NMR Studies of Inclusion Compounds Stockholm University

NMR Studies of Inclusion
Compounds
Sahar Nikkhou Aski
Stockholm University
© Sahar Nikkhou Aski, Stockholm 2008
ISBN 978-91-7155-715-5
Printed in Sweden by US-AB, Stockholm 2008
Distributor: Department of Physical, Inorganic and Structural Chemistry
Stockholm University
ii
NMR Studies of Inclusion Compounds
Sahar Nikkhou Aski
Abstract
This thesis presents the application of some of the NMR methods in studying hostguest complexes, mainly in solution. The general focus of the work is on
investigating the reorientational dynamics of some small molecules that are bound
inside cavities of larger moieties. In the current work, these moieties belong to two
groups: cryptophanes and cyclodextrins. Depending on the structure of the cavities,
properties of the guest molecules and the formed complexes vary. Chloroform and
dichloromethane are in slow exchange between the cage-like cavity of the
cryptophanes and the solvent, on the chemical shift time scale, whereas
adamantanecarboxylic acid, quinuclidine and 1,7-heptanediol in complex with
cyclodextrins are examples of fast exchange. Kinetics and thermodynamics of
complexation are studied by measuring exchange rates and translational selfdiffusion coefficients by means of 1-dimenssional exchange spectroscopy and
pulsed-field gradient (PFG) NMR methods, respectively. The association constants,
calculated using the above information, give estimates of the thermodynamic
stability of the complexes. Carbon-13 spin relaxation data were obtained using
conventional relaxation experiments, such as inversion recovery and dynamic NOE,
and in some cases HSQC-type (Hetereonuclear Single Quantum Correlation
Spectroscopy) experiments. Motional parameters for the free and bound guest, and
the host molecules were extracted using different motional models, such as LipariSzabo, axially symmetric rigid body, and Clore models. Comparing the overall
correlation times and the order parameters of the free and bound guest with the
overall correlation time of the host molecule, one can estimate the degree of the
motional restriction, brought by the complexation, and the coupling between the
motion of the bound guest and the reorientation of the host molecule. In one case,
the guest motions were also investigated inside the cavities of a solid host material.
iii
iv
Contents
List of papers......................................................................................................vii
Preface ................................................................................................................ 1
1- Supramolecular structures............................................................................. 2
1.1
Classification ......................................................................................................2
1.1.1 Complex or clathrate.......................................................................................3
1.1.2 Interactions .....................................................................................................4
1.1.3 Host and guest types ......................................................................................6
1.2 Selectivity..............................................................................................................21
1.3 Application ............................................................................................................22
2- NMR spectroscopy....................................................................................... 24
2.1 - Spin Hamiltonians ...............................................................................................24
2.2 Relaxation - A very brief introduction.....................................................................27
2.2.1 Relaxation mechanisms................................................................................27
2.2.2 Spectral density functions .............................................................................29
2.2.3 Relaxation parameters..................................................................................31
2.2.4 Experimental methods ..................................................................................34
2.3
Chemical exchange ..........................................................................................39
2.4 Translational diffusion ...........................................................................................41
3- Dynamics of cyclodextrins and cryptophanes studied by NMR ................ 44
3.1 Stoichiometry and binding constant.......................................................................44
3.2 Nuclear magnetic relaxation..................................................................................46
4- Discussion of the papers ............................................................................. 48
4.1 Papers I-II .............................................................................................................49
4.2 Papers III-V ...........................................................................................................50
Acknowledgment .............................................................................................. 53
References ........................................................................................................ 54
v
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List of papers
This thesis is based on the following publications and manuscripts.
I. Exchange kinetics and 13C NMR relaxation studies of inclusion
complexes of dichloromethane and some cryptophanes
S. Nikkhou Aski, A.Y.H. Lo, T. Brotin, J.-P. Dutasta, M. Edén
and J. Kowalewski,
Journal of Physical Chemistry C, in press
Reproduced with kind permission from American Chemical Society ©2008
II. Inclusion complexes of cryptophane–E with dichloromethane and
chloroform: A thermodynamic and kinetic study using the 1DEXSY NMR method
S. Nikkhou Aski, Z. Takacs and J. Kowalewski
Magnetic Resonance in Chemistry, in press
Reproduced with kind permission from John Wiley & Sons Limited ©2008
III. Reorientational dynamics of adamantanecarboxylic acid in
complex with β-cyclodextrin
Z. Tosner, S. Nikkhou Aski and J. Kowalewski
Journal of Inclusion Phenomena and Macrocyclic Chemistry 55
59-70 (2006)
Reproduced With kind permission from Science+Bussiness Media
IV. Quinuclidine compelx with α-cyclodextrin: a diffusion and 13C
NMR relaxation study.
S. Nikkhou Aski and J. Kowalewski
Magnetic Resonance in Chemistry 46 261-267, (2008)
Reproduced with kind permission from John Wiley & Sons Limited ©2008
V. Interaction between α-cyclodextrin and 1,7-heptanediol. An NMR
study of diffusion and carbon-13 relaxation
S. Nikkhou Aski, Z. Takacs and J. Kowalewski
Manuscript
vii
The following articles are not included in the thesis.
- The effect of pendant-arm modification and ring size on the
dynamics of cyclic polyamines
J. Wyrwal, G. Schroeder, J. Kowalewski and S. Nikkhou Aski
Journal of Molecular Structure 274-279, (2006)
- Cross-correlated and conventional dipolar carbon-13 relaxation in
methylene groups in small, symmetric molecules
L. Ghalebani, P. Bernatowicz, S. Nikkhou Aski and J. Kowalewski
Concepts in Magnetic Resonance Part A 30A 100-115, (2007)
- Extensive NMRD studies of Ni(II) salt solutions in water and watergrycerol mixtures
J. Kowalewski, A. Egorov, D. Kruk, A. Laaksonen, S Nikkhou
Aski, G. Parigi and P.-O. Westlund
Submitted
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Preface
The research work described in this dissertation is the result of my PhD
study at the division of physical chemistry during the period 2004 - 2008.
The thesis is mainly centered on the issue how the motional properties of
small molecules change in complexation with somewhat larger moiety
named host molecules in liquids. Since the discovery of the naturally
occurring supramolecules, there has been an intense interest in studying
them. During the past decades, researchers have been doing great amounts of
work and investigation in synthetic chemistry to approach the artistic way
that nature has designed the functional aggregations of molecules1.
The central approach used in this work is NMR nuclear spin relaxation, in
particular, relaxation of the 13C spin. As complementary tools, it is also taken
advantage of some other techniques such as diffusion measurements and
kinetic studies using NMR to partly cover the kinetics and thermodynamics
of the chemical exchange going on in the systems under study. I would like,
however, to emphasize that the most looked forward to aspect of the work
was to investigate the effect of complexation on the motion rather than the
thermodynamics of inclusion. The main body of the summary is split into
two parts: an account of NMR spectroscopy theory and methods, and the
systems undergone investigation. The thesis starts with an explanation of
inclusion phenomena and the systems chosen to be studied. To maintain
briefness, this part is limited mainly to two classes of host molecules. In the
following chapter I present the outlines of nuclear magnetic resonance
spectroscopy and nuclear spin relaxation. In the same chapter, the
experimental approaches employed to obtain the relaxation parameters of the
components of the systems is reviewed. In the next part, kinetics and
thermodynamics of the complexation and their significance in the
applicability of the relaxation study of the system is discussed. There is at
last a final conclusion and discussion chapter. This chapter covers the
concluding remarks of the papers on which this thesis is set up.
1
1- Supramolecular structures
Molecular recognition2 is the study of a very interesting group of compounds
in which the components are held together by non-covalent bonds3.
Although non-covalent bonds are of much weaker strength than covalent
analogues, the constructed assemblies can be quite complicated.
Recognition may occur in all phases of gas, liquid, solid and even interface.
Molecular assemblies are formed in well-defined conditions and their
stability is under thermodynamic control. A very general classification
divides supramolecules into two main groups4. One class comprises of selfassemblies of molecular units of the same size providing compounds that can
accept smaller molecules in the formed spaces within them. The other class
includes a group of large molecules that are organized prior to inclusion in
such a way that they can provide enclosed spaces or binding sites for
accommodation of smaller components. However, some consider these
classifications as just different nomenclatures given by Cram (host–guest
chemistry) and Lehn (supramolecular chemistry)5 with the common feature
of non-covalent bonding.
The first report of this type of research dates back to the 1950s when
Cramer introduced the inclusion complexes of cyclodextrins6. The field was
further developed by the vast research of Cram and co-workers on molecular
containers7. Cyclodextrins and some other biologically important molecules,
