22 30.0 -11.61
20.0 -12.93 35.0 -11.57
25.0 -12.57 40.0 -11.47
30.0 -12.36
35.0 -12.23
40.0 -12.04

 

96

x2"
Cs+(18C6) + 12C4 =4: Cs+(18C6)(12C4)

ip

 

Cs+(18C6) + SCN' Cs+(18C6)SCN'

 

The results are given in Table 3-5 and in Figure 3-2. The plots in
Figure 3-2 show a gradual paramagnetic shift upon addition of 15-
crown-S or 12-crown-4, clearly indicating the formation of mixed
sandwich complexes of Cs+(18C6)(15C5) and Cs+(18C6)(12C4) in
nitromethane solution. A third possible complexation reaction was
also investigated by addition of 15-crown-5 to a solution with the
[l8C6]/[Cs+] mole ratio of two in order to determine directly whether
complexed Cs+(18C6)2 or Cs+(18C6)(15C5) ion is more stable. This

reaction equation may be expressed as

 

Cs+(18C6)(15CS) + 18C6

 

Cs+(18C6)2 + 15C5

The formation constants of the two mixed sandwich complexes
obtained from computer fitting of the data with the KINFIT program
are listed in Table 3-6. It was found from all formation constants
that the overall stability of the sandwich complexes varies in the
order Cs+(l8C6)2 > Cs+(18C6)(15C5) > Cs+(18C6)(12C4) > Cs+(15C5)2 >
Cs+(12C4)2. This order nicely reflects the decrease of the oxygen
number in crown ethers and the sizes of the crown ether molecules.
Because the size of the Cs+ ion(3.38 A)[58, 81] is larger than the

cavity of all three crown ethers, observation of the above correlation

is 1
CW
despi
atoms
of thi
cavity
molec
Cs+(1
is ex;
3 K v

more 1

Tab]:

97

is not surprising. However, the overall stability of the
Cs+(18C6)(12C4) complex is much higher than that of Cs+(15C5)2,
despite the equal number of donating oxygen atoms(10 oxygen
atoms) involved in the complex formation. This is probably because
of the much better coordination condition of Cs+ ion inside the larger
cavity of 18-crown-6 molecule than that of the smaller lS-crown-S
molecule. Since the complexed Cs+(18C6)2 ion is more stable than
Cs+(l8C6)(15C5), a very small K value for the third reaction equation
is expected. In fact, computer fitting with the data in table 3-5 gives
a K value of 0.3, indicating that the complex of Cs+(18C6)2 is indeed
more stable than that of Cs+(18C6)(15C5).

Table 3-6. Formation Constants for Cs+ Ion Complexes with Mixed

Crown Ethers in Nitromethane Solvent at 25°C.

 

 

Complexed Ions K1 162*
Cs+(18C6)(12C4) (1.6i0.2)><105 (2.1i0.4)><10
Cs+(18C6)(15C5) (1.6i0.2)><105 (6.7i0.3)><10
Cs+(HMHCY)(12C4) >105 (3.7i1 .8)>< 103
Cs+(HMHCY)(15C5) >105 (7.9:1 .5)>< 103
Cs+(I-IMHCY)2 >105 (1.6i0.1)><103

 

* K2 represents the 162', 162", or 362 .

The variation of the 133Cs chemical shifts as a function of the

[HMHCY]/[Cs+], [15C5]/[Cs+(HMHCY)], and [l2C4]/[Cs+(HMHCY)] mole

98

Table 3-7. Mole Ratio Studies of Mixed Sandwich Complexes with
CsSCN in MeNOz Solvent by 133Cs NMR at 250C. [CsSCN]1~=0.005M.

 

[HMHCY]=0.005M [HMHCY]=0.005M

 

 

HMH Y fl5_C_§l [M
[Cs+] 8ppm [Cs+] 8ppm [Cs+] 8ppm
1.0 9.90 0.0 9.90 0.0 9.90
1.2 16.33 0.2 3.82 0.2 6.42
1.4 21.06 0.4 -1.28 0.4 3.90
1.6 25.39 0.6 -6.24 0.6 1.89
1.8 28.30 0.8 -11.09 0.8 -0.21
2.0 31.16 1.0 -l4.28 1.0 —1.61
2.4 34.47 1.4 ~15.96 1.4 -2.60
3.0 36.82 2.0 -16.77 2.0 -3.02
4.0 37.41 3.0 -l7.24 3.0 -3.26
5.0 37.81 4.0 -17.03 4.0 -2.95
7.0 38.26 5.0 -l7.33 5.0 -3.20
8.0 38.37 7.0 -l7.40 7.0 -3.51

10.0 38.62 9.0 -l7.38 9.0 -3.37

 

99

 

60

 

 

 

 

 

E
a.
fl.
:7
z:
8
m
3
.2
E
0
S
o
fl
(‘5
F
.3 I A HM-tcv
0 4m! + HMHCY+1SC5
I I HMHCY+IZC4
'60 r T I ' r ‘ I ' r '
o 2 4 6 a 10 12

Mole Ratlo([L]/[Cs+])

Figure 3-5. 133Cs chemical shifts VJ, [Ll/[Cs+] mole ratio in
nitromethane at 25°C. L = HMHCY, lS-crown-S, or 12-crown-4.

The solid lines are least-squares plots.

100

ratios in nitromethane is given in Table 3-7 and shown in Figure 3-5.
It is interesting to note that, between [HMHCY]/[Cs+] mole ratio of
zero and one, two broad 133Cs peaks were observed and the
corresponding chemical shift values could not be measured
accurately. Nevertheless, these broad peaks indicate the existence of
a rather slow exchange between the free and complexed Cs+ ions, and
the formation of a very stable 1:1 complexed Cs+(HMHCY) ion.
However, after the mole ratio of one, only one population-averaged
broad NMR peak was observed and this peak showed a paramagnetic
shift upon further addition of HMHCY. The plot in Figure 3-5 also
shows that the 133Cs chemical shift starts to level off at a
[HMHCY]/[Cs+] mole ratio of about two. This behavior is clearly
indicative of the formation of a stable 2:1 sandwich complex of
Cs+(HMHCY)2 in nitromethane solution.

The formation of mixed sandwich complexes of Cs+ ion with
HMHCY and crown ethers was investigated by the addition of either
15-crown-5 or 12-crown-4 to the nitromethane solution with a
[HMHCY]/[Cs+] mole ratio of one. In these cases, the 133Cs peak shifts
diamagnetically upon addition of the crown ethers. and tends to level
off at mole ratio of about two as shown in Figure 3-5, indicating the
formation of mixed sandwich complexes of Cs+(HMHCY)(15C5) and
Cs+(HMHCY)(12C4) respectively.

All three 2:1 complexation reactions involving the HMHCY 1:1

complex may be expressed by the one step reaction equation,

x "I
Cs+(I-IMHCY) + L :2 Cs+(HMHCY)(L)

101

where L represents the complexant, HMHCY, 15-crown-5 or 12-
crown-4. Computer fittings of the data with the KINFIT program

were carried out in order to evaluate the x2 values of the three 2:1
complexes and the results are included in Table 3-6. These results
show that the 162'" values of complexed Cs+ ions varies in the order
Cs+(HMHCY)(15C5) > Cs+(HMHCY)(12C4) > Cs+(HMHCY)2. In contrast to
the Cs+-18C6 sandwich complexes, the complexed Cs+(HMHCY)2 is the
least stable 2:1 complex in the series, probably due to the existence
of the six bulky -CH3 groups on the nitrogen atoms of the macrocyclic
ring. These methyl groups can prevent the convenient approach of
the second HMHCY molecule to the previously complexed Cs+ ion. On
the other hand, a smaller molecule, such as 15-crown-5 can better
cap the bowl-shaped 1:1 complex of Cs+(HMHCY) without
considerable spatial interferance, giving a very stable mixed
sandwich complex. The small size and lower coordination number of
the 12-crown-4 molecule gives a relatively weaker mixed sandwich
complex of Cs+(HMHCY)(12C4), but it is still more stable than the
complex of Cs+(HMHCY)2. It is interesting to note that, in the solid
state, no alkalide or electride could be made that contained 2:1
complexes, such as Cs+(HMHCY)(12C4), Cs+(HMHCY)(15C5), or
Cs+(HMHCY)2. The only compound prepared was Cs+(HMHCY)Na'
which has a cation-anion contact ion pair to coordinate the Cs+
ion[55]. Therefore, the existence of the 2:1 complexes and their large
362'" values in nitromethane can be attributed to the very poor

solvation power of nitromethane and the weak ion pair formation

between Cs+ and SCN' ions.

102

Comparison of the K2 values shows that, while the second step
formation constants are about the same for complexed Cs+(18C6)2
and Cs+(HMI-ICY)2 ions, the 362 values for complexed
Cs+(HMHCY)(15C5) and Cs+(HMHCY)(12C4) ions are much larger than
those of the Cs+(18C6)(15C5) and Cs+(18C6)(12C4) complexes.
According to the crystal structure of Cs+(HMHCY)Na'[55], the
configuration of the HMHCY molecule is a rigid hemisphere or bowl-
shaped structure. In this structure, one side of the HMHCY molecule
is completely surrounded by the hydrogen atoms on the HMHCY ring
and the Cs+ ion sits inside the hemisphere and is coordinated to all
six nitrogen atoms of the HMHCY molecule. The Na' anion also forms
a cation-anion contact ion pair with the Cs+ ion, directly from the
Open side. In solution, the complexed Cs+(HMHCY) ion probably has
the same structure and a 15-crown-5 molecule can easily cover the
open side of the hemisphere to form a three-dimensional cavity. In
this conformation, there is no open space for the penetration of the
solvent molecule or the counter-anion, SCN', toward the Cs+ cation
and the complex can be very stable, especially when the solvent is a
very poor solvated solvent and the ion-pairing is weak.

In contrast to HMHCY, 18-crown-6 has a two-dimensional
cavity and the Cs+ ion can only partially fit inside the cavity because
of the larger size of the cation. If the complexed Cs+(18C6) is covered
by a 15-crown-5 or 12-crown-4 molecule, there is still some open
space so that the complexed Cs+ ion remains exposed to the solvent
molecules. Therefore, complexed Cs+(HMHCY)(15C5) and
Cs+(HMHCY)(12C4) ions are expected to be more stable than
complexed Cs+(18C6)(15C5) and Cs+(18C6)(12C4).