such as carbohydrates in general, nucleotides, steroids, and oligopeptides all
occur in nature. After a while scientists began to synthesize8 similar
functional systems, highly analogous to the naturally existing ones. This
activity started with the synthesis of hollow calixarenes by Collet and Cram
in the early 1980s9, 10. The main motive was to produce host molecules with
controlled cavity size and shape11-13.
1.1 Classification
Over the years, since the discovery of the first host molecule, the number of
structures that are identified or newly synthesized has been growing quickly,
resulting in various nomenclatures and classifications. There have been
several attempts to sort this class of compounds into different families.
However, there are always grey areas where different groups and definitions
2
overlap. According to the topology, type, application and interactions
involved, they may be divided into different classes14.
1.1.1 Complex or clathrate
A very fundamental classification assigns supramolecular systems to one of
two groups. At one extreme, as mentioned above, there are pre-organized
lattice of molecules, called clathrates, which retain smaller compounds by
steric barriers. Some examples are urea and graphite15, illustrated in figures
1.1a and b. These compounds normally exist in solid phase and decompose
upon dissolution. At the other extreme, there are complexes that are basically
coordinated systems of host and guest, which do not lose their structures
when dissolved. Crown ethers and cryptophanes are among the typical
examples of this category (see figures 1c and d). There are of course other
types of aggregations that fall in between these two limiting situations and
usually take a hybrid name of both mentioned categories.
a)
b)
N
NN
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
3
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
c)
d)
O
O
O
O
C+
N
O
H3CO
O
N
O
N
O
O
O
O
O H3 O H3
CH2Cl2
H3CO H CO
3
O
O
O
OCH3
O
Figure 1.1. Schematic representation of a) Graphite and b) Urea clathrates,
and c) 27-crown-9 and d) cryptophane-A complexes.
1.1.2 Interactions
Another criterion for defining supramolecular systems is based on the forces
operating between the components. Strong and specific recognition takes
place by means of involving several non-covalent bonds depending on the
structures and functions. For instance, “biologically important guest
molecules” have different hydrogen bonding sites. In order to form hydrogen
bonds, host and guest molecules must be perfectly aligned. Consequently,
the complexation produces directed molecular building blocks. On the other
hand, while the organization and selectivity are provided by hydrogen
bonding, other types of interactions such as hydrophobic effects enhance the
complexation16.
Table 1.1 Strength of covalent bonds in comparison with several noncovalent interactions.
Type of interaction
Strength
kJ.mol-1
covalent bond
350–950
Coulomb
250
ion–dipole
50–200
hydrogen bond
10–65
dipole–dipole
5–50
cation–π
5–80
π–π
0–50
van der Waals forces
<5
hydrophobic effects
Hardly assessable
metal–ligand
0–400
4
Compared to the strength of covalent bonds, covering the range of 350
kJmol-1 for a single bond to 942 kJmol-1 for the triple bond in N2, interactions
involved in molecular recognition are of weaker magnitude1. The strength of
covalent and non-covalent bonds is presented in Table 1.117.
Electrostatic forces, such as ion–ion, ion–dipole and dipole–dipole are
based on Columbic attraction. Strong bindings are achieved when these
types of interactions are involved in attaching the guest to the host. Another
feature of electrostatic forces, in the case of dipoles, is that suitable
alignment is of great importance to high binding efficiency17.
Hydrogen bonding is a very common interaction in biological systems.
Many proteins retain their shape by means of hydrogen bonding and the
double helix structure of DNA is stabilized by hydrogen bonds. They have
the same directional nature as exists in the case of two dipoles. In fact, the
hydrogen bonding relation can be considered as an attraction between two
dipoles18.
Cation–π interaction is also known to be relevant in structural biology. As
an example, one can consider the association of K+ with benzene19 and the
binding of acetylcholine20 in biological systems.
π–π Stacking forces act between aromatic rings of molecules containing
them. The relative ring positions may be “face to face” or “face to edge”, of
which the latter one is weaker17.
Van der Waals forces refer to the attraction between induced dipoles of
different species or with non-polar molecules. Small organic molecules are
usually included loosely into cavities or within crystalline lattices by means
of van der Waals interactions18.
The expulsion of non-polar weakly dissolved molecules by solvent
molecules, particularly water, is called hydrophobic effect. The attraction
between the water molecules in their hydrogen-bonded network is so strong
that non-polar organic molecules are forced out of the network. Inclusion of
organic molecules in cyclodextrins is a well-known example of hydrophobic
effects in supramolecular chemistry. Hydrophobic effects result in favorable
free-energy changes in solution. The presence of water inside the
hydrophobic cavities of host molecules such as cyclodextrins is energy
expensive. Upon guest incorporation, water molecules are driven out of the
cavity. These water molecules are stabilized by joining to the pool of solvent
molecules. It is also more entropy-favored when the organic guest molecules
are replaced with the water molecules in the bulk solvent by complexing to
the host molecules17.
An important factor influencing the host–guest interactions in solution is
the solvent. As discussed above, for example hydrophobic effects arise from
solvent–solvent or solvent–components relationships. The solvent can
modulate the thermodynamic stability of the complex to a great extent.
Moreover, the dielectric constant of the solvent is defined by the polarity of
solvent molecules, and consequently controls the electrostatic interactions
5
between components in solution. This can particularly be very crucial in ion
recognition. Sometimes the solvent can be a strong competitor in hydrogen–
bonded host–guest systems if the individual solvent molecules are good
hydrogen bond donors and acceptors. In such cases, guest or host molecules
are preferentially solvated rather than complexed18.
1.1.3 Host and guest types
Guest molecules can be in the forms of cation, anion or neutral molecules.
One way of classification is according to complexation ability of different
host molecules with each group of the mentioned guest molecules.
1.1.3.1 Cation binding hosts
Cation guests are bound to hosts through electrostatic ion–dipole
interactions. In many cases hydrogen bonds enhance the complexation even
more. The cations can be of either metal or nonmetal type. There are many
examples of cation binding, furnished particularly by the life sciences, and
among synthetic host molecules. In the B12 vitamin, a corrin macrocycle
binds cobalt ion and iron is complexed with porphyrin macrocycles in haem
groups. In MRI, Gd3+complexes are used as contrast agents, and
coordination of platinum to DNA hinders the growth of cancerous cells21.
Some of the general groups of host molecules that are able to bind cations,
such as crown ethers, cryptands, spherands, calixerenes and siderophores are
discussed briefly below.
Crown ethers, considered as the simplest macrocyclic ligands, were first
introduced by Charles Pedersen in 1967. Their structure is composed of
ether oxygen atoms linked together via organic linkers such as methylene
groups. When complexing transition metals, the oxygens can be replaced by
some softer donors such as sulfur and nitrogen atoms. There is an ion–dipole
attraction between the cation and the oxygen donor atoms of the rings. The
most stable complexes form when there is an optimal fit between the
cationic radius and the cavity size. This optimal spatial fit concept results in
selective complexation of crown ethers with certain cations. In figure 1.2,
two crown ethers of different cavity diameters are presented, which form
complexes selectively with two different cations22.
6
O
O
O
O
O
O
K
+
+
O
O
Cs
O
O
O
Cavity diameter = 2.6 - 3.2 Å
O
O
Cavity diameter = 3.4 - 4.3 Å
+
+
K diameter = 2.66 Å
Cs diameter = 3.34 Å
18-crown-6
21-crown-7
Figure 1.2 Role of size in selective complexation of crown ethers with
cations.
The preference for binding a cation with a certain diameter maximizes the
electrostatic interaction between the two species. Most of the complexes are
of 1:1 stoichiometry, although there are some examples where large crowns
complex two cations simultaneously. Besides metallic cations, crown ethers
can encapsulate ammonium and alkyl ammonium cations through hydrogen
bonding. Therefore, a combination of electrostatic and hydrogen bonding
stabilizes the complexation. The key point to this type of complexes is the
complementary orientation of the oxygen atoms in the crown ether to form
the hydrogen bonds17. The role of symmetry in efficient complexation is
illustrated in figure 1.3.
O
O
Me
O
O
Me
O
H
+ H
Me
Me
H
O
O
+ H
Me
Me
O
O
H
O
O
18-crown-6
15-crown-5
H
Figure 1.3 Role of symmetry in selective complexation by crown ethers.
Cryptands are three-dimensional, cage-like analogues to crown ethers.
They have high affinity for complexing group 1 and 2 metal cations.
7
Compared to crown ethers, cryptands encapsulate the cation entirely in a
more selective way. This is due to their bicyclic structure and their more
enhanced ionophore-like properties. Higher stability constants are therefore
attained for cation complexes compared to those of analogous crown ethers.
This is ascribed to favorable enthalpy and entropy changes when the cation
is shielded from the solvent molecules inside the sphere of cryptand. The
complexes are commonly named cryptates23. The most famous and
commercially available cryptand, [2.2.2]cryptand, is shown in figure 1.4.
N
O
O
O
O
O
O
N
Figure 1.4 [2.2.2]cryptand
First discovered by Donald Cram, spherands are another group of
macrocyclic cation hosts, synthesized with a preorganized structure. In
contrast to crown ethers and cryptands, which have flexible structures in
solution, these molecules have a convergent pocket-shape cavity for cation
guests. This structure rigidity enables them to have better selectivity and
bonding strength compared to crown ethers and cryptands. Higher bonding
strength gives rise to slower complexation – decomplexation kinetics in
these systems. However, their preorganized rigid structures limit them to
binding small-size cations only, such as sodium ions. Figure 1.5 illustrates
how oxygen atoms are in an octahedral configuration for binding cations24.
O
O
O
O
O
O
Figure 1.5 One of the first synthesized spherand host molecules.
8
Calixarene structure is composed of phenol parts, linked by methylene
groups. They exist in four different conformations, namely, cone, partial
cone, 1,3- alternate and 2,2- alternate (see figure 1.6). Depending on the
polarity of the solvent, the amount of each conformation may vary in
solution. In a polar solvent, for example, the cone conformation constitutes
the highest amount. The reason is that the cone is the most polar of all four
conformations, by having all OH groups located to one side of the molecule.
In this conformation, cations can either be held by the OH groups of the
lower rim or be involved in a π-cation interaction with the aromatic rings17.
RO
OR
OR
OR OR RO
Cone
OR OR
Partial Cone
OR
RO
OR
OR
OR OR
1,3-alternate
OR
OR
1,2-alternate
Figure 1.6 Different conformations of Calixarenes molecules.
Siderophores exist both in natural and synthetic form. Their general name
means “iron bearer” reflecting the fact that their ability to complex iron ions
is enormous. The most frequent naturally occurring oxidation state of iron,
Fe(III), is not soluble in water. This is a problem when, at physiological pH
of about 7, a concentration of 10-7 mol dm-3 is needed. To tackle this
difficulty, in plants, bacteria and some higher organisms the Fe3+ delivery to
the cell is accomplished effectively by siderophores. Siderophores complex
with iron(III) through oxygen atoms in hydroxamate or catecholate groups.
Figure 1.7 shows how enterobactin, a bacterial siderophore, makes a ∆
configuration around the metal ion by catecholates18.
9
OH
O
OH
NH
O
O
O
Fe
O
O
3+
O
O
O
O
H
N
O
HN
HN
OH
HO
O
O
O
O
N
H
NH
O
O
∆ configuration
enterobactin
O
HO
OH
Figure 1.7 Enterobactin makes a ∆ configuration around Fe(III).
1.1.3.2 Anion binding hosts
Anion binding is an important process that benefits different areas such as
chemistry, environmental chemistry, biology and medicine. Anion reactivity
as catalyst or base can be altered by binding to a host molecule. Anion
pollutants and toxic byproducts can be selectively sensed and extracted by
recognition processes. 70 to 75 per cent of biologically important molecules
such as adenosine triphosphate(ATP) and deoxyribonucleic acid (DNA) are
negatively charged18.
In extending the discussion from cation binding to anion complexation,
some new aspects emerge which can be attributed to the special features of
anion moieties. The new features of anions compared to cations comprise of
their size, pH dependence of properties, the way they interact with solvent
molecules, and their geometry. Compared to their isoelectronic cations,
anions are relatively larger. This means that the receptors encapsulating them
must have larger cavities. Many anions, such as carboxylates, and
phosphates, exist in a narrow region of pH. Changing the pH can make them
lose their negative charges. Anion solvation depends on size, charge and the
pH range in which the ion exists. In general, anions have higher solvation
free energies than cations of similar sizes. Anions come in different shapes
and geometries. They may exhibit, e.g. spherical (F-, Cl-, Br-, I-,), linear (N3-,
CN-, SCN-, OH-), planar (NO3-, PtCl4-), tetrahedral (PO43-, SO42-, MnO4-),
10
and octahedral (PF6-, Co(CN)63-) geometries, and even some complicated
shapes which are common among biologically important anions17.
The main similarity between cation binding and anion recognition is that
electrostatic forces again play an important role in strengthening the
recognition. The simplest way of hosting an anion could be an electrostatic
ion–ion interaction. There are other options, however, such as arrays of
hydrogen bonding groups acting as electron pair acceptors. The
directionality property of hydrogen bonds makes it possible to differentiate
between anions with different geometries using specifically shaped host
molecules. Another option that works in a similar way to hydrogen bonding
is binding to the Lewis-acid hosts. They also can accept electron pairs into
their vacant orbitals17.
As mentioned above, anion complexation is sensitive to the range of pH.
This issue, however, can be used as a tool to transform a cation receptor to
an anion host. A vast number of cryptand molecules that complex cations
through the nitrogen bridgeheads, and secondary amine chains can bind
anions through protonating the amine groups by varying the solution pH.
However, only cryptands that have large cavities are suitable for this
purpose. The macrotricyclic cryptand in figure 1.8 is a versatile example,
which is commonly named “soccer ball” because of its perfectly spherical
shape. The presence of nitrogen atoms gives it Lewis-base properties so that
it can bind cations. In its tetraprotonated form it is also a good receptor for
ions such as Cl-, forming hydrogen bonds from one side and strengthening
the complexation from the other side by electrostatic interactions with ether
oxygen atoms. In its diprotonated form it can also bind neutral molecules
such as water17.
N
O
O
N
O
O
N
O
O
N
Figure 1.8 The “soccer ball”-shaped cryptand complexing both cations and
anions at different pH.
Two-dimensional macrocycles such as those depicted in figure 1.9, which
are nitrogen analogues of the crown ethers, are the very first anion-binding
hosts. However, the cavity of hexacyclen is partially filled by the NH
protons and cannot accept any anion. There are some large-ring species that
can accommodate large anions such as [Fe(CN)6]4– 17.
11
O
N
H
NH
N
H
NH
HN
NH
NH
HN
H
N
HN
H
N
HN
O
Hexacyclen
Figure 9.1 Crown ethers binding anions.
Expanded porphyrin macrocycles are another interesting class of anion
receptors with protonated nitrogens. They provide the guests with a rigid
cavity of about 5.5 Å diameter. However, a typical example such as
sapphyrin is only able to bind the smallest anion, F–. For the larger chloride
anion, due to poorer fit, the stability is much lower. In contrast, a similar
host with a somewhat larger cavity yields stronger complexation with
chloride anion than with fluoride (see figure 1.10)18.
R
R
2
R
2
N
R
+
1
R
1
R
N
N
H
H
H
H
2
N
N
R
+
1
R
2
N
+
+
H
H
H
H
H
2
R
N
R
1
2
R
2
R
N
R
+
R
N
2
R
2
+
H
2
1
R = Me, R = Et
N
2
R
2
2
2
R = Me, R = Et
Figure 1.10 Expanded porphyrin macrocycles
There are two disadvantages to charged hosts, which can be avoided by
employing neutral receptors. The disadvantages originate from the
nondirectional nature of electrostatic interactions and the presence of
12
1
counter-ions of the hosts. Despite strong binding by electrostatic interaction,
charged hosts can bind to almost all anions with different strength of
complexation, which results in reduced selectivity. The counter-ion itself
could be a competitor of the target anion guest and reduces the affinity of the
host for other anions. A very practical replacement for electrostatic
interaction could be the hydrogen binding interactions that are at the same
time directional and strong. An example is calyx[4]pyrrole, shown in figure
1.11, which has a very small cavity in which it is possible to bind small
anions. In CH2Cl2, it binds fluoride with a binding constant of 1.7×104 M-1
with a high selectivity factor of 50 over chloride inclusion. Another
interesting feature of this host is that it adopts different conformations when
empty or bound to the anion, which is an indication of conformation
rearrangement induced by complexation17.
N
H
NH
HN
H
N
calix[4]pyrrole
Figure 1.11 calyx[4]pyrrole binds fluoride selectively.
Another well-known group of neutral receptors is named zwitterions,
which are both positively and negatively charged so that the overall charge is
zero. Many anion-binding enzymes and proteins are zwitterionic. Some
examples are the amino acids phenylalanine and tryptophan in which the
CO2H protonates the NH2 group. This also facilitates the proteins membrane
solubility18.
1.1.3.3 Hosts binding neutral molecules
In comparison to strong, permanent electrostatic interactions that hold ions
to the receptors, neutral (mostly organic) molecules may be bonded with
weaker interactions such as hydrogen bonds, van der Waals and hydrophobic
effects. Neutral guests may be either captured in solid-state networks in the
form of clathrates or be embedded within the cavity of cavitands17.
13
Solid state clathrates are made up of both organic and inorganic
compounds. Clathrate hydrates are examples of inorganic clathrate
compounds that form under very specific conditions of pressure and
temperature. For example, there is no cavity in the normal ice structure, but
in the presence of some hydrate-forming guests, such as Cl2, H2S and CS2, a
polyhedral cavity is formed via a template reaction. This new conformation
alters some of the physical properties of ice such as rigidity at different
temperatures, and thermal conductivity17.
Porous aluminosilicates, known as zeolites, exist in two main categories
according to the Si/Al ratio. The featured property of zeolites is their
strongly built channels and cavities which are not disrupted by the guest
species entering or leaving. This feature makes them favorable molecular
sieves and reaction vessels with high selectivity25.
Cycloteriveratrylene (CTV) (shown in figure 1.12) is both a versatile host
molecule and an important building block in two forms, bowl-shaped and
saucer-shaped, used for constructing a vast range of hosts that can bind
either neutral guests or anionic compounds in solid phase and in solution.
H3C
O
O
CH3
O
O
O
O
CH3
Figure 1.12 CTV building block
A wide range of small molecules, such as benzene, water, toluene and
CS2 can be included in CTV in the solid-state. CTV is predominantly a
hydrogen bond acceptor. Even weak hydrogen-bond donor guests such as
benzene can provide hydrogen to methoxy groups oxygens. Otherwise, in a
less probable mode, the methoxy group acts as the hydrogen-bond donor to
the hydrogen bond acceptor guests. These two modes of inclusion are known
as α and β phase of CTV. A new clathrate phase of γ is also known, with a
single example of (CTV)4.acetone. The interesting aspects of the (CTV)4
arrangement are its intracavity inclusion form and its being the non-covalent
analogue of cryptophanes(see below). Buckminsterfullerene (C60) has also
14
been shown to form an intracavity complex with CTV. Highlights of this
inclusion system are a good curvature match between guest and host
structures and complementation of C60 electron deficiency with electron-rich
methoxy groups17.
The inclusion systems discussed above are the results of intermolecular
interactions between the host and guest, so that the guest species fill the
spaces left between the host molecules in their crystalline form. Hosts
possessing permanent cavities can form complexes in the solid state and in
solution. In this way the host can encapsulate the guest in its intrinsic
curvature. These groups of hosts, termed cavitands, are molecular containers
with permanently concave surfaces. They are commonly classified according
to the building blocks that construct them. Besides having intrinsic
curvatures, sometimes the walls of the container may be formed by aryl rings
and a variety of spacers. This series of containers is named cyclophanes. The