CHAPTER 4. SINGLE-CRYSTAL 133Cs NMR STUDY
OF Cs+(l8C6)2e‘

I. Introduction

The nuclear spin Hamiltonian can be expressed in the following
tabular form:

Term Coupling of nuclear spins with

 

J~I=J~lz external static magnetic fields

+J‘Irf external rf magnetic fields

+J~lcs induced magnetic fields originating from orbital
motions of electrons

+J~IQ electric field gradients

+J~ISR magnetic moment associated with the molecular
angular momentum

+J~ID each other, directly through their dipole moments

+J‘IJ each other, indirectly via electron spins

 

where «Hz and J‘Irf are Hamiltonians from external magnetic fields
which are much larger than internal fields and can be controlled by
experiments. Detailed descriptions of each term can be found from
many books[82-85]. For 133C3 NMR studies of Cs+(18C6)2e',
quadrupolar coupling and chemical shielding interaction are the two

most important terms among the internal Hamiltonians. Therefore,

103

104

the total Hamiltonian, J4, which governs the NMR spectrum of a

quadrupolar nucleus of Cs, may be expressed by

J4=J~Iz+J~Ics+eHQ (4-1)

where Z, CS, and Q represent the Zeeman, chemical shielding and
quadrupolar interactions, respectively. The dominant Zeeman term is
from the interaction between the nuclear magnetic moment and the
applied magnetic field. The terms Jigs and «HQ can be treated as
perturbations and are sensitive to the electronic environment around
the nucleus. The dipolar term JID, while smaller, causes broadening
and 'smoothing' of the spectra.

The chemical shielding interaction results from the motion of
electrons around a nucleus induced by the applied external magnetic
field, B0. The local magnetic fields induced by this motion change the
total field experienced by the nucleus. The chemical shielding

Hamiltonian, therefore, can be expressed as

chsz'ylo-Bo (4-2)

where yis the magnetogyric ratio of the nucleus and I and o are the
nuclear spin angular momentum vector and the chemical shielding
tensor, respectively. This tensor describes the three-dimensional
nature of the electronic shielding of the nucleus. The shielding
usually varies with the orientation of a crystal or molecule in the
magnetic field. In its principal-axis system(PAS), the diagonalized

tensor is described by three orthogonal principal components, on, on,

105

and 033, with, by convention, ans 0225 033. Three angles are required
to describe the chemical shielding PAS with respect to the crystal

axis system. The isotropic chemical shielding is given by

0130 = ((511+ C322+ 033)/3 (4'3)

A nucleus with nuclear spin quantum number I 21 possess a
nuclear quadrupole moment. The nuclear quadrupole coupling is an
electrostatic interaction between the nuclear quadrupole moment
and the electric field gradient at the nucleus. The quadrupolar

Hamiltonian can be expressed as

.1th = [eQ/21(21-1)h] I.v.I (4-4)

where eQ is the nuclear quadrupole moment and I and V are the
nuclear spin angular momentum vector and the quadrupolar tensor,
respectively. In the principal-axis system, the principal components
of V are defined again by convention as |V33| 2 |V22| 2 |V11| and the
electric field gradient tensor is traceless with V33 + V22 + V11 = 0.
Therefore, two parameters, the quadrupolar coupling constant, x, and
the asymmetry parameter, "lQ, can completely define the magnitudes
of its principal components. The quadrupolar coupling constant and

asymmetry parameter are given by

x : eZqQ/h (4'5)

and T1Q = (V11- V22)/V33 (4-6)

106

where eq = V33. Like the chemical shielding interaction, three angles
are also required to define the orientation of the quadrupolar PAS
with respect to the crystal axis system.

Because 133Cs has a small nuclear quadrupole moment, it is
sufficient to consider the influence of the quadrupolar interaction on
the solid-state NMR spectra by using only first-order perturbation
methods. The NMR spectrum that results from magnetically
equivalent 133Cs nuclei in a single crystal that shows the effects of
anisotropic chemical shielding and quadrupolar coupling is given
by[861

+1

1(V) = 2 P(m)g(V-Vm) (4-7)

m=-I+1

where p(m) is the probability of the (m <—) m-l) transition, g is a line-

broadening function, and
vm = vo[1 - (onsinzfi cosch + 0228111213 sinch + 033coszfi )]
- (vQ/2)[(3c0529 - 1) - Tlein26 cos2¢)](m-l/2) (4-8)
V0 = 730/21! (4-9)
m = 3e2qQ/21(21-1)h

= 3x/2I(21-1) (4-10)

107

The angles 1‘) and (p define the orientation of the PAS of the chemical
shielding tensor with respect to the magnetic field, while the angles 9
and 0 define the orientation of the PAS of the quadrupolar electric
field gradient tensor with respect to the magnetic field.

Since the chemical shielding results in an overall shift of the
nuclear spin energy levels, only the quadrupolar interaction
determines the splitting between any pair of satellite transitions. For
a first order quadrupolar interaction, the central transition is not
affected and this central transition depends only on the chemical
shielding. Because of these characteristics of a nucleus which has a
small quadrupole moment, the quadrupolar and chemical shielding
influences on a single-crystal NMR spectrum can easily be separated.
The position of the central transition peak and the magnitude of the
satellite splitting can be used to determine the chemical shielding
and quadrupole coupling, respectively, as a function of the
orientation of the single crystal in the magnetic field. From these
data one can determine the chemical shielding and quadrupolar
tensors.

In general, the frequency of an observed resonance is
determined only by the secular contribution, the 2 component of a
tensor in the laboratory frame. The chemical shielding or
quadrupolar tensor, in the reference frame of a cubic box inside of
which the crystal is mounted, can be constructed from the angular
dependence of the z component. By a series of unitary
transformations, the chemical shielding or quadrupolar tensor can be
rotated to its principal axis system in which the tensor is in the

diagonal form. Therefore, the eigenvalues of the tensor and the

108

corresponding eigenvectors, which are the direction cosines with
respect to an orthogonalized crystal axis frame, may be obtained in
this way. In the crystal frame, the directions of the tensor elements
may then be correlated with the molecular structure, which
ultimately determines both the magnitude and direction of the
tensor elements. The series of transformations required to determine
the chemical shielding or quadrupolar tensor in the PAS frame may
be expressed as in Figure 4-1[87].

The laboratory system in which data are obtained can be
related to the goniometer system by a rotation angle. A cubic box
inside of which a single crystal will be placed can be mounted into
the goniometer. The coordination between the cubic box and the
goniometer is related by simple rotation with a rotating angle of 90°,
180°, or 270°. The cubic box has an orthogonal coordinate system
and this system must be related to the crystal axis system by
crystallography because the crystal is randomly mounted inside the
cubic box. Finally, matrix diagonalization gives the principal
components of the tensor, and the orientation of the tensor in the
crystal system.

Although single-crystal NMR studies[86-90] have become more
and more popular and have been shown to be a very useful method
to extract information about a nucleus of interest, there has been
only one such study made of an alkalide or electride, that of
Na+(C222)Na' by J. Kim[46]. The scarcity of such studies is due to the
difficulties of crystal growth and sample handling, because these
compounds are extremely air- and temperature-sensitive.

Cs+(18C6)2e' was selected as a candidate for single-crystal NMR

109

Laboratory Axis System

U R(¢, 90, 90)

Goniometer Axis System

U Rta”, 13". Y’)

Cube Axis System

U R(a’. 15'. Y)

Crystal Axis System

U Rta, 13, 7)

Principal Axis System

Figure 4-1. The series of transformations required to determine the
chemical shielding or quadrupolar tensor in the PAS frame from the

experimental data obtained in the laboratory frame.

 

110

 

Figure 4-2. Crystal structure of Cs+(18C6)2e'. A) Single molecule
diagram; B) ORTEP stereo packing diagram. The anionic hole

centers are indicated by the symbol 0.

111

study for several reasons. First, it is an electride and it is the most
stable of the electrides. Second, its crystal structure in the low-
temperature phase is known, as shown in Figure 4-2[6]. Third, single
crystals of Cs+(18C6)2e' can occasionally be grown large enough to be
used for single-crystal NMR studies. Finally, and most importantly,
this compound has demonstrated unique physical properties from
powder NMR, EPR, conductivity, and magnetic susceptibility studies.
Especially relevant to this study, the powder MAS NMR shows that
this electride slowly goes through an irreversible transition from a
low-temperature phase to a disordered high-temperature phase at
about -50°C, during which the observed single NMR peak shifts
diamagnetically by about 80 ppm[9l-92]. For the high-temperature
Phase, a reversible first order phase transition occurs at about -50°C.
Above -50°C, the MAS NMR spectra show a single peak, but two
Peaks were observed below -50°C, indicating two 'frozen' chemically
inecluivalent sites for Cs+ ions below this temperature. This further
indicates that the crystal structure has been changed from the low-
tel'l'lperature phase to high-temperature phase. Although what
cllalrnge occurs in the crystal is not known, a single-crystal 133Cs NMR
Study of Cs+(18C6)2e' may be able to ascertain whether Cs+ ions in
the high-temperature phase are all magnetically equivalent or not
above -50°C. This study may also indicate how many magnetically
i1me'cluivalent Cs+ ions are present in each of the two chemically
it~"3-Cluivalent sites. This information will certainly be useful in
understanding the local environment of the Cs+ ions in the high-

t . . . .
gmperature phase and may provrde information about changes in

t
he crystal structure.

157-- x-.._n1

112

II. Experimental

Since electrides are air-sensitive and are thermally unstable at
higher temperature, the synthesis and single-crystal growth were
carried out at -78°C after prior evacuation of the cell to 10'5 torr. A
mixed solvent of dimethyl ether and trimethylamine and a K-cell
were used for the synthesis and single-crystal growth. After
Cs+(18C6)2e' had been synthesized, the solvent was slowly
evaporated into a liquid nitrogen trap through a series of frits for
about seven days. Single crystals as large as 4x4 x4 mm3 were
obtained. An appropriate single crystal which had the approximate
dimensions of 3x4 x4 mm3 was selected under a microscope in a dry
nitrogen-filled glove bag and then the crystal was mounted into a
cubic box, machined from Rexalite polymer. The cubic box with the
Crystal was then inserted into a supporting frame inside the
receiving coil on the NMR probe. Dow Corning vacuum grease was
uSed for crystal mounting.

NMR measurements were carried out at 52.468 MHz with a
Varian VXR-400 superconducting NMR spectrometer. A single-pulse
sequence was used with pulse width 0f 0.7 us. All 133Cs spectra were
referenced with respect to infinitely dilute aqueous solution of Cs+
ion. A home-built NMR probe with angle rotating capability was

used. Angle rotations were performed in ten-degree intervals with a
Possible i0.l degree deviation from the goniometer which has a
minimum scale of 0.2 degree. The single-crystal NMR data of 133Cs in
Cs+(18C6)2e' were collected at about -50°C and under a nitrogen

atmosphere. A precooled nitrogen gas stream kept the sample

113

temperature at about -50°C. Although the average temperature
seldom differed by more than i2°C from -50°C., excursions of up to
about i4°C sometimes occurred during the 30 hours or so required
for a single orientation of the cubic box, since there is no
temperature controller in the home-built single-crystal NMR probe.
By repeating the measurements with the cubic box turned so that
successive rotations could be made about the x, y, and z coordinates
of the box, enough data could be obtained to determine the crystal
orientation. The orientation of the unit cell axes of the crystal with
respect to the cubic box axis system could not be determined
independently because of the large size and thermal instability of the

Crystal. The least-squares KINFIT program and a subroutine

program, XTAL[9], were used to fit the data.

111. Results and Discussion

The low-temperature phase of crystalline Cs+(l8C6)2e' belongs
t0 the monoclinic space group C2/c. The four Cs+ ions in the unit cell
lie on special positions on the two-fold axis, with the coordinates (1)
0. y, 1/4; (2) 0, -y, 3/4; (3) 1/2, y+1/2, 1/4; (4) 1/2, -y+l/2, 3/4.

Positions (1) and (2) are related by an inversion center as are (3) and

(4), while the first pair is related to the second pair by a two-fold
Screw axis. Therefore, all four Cs+ ions are crystallographically
equivalent and must have identical isotropic chemical shifts as
observed in this laboratory[91-92]. Since (1) and (2) are related by
an inversion center, they are magnetically equivalent, as with (3)

and (4). Furthermore, the site symmetry constraint due to the two

114

fold axis indicates that all four Cs+ ions in the unit cell of the low-
temperature phase are magnetically equivalent. This also has
possibly been confirmed[93]. One of the objectives of the present
work was to carry out a single-crystal NMR study of the low-
temperature phase at low temperatures. Unfortunately, the presence
of the disordering transition was not known at the time of this study
and the crystal used was warmed to slightly above -50°C, so that
only single-crystal NMR spectra of the high-temperature phase were
obtained. It is clear from the results, however, that the original
crystalline orientation was preserved rather than the formation of a
random powder.

Two distinct sets of 133Cs NMR patterns were observed at -50°C
as shown in Figure 4-3. All seven transitions for one set and five
transitions for another one are clearly shown in the lower spectrum,
While a total of seven transitions can be observed from the upper
Spectrum, indicating that the two sites coalesce at this orientation.
The crystal was independently rotated around three orthogonal axes,
designated as 1, 2, and 3. The orientation plots of half the splitting of
the first two satellite transitions for each of the two sites of Cs+
Versus the angle of rotation about the three orthogonal axes are
given in Figure 4-4 and 4—5. Figure 4-6 and 4-7 show the angular
dependence of the chemical shifts of the central transitions for both
Sites. The least-squares KINFIT multiple-data-set fitting of the data

from all three orthogonal axes with program XTAL gave the results
summarized in Table 4-1. The chemical shifts vary with the
orientation of the crystal as expected. Because of the temperature

fluctuations during the experiment, the chemical shifts from the

w; 3

115

Figure 4-3. Single-crystal 133Cs NMR spectra of the high-temperature

phase of Cs+(l8C6)2e' at two different orientations at VL=52.468MH2
and at -50°C.

116

 

 

 

 

600
a a
D a ‘
a 9 ‘
400 A
a n
a A
A
5 9 a
O 200 . ‘ . Q
3 a
E 4 O ‘ O O
8 a .A 0
0-1 ° °
3 ° °
'2 no
4 . ‘ .
o A
s ~200- A 0
IL . A
A
i ‘5 o
o 0 m1
400‘ . ° m2
0
‘ 0‘ A ms
400 v I '
0 100 200

Anal. at RotntloMDogm)

Figure 4-4. Angular dependence of half the splitting of the two first
sa‘iellite transitions of Cs+ in site 1 from the high-temperature phase

0f single crystal Cs+(18C6)2e‘.

ll7

 

 

 

 

 

600
a D
O O
A
2 a o . A 7
o

400 0 A
E 1 . o O
a.
z A a n
a) 0 A o I:
b 0
§ 0+ ‘ . a

o

O ‘ a I: o
3' A
.3 A

200‘ I) exist °

0 0 m2 0
0 mass ° °
400 . I '
O 100 200

Angle of BotatloMDogm)

Figure 4-5. Angular dependence of half the splitting of the two first
satellite transitions of Cs+ in site 2 from the high-temperature phase

of single crystal Cs+(l8C6)2e‘.

118

 

 

 

 

180
1: 9 a
160‘ a :-
n ‘-“
‘s‘ * a
a. h.
a. a 1
"' 140- , .
= 0 O . . a . . .
“4A. 0.000. OAAA
_ A
a ‘ A A A
3 120‘ a ‘ A A A ‘ 7
5
.1: a
0 II
a
1007 n D exist
a a -
‘ a 0 0:32
A 0033
80 v r v
0 100 200

Angle of Rotation (Degree)

Figul‘e 4-6. Angular dependence of the chemical shift of the central
t1-a"‘sition of Cs+ in site 1 from the high-temperature phase of single

‘2‘ yStat Cs+(18C6)2c-.

119

 

 

 

 

180
a a
1601 D a
‘ a
E 0 . a . O .
a . °
" 140.. ‘
e
:2 e a ’
2 ° . °
0) ‘ .
e
_ A ‘ a ° 0 O . A A A
8 12m ‘ . . ‘ a
5 . .
.c t . U A o
0 ‘ ‘ ‘
100‘ ‘ O u u an“
a a a e axisz
. A axis3
so r r *
0 100 200

Angle of flotation (Degree)

Figun 4-7. Angular dependence of the chemical shift of the central

transition of Cs+ in site 2 from the high-temperature phase of single

crystal Cs+(18C6)2e-.

120

Table 4-1. Results* Obtained from a Single-Crystal 133Cs NMR Study
of the High-Temperature Phase of Cs+(l8C6)2e' at 60°C.

 

 

Site 1 2

9g.-
0’11 92i5ppm 93:5ppm j
022 125i5ppm 125i5ppm 5
G33 162i5ppm 165i5ppm
QCC 0.5 8:0.04MH2 05710.05 MHz
nQ O.57i0.10 0.45:0.07

 

* Results are from simultaneous least-squares KINFIT fitting of all

three data sets for each site.

121

spectra are not as accurate as expected from the instrument

specifications. This is because this electride is a paramagnetic

compound and its chemical shift is strongly temperature dependent.
Nevertheless, an important result was obtained from the central line
chemical shifts. The simultaneous presence of both lines for some
orientations showed that the isotropic chemical shifts, disc, for the
two sites are 126 ppm and 128 ppm at -50°C. Since the two peaks
observed at lower temperature by powder MAS measurements have
chemical shifts that differ by about 20 ppm, the present result shows
that this is only a single type of chemical environment for the two
magnetically inequivalent Cs+ sites in this higher temperature region
of the high-temperature phase.

The quadrupolar coupling constants and the asymmetry

parameters for the two sites are QCC=O.58i0.04MHz and

1'1Q=O.57iO.10, and QCC=O.57:O.05MH2 and nQ=O.45iO.O7, respectively.

‘I‘he similarity of these values for the two sites as well as the
chemical shifts reinforce the assumption that there is only a single

average chemical environment for each of the complexed cesium

cations in the high-temperature phase at this temperature.

CHAPTER 5. CONCLUSIONS

Five new alkalides have been synthesized and their crystal
structures have been determined. Three of them were synthesized
with large crown ethers such as 21-crown-7 or dicyclohexano-24-
crown-8. These three compounds showed very unusual crystal
structures and some interesting features. (Cs+)2(21C7)2(Na')2 has
twin cation-anion ion pairs in which the Cs+-Na‘ distances are only
4-44(2)A and 4.52(3)A respectively. But optical absorption
spectroscopy and 23Na NMR show no charge transfer between Na'
and Cs+. Each Cs+ cation in the molecule is bonded to all seven oxygen
atoms in one 21-crown-7 and to one of the seven oxygen atoms from
another 21-crown-7, giving the Cs+ cations a coordination number of
eight and connecting the two Cs+(21C7)Na' units together to form
( Cs+)2(21C7)2(Na')2. (K+)2(21C7)3(MeNH2)(Na‘)2 has a third 21-
crown-7, which serves as a bridge connecting the two K+ cations in
the molecule while a solvent molecule, MeNHz, forms a bond to one
Of the two K+ cations. By contrast, K+(dicyclohexano-24C8)Na' has a
l =1 ratio of K+ ion to complexant, although dicyclohexano-24-crown-8
is a larger crown ether. The crystal structure of this compound shows
that dicyclohexano-24-crown-8 twists around the K+ cation in order
to have all eight oxygen atoms coordinated to the cation, giving a
'Wl‘ap around' complex. These alkalides are stable in spite of the
laI‘ge cavity sizes of the crown ethers compared to the relatively
S“hall sizes of the Cs+ and K+ cations. The stability of these

compounds is attributed to their unusual structural feature in which

122

123

the cations can be fully coordinated in different ways. Five more new
compounds have also been synthesized with dicyclohexano-BO-
crown-10 and dicyclohexano-24-crown-8. These alkalides appear to
be amorphous materials. Attempts to crystallize these compounds
failed, probably because they are too 'soft' and disordered as a result
of the flexible nature of the large crown ethers. The successful
synthesis and crystal structure determination of alkalides that
contain large crown ethers showed that large crown ethers could be
used as complexants for the synthesis of alkalides. Furthermore,
large cryptands such as C322 and C332 may be good candidates for
the synthesis of alkalides and even new electrides since they have 3-
dimensional cavities which appears to be important for the stability
of electrides.

Two new mixed sandwich complexes, Rb+(18C6)(12C4)Na' and
Rb+(l8C6)(12C4)Rb', have also been synthesized and their crystal
structures have been determined. These two compounds show very
interesting optical properties and Rb+(18C6)(12C4)Na' even has a
shiny green color while other sodides generally are golden or reddish
in color. The optical absorption spectra of Rb+(18C6)(12C4)Na' and
R b‘+(18C6)(12C4)Rb' have two and three absorption peaks while

mOSt of alkalides only have one. It is, however, unclear what causes
th'E-Ese absorption peaks. One possible explanation is that these
I"“llsual optical absorption spectra may result from the effect of the
asymmetry of the excited states of Na‘ and Rb' ions in the
compounds. In order to answer this question, polarized single crystal

reflectance studies need to be carried out.