presence of aromatic rings linked by aliphatic chains provides a hydrophobic
cavity for non-polar guests particularly in water. Among cyclophanes those
with well-defined cavities set up by parallel aromatic rings are of special
interest. The aromatic groups in the wall empower the receptor with a
preorganized rigid cavity17.
Cyclodextrins(CDs) – CDs are cyclic oligosaccharides composed of six to
eight D-glucopyranoside units that are linked by 1,4-glycosidic(depicted in
figure 1.13) bonds. Cavitands of this group are able to bind neutral, charged
and even radical guests in solid and solution phases26. The three important
naturally occurring ones are α-, β-, and γ-cyclodextrins. These three
members of the family contain six, seven and eight glucopyranoside units,
respectively.
OH
OH
2
4
1
HO
3 O
4
5
O6
2
O
O
HO
3
5
OH
1
O
6
OH
Figure 1.13 1,4-Glycosidic link
Cyclodextrin resembles a truncated funnel with upper and lower rims,
similar to the calixarene cone. The narrower rim is composed of primary
hydroxyl groups while the secondary rim is built up of -CH2OH groups. The
schematic shape of CDs is presented in figure 1.1417.
15
13.70 Å
15.30 Å
16.90 Å
5.70 Å
7.80 Å
9.50 Å
a-CD
β-CD
γ-CD
Figure 1.14 Schematic presentation of CDs.
From α- to γ-CD, physical and chemical properties change smoothly
except for the solubility in water which is much lower for β-CD, than for the
other two and even larger cyclodextrins such as δ-CD. Several arguments
have been put forward to explain this abnormal trend. One explanation is
that, since the water molecule has even numbers of hydrogen bond donors
and acceptors the six- and eight- fold symmetries of the two other CDs are
more compatible with the solvent cage, resulting in more favorable hydration
enthalpy and entropy values. Another explanation states that the
intramolecular hydrogen bonding on the secondary rim of β-CD limits its
interaction with solvent molecules26, 27.
As discussed above, having a rigid and deep cavity is advantageous in
forming stable complexes with non-polar guests, which is based on weak
interactions. For a long time it was thought that cyclodextrins with fully
saturated rings could also offer such rigidity because of their highly curved
surfaces. This understanding relied on X-ray studies28,29. But many
experimental data, mostly acquired using solution and solid-state NMR, and
theoretical investigations proved that cyclodextrins cannot be rigid moieties.
One of the first experimental and theoretical proofs was the low barrier of
internal rotation obtained for the ether C-O bond connecting the rigid
glucopyranose rings30. This is also in agreement with the fact that CDs
should be flexible to some extent to be able to include a variety of guests
with different shapes. However, higher equilibrium constants are also
observed for guests with saturated structures that benefit from higher degree
of freedom, and therefore higher flexibility, to fit into the cavity of the CD31.
CDs are obtained from biochemical degradation of starch, and they
crystallize from water as hydrates with some varying amount of water
captured inside their cavities. Being hydrophobic, the cavity has little
interaction with these water molecules, and therefore these high-energy
16
water molecules are driven out in the process of guest binding. Upon the
release of water molecules, most frequently, a 1:1 inclusion complex is
formed. A common relationship of thermodynamic equilibrium may be
written for the process:
CD.G
CD + G
K=
[CD.G ]
[CD] [G ]
1.1
1.2
where K is the stability constant of the complex.
However, it is possible that higher equilibria exist simultaneously. The
important factors that drive the complexation are steric fit, release of highenergy water molecules, hydrophobic effects, van der Waals interactions,
dispersive forces, dipole–dipole interactions, charge-transfer interactions,
electrostatic interactions (in the case of ionic species) and hydrogen bonding.
Inspecting the sizes of typical guests binding CDs, it appears that there is a
proportion between the sizes of the host and the guest occupying its cavity.
Several phenomena in cyclodextrin complexation could result in either
favorable or unfavorable entropy and enthalpy changes. For example, release
of high-energy solvent molecules and their rejoining the bulk sometimes
creates enthalpy gain. Entropy loss is also obtained when two holes in the
network of the solvent molecules, produced by the presence of host and free
guest molecules, coalesce to one as they non-covalently bind. There are
some other sources of enthalpy gain, such as hydrogen binding between the
guest and hydroxyl groups of CDs and dipolar interactions. For example,
when aliphatic guests of type CH3(CH2)nX bind to CD, if X is a polar group,
such as –COOH or –OH, the binding is much stronger than when X is for
example a methyl group. Moreover, due to presence of –OH groups in the
structure of CDs, the cavity is not 100 per cent non-polar but rather semipolar. This fact controls the favorability of the interactions operating
between host, guest and solvent molecules. Consequently an enthalpyentropy compensation process averages out the influence of different factors
altering the energetics of the encapsulation. Thus the change in the
association constant, K, is less than what expected from the enthalpy
variation observed in experiments32.
CDs are eminently applicable in different areas, mainly because they are
selective host molecules. CDs are the cheapest commercially available hosts
that cover a large range of industrial applications. Having very low toxicity,
even in high doses, and excellent temperature stability, 70 to 80 per cent of
their production volume is devoted to food industry. They also have
extensive application in pharmaceuticals industry as drug-delivery systems.
They can be used as protecting agents to prevent any early metabolism of the
17
drug. CDs can modify and enhance the solubility of the drug without any
need for modifying the drug itself. Another field of extensive application is
analytical chemistry, particularly in chromatographic methods such as highpressure liquid chromatography (HPLC) and gas chromatography. They are
used either as part of the mobile or stationary phase to assist in the
separation of closely related compounds, especially enantiomers. In the case
of selecting and separating enantiomers, the process is commonly referred to
with the term “chiral recognition”17. CDs can be used both as homogenous
and heterogeneous catalysts. There have been several reports on catalytic
activities of cyclodextrins mimicking enzymes. They are usually used to
model the function of the enzymes in order to elucidate the mechanism with
which the enzymes operate. However, CDs mostly influence the
stereoselectivity of the reaction rather than its yield27. This vast range of
applications has encouraged the synthesis of chemically and enzymatically
modified cyclodextrins, so that the number of synthesized CDs has already
passed 1500 derivatives33.
Cryptophanes – CTVs (shown in figure 1.12) are the building blocks of the
cryptophanes. As discussed before, CTVs, with their saucer-like shape, are
good anion receptors, whereas they do not have any considerable ability to
include neutral guests. However, there are limited examples such as
intracavity complexation of C60 and spherical carborane, o-C2B10H12. The
low solution-binding ability of the CTV is sometimes ascribed to its
shallowness. Deepening the CTV cavity might enhance its binding
properties in solution, but a modification will be much more effective if the
formed structure is a three-dimensional closed shell that can protect the guest
from the solvent medium and slow down the exchange of the guest with the
bulk solvent. The first series of three-dimensional hosts were synthesized by
Collet34, using two CTV units facing each other and linked covalently by –
(CH2)n-, -CH2 -CH=CH-CH2- or –CH2-C≡C-CH2- bridges with n = 3–8.
They were named cryptophanes and are usually of two distinct forms, with
D3-anti or C3h-syn symmetry (see figure 1.15). The first series comprises
cryptophane-A and –B, which are the anti/syn derivatives with X = -(CH2)2bridges, and cryptophane-E and -F where X = -(CH2)3-. Afterwards came
cryptophane-C and –D, with the same bridges as cryptophane-A/B but
lacking methoxy groups in one hemisphere12.
18
O
O
O
X
O
O
X
O
O
O
O
O
O
X
X
O
O
O
X
O
O
O
O
O
O
O
O
X
O
O
C3h-syn
D3-anti
X = -(CH2)n-, -(CH2)-CH=CH-CH2-, alkyne, C6H4
Figure 1.15 Two forms of cryptophane derivatives.
Small, tetrahedral molecules such as methane and halogenated derivatives
are the best choices of guest to fit in the cavity of the cryptophanes. In a nonpolar solvent medium, a binding constant of 470 M-1 is obtained for a
complex of CHCl3@cryptophane-E which, considering the absence of
hydrophobic effects, is still very strong bonding. This is brought out by the
large binding constant of 7700M-1 for chloroform in water with a host
similar to cryptophane-E, with the difference that the methoxy groups are
replaced by hydrophilic carboxyl groups17.
Cryptophanes are apparently able to discriminate among guests on the
basis of van der Waals volume differences less than 5%35. For instance, as a
comparison between cryptophane-E and -C, the smaller CH2Cl2 molecule is
preferred by cryptophane-C where, compared to cryptophane-E, the bridges
are shorter and accordingly the cavity should be of smaller size.
Cryptophane-E shows selectivity for the larger chloroform molecule.
However, it is worth breaking down the free energies into their enthalpy and
entropy parts to get a better insight into the size-fit conception of the
complexation. The results of a van t’Hoff plots for CH2Cl2 and CHCl3
binding by the above mentioned cryptophane derivatives are listed in the
Table 1.217. It is clear from the Table that, although a favorable enthalpy
contribution is produced when cryptophane-C binds CHCl3 but an
unfavorable entropy change makes this host more selective for the smaller
dichloromethane molecule. This implies that chloroform probably fits too
well into the cryptophane-C cavity, so that its degree of freedom becomes
19
highly restricted, resulting in a dramatic entropy decrease. On the other
hand, CHCl3 finds somewhat larger room to move around inside the cavity
of cryptophane-E, which yields a more stabilized complex in solution.
Table 1.2 Thermodynamic parameters obtained for the complexes at 300K in
tetrachloroethane.
Host
Guest
∆G0
∆H0
∆S0
-1
-1
-1
kJ.mol
kJ.mol
JK .mol-1
Cryptophane-C
CH2Cl2
-15.1
-16.3
-4
CHCl3
-6.7
-26.8
-67
Cryptophane-E
CH2Cl2
-11.7
+4.2
+25
CHCl3
-15.5
-25.1
-29
Another interesting example of cryptophane complexes is
methane@cryptophane-A. Methane, with its highly symmetrical, uncharged
and non-polar structure, can only interact with its environment via very weak
van der Waals forces. However, cryptophane-A is found to be very effective
in binding methane, with a binding constant of 130 M-1 at 300 K in