124

133Cs NMR studies were performed on the concentration
dependence of the 133Cs chemical shifts of Cs+SCN', Cs+(18C6)SCN',
and Cs+(18C8)zSCN‘ in nitromethane. Studies of 133Cs chemical shift
versus [L]/[Cs+] mole ratio (L = 18-crown-6, 15-crown-5, lZ-crown-
4, or HMHCY) were also carried out. These studies showed the
formation of stable 2:1 sandwich complexes of Cs+(18C6)2,
Cs+(15C5)2, and Cs+(HMHCY)2 in nitromethane. In the case of
C s+(18C6)2, the formation of an intermediate 'club sandwich',
(Cs+)2(18C6)3, is possible in nitromethane solvent. By contrast, the
Cs+-12C4 system was considered only as a one step complexation.
Finally, evidence for the formation of mixed sandwich complexes of
C s‘*‘(18C6)(15C5), Cs+(18C6)(12C4), Cs+(HMHCY)(15C5), and
Cs+(HMHCY)(12C4) were observed in nitromethane solvent.

A single-crystal 133Cs NMR study of an electride, Cs+(18C6)2e',
was carried out for the first time. The crystal of Cs+(18C6)2e' used
for this study was allowed to warm to above -50°C and only single-
Cry stal NMR spectra of the high-temperature phase were obtained. It
is clear from the results, however, that the original crystalline
Orientation was preserved rather than the formation of a random
Powder after the phase transition. This study demonstrated that
Sil'lgle-crystal NMR study of an electride is possible although
electrides are extremely air- and temperature-sensitive. In order to
understand better the NMR properties of Cs+(18C6)2e', more single-
cl‘ystal NMR studies need to be carried out, especially for the low-

temperature phase of this electride at low temperatures.

APPENDICES

APPENDIX A

Crystal Structure Data of (Cs+)2(21C7)2(Na')2,

(K+)2(21C7)3(MeNH2)(Na')2, K+(dicyclohexano-24C8)Na',

Table

A-1.

A-2.

A-3.

A-4.

A-S.

A-6.
A-7.

A-8.

A-9.
A-lO.

Rb+(l 8C6(12C4)Na' and Rb+(18C6(12C4)Rb‘.

Positional Parameters and Their Estimated Standard
Deviations for (Cs+)2(21C7)2(Na')2.

Bond Distances (in Angstroms) for (Cs+)2(21C7)2(Na‘)2.
Bond Angles (in Degrees) for (Cs+)2(21C7)2(Na')2.
Positional Parameters and Their Estimated Standard
Deviations for (K+)2(21C7)3(MeNH2)(Na’)2.

Bond Distances (in Angstroms) for
(K+)2(21C7)3(M6NH2)(Na')2.

Bond Angles (in Degrees) for (K+)2(21C7)3(MeNH2)(Na’)2.
Positional Parameters and Their Estimated Standard
Deviations for K+(dicyclohexano-24C8)Na'.

Bond Distances (in Angstroms) for
K+(dicyclohexano-24C8)Na'.

Bond Angles (in Degrees) for K+(dicyclohexano-24C8)Na‘.
Positional Parameters and Their Estimated Standard

Deviations for Rb+(18C6)(12C4)Na‘.

A-ll. Bond Distances (in Angstroms) for Rb+(18C6(12C4)Na'

(I) and Rb+(18C6(12C4)Rb‘(II).

A-12. Bond Angles (in Degrees) for Rb+(18C6(12C4)Na'(I) and

125

126

Rb+(18C6(12C4)Rb'(II).
A-13. Positional Parameters and Their Estimated Standard

Deviations for Rb+(18C6)(12C4)Rb'.

The parameters for hydrogen atoms have not been included, as
they were constrained in all five structures to ride on the carbon

atoms to which they belong in all five structures.

 

127

 

 

Table A-1. Positional Parameters and Their Estimated Standard
Deviations for (Cs+)2(21C7)2(Na’)2

Atom x y z 13(A2)

Csl 0.8398 0.5070 0.5043 4.9(3)*
Cs2 0.3975(2) 0.3116(2) 0.8516(2) 4.2(3)*
Nal 1.253(2) 0.836(2) 0.394(2) 7(2)*

Na2 0.975(3) 0.978(3) 0.968(2) 9(2)*

01 0.266(3) 0.584(3) 0.837(2) 6.9(8)
04 0.353(3) 0.449(3) 0.634(2) 3.3(7)
07 0.531(3) 0.276(3) 0.575(2) 7.0(9)
010 0.524(2) 0.070(2) 0.756(2) 2.9(4)
013 0.482(2) 0.112(2) 0.984(1) 3.7(4)
016 0.492(2) 0.373(3) 1.087(2) 6.1(6)
019 0.351(3) 0.570(3) 1.031(3) 10(1)

0101 0.953(2) 0.245(2) 0.492(2) 2.0(4)
0104 0.918(2) 0.335(2) 0.296(2) 4.8(5)
0107 0.754(2) 0.532(3) 0.256(2) 5.6(6)
0110 0.751(2) 0.773(2) 0.404(2) 4.6(5)
0113 0.712(3) 0.758(3) 0.642(2) 5.9(7)
0116 0.694(3) 0.535(3) 0.783(2) 2.8(7)
0119 0.904(3) 0.370(3) 0.700(2) 3.4(7)
C2 0.224(4) 0.578(4) 0.744(3) 5(1)

C3 0.335(5) 0.601(6) 0.652(5) 7(2)

C5 0.425(3) 0.427(3) 0.527(2) 2.9(8)
C6 0.422(3) 0.284(3) 0.522(3) 7.5(8)
C8 0.568(4) 0.140(4) 0.568(3) 3.5(8)
C9 0.465(4) 0.029(4) 0.661(3) 4.1(8)
C11 0.445(3) -0.042(3) 0.842(3) 4.7(7)
C12 0.540(4) -0.019(4) 0.915(3) 7(1)

C14 0.549(4) 0.152(4) 1.071(3) 6(1)

C15 0.442(5) 0.244(6) 1.147(4) 11(2)
C17 0.438(4) 0.472(4) 1.152(3) 5.3(9)
C18 0.459(5) 0.574(5) 1.097(4) 11(1)

 

 

Table A-1.

128

Positional Parameters and Their Estimated Standard
Deviations for (Cs+)2(21C7)2(Na')2 (Continued)

 

 

Atom x y z B(A2)
C20 0.264(7) 0.621(6) 1.038(5) 11(2)
C21 0.171(4) 0.576(4) 0.944(3) 5(1)
C102 1.044(3) 0.245(3) 0.381(3) 3.4(8)
C103 0.980(6) 0.239(5) 0.311(4) 7(1)
C105 0.841(4) 0.306(4) 0.218(3) 6(1)
C106 0.837(4) 0.446(4) 0.173(3) 6(1)
C108 0.782(4) 0.660(4) 0.225(3) 5.9(9)
C109 0.704(4) 0.741(4) 0.307(3) 7(1)
C111 0.721(5) 0.859(5) 0.480(4) 9(1)
C112 0.771(3) 0.887(3) 0.565(3) 5.4(8)
C114 0.747(4) 0.773(4) 0.737(3) 5(1)
C115 0.658(4) 0.663(4) 0.824(3) 5(1)
C117 0.797(4) 0.511(4) 0.845(3) 1.4(9)
C118 0.802(3) 0.352(3) 0.811(3) 3.5(8)
C120 0.934(3) 0.244(3) 0.700(3) 3.3(6)
C121 1.043(3) 0.251(3) 0.575(3) 3.4(7)

 

Starred atoms were refined anisotropically.

129

Table A-2. Bond Distances (in Angstroms) for (Cs+)2(21C7)2(Na’)2

 

Atom 1

(381
(381
(:81
(381
(:81
(381
(:81
(:81
(382
(:82
(CS2
(:S2
(382
<3S2
(382
(3S2
()1
()1
()4
()4
()7
()7
()10
()10
()13
()13
()16
()16
()19
()19
0101

we.

(37
0101
0104
0107
0110
0113
0116
0119
CH
(34
(37
()10
()13
016
()19
0116

(321

C5
C8
C9
CHI
(:12
(314
(315
CH7
(318
(:20
C102

Distance
3.25(3)
3.18(2)
3.18(2)
3.55(2)
3.44(2)
3.43(2)
3.47(3)
3.18(3)
3.44(3)
3.32(3)
3.45(3)
3.16(2)
3.10(2)
3.40(2)
3.48(3)
3.13(3)
1.38(4)
1.43(4)
.59(6)
.41(4)
.49(4)
.52(4)
.50(4)
.46(3)
.73(5)
.46(4)
.39(6)
.43(4)
.59(5)
.14(6)
.45(3)

p—AHHp‘HHy—Ay—AHp—eg—At—Ap—A

 

130

Table A-2. Bond Distances (in Angstroms) for (Cs+)2(21C7)2(Na')2

 

 

(Continued)
61m; Ami Manse
0101 C121 1.60(4)
0104 C103 135(5)
0104 C105 1.43(4)
0107 C106 1.60(5)
0107 C108 1.27(4)
0110 C109 1.45(4)
0110 C111 1.31(5)
0113 C112 1.49(4)
0113 C114 1.35(4)
0116 C115 1.49(5)
0116 C117 l.58(4)
0119 C118 1.48(4)
0119 C120 1.39(4)
C2 C3 1.36(6)
C5 C6 1.43(5)
C8 C9 1.55(5)
C11 C12 1.52(5)
C14 C15 1.74(6)
C17 C18 1.18(S)
C20 C21 1.73(7)
C102 C103 1.24(6)
C105 C106 1.55(5)
C108 C109 1.51(5)
C111 C112 l.32(5)
C114 C115 1.46(5)
C117 C118 l.66(5)
C120 C121 l.65(4)

 

Estimated standard deviations in the least significant figure are
given in parentheses.

131

Table A-3. Bond Angles (in Degrees) for (Cs+)2(21C7)2(Na')2

 

Atom 1 Atom 2 Atom 3 Angle
07 CS] 0101 85.2(7)
07 CS] 0104 87.5(7)
07 CS1 0107 81.5(7)
07 C81 0110 97.8(7)
07 CS] 0113 91.9(7)
07 CS] 0116 73.9(7)
07 C81 0119 88.0(7)
0101 CS] 0104 52.5(5)
0101 C81 0107 106.5(6)
0101 CS] 0110 156.5(5)
0101 CS] 0113 153.0(5)
0101 C81 0116 105.7(6)
0101 CS1 0119 54.0(6)
0104 C81 0107 54.9(6)
0104 CS] 0110 104.1(5)
0104 CS] 0113 154.3(6)
0104 CS] 0116 153.2(6)
0104 C81 0119 106.5(6)
0107 CS] 0110 51.5(6)
0107 CS] 0113 99.5(6)
0107 CS] 0116 137.2(6)
0107 CS] 0119 158.8(7)
0110 CS] 0113 50.5(5)
0110 C81 0116 97.5(6)
0110 CS1 0119 149.0(6)
0113 CS] 0116 48.2(6)
0113 C81 0119 99.2(7)
0116 CS1 0119 54.8(6)
01 CS2 04 51.5(7)
01 CS2 07 100.1(7)
01 C82 010 154.9(6)
01 CS2 013 151.1(6)

 

132

Table A-3. Bond Angles (in Degrees) for (Cs+)2(21C7)2(Na')2

 

 

(Continued)

Ami Atom 2 m4 A113];
01 C82 016 100.5(6)
01 CS2 019 48.8(7)
01 C82 0116 86.6(7)
O4 C82 07 49.8(7)
04 C82 010 103.5(6)
04 CS2 013 157.5(6)
04 C82 016 146.6(6)
04 C82 019 98.8(7)
04 C82 0116 85.2(7)
07 C82 010 55.5(7)
07 C82 013 108.2(6)
07 C82 016 142.1(6)
07 C82 019 140.0(8)
07 C82 0116 75.7(6)
010 C82 013 54.0(5)
010 C82 016 103.1(5)
010 CS2 019 154.4(7)
010 C82 0116 91.7(6)
013 C82 016 52.6(6)
013 C82 019 103.1(7)
013 C82 0116 94.5(6)
016 C82 019 51.8(7)
016 C82 0116 74.1(6)
019 C82 0116 77.7(7)
C82 01 C2 109(2)
C82 01 C21 103(2)
C2 01 C21 122(3)
C82 04 C3 113(2)
C82 04 C5 120(2)
C3 04 C5 116(3)
C81 07 C82 104.2(8)

 

133

Table A-3. Bond Angles (in Degrees) for (Cs+)2(21C7)2(Na‘)2

 

(Continued)

Atom 1 Atom 2 Atom 3 Angle
CS1 07 C6 121(2)
CS1 07 C8 101(2)
C82 07 C6 106(2)
C82 07 C8 106(2)
C6 07 C8 117(3)
CS2 010 C9 103(2)
CS2 010 C11 101(2)
C9 010 C11 105(2)
CS2 013 C12 118(2)
C32 013 C14 125(2)
C12 013 C14 109(2)
CS2 016 C15 106(2)
C82 016 C17 115(2)
C15 016 C17 109(3)
C82 019 C18 102(2)
C82 019 C20 122(4)
C18 019 C20 135(4)
CS1 0101 C102 109(2)
C81 0101 C121 112(1)
C102 0101 C121 108(2)
C81 0104 C103 114(3)
C81 0104 C105 123(2)
C103 0104 105 116(3)
CS] 0107 C106 105(2)
CS1 0107 C108 110(2)
C106 0107 C108 115(3)
CS1 0110 C109 114(2)
CS] 0110 C111 112(3)

.C109 0110 C111 129(4)
C81 0113 C112 107(2)
C81 0113 C114 108(2)

 

134

Table A-3. Bond Angles (in Degrees) for (Cs+)2(21C7)2(Na')2

 

(Continued)

Atom 1 Atom 2 Atom 3 Angle
C112 0113 C114 115(3)
CS1 0116 CS2 106.2(7)
CS1 0116 C115 122(2)
CS] 0116 C117 107(2)
C82 0116 C115 101(2)
CS2 0116 C117 114(2)
C115 0116 C117 107(2)
CS1 0119 C118 118(2)
C81 0119 C120 126(2)
C118 0119 C120 99(2)
01 C2 C3 111(4)
04 C3 C2 103(4)
04 C5 C6 109(3)
07 C6 C5 104(3)
07 C8 C9 112(3)
010 C9 C8 102(3)
010 C11 C12 102(3)
013 C12 C11 95(3)
013 C14 C15 100(3)
016 C15 C14 103(4)
016 C17 C18 110(4)
019 C18 C17 117(4)
019 C20 C21 116(5)
01 C21 C20 109(3)
0101 C102 C103 112(4)
0104 C103 C102 124(5)
0104 C105 C106 108(3)
0107 C106 C105 117(3)
0107 C108 C109 114(3)
0110 C109 C108 116(3)
0110 C111 C112 127(5)

 

135

Table A-3. Bond Angles (in Degrees) for (Cs+)2(21C7)2(Na')2

 

(Continued)

Atom 1 Atom 2 Atom 3 Angle
0113 C112 C111 108(3)
0113 C114 C115 114(4)
0116 C115 C114 104(3)
0116 C117 C118 101(2)
0119 C118 C117 106(3)
0119 C120 C121 103(2)
0101 C121 C120 105(2)

 

given in parentheses.

Estimated standard deviations in the least significant figure are

136

 

 

Table A-4. Positional Parameters and Their Estimated Standard
Deviations for (K+)2(21C7)3(MeNH2)(Na')2
Atom x y z B(A2)
K1 0.9729(5) 0.2507(1) 0.2523(2) 3.2(1)
K2 0.6495(6) 0.5117(2) 0.2490(3) 6.2(2)
Nal 0.536(1) 0.1180(3) 0.4702(5) 6.9(3)
Na2 0.458(1) 0.1169(3) 0.0473(5) 6.3(3)
01 0.462(1) 0.2376(4) 0.3141(7) 3.9(4)
04 0.409(2) 0.2991(4) 0.4087(7) 3.7(4)
07 0.437(2) 0.3783(4) 0.3686(7) 4.2(4)
010 0.502(2) 0.4424(4) 0.2705(8) 6.2(4)
013 0.523(2) 0.3883(4) 0.1584(8) 5.6(4)
016 0.608(2) 0.3131(4) 0.1103(6) 3.7(4)
019 0.645(1) 0.2433(4) 0.1963(7) 4.0(4)
0101 1.144(2) 0.3172(4) 0.2635(7) 4.1(4)
0104 1.189(2) 0.2697(4) 0.1521(8) 4.9(4)
0107 0.982(1) 0.2139(4) 0.1195(7) 3.5(3)
0110 1.039(2) 0.1745(3) 0.2491(8) 4.4(4)
0113 1.038(2) 0.2078(4) 0.3794(7) 4.0(4)
0116 0.835(1) 0.2662(4) 0.3777(7) 3.6(4)
0119 0.835(2) 0.3195(3) 0.2663(7) 3.6(4)
0201 0.871(4) 0.472(1) 0.167(2) 19(1)*
0204 0.902(3) 0.4681(8) 0.312(2) 18(1)*
0207 0.751(4) 0.512(1) 0.402(2) 21(1)*
0210 0.453(4) 0.550(1) 0.336(2) 18(1)*
0213 0.285(5) 0.536(1) 0.232(3) 20(2)*
0216 0.364(2) 0.5208(6) 0.103(1) l8.2(7)*
0219 0.637(3) 0.5167(8) 0.097(1) 16(1)*
N1 0.828(2) 0.5783(5) 0.244(1) 5.7(5)
C2 0.449(2) 0.2352(5) 0.390(1) 3.4(5)
C3 0.332(2) 0.2645(6) 0.406(1) 3.4(5)
C5 0.306(2) 0.3288(6) 0.424(1) 3.9(6)
C6 0.396(2) 0.3635(5) 0.434(1) 2.9(5)

 

Table A-4.

Positional Parameters and Their Estimated Standard

137

Deviations for (K+)2(21C7)3(MeNH2)(Na')2 (Continued)

 

 

Atom x y z B(A2)

C8 0.543(3) 0.4087(6) 0.378(1) 4.7(6)
C9 0.604(3) 0.4169(6) 0.308(1) 5.3(7)
C11 0.377(3) 0.4276(6) 0.229(1) 5.1(7)
C12 0.414(3) 0.4195(6) 0.154(1) 5.2(6)
C14 0.556(2) 0.3774(6) 0.088(1) 4.1(6)
C15 0.678(3) 0.3485(6) 0.100(1) 4.8(6)
C17 0.721(2) 0.2841(6) 0.107(1) 3.7(5)
C18 0.635(2) 0.2481(6) 0.119(1) 3.4(5)
C20 0.555(2) 0.2115(6) 0.214(1) 3.8(5)
C21 0.569(2) 0.2115(6) 0.295(1) 3.5(5)
C102 1.291(3) 0.3133(6) 0.232(1) 5.1(6)
C103 1.258(3) 0.3054(6) 0.160(1) 5.2(6)
C105 1.130(2) 0.2621(5) 0.083(1) 3.2(5)
C106 1.107(2) 0.2220(5) 0.078(1) 3.3(5)
C108 0.966(2) 0.1741(6) 0.129(1) 3.6(5)
C109 1.083(2) 0.1594(5) 0.183(1) 3.6(6)
C111 1.150(2) 0.1645(6) 0.306(1) 4.6(6)
C112 1.069(2) 0.1696(6) 0.371(1) 4.7(6)
C114 0.951(2) 0.2148(5) 0.438(1) 2.9(5)
C115 0.927(2) 0.2556(6) 0.443(1) 3.2(5)
C117 0.764(2) 0.3028(6) 0.381(1) 3.0(5)
C118 0.710(2) 0.3139(5) 0.309(1) 3.2(5)
C120 0.928(2) 0.3497(6) 0.292(1) 3.7(6)
C121 1.061(2) 0.3502(6) 0.243(1) 4.6(6)
C202 0.928(4) 0.447(1) 0.204(2) 10(1)*
C203 0.997(4) 0.4589(9) 0.272(2) 10(1)*
C205 0.957(4) 0.4796(9) 0.380(2) 10(1)"‘
C206 0.837(5) 0.489(1) 0.421(2) 17(2)*
C208 0.622(4) 0.524(1) 0.424(2) 12(1)*
C209 0.557(6) 0.555(1) 0.404(3) 18(2)*

 

Table A-4.