(CDCl2)2. Molecular modeling data show that the mean distance between
carbon atoms in the host and carbon atoms in the guest is 4.5 Å which is 20
per cent longer than the sum of their radii. This distance is related to the
maximum attractive forces in van der Waals interactions, and may be
considered as the reason for the high affinity of cryptophane-A for methane
molecules. The same study was performed for some other cryptophane
derivatives complexing similar guest molecules36. The ratio of the cavity size
to guest molecular volume was defined as the occupancy factor (ρ). A ρ
value of 1 means the cavity is completely filled by the guest. Table 1.3
presents different ρ values for the cryptophane complexes discussed above.
The ρ value of methane@cryptopthane-A is similar to its packing factor in
its supercritical fluid form, while for CHCl3 inside the same cavity it equal to
a densely packed crystal of chloroform. This indicates that the change in
enthalpy and entropy of binding follows the same trend as the state of matter
they resemble. Rebek et al.37 calculated the packing factors, using their own
methodology. Some of their results are included in Table 1.317. They
concluded that a range of 0.55±0.09 for the packing factor is expected for the
occurrence of complexation in solution, which is similar to the packing
factors of organic liquids.
20
Table 1.3 Packing factor for cryptophanes complexes.
Guest
Cryptophane-A
Cryptophane-C
CH4
0.35
0.70
CH2Cl2
0.70
0.60a
CH2Br2
0.80
0.89
CHCl3
0.89
0.75a
a
Cryptophane-E
0.65
0.49a
0.81
0.61a
Data from Rebek et al37.
In accordance with the factors governing supramolecular recognition
strength in solution, cryptophane complexation is also significantly
influenced by solvent effects. Early studies of cryptophane complexes were
carried out in CDCl3 solvent, assuming that solvent molecules cannot pass
through the effectively closed surface of the cryptophane structure.
However, very low binding constants of 1–2 M-1 were obtained for guests
such as dichloromethane that were similar in size to the solvent molecules.
This is an indication of a significant solvation effect originating from guest
encapsulation. In the case of water as solvent, this effect reinforces the
binding by benefiting from the hydrophobic effects and restoring the strong
hydrogen bonds between water molecules. However, the chloroform
molecule is a potent competitor of similar-sized guests, resulting in reduced
binding constants.
The first application of cryptophanes was the separation of enantiomers of
CHFClBr, which is the simplest chiral compound. Using the intrinsic
chirality of the D3-anti cryptophanes, complexation of a partially resolved
sample of (±)-CHFClBr with a resolved sample of (+)-cryptpohane-C was
examined by Collet et al.38. Separate signals for (+)host:(+)guest and
(+)host:(-)guest were observed in NMR spectroscopy, and the optical
rotation of the guest was defined. Cryptophanes are very promising synthetic
hosts, and the research is going on towards the stage where their remarkable
recognition properties can be used in different areas of separation, molecular
delivery and sensing.
1.2 Selectivity
Discriminating among different guests in binding is called selectivity which
is in fact the main goal of supramolecular chemistry. This criterion is
requested both in nature and synthetic systems. The first assessment of the
selectivity of a host for a particular guest is their equilibrium constant. One
can therefore consider the selectivity, in thermodynamic terms, as below:
21
Selectivity =
K Guest1
K Guest 2
1.3
For example, in blood it is important that haemoglobin should selectively
take up O2, from the mixture of oxygen with water, CO2 and N217.
However, there is another kind of assessment in which one looks at the
rate of the transformation of one particular guest along a reaction path, in
comparison with other guest species. In this way the kinetic selectivity of the
host is examined and the guest which is transferred fastest is considered to
be effectively selected by the host. This kind of selectivity is needed in
processes such as supramolecular catalysis and guest sensing. Therefore in
the application where the kinetics of the process is of importance the
thermodynamic selectivity, i.e. high equilibrium constant, is inhibitory and is
not favored17.
1.3 Application
Application of molecular recognition is progressing in two fields in parallel.
Molecular biology and nanotechnology both benefit from the new horizons
opening in this area. Supramolecules such as crown ethers can be used as
phase transfer agents to solubilize salts in non-polar solvents. A number of
organic reactions became feasible by means of these agents. Molecular
recognition may be used in separation of one species from a mixture of many
components. For example, in removal of pollutants such as toxic metal ions
from aqueous solutions, supramolecular chemistry is of great use. As another
instance, purification of C60 from C70 impurities using p-tertbutylcalix[8]arene in toluene can be mentioned. Benefiting from the shape fit
of spherical C60 into the cup-shaped cavity of calixarene, the complex is
precipitated from the solvent while C70 and other impurities remain in the
mixture. In the next step, the complex can be transferred to a solvent such as
chloroform, where the host is soluble but the guest is not, and therefore can
be filtered off. Some receptors are able to report the presence of guests
bound to them by some physical means. This group of hosts may be used as
molecular sensors. They are usually selective to some guests and can
moreover be used to estimate the concentration of the sensed molecule. The
receptor can be appended to a polymer electrode and produce a response
when placed in contact with the relevant guest species. Alternatively there
could be a functional group in the host structure that has a special
electrochemical or spectroscopic property which can be altered by including
a special guest compound. Instead of silicone chips, molecular hosts may
one day be used as on-off switches and logic gates. In particular, nanoscale
22
molecules that use light as input or output are of interest, since light has high
velocity and is easily controllable using fiber optics. For example, as
depicted in figure 1.16, the anthracene group is not fluorescent when, in the
absence of hydrogen, photoinduced electron transfer (PET) occurs from the
nitrogen group to the aromatic rings. But as soon as the nitrogen group is
protonated PET is prevented and therefore emission from the anthracene unit
is observed18.
O
PET
No
PET
N
O
HN
+
+
H
Cl
Cl
not fluorescent
fluorescent
Figure 1.16 A molecular ‘on-off’ switch.
In biological application of supramolecules, an important feature that
attracts great attention is the catalytic influence of the hosts on the substrate.
One usually wishes to gain control over regio- and stereoselectivity in
catalytic reactions. In pharmaceutical research, molecular and especially
chiral recognition is highly appreciated in drug design. Some examples are
the application of inclusion complexes as MRI contrast and anti-cancer
agents and anti-HIV products18.
23
2- NMR Spectroscopy
In this chapter a number of topics in nuclear magnetic resonance
spectroscopy, related to the research presented in the attached articles and
drafts, are briefly discussed.
2.1 - Spin Hamiltonians
A nucleus with non-zero nuclear spin possesses a total angular momentum:
Iˆ = h.I
2.1
I is a dimensionless angular momentum operator.
A nuclear magnetic moment, µ̂ , is attributed to the total angular momentum:
µˆ = γ.Iˆ
2.2
From the sum of individual magnetic moments in an ensemble of identical
nuclei, a macroscopic total magnetic moment is produced, constituting a
molecular spin system39.
Through µ̂ , the spin can interact with the magnetic fields present in its
environment. Magnetic fields can be either external, such as the static Bo
field or the radiofrequency B1 field, or internal due to presence of other spins
within the sample. The total Hamiltonian for spin interactions can be written
as:
Hˆ = Hˆ o + Hˆ 1(t) + Hˆ R (t)
2.3
Ĥ o consists of the time-independent interaction with Bo and all other
relevant time-independent contributions. Hˆ 1(t) is the Hamiltonian that
describes the interaction of the spin with the fluctuating B1(t) field. Due to
the interaction with this field, spin rotates and consequently deviates from its
equilibrium position. Any interaction that can drive the spin back to its initial
position is considered as a relaxation interaction, represented by Hˆ R (t) 40.
In the case of spin-1/2, the components of the time-independent
Hamiltonian are as follows:
24
Hˆ o = Hˆ z + Hˆ σ + Hˆ J + Hˆ D
2.4
The interaction of each nuclear spin with the Bo field, aligned along the z
direction of the laboratory frame, is called nuclear Zeeman interaction, and
the Hamiltonian for the spin system is given by41:
Hˆ z = ∑ −γ k .Bo .Iˆzk
2.5
k
γk is the gyromagnetic ratio and k enumerates individual spins in the
molecular spin system.
The presence of electrons in the system changes the magnitude of the
local field at the site of the nucleus. In an external magnetic field, electrons
produce an induced magnetic field that changes the local effect of Bo, a
phenomenon known as chemical shielding. The related Hamiltonian is
written as41:
Hˆ σ = ∑ γ k .Bo .σ k .I k
2.6
k
k
k
k
k
k
I is a vector with the components Î x, Î y and Î z, and σ is the chemical
shielding tensor.
Magnetic moments can also magnetically perturb each other either
through space or via the electronic structure. The Hamiltonian for the direct
through space dipolar coupling of two spins41 reads:
Ĥ D =
∑I
k
.D kl .I k
2.7
k,l > k
The interaction depends on the inverse third power of the distance between
the spins, rkl-3, which is included in the coupling tensor, Dkl.
In the case of indirect coupling of spins that are connected via the
electronic bonds, the interaction Hamiltonian is written as41:
Hˆ J =
∑ 2π .I
k
.J kl .I l
2.8
k,l > k
Another important feature of the spin interactions is that they can be
either isotropic, meaning they are the same in all directions in space, or
anisotropic, i.e., they depend on the direction. If the molecule is fixed with
respect to the laboratory frame, the anisotropy of interactions is important.
This is actually the case in the solid state or in highly viscous systems. When
the directions in space matter, we deal with the tensor-type quantities.
Anisotropic interactions are therefore characterized as second-rank tensors.
A second-rank Cartesian tensor (3×3 matrix) can be broken up into three
irreducible tensors, which are of zero, first and second rank. In solution, on
25
the other hand, interactions become isotropic due to isotropic molecular
motions. One can characterize the isotropic interactions by a scalar value,
which is the zero-rank component of the interaction tensor. The zero-rank
component of the tensor is the average value of the tensor. This component
of the dipolar interaction tensor is zero, and the interaction thus plays no role