138

Positional Parameters and Their Estimated Standard

Deviations for (K+)2(21C7)3(MeNH2)(Na')2 (Continued)

 

 

Atom x y z B(A2)
C211 0.374(6) 0.534(1) 0.371(3) 18(2)*
C212 0.256(4) 0.546(1) 0.302(2) 15(1)*
C214 0.247(9) 0.551(2) 0.188(4) 40(4)*
C215 0.186(6) 0.515(2) 0.127(3) 29(2)*
C217 0.430(4) 0.555(1) 0.105(2) 16(1)*
C218 0.571(4) 0.541(1) 0.060(2) 14(1)*
C220 0.768(4) 0.504(1) 0.071(2) 10(1)*
C221 0.820(5) 0.476(1) 0.115(2) 13(2)*
C301 0.725(3) 0.6079(7) 0.243(1) 7.3(8)

 

Starred atoms were refined isotropically.

139

Table A-5. Bond Distances (in Angstroms) for
(K+)2(21C7)3(M6NH2)(Na')2

 

Atgm 1 Atgm 2 Digtange
K1 019 3.12(1)
K1 0101 2.89(1)
K1 0104 2.97(2)
K1 0107 2.92(1)
K1 0110 2.85(1)
Kl 0113 2.95(1)
K1 0116 2.89(1)
K1 0119 2.84(l)
K2 010 2.92(2)
K2 0201 305(4)
K2 0204 2.99(3)
K2 0207 3.04(3)
K2 0210 2.92(4)
K2 0219 2.95(3)
K2 N1 2.94(2)
01 C2 1.49(2)
01 C21 1.44(3)
04 C3 1.45(3)
04 C5 1.49(3)
07 C6 1.46(2)
07 C8 1.48(3)
010 C9 1.47(3)
010 C11 1.45(3)
013 C12 1.51(3)
013 C14 1.48(3)
016 C15 1.46(3)
016 C17 1.49(3)
019 C18 1.52(2)
019 C20 1.48(3)
0101 C102 1.53(3)
0101 C121 1.47(3)

 

140

Table A-5. Bond Distances (in Angstroms) for
(K+)2(21C7)3(MeNH2)(Na')2 (Continued)

 

Atom mm Maw
0104 C103 1.45(3)
0104 C105 1.44(2)
0107 C106 1.48(3)
0107 C108 1.48(3)
0110 C109 1.49(3)
0110 C111 1.49(3)
0113 C112 1.44(3)
0113 C114 1.46(2)
0116 C115 151(2)
0116 C117 1.49(2)
0119 C118 1.48(3)
0119 C120 1.46(2)
0201 C202 1.24(5)
0201 C221 1.09(6)
0204 C203 1.26(5)
0204 C205 1.45(5)
0207 C206 1.19(6)
0207 C208 1.37(6)
0210 C209 l.58(6)
0210 C211 1.20(6)
0213 C212 1.46(7)
0213 C214 107(9)
0216 C215 1.73(6)
0216 C217 1.39(4)
0219 C218 1.27(5)
0219 C220 1.42(5)
N1 C301 1.43(3)
C2 C3 1.56(3)
C5 C6 1.51(3)
C8 C9 1.54(3)
C11 C12 1.55(3)

 

141

Table A-5. Bond Distances (in Angstroms) for
(K+)2(21C7)3(MeNH2)(Na')2 (Continued)

 

Atgm 1 Atom 2 Distange
C14 C15 1.54(3)
C17 C18 1.56(3)
C20 C21 l.58(3)
C102 C103 1.45(3)
C105 C106 1.49(3)
C108 C109 1.53(3)
C111 C112 1.53(3)
C114 C115 l.51(3)
C117 C118 l.51(3)
C120 C121 1.60(3)
C202 C203 1.48(5)
C205 C206 1.45(6)
C208 C209 1.32(7)
C211 C212 1.71(7)
C214 C215 1.8(1)
C217 C218 1.68(5)
C220 C221 1.40(6)

 

Estimated standard deviations in the least significant figure are
given in parentheses.

142

Table A-6. Bond Angles (in Degrees) for (K'*')2(21C7)3(MeNH2)(Na‘)2

 

Atom 1 Atom 2 Atom 3 Angle
019 K1 0101 126.8(4)
019 K1 0104 117.5(4)
019 K1 0107 75.2(4)
019 K1 0110 96.1(4)
019 K1 0113 111.8(4)
019 K1 0116 80.9(4)
019 K1 0119 71.8(4)
0101 K1 0104 57.8(4)
0101 K1 0107 113.6(4)
0101 K1 0110 135.2(4)
0101 K1 0113 108.2(4)
0101 K1 0116 92.4(4)
0101 K1 0119 59.3(4)
0104 K1 0107 57.2(4)
0104 K1 0110 93.5(4)
0104 K1 0113 125.1(4)
0104 K1 0116 150.1(4)
0104 K1 0119 100.3(4)
0107 K1 0110 60.6(4)
0107 K1 0113 118.6(4)
0107 K1 0116 152.0(4)
0107 K1 0119 122.5(4)
0110 K1 0113 58.0(4)
0110 K1 0116 108.5(4)
0110 K1 0119 164.7(5)
0113 K1 0116 57.9(4)
0113 K1 0119 116.9(4)
0116 K1 0119 61.2(4)
010 K2 0201 89.6(8)
010 K2 0204 80.0(7)
010 K2 0207 88.0(8)
010 K2 0210 91.3(8)

 

143

Table A-6. Bond Angles (in Degrees) for (K+)2(21C7)3(MeNH2)(Na')2

 

(Continued)

Atom 1 Atom 2 Atom 3 A_ng1o
010 K2 0219 102.6(7)
010 K2 N1 171.6(5)
0201 K2 0204 55.6(9)
0201 K2 0207 110(1)
0201 K2 0210 176(1)
0201 K2 0219 58.6(9)
0201 K2 N1 89.2(8)
0204 K2 0207 55(1)
0204 K2 0210 121(1)
0204 K2 0219 114.2(9)
0204 K2 N1 92.5(7)
0207 K2 0210 66(1)
0207 K2 0219 164(1)
0207 K2 N1 84.6(8)
0210 K2 0219 124.9(9)
0210 K2 N1 89.4(8)
0219 K2 N1 83.8(7)
C2 01 C21 109(1)
C3 04 C5 109(1)
C6 07 C8 113(1)
K2 010 C9 110(1)
K2 010 C11 127(1)
C9 010 C11 119(2)
C12 013 C14 110(2)
C15 016 C17 108(2)
K1 019 C18 109(1)
K1 019 C20 121(1)
C18 019 C20 109(1)
Kl 0101 C102 112(1)
K1 0101 C121 114(1)
C102 0101 C121 115(2)

 

144

Table A-6. Bond Angles (in Degrees) for (K+)2(2lC7)3(MeNH2)(Na‘)2

 

 

(Continued)

Atom 1 Atom 2 Atom 3 Anglo
K1 0104 C103 117(1)
K1 0104 C105 111(1)
C103 0104 C105 113(2)
K1 0107 C106 118(1)
Kl 0107 C108 110(1)
C106 0107 C108 111(1)
K1 0110 C109 117(1)
K1 0110 C111 111(1)
C109 0110 C111 110(1)
K1 0113 C112 117(1)
K1 0113 C114 118(1)
C112 0113 C114 112(2)
K1 0116 C115 114(1)
K1 0116 C117 116(1)
C115 0116 C117 114(1)
K1 0119 C118 108(1)
K1 0119 C120 117(1)
C118 0119 C120 111(1)
K2 0201 C202 108(3)
K2 0201 C221 100(3)
C202 0201 C221 140(4)
K2 0204 C203 116(2)
K2 0204 C205 115(2)
C203 0204 C205 116(3)
K2 0207 C206 117(3)
K2 0207 C208 96(2)
C206 0207 C208 134(4)
K2 0210 C209 101(3)
K2 0210 C211 121(3)
C209 0210 C211 85(4)
C212 0213 C214 123(6)

 

145

Table A-6. Bond Angles (in Degrees) for (K+)2(21C7)3(MeNH2)(Na')2

 

(Continued)

Atom_1_ Atom 2 Atom 3 Anglo
C215 0216 C217 121(3)
K2 0219 C218 126(2)
K2 0219 C220 112(2)
C218 0219 C220 114(3)
K2 N1 C301 105(1)
01 C2 C3 106(1)
04 C3 C2 106(2)
04 C5 C6 107(2)
07 C6 C5 112(2)
07 C8 C9 108(2)
010 C9 C8 108(2)
010 C11 C12 112(2)
013 C12 C11 106(2)
013 C14 C15 104(2)
016 C15 C14 108(2)
016 C17 C18 103(2)
019 C18 C17 105(1)
019 C20 C21 103(2)
01 C21 C20 105(2)
0101 C102 C103 107(2)
0104 C103 C102 110(2)
0104 C105 C106 107(2)
0107 C106 C105 106(2)
0107 C108 C109 111(2)
0110 C109 C108 104(2)
0110 C111 C112 104(2)
0113 C112 C111 109(2)
0113 C114 C115 108(2)
0116 C115 C114 106(1)
0116 C117 C118 108(2)
0119 C118 C117 111(2)

 

146

Table A-6. Bond Angles (in Degrees) for (K+)2(21C7)3(MeNH2)(Na')2

 

(Continued)

Atom 1 Atom 2 Atom 3 Anglo
0119 C120 C121 105(2)
0101 C121 C120 103(2)
0201 C202 C203 116(3)
0204 C203 C202 111(3)
0204 C205 C206 110(3)
0207 C206 C205 119(4)
0207 C208 C209 125(4)
0210 C209 C208 113(4)
0210 C211 C212 78(3)
0213 C212 C211 121(4)
0213 C214 C215 102(6)
0216 C215 C214 81(4)
0216 C217 C218 94(3)
0219 C218 C217 106(3)
0219 C220 C221 106(3)
0201 C221 C220 140(5)

 

Estimated standard deviations in the least significant figure are
given in parentheses.