in the appearance of liquid samples. The first rank component is also zero.
However, the second rank components contribute significantly to the process
of spin relaxation, which is discussed in the next section. Even though
indirect dipolar interaction is basically an anisotropic interaction, only the
isotropic component is taken into account because the anisotropies are
usually small.
The chemical shielding tensor can be illustrated as an ellipsoid, as shown
in figure 2.1a41.
a)
σzz
b)
θ
σxx
φ
σzz
Y
Z
B0
β
σyy
σxx
α
σyy
γ X
N
Figure 2.1 a) Pictorial representation of chemical shielding tensor b)
Relationship between other anisotropic interaction tensors: line N is the
intersection of the XY and σxxσyy coordinate planes. Looking down from N
toward origin, σzz and Z axes can rotate about N.
To obtain the magnitude of the interaction in any direction, σ(θ,φ) is
defined as:
2.9
σ(θ,φ) = σ xx cos 2 φ sin 2 θ + σ yy sin 2 φ sin 2 θ + σ zz cos 2 θ
Relative values of σxx, σyy and σzz define different powder patterns in solidstate NMR. The molecular frame of the system is defined according to the
properties of this tensor. Other anisotropic interaction tensors, if any, are
defined using α, β and γ Euler angles with respect to this tensor (see figure
2.1b.).
26
2.2 Relaxation - A very brief introduction
Besides the magnetic fields discussed previously, Bo and B1, there are some
other fluctuating local magnetic fields present at the sites of the nuclei.
These fields are produced by the interactions of spins with one another or
with their environments. These interactions act as weak perturbations of the
energy levels induced for spins by Bo. Following a perturbation caused by
radio-frequency field at the Larmor frequency, which causes transitions
between states, spins start to relax by exchanging the absorbed energy
among themselves and also releasing it to the surrounding medium; these
processes are the so-called spin–spin and spin–lattice relaxation,
respectively. In liquids, the relaxation process is caused by rapid and
stochastic molecular motions. The influence of molecular motions on the
local magnetic fields is to make them time-dependent. The most important
motions are rotations which modify those (anisotropic) local magnetic fields.
Due to reorientation of internuclear axes with respect to each other and the
stationary field, local magnetic fields fluctuate with time. To play an active
role in a relaxation process, oscillations should reach the transition
frequencies of spin energy levels. For small molecules in isotropic liquids,
the rotational motion may take place at rates comparable to the Larmor
frequency of the nuclei42.
2.2.1 Relaxation mechanisms
Usually, all the time-dependent random interactions may contribute to
relaxation. In the absence of quadruploar nuclei (I > 1/2) or paramagnetic
impurities, there are two major mechanisms involved. The first one is the
chemical shift anisotropy (CSA). As mentioned earlier, chemical shift
originates from the shielding effect of surrounding electrons. When the
distribution of electron density around the nucleus is non-spherical, the
nuclear spin feels a fluctuating field when the molecule tumbles. For nonprotonated carbons, such as carbonyl or olefinic carbons, this is the dominant
mechanism leading to relaxation. Since CSA comes from the shielding
effect, its strength is proportional to the strength of the applied magnetic
field.
The other mechanism is the dipole–dipole interaction through space
between pairs of spins, which is considered as the dominant mechanism for
relaxation in the case of 13C-nuclei with directly bonded protons. Protons, as
high natural abundance nuclei with a large gyromagnetic ratio, are
particularly important. In the absence of motion, a simplified form of the
local field induced by a proton spin that is close enough to the corresponding
carbon can be expressed as:
27
Bdip =
µ µ ( 3 cos 2 θ − 1 )
o
2.10
1
r3
4π
r is the length of the relaxation vector, i.e. the axis connecting two spins, and
θ defines the orientation of that axis with respect to the static magnetic field.
Through molecular tumbling, the angle varies randomly, and a fluctuating
field is induced at the site of the other spin (figure 2.2a). In figure 2.2b the
orientation of the relaxation vector in the molecular frame is shown with
spherical coordinates. θ and φ are equivalent to the α and β Euler angles,
respectively. Assuming a symmetric interaction around the relaxation vector,
φ is normally defined to be zero43.
Bo
a)
b)
z
Spin 2
θ
Bdip
r
θ
r
[0,π] € θ
[0,2π] € φ
Spin1
y
φ
x
Figure. 2.2 a) The field induced by spin 1(1H) at the site of spin 2(13C). b)
The relaxation vector in a spherical coordinate system.
The classical interaction energy of the carbon-13 dipole moment with Bdip
is given by:
E dip = − µ 2 .Bdip
2.11
The Hamiltonian is obtained by replacing all variables with their quantum
mechanical operator equivalents. Its simplified form under secular
approximation is:
µ γ γ ( 3 cos 2 θ − 1 ) ˆ1 ˆ 2
Hˆ D = − o 1 2
.I z I z
4πr 3
2.12
This approximation is applied in high magnetic fields where the Zeeman
interactions are dominant. In such a case only those terms in the Hamiltonian
are retained that commute with the Zeeman Hamiltonian44.
28
In solid-state NMR, where the rotational motion is frozen, dipolar
interaction gives direct information on the geometry of the molecule. In an
isotropic liquid, however, the anisotropy is averaged out:
( 3 cos
2
θ −1 )
/2
=0
2.13
This happens because molecular tumbling changes the orientation of the
relaxation vector on a time scale that is faster than the dipolar coupling.
However, this means that the ensemble averaged dipolar Hamiltonian is zero
at every moment, i.e. Hˆ D (t ) = 0 whereas, in relaxation theory, we deal with
the expression of the type Hˆ D (t1 ) Hˆ D (t 2 ) . t1 and t2, are the time points at
which Ĥ (t ) is still correlated44.
In a more general fashion, the dipolar Hamiltonian may be rewritten as a
scalar product of two tensors:
µ0 γ1γ 2 h 2
2
m
ˆ
H D (t ) =
∑ (− 1) Y2 ,- m (Ω (θ )),Tˆ2 ,m I I
3
1 2
4π r
m= - 2
( )
2.14
One tensor introduces the spin operator functions described by second-rank
irreducible spherical tensor operators, T2,m(I1,I2). Irreducibility means that the
tensor has no components of ranks 0 and 1. This tensor gives information on
the spin operators. The other one incorporates the spatial functions, which
are second-rank spherical harmonics, Y2,m(Ω(θ)). Spherical harmonics are
components of a tensor defining the direction of the relaxation vector in
spherical coordinates, Ω(t) = (θ(t)φ(t)), with respect to the laboratory frame.
Ω(t) represents the time-dependent orientation of the relaxation vector. In
fact, the C–H vector is fixed in the molecular frame, and it is the frame that
varies with time with respect to the fixed-in-space laboratory coordinate
system. The two coordinate systems are associated through Euler
transformation41, 45.
2.2.2 Spectral density functions
As noted above, if rotational motion of the molecule has the suitable
frequency, it can stimulate transitions in the eigenstate of the spins. The
probability of a transition depends on the different frequencies that are
provided for the system by thermal motion of the molecules. The probability
of finding the desired frequency is given by the spectral density function,
J(ω). J(ω) is obtained as the Fourier transform of the correlation function,
C(τ), of the spherical harmonics, Y2m(Ω):
29
J (ω ) =
∞
∫ C (τ )e
-∞
itω
∞
dt = ∫ Y2 m [Ω (0)]Y2∗m [Ω (t )] e itω dt
-∞
2.15
< > denotes an equilibrium ensemble average41.
In infrared and Raman spectroscopy, Fourier transforms of band shapes
can be associated with correlation functions, while in the case of NMR
spectroscopy one needs J(ω) to describe relaxation processes41,45.
Correlation functions tell us how “self similar” Y2m(Ω) is after a certain time.
Correlation functions examine the values of Y2m(Ω) in short time intervals,
comparable to the timescale of the fluctuations, and these values tend to be
similar. If one probes after a longer time, the function has already lost its
memory since this is the nature of being random and fluctuating.
In the simplest case, time correlation function is proportional to a single
exponential, corresponding to the reduced Lorentzian spectral density
function given by44:
J (ω) =
2τ c
1
2π 1 + ω 2 τ c2
2.16
τc is the correlation time of rank-two spherical harmonics and ω is a
frequency. The correlation time represents the duration in which the
orientation of the relaxation vector has changed by a significant amount,
approximately 1 radian. In such a case, equation 2.16 is valid for isotropic
reorientation of a rigid body, excluding any internal motion.
Spectral density with one characteristic time is Lorentzian. In the cases
where the motion of the system needs to be expressed with more
characteristic times, we would deal with more complex formulae.
Calculation of the correlation function is based on a physical model for the
rotational motion of the molecules in liquids. According to small-step
Brownian rotational diffusion theory, the correlation time is related to the
rotational diffusion constant, DR:
τc =
1
8πr 3 η
=
6 D R 6k B T
2.17
η is the solution viscosity, kB is the Boltzmann’s constant, T is the absolute
temperature and r is the radius of the sphere. This is the case, however when
the relaxation vector diffuses isotropically around the x, y and z molecular
coordinate axes. Generally speaking, each system can be characterized by a
rotational diffusion tensor in the molecular frame. Then, there will be three
non-zero principal elements in the tensor, Dx, Dy and Dz. If the molecule is a
symmetric top, that is, it diffuses at the same rate around the x and y axes the
number of diffusion coefficients reduces to two quantities, D x = D y = D ⊥ ,
and Dz = D||. D_|_ defines the tumbling of the symmetry z axis, whereas D||
30
describes the motion around the z axis. The spectral density function is then
written as44:
J (ω ) =
6 D⊥
2
1 1
[ cos 2 θ − 1
+
2π 4
(6D⊥ )2 + ω 2
(
2
)
5D⊥ + D||
2
3 cos θ sin θ
(5D
+ D|| )
2
⊥
2 D⊥ + 4 D||
3
+ sin 4 θ
]
2
4
+ω
(2D⊥ + 4D|| )2 + ω 2
2.18
If the molecule cannot be modeled as a rigid body, i.e. it enjoys internal
degrees of freedom, one should switch to the types of spectral densities
where extra parameters are involved to identify the segmental motions in the
system. One of the very popular ones is the model-free approach of Lipari
and Szabo46, 47. In this model the overall reorientation, described by a global
correlation time, τM is considered to be either isotropic or anisotropic while
some part of the system is undergoing fast internal motions, characterized by
a local correlation time, τe. A generalized order parameter, S, defines the
degree of spatial restriction. Order parameter lies in the range of 0≤ S2 ≤1, in
which lower values indicate higher freedom for internal motion. The relevant
spectral density is written as44:
J (ω ) =
(
)
1  S 2τM
1− S2 τ 
+


2π 1 + ω 2 τ M2 1 + ω 2 τ 2 
2.19
where τ-1 = τ e-1 + τ M-1. If the internal motion is very slow, so that τe-1
approaches zero, equation 2.19 reduces to the same form as equation 2.16.
Sometimes the relaxation data cannot be accounted for by the simple twoparameter Lipari-Szabo model. Clore et al. 48 proposed a model, originally
for interpretation of 15N relaxation data in proteins, to tackle this issue. In
their approach two types of local motion, slow and fast, are allowed, each
characterized by an order parameter and a local correlation time. The
spectral density considering and isotropic overall reorientation is:
(
)
(
)
( )
1 − S 2f τ 'f
S 2f − S 2 τ 's 
1  S 2τM


J (ω) =
+
+
' 2
2π 1 + ω 2 τ M2 1 + ωτ 'f 2

1
+
ωτ
s


(
)
2.20
2.2.3 Relaxation Parameters
Relaxation parameters, measured using NMR spectroscopic methods, are the
macroscopic properties that provide the link to the properties at molecular
31
level. They correspond to the rates at which the populations of nuclear
energy states change or the coherence of individual magnetic moments is
lost. From the spectral densities one can obtain the relaxation parameters.
The equations below describe the case of 13C–H dipolar interaction if the 13C
and 1H are defined as S and I, respectively44.
π 2
bIS [J (ωI − ωS ) + 3 J (ωS ) + 6 J (ωI + ωS )]
5
π
1
3
= bIS2 [2 J (0) + J (ωI − ωS ) + J (ωS )
5
2
2
+ 3 J(ωI ) + 3J (ωI + ωS )]
T1−1 =
2.21a
T2−1
2.21b
π 2
bIS [6 J (ωI + ωS ) − J (ωI − ωS )]
5
µγ γh
bIS = − 0 S I
4π rSI
σ IS =
2.21c
T1 and T2 are the longitudinal and transverse relaxation rates, respectively
and σIS is the cross-relaxation rate. Spectral densities involve three important
frequencies, ωS, ωI and zero. Assuming the simple spectral density in
equation 2.16, if the molecular reorientation is in a motional regime that is
called extreme narrowing, where ω2τC2 is much less than unity, then the
spectral density function and the relaxation parameters will be independent
of the magnetic field strength. At longer correlation times, the product
approaches unity, i.e. ωτC ≈ 1, and T1−1 obtains a maximum value as well. In
contrast, with J(ω=0), T2−1 contains a term proportional to the correlation
time. J(ωc) describes the contribution of a single transition, implying an
energy exchange with the lattice, while the two other terms represents a
cooperative energy exchange of both spins with the lattice. This behavior is
the origin of another important phenomenon, namely cross relaxation, which
takes place only when relaxation is through the dipolar interaction
mechanism. The equations can become quite complicated with more than
one mechanism for the relaxation.
If CSA contributes to the relaxation rate, the equation will be the sum of
the rates induced by both mechanisms:
1
1
T1−1 = T1−Dip
+ T1−CSA
1
=
T1−CSA
2.22a
2π
(γ S B0 σ )2 J (ωS )
5
2.22b
For axially symmetric CSA :
σ = 2 / 3 (σ ||−σ _|_ ) σ ||= σ zz and σ _|_ = σ xx = σ yy
32
Considering the complexity of the spin system and the type of
information desired, one can study the relaxation phenomenon from a
classical, vector-model point of view or involve more complicated quantum
mechanical concepts. The simplest approach is to treat an ensemble of
isolated spins, using Bloch equations. In the absence of the radio-frequency
field, relaxation processes are characterized by two first-order rate constants:
d < M z (t ) >
= − R1 < M z (t ) > − < M z0 >
dt
d < M + (t ) >
= − R2 < M + (t ) >
dt
(
)
2.23a
2.23b
Mz0 is the equilibrium macroscopic magnetic moment, which is the sum over
all magnetic moments of individual spins, Mz is the component along the z
direction of the laboratory frame, and M+ is the observable transverse
magnetization in the rotating frame (the frame rotating at the Larmor
frequency), induced by the influence of the r.f. field. R1 describes the
recovery of the longitudinal magnetization to thermal equilibrium, or the
return of the population of the energy levels to the Boltzmann distribution.
R2 describes the decay of the observable magnetization to zero. The Bloch
formulation can be the basis for experimental measurements of relaxation
rates, which are discussed in next section.
.
βIβS
W1S
W1I
W2
βIαS
W0
W1I
αIβS
W1S
αIαS
Figure 2.3 Rate constant diagram for an interacting two-spin system.
For interacting spins, relaxation parameters can be obtained using
Solomon equations. When a liquid sample is placed in the strong external
magnetic field of Bo, spins are distributed between different energy levels. A
relaxation process takes place by transition of spins between these energy
levels. Figure 2.3 shows the rate constants between the Zeeman energy
33
levels of a system of two spin-1/2 nuclei, labeled as I and S; α and β denote
the eigenstates of isolated spin-1/2 nuclei44. The rate constants, W1I and W1S,
determine the rates of the transitions where only one type of spin is flipped,
and the other two, W0 and W2 govern the transition where both spin types
are involved42. Iz and Sz components are proportional to the population
differences between the eigenstates. The rate of the change of populations
yields differential equations for ∆Iz and ∆Sz as below:
where
d∆I z (t )
= − ρI ∆I z (t ) − σ IS ∆S z (t )
dt
d∆S z (t )
= − ρS ∆S z (t ) − σ IS ∆I z (t )
dt
2.24a
2.24b
ρ I = W0 + 2W 1I + W2
ρ S = W0 + 2W 1S + W2
σ IS = W 2 − W0
∆K =< K z (t ) > − < K z0 >
K = I or S
<Kz0> is the equilibrium value of the z component of the magnetizations.
ρI and ρS are equivalent to the R1I and R1S relaxation rate constants in the
Bloch terminology, and σIS is the cross-relaxation rate constant for the
exchange of magnetization between the two spins42. The cross-relaxation
rate is related to the phenomenon of nuclear Overhauser enhancement, see
below.
2.2.4 Experimental methods
The conventional experiment to measure longitudinal relaxation time is the
inversion recovery method. The pulse sequence is:
π_
π
S
I
D1
2
t
decoupling
Figure 2.4 Pulse scheme of an inversion recovery experiment.
34
D1 represents the time needed for the magnetization to fully recover to
thermal equilibrium. With a 180 degree r.f. pulse, an initial state is prepared
for the magnetization. During the delay time t, magnetization relaxes back to
the equilibrium. At the end of time t, the magnetization vector is tipped to a
transverse position and recorded during the acquisition time. Irradiation of I
spins by a weak r.f. pulse during the experiment saturates the I energy levels,
leaving no net I magnetization along the z axis. In this situation, <Iz(t)> = 0,
and the slope of the recovery curve is obtained as:
d < S z > (t)
= − ρ S < S z > (t)− < S z0 > + σ < I z0 >
dt