147

 

 

Table A—7. Positional Parameters and Their Estimated Standard
Deviations for K+(dicyclohexano-24C8)Na'

Atom x y z B(A2)
K1 0.000 0.500 0.1444(4) 2.8(2)
K2 0.000 0.000 0.3562(6) 8.0(4)
Nal 0.500 0.000 0.147(1) 16(1)
Na2 0.000 0.000 0.6479(8) 6.0(6)
01 -0.040(2) 0.709(2) 0.0895(7) 4.0(6)
04 0.059(2) 0.736(1) 0.1796(6) 1.4(4)
07 0.186(2) 0.525(2) 0.2125(7) 3.1(5)
010 0.266(3) 0.452(2) 0.125(1) 6.8(8)
O21 -0.084(3) 0.205(3) 0.415(1) 10(1)
024 0.078(3) 0.233(3) 0.313(1) 10(1)
027 0.189(3) 0.012(3) 0.2848(9) 6.6(7)
O30 0.254(3) -0.066(2) 0.380(1) 7.4(8)
C2 -0.05 2(4) 0.836(4) 0.115(2) 9(2)
C3 0.103(3) 0.827(3) 0.136(1) 5(1)
C5 0.182(3) 0.764(3) 0.213(1) 6(1)
C6 0.185(3) 0.635(3) 0.243(1) 5(1)
C8 0.315(3) 0.504(3) 0.202(1) 3.5(7)
C9 0.331(3) 0.402(3) 0.161(1) 4(1)
C11 0.287(4) 0.362(4) 0.087(1) 8(1)
C12 -0. 176(3) 0.707(3) 0.065(1) 3.0(7)
C13 -0.27 9(7) 0.770(6) 0.026(2) 23(3)
C14 -0.134(4) 0.660(4) -0.006(2) 11(1)
C15 -0.244(5) 0.568(3) -0.008(2) 9(1)
C16 -0.263(4) 0.505(4) 0.044(1) 11(1)
C22 -0.038(4) 0.319(3) 0.389(1) 5(1)
C23 0.063(3) 0.327(3) 0.353(1) 5(1)
C25 0.168(3) 0.223(3) 0.282(1) 3.5(8)
C26 0.147(3) 0.121(3) 0.254(1) 3.1(8)
C28 0.329(4) 0.028(4) 0.308(1) 8(1)
C29 0.321(4) -0.088(4) 0.330(2) 8(1)

 

148

 

 

Table A-7. Positional Parameters and Their Estimated Standard
Deviations for K+(24C8)Na‘ (Continued)
Atom x y z B(A2)
C31 0.259(3) -0.206(2) 0.4126(9) 1.9(6)
C32 -0.184(4) 0.261(4) 0.478(1) 10(1)
C33 0.405(4) -0.160(4) 0.444(1) 10(1)
C34 0.370(3) -0.068(3) 0.480(1) 7(1)
C35 0.257(4) -0.112(4) 0.514(2) 8(1)
C36 0.147(3) -0.079(3) 0.466(1) 8(1)

 

All atoms were refined isotropically.

149

Table A-8. Bond Distances (in Angstroms) for
K+(dicyclohexano-24C8)Na'

 

Atom 1 Atom 2 Distance
K1 Ol 2.79(2)
Kl O4 2.83(2)
K1 O7 2.71(3)
K1 010 2.81(3)
K2 021 2.87(4)
K2 024 2.92(3)
K2 027 2.81(3)
K2 O30 2.90(3)
01 C2 155(4)
01 C12 150(4)
04 C3 1.46(4)
04 C5 163(4)
07 C6 1.44(4)
07 C8 1.40(4)
010 C9 1.43(4)
010 C11 150(5)
021 C22 1.44(5)
021 C32 162(5)
024 C23 164(5)
024 C25 1.24(4)
027 C26 .1 .53(4)
027 C28 1.53(5)
030 C29 150(5)
030 C31 1.67(3)
C2 C3 l.65(5)
C5 C6 1.60(5)
C8 C9 1.63(4)
C11 C 12 1.5 1(4)
C11 C16 1.75(6)
C12 C13 1.71(5)

 

150

Table A—8. Bond Distances (in Angstroms) for
K+(dicyclohexano-24C8)Na' (Continued)

 

Atom 1 Atom 2 Distanoo
C13 C14 1.67(5)
C14 C15 1.67(5)
C15 C16 1.54(6)
C22 C23 1.49(5)
C25 C26 1.36(5)
C28 C29 1.31(5)
C31 C32. 1.57(5)
C31 C33 1.77(5)
C32 C36 1.6l(5)
C33 C34 l.58(6)
C34 C35 1.62(6)
C35 C36 1.77(5)

 

Estimated standard deviations in the least significant figure are
given in parentheses.

151

Table A-9. Bond Angles (in Degrees) for K+(dicyclohexano-24C8)Na'

 

Atom 1

0 1
01
01
01
01
01
01
04
04
04
04
04
07
07
07
010
021
021
021
021
021
021
021
024
024
024
024
024
027
027
027

At_om_2

K1
K1
K1
K1
K1
K1
K1
K1
K1
K1
K1
K1
K1
K1
K1
K1
K2
K2
K2
K2
K2
K2
K2
K2
K2
K2
K2
K2
K2
K2
K2

Atom 3

01

04

04

07

07

010
010
04

07

07

010
010
07

010
010
010
021
024
024
027
027
030
030
024
027
027
030
030
027
030
030

Anglo

113(1)
59.0(6)
154.1(6)
114.1(7)
110.9(7)
100.6(7)
66.5(7)
139.4(9)
60.0(6)
91.2(7)
90.1(6)
97.6(6)
93(1)
57.3(7)
143.8(9)
158(1)
115(1)
66.4(9)
147.1(9)
123(1)
102.8(9)
110.7(9)
54.1(8)
132(1)
59.2(9)
86.4(9)
93.7(7)
96.3(8)
90(1)
60.2(7)
143.5(9)

 

152

Table A-9. Bond Angles (in Degrees) for K+(dicyclohexano-24C8)Na'

 

(Continued)

Atom; ALQLL; Atom; Angle
O30 K2 O30 155(1)
K1 0] C2 121(2)
K1 01 C12 109(2)
C2 01 C12 101(3)
K1 04 C3 117(2)
K1 04 C5 120(2)
C3 04 C5 93(2)
K1 07 C6 119(2)
K1 07 C8 124(2)
C6 07 C8 106(3)
K1 010 C9 115(2)
K1 010 C11 118(2)
C9 010 C11 99(3)
K2 021 C22 111(3)
K2 021 C32 125(3)
C22 021 C32 119(4)
K2 024 C23 102(2)
K2 024 C25 116(3)
C23 024 C25 130(3)
K2 027 C26 101(2)
K2 027 C28 109(2)
C26 027 C28 113(3)
K2 030 C29 105(2)
K2 030 C31 113(2)
C29 030 C31 115(3)
01 C2 C3 104(3)
04 C3 C2 102(3)
04 C5 C6 99(3)
07 C6 C5 111(3)
07 C8 C9 109(3)

 

153

Table A-9. Bond Angles (in Degrees) for K+(dicyclohexano-24C8)Na‘

 

(Continued)

Atom 1 Atom 2 Atom 3 Anglo
010 C9 C8 98(3)
010 C11 C12 111(3)
010 C11 C16 93(3)
C12 C11 C16 104(3)
01 C12 C11 132(2)
01 C12 C13 120(3)
C11 C12 C13 105(3)
C12 C13 C14 85(3)
C13 C14 C15 95(3)
C14 C15 C16 117(4)
C11 C16 C15 107(4)
021 C22 C23 112(4)
024 C23 C22 113(3)
024 C25 C26 111(4)
027 C26 C25 113(3)
027 C28 C29 99(4)
030 C29 C28 111(4)
030 C31 C32 116(3)
030 C31 C33 99(2)
C32 C31 C33 95(2)
021 C32 C31 79(3)
021 C32 C36 92(3)
C31 C32 C36 102(3)
C31 C33 C34 107(3)
C33 C34 C35 112(4)
C34 C35 C36 86(3)
C32 C36 C35 73(2)

 

Estimated standard deviations in the least significant figure are
given in parentheses.

154

 

 

Table A-10. Positional Parameters and Their Estimated Standard
Deviations for Rb+(18C6)(12C4)Na'
Atom x y z B(A2)
Rb 0.3930(1) 1/4 0.35033(8) 3.00(5)
Na 0.1019(6) 3/4 0.3595(4) 8.3(4)
Ol 0.5803(6) 1/4 0.4434(5) 4.4(5)
O4 0.5076(4) 0.0667(5) 0.3872(5) 5.2(4)
07 0.4262(5) 0.0756(6) 0.2349(5) 6.3(5)
010 0.3476(6) 1/4 0.1765(6) 6.6(7)
011 0.2055(4) 0.3545(5) 0.3433(4) 6.0(4)
014 0.2951(5) 0.3518(6) 0.4968(5) 7.6(5)
C2 0.5781(7) 0.1645(9) 0.4916(6) 6.5(7)
C3 0.5873(7) 0.0769(9) 0.4386(7) 6.2(7)
C5 0.518(1) -0.0084(9) 0.3293(9) 8.0(9)
C6 0.431(1) -0.015(1) 0.279(1) 10(1)
C8 0.350(1) 0.075(1) 0.1795(9) 11(1)
C9 0.358(1) 0.162(1) 0.1266(7) 10(1)
C12A 0.151(1) 0.396(1) 0.400(1). 3.3(4)*
C12B 0.215(2) 0.437(2) 0.414(1) 4.4(6)*
C13A 0.222(2) 0.383(2) 0.499(2) 6.4(7)*
C13B 0.228(2) 0.440(2) 0.457(1) 4.0(5)*
C15A 0.302(1) 0.260(6) 0.574(1) 7.6(8)*
C15B 0.246(1) 0.326(1) 0.561(1) 4.6(5)*
C16A 0.136(1) 0.278(1) 0.2907(7) 2.6(4)*
C16B 0.125(1) 0.312(1) 0.344(1) 4.7(5)*

 

Starred atoms were refined isotropically and the multiplicities are

all 0.5.

155

Table A-ll. Bond Distances (in Angstroms) for
Rb+(18C6(12C4)Na‘(I) and Rb+(l8C6(12C4)Rb‘(II)

 

 

Atom 1 Atom 2 Distance
1 II
Rb Ol 3.046(8) 3.05(1)
Rb O4 3.038(7) 3.004(8)
Rb O7 3.101(8) 3.08(1)
RB 010 2.969(9) 2.98(2)
Rb 011 2.988(6) 2.964(7)
RB 014 3.128(7) 3.155(9)
01 C2 1.42(1) 1.40(1)
04 C3 1.41(1) 1.41(2)
04 C5 1.42(1) 1.43(2)
07 C6 1.44(2) 1.41(3)
07 C8 1.41(1) 1.42(3)
010 C9 1.47(1) 1.44(3)
011 C12A 1.34(2) 1.27(2)
011 C12B 1.64(2) 1.55(3)
011 C16A 1.68(1) l.78(2)
011 C16B 1.27(2) 1.26(2)
014 C13A 1.11(2) 1.12(3)
014 C13B 1.67(2) 1.70(3)
014 C15A 1.80(5) 1.67(3)
014 CISB 1.33(2) 1.29(2)
C2 C3 1.49(1) 1.49(2)
C5 C6 1.48(2) 1.48(3)
C8 C9 1.49(2) 1.52(5)
C12A C13B* 1.56(3) 1.69(4)
C128 C13A* 1.60(3) l.51(4)
C15A CISB* 1.43(6) 1.60(3)
C16A C16B* 1.53(2) 1.41(3)

 

* Atoms at X, 0.5-Y, Z position. Estimated standard deviations in
the least significant figure are given in parentheses.