σ 

= − ρ S < S z > (t)− < S z0 > 1 +
ρ S 


< S z > (t)
σ 
σ 
 exp ( − ρ S t)
= 1+
−  2 +
0
ρ
ρ
< Sz >
S
S 

[
(
d < S z > (t) / < S z0 >
dt
]
)
2.25a
2.25b
2.25c
= 2 ρS + σ
t =0
This shows that the recovery curve is mono-exponential42. By having a
mono-exponential curve, one can alternatively consider the cross relaxation
negligible and obtain the rate constant from Bloch equations:
< M z (t) >= −2 < M z0 > exp ( − tR1 )+ < M z0 >
2.26
The standard method for measuring transverse relaxation time is the Carr–
Purcell–Meiboom–Gill (CPMG) method with the sequence depicted below:
(
S
π
_
)
(π )
2 x
[
t
y
t
]
c
decoupling
I
Figure 2.5 CPMG pulse sequence.
35
(t – πy –t)c is the refocusing sequence, the spin-echo, where any contribution
from inhomogeneity of the magnetic field to the value of the R2 rate is
eliminated. Again the R2 rate can be obtained using Bloch formalism:
< M z (t) >=< M z0 > exp ( − tR2 )
2.27
However chemical exchange during the spin-echo sequence can affect the
value of the measured transverse relaxation rate 42:
R2 = R2Dip + Rex
2.28
Rex is the exchange contribution to the decay of transverse magnetization. If
the exchange occurs between two equally populated sites, Rex depends on the
first-order rate constant of the exchange process, kex.
Another relaxation parameter, complementary to R1 and R2 rates, is the
NOE. The heteronuclear NOE is used, along with R1 and R2, to characterize
molecular dynamics. Homonuclear (proton) NOE is used to determine the
distance between two interacting spins in biological system, and thus the
molecular structure. The cross-relaxation rate is proportional to the inverse
sixth power of rSI. NOE is either characterized by σIS in Solomon equations
or an enhancement factor, η. These two parameters are measured in transient
and steady-state NOE experiments, respectively. In steady-state NOE
measurement, irradiating the I spins for a time period much longer than the
relaxation rates of both spins puts the I spins in a saturated situation. By
setting d∆Sz/dt=0 and <Iz0>=0 one obtains the steady-state I as below:
d
Sz
(
)
(
= − ρ S S z − S z0 + σ IS I z0 = 0
dt
S z / S z0 = 1 + σ IS I z0 / ρ S S z0
S z / S z0 = 1 +
)
σ IS γ I
= 1+ η
ρS γS
2.29a
2.29b
2.29c
1+η is the nuclear Overhauser enhancement factor. A pulse sequence for
measuring NOE is shown in figure 2.649, which is called dynamic NOE. To
measure the enhancement factor, the experiment is repeated twice with
different values of the time interval t. In the first experiment, t is set to a
negligible value, and in the second experiment it is defined to be much
longer than the relaxation time of the S nuclei. Cross relaxation through
dipolar coupling between I and S spins results in the NOE enhancement.
36
π_
2
S
t
decoupling
I
Figure 2.6 Dynamic NOE pulse scheme.
Sometimes, a need of higher signal-to-noise for nuclei with small
gyromagnetic ratio, or a demand for more highly resolved spectra, has led to
application of two-dimensional methods for measurement of relaxation
parameters44. There is a two-dimensional analogue of the NOE experiment,
called NOESY, for measuring the cross-relaxation. Since σIS is proportional,
to the inverse sixth power of the interspin distance, for a quantitative
measurement of the distance one should directly measure the cross
relaxation rate. In this experiment, the intensity of the cross peak is under
certain conditions proportional to σIS. The NOESY sequence is illustrated in
figure 2.7a. During the first π/2–t1–π/2 block of the sequence, magnetization
is labelled with a chemical shift and returned back to the z axis. During τM,
the mixing time, magnetization transfer occurs via dipolar coupling, and is
observed with the final read pulse.
a)
_
π
2
t1
I
b)
τm
t2
π
_
2
spinlock
t1
I
τm
t2
Figure 2.7 a) NOESY and b) ROESY pulse sequences.
37
The problem with the NOESY experiment is that chemical exchange can
also lead to cross peaks if the exchange rate is not slow compared to the
mixing time. Depending on the magnitude of the overall correlation time,
cross peaks from cross relaxation could have the same sign as the exchange
cross peaks. Thus it is hard sometimes to distinguish between the cross peaks
from exchange and cross relaxation. There is another sequence, rotating
frame Overhauser effect spectroscopy (ROESY), with the advantage that the
sign of the ROE cross peaks is always positive and therefore opposite in sign
to the exchange cross peaks at all correlation times. In this experiment the
cross relaxation between spin-locked spins using r.f. pulses is followed50, 51.
The ROESY sequence is shown in figure 2.7b in which the spin-lock
operates on the spins during the mixing time.
Heteronuclear single-quantum correlation spectroscopy (HSQC) is
another two-dimensional method that can be used for measuring relaxation
parameters, using indirect detection of the less sensitive nucleus. In these
methods, magnetization transfer to more sensitive nuclei through scalar
couplings results in better resolution and shorter experimental time44. A
general form of the pulse sequence is presented in figure 2.852.
Refocused INEPT
Reversed INEPT
t2
I
t1
S
Dec.
Relaxation
delay
Figure 2.8 The general pulse scheme of the HSQC type experiments. To
perform T1 measurements, the relaxation delay block is an inversion
recovery. For measuring T2 or T1ρ it is replaced with a train of π pulses or
spin-lock respectively. For NOE measurement, two experiments are done
with one of them containing a 1200 pulses at the beginning of I channel and a
long “Relaxation delay” to perform the NOE saturation. In the second
experiment “Relaxation delay” is set to zero and the 1200 pulse is off.
The pulse sequences contain some INEPT (insensitive nuclei enhanced by
polarization transfer) blocks. In INEPT, the I spin polarization is transferred
38
to S nuclei. The enhancement ratio is ±γI / γS. The next part of the sequence
is a relaxation delay. It may contain a π pulse to measure T1, a train of π
pulses for T2 measurement or a spin-lock for measuring T1ρ. A reversed
INEPT block returns the magnetization back to the I nuclei channel for
detection.
2.3 Chemical exchange
The resonance positions of nuclei in NMR spectroscopy are sensitive to the
magnetic environments. Changes in magnetic environment of the nuclei
owing to some dynamic process are reflected in the NMR spectrum53. NMR
provides the opportunity of studying the exchange process without
perturbing the chemical equilibrium42. That is why it is called chemical
exchange. One can classify chemical exchange in different groups. In these
groups, spin systems can be coupled or uncoupled, and the exchange can be
mutual or non-mutual. The non-mutual exchange refers to the case where
two sites are not chemically equivalent. Exchange can also be either
intermolecular, that is between sites in different molecules, or between
different conformations of the same molecule53.
Exchange can affect the relaxation time measurements. If the spin–lattice
relaxation time of a spin is different at two sites but the peaks are not
resolved, the observed relaxation rate will be a weighted average of the two
relaxation rates in the absence of the exchange54. If the exchange is fast
enough, the curve will be single exponential.
Exchange will influence the relaxation rates even in the slow exchange. In
the case of uncoupled spins, modified Bloch equations are used, which are
called Bloch-McConnell if we deal with chemical reactions44. For a two-site
chemical exchange, the first-order chemical reaction is described as:
A1
k1
k-1
A2
The rate laws in matrix format can be formulated as42:
d  [A1 ](t ) − k1
=
dt [A2 ](t )  k1
k −1  [ A1 ](t )
− k −1  [A2 ](t )
2.30
The modified Bloch equation can be written by introducing the matrix
above:
39
d  M A1 (t)   − R A1 − k1

=
k1
dt  M A2 (t)  
M Ai (t) = M ×
k −1
 M A1 (t)   R A1

+
− R A2 − k −1  M A2 (t)   0
0  M A01 


R A2  M A02 
Ai (t)
∑ Ai (t)
2.31
i
Here, MA(t) and MA0 for species in the two sites, are the magnetizations at
time t and at equilibrium, respectively, and RA values for 1 and 2 are the
corresponding spin–lattice relaxation rates. The effect of exchange on spin–
spin relaxation time is briefly discussed in the previous section.
Depending on the time scale of the exchange process, it can be measured
using different techniques. In the coalescence regime, where two signals
from two sites merge into one, the classical line-shape analysis is the
technique of choice. This is the region where the line shape is most affected
by the exchange. In the fast exchange region the signal is a single Lorentzian
but it is still broadened by the exchange. However this broadening is
comparable to the natural line-width and the broadening due to magnetic
field inhomogeneity. Thus the contribution of exchange can be measured
with a T2 experiment. In the presence of exchange, T2 is in certain situations
dependent on the time intervals between the refocusing π pulses in the
CPMG experiment. The equation for a two-site fast exchange is given by44:

 k ex τ cp
2
tanh 
T2−1 (1/τ cp ) = T2−1( 1/τ cp → ∞) + p A p B ( 2δ)2 1 −
 2
 k ex τ cp

 2.32

T2 is the apparent spin–spin relaxation time, τcp presents the time intervals in
the CPMG experiment, pA and pB are the populations of the two sites, kex is
the exchange rate, and 2δ is the frequency difference between the signals
from two sites.
π
_
2
π
π
Selective pulse
S
Mixing time
G
Figure 2.9 Pulse scheme for the selective inversion experiment. G stands for
pulsed-field gradient.
40
In the slow–exchange regime, excellent rate data are obtained using selective
inversion experiments. The pulse sequence is depicted in figure 2.9. During
the first block of the sequence, which is based on the so-called excitation
sculpting procedure, one site is selectively inverted. In the second block,
during the mixing time, two processes can lead to magnetization transfer.
The first one is the dipolar interaction between nearby nuclei, which may
lead to NOE effects, and the second one is the transfer due to exchange
process. The inverted signal travels to the second site through the exchange
process, and a signal is detected from the second site by the last 900 pulse.
2.4 Translational diffusion
The random Brownian motion of the molecules or ions, driven by internal
thermal energy, in isotropic liquids is called diffusion55. Diffusion
measurement using NMR-based techniques has some advantages over other
methods. NMR can monitor the random motion of an ensemble of particles,
and therefore the diffusion itself, whereas many other methods rely on
detecting a concentration gradient to probe the diffusion55. NMR is also able
to investigate diffusion phenomena related to formation of guest-host
complexes.
According to the Stokes-Einstein equation, diffusion in the isotropic
solutions is related to the size of the molecule44:
D = (kBT)/6πηr
2.33
in which D is the molecular self-diffusion coefficient, kB is the Boltzmann
constant, T is the absolute temperature, η is the viscosity of the solution and r
is the hydrodynamic radius of a spherical particle. The relation between the
temperature and diffusion is not linear, as it appears from the equation
above, since the viscosity is sensitive to the temperature. Therefore an
exponential variation of the diffusion coefficient with change of the
temperature may be expected:
D = D∞ e