Table A-12. Bond Angles (in Degrees) for Rb+(18C6(12C4)Na'(I) and

156

Rb+(18C6(12C4)Rb'(II)

 

Atom 1
01

01
01
01
01
04
04
04
04
04
07
07
07
07
010
010
011
011
014

C3

C6 -
C9
C12A
C12B
C13A
C13B
01
04
04
07

Atom 2

 

§§§§§§§§§§§§§§§§§§§

OOO
\l-bH

010
011
011
014
014

C3
C5
C6

Atom 3
04
07
010
011
014
04*
07
010
011
014
07*
010
011
014
011
014
011*
014
014*

C5
C8
C9
C16A
C16B
C15A
C15B
C3

C6
C5

Angle I
56.1(1)

1(KL8(2)
133.0(2)
140.8(2)
881x2)
111.2(3)
541x2)
108.1(2)
94.4(2)
72.9(2)
100.6(3)
5449(2)
74.9(2)
102.0(2)
76.9(2)
132.0(2)
57.1(3)
55.5(2)
52.9(3)
111(1)
113.9(9)
111(1)
110(1)
108(1)
112(1)
107(2)
103(1)
108.9(9)
111.7(9)
110(1)
106(1)

Anglo n
55.8(2)
101.1(3)
134.2(4)
140.2(3)
88.7(3)
110.5(4)
54.7(4)
108.9(3)
94.6(3)
72.2(2)
99u8(6)
54.9(3)
75.4(2)
101.6(4)
76.6(3)
130.7(3)
57.1(4)
5446(3)
54.5(5)
113.2(2)
112(1)
110(3)
110(3)
100(2)
110(2)
112(2)
107(2)
110(2)
109(2)
109(2)
109(2)

 

Table A-12. Bond Angles (in Degrees) for Rb+(l8C6(12C4)Na'(I) and

157

Rb+(18C6(12C4)Rb'(II) (Continued)

 

Atom 1 Atom 2 Atom 3 Angle I Anglo II
07 C8 C9 110(1) 108(3)
010 C9 C8 108.1(9) 108(2)
011 C12A C13B 101(1) 90(2)
011 C12B C13A 109(2) 116(3)
014 C13A C12B 102(2) 110(3)
014 C13B C12A 102(2) 106(2)
014 C15A C15B* 116(2) 117(2)
014 C15B C15A* 93(2) 93(2)
011 C16A C16B* 105(1) 105(1)
011 C16B C16A* 106(2) 111(2)

 

* Atoms at X, 0.5-Y, 2 position.
Estimated standard deviations in the least significant figure are
given in parentheses.

158

 

 

Table A-13. Positional Parameters and Their Estimated Standard
Deviations for Rb+(18C6)(12C4)Rb'
Atom x y z B(A2)
Rb 0.3921(1) 1/4 0.3540(1) 3.8(1)
Rb' 0.1032(2) 3/4 0.3520(1) 8.6(2)
01 0.5780(8) 1/4 0.4458(7) 6.3(9)
O4 0.5055(6) 0.0757(6) 0.3906(7) 7.1(6)
07 0.4250(8) 0.0837(9) 0.2407(8) 8.9(8)
010 0.343(1) 1/4 0.181(1) 10(1)
011 0.2070(6) 0.3500(6) 0.3489(6) 7.3(6)
014 0.2941(6) 0.3520(9) 0.4974(6) 10.3(8)
C2 0.575(1) 0.168(1) 0.491(1) 9(1)
C3 0.586(1) 0.083(1) 0.439(1) 12(2)
C5 0.516(1) 0.002(1) 0.334(1) 11(1)
C6 0.430(2) -0.001(2) 0.284(2) 14(2)
C8 0.346(2) 0.082(3) 0.189(1) 17(3)
C9 0.353(1) 0.167(3) 0.136(1) 19(3)
C12A 0.145(2) 0.378(2) 0.398(2) 4.7(6)*
C12B 0.201(3) 0.423(3) 0.416(2) 8(1)*
C13A 0.223(2) 0.387(2) 0.497(2) 6.3(9)*
C13B 0.231(2) 0.436(2) 0.449(2) 3.8(7)*
C15A 0.302(1) 0.271(3) 0.568(1) 5.4(8)*
C15B 0.242(2) 0.324(2) 0.555(1) 5.2(7)*
C16A 0.137(1) 0.271(2) 0.2918(9) 4.2(7)*
C16B 0.128(2) 0.311(2) 0.339(2) 4.7(7)*

 

Starred atoms were not refined and the multiplicities are all 0.5.

APPENDIX B

The Subroutine Program for the Multiple Data Set Fitting

0000

00000000

..EQN_2.INC
..Please enter the equations for CALC and CALCF(i)
.(i=l,2,....,50)

.Consider the input format of FORTRAN 77.

GO TO (1000,1001,1002) JDAT

1000 CONTINUE

R=DEXP((- 3. 645d0*SQRT(l. 0d0*XX( (1)) )/
& (l. Od0+2. 88d0*DSQRT(l. 0d0*XX(l))))
A: (- 1. 0d0+DSQRT(DABS(1. 0d0+4. Od0*U(3)*XX(l)*R*R)))/

& (2. Od0*U(3 )*R*R)
B=U(3)*A*A*R*R
C=DSQRT(DABS(A/(U(2)*(l.0d0+U(5)*A))))

D=U(S)*A*C
CALC=(U(6)*C+U(7)*D+A*U(l)+B*U(4))/XX(1)
CALCF(1) = CALC

IF(IMETH.NE.-l) GO TO 35

RETURN

1001 CONTINUE

R=DEXP({-3.645d0*SQRT(l.0d0*XX(1)))/

& (l.0d0+2.88d0*DSQRT(1.0dO*XX(l))))
A=-1.0d0+SQRT(ABS(1.0dO+4.0d0*U(5)*XX(1)*R*R))
B=2.0d0*U(5)*XX(1)*R*R
CALC=(A/B)*(U(6)-U(7))+U(7)

CALCF(3) = CALC
IF(IMETH.NE.-l) GO TO 35
RETURN

1002 CONTINUE

R=DEXP((-3.645d0*SQRT(1.0dO*XX(1)))/

& (1.0d0+2.88d0*DSQRT(l.Od0*XX(1))))
X=ABS(U(11)+XX(1)*U(11)*U(8)*R*R)
A:(-1.0d0+SQRT(l.0d0+4.0d0*XX(1)*X))/(2.0d0*X)
B=U(ll)*A*A
C=U(3)*A*(A+B)

D=U(8)*R*R*B*(A+B)
CALC=(A*U(1)+B*U(9)+C*U(4)+D*U(10))/XX(1
CALCF(4) = CALC

..XX(l) = independent variable.
..CALC = computer calculated value of Y
..XX(NOVAR) = refers to an experimental value of Y
.( X(NOVAR,I) )
.CALCF(1), CALCF(2), ...... , CALCF(50) are

..available for functions
..which can be plotted.
.constant value are labeled CONST(l), ... CONST(16)

159

APPENDIX C

The Subroutine Program for the KINFIT Fitting

C...EQN_2.INC
C...Please enter the equations for CALC and CALCF(i)
C

0000

.Consider the input format of FORTRAN 77. Do not
.write before or after

.(i=1,2,....,50)

C...the I marks indicated below
C23456789012345678901234567890123456789012345678901234
C567890123456789012345

1001

1002

1003

1005

6001

6002

IF (XX(1).EQ.0.0) GOTO 1007

A=2.0*XX(1)-CONST(1)+U(3)/U(l)

B=(l.0+U(3)*XX(1)-CONST(1)*U(3))/U(l)

C=-CONST(1)/U(1)

Q=(A*A-3.0*B)/9.0

Q3=Q**3

R=(2.0*A**3-9.0*A*B+27.0*C)/54.0

R2=R*R

IF (R2.LT.QB) GOTO 1001

=-(R+SQRT(R2-Q3))**(1/3)

GOTO 1005

CONTINUE

AN=R/SQRT(Q3)

ANG=ACOS(AN)

X1=-2.0*SQRT(Q)*COS(ANG/3.0)-A/3.0

IF (X1.GT.0.0) GOTO 2001

CONTINUE

X2=-2.0*SQRT(Q)*COS((ANG+2.0*3.1415926)/3.0)-
(A/3.0)

IF (X2.GT.0.0) GOTO 2002

CONTINUE

X3=-2.0*SQRT(Q)*COS((ANG-Z.0*3.l415926)/3.0)-
(A/3.0)

IF (X3.GT.0.0) GOTO 2003

GOTO 2004

CONTINUE

IF (AA.EQ.0.0) GOTO 6001

BB=Q/AA

GOTO 6002

CONTINUE

RO0T=-A/3.0

GOTO 1008

CONTINUE

RO0T=AA+BB-A/3.0

GOTO 1008

160

C

00000000

2001

2002

2003

2004

1007

1008

1006

..XX(1)
..CALC
..XX(NOVAR)
..( X(NOVAR,I) )
.CALCF(1), CALCF(2), ...... , CALCF(50) are
..available for functions

..which can be plotted.

.constant value are labeled CONST(l), ... CONST(16)

161

CONTINUE

ROOT=X1

IF (RO0T.LT.0.005) GOTO 1008

GOTO 1002

CONTINUE

ROOT=X2

IF (ROOT.LT.0.005) GOTO 1008

GOTO 1003

CONTINUE

ROOT=X3

IF (RO0T.LT.0.005) GOTO 1008

CONTINUE

WRITE(*,*) ’NO SOLUTION FOUND’

CONTINUE

RO0T=0.005

CONTINUE

A1=ROOT

XY=1.0+U(1)*A1*A1+U(3)*Al

XYZ=XX(l)/XY

A2=U(3)*A1*XYZ

A3=U(l)*XYZ*Al*A1

CALC:(A1*CONST(2)+A2*CONST(3)+2.0*A3*U(2))/
CONST(l)

WRITE(LUNOUT,1006)A1,A2,A3

CALCF (1) = CALC

FORMAT(3F20.16)

independent variable.

computer calculated value of Y

refers to an experimental value of Y

LIST OF REFERENCES

10.

11.

12.

13.

14.

15.

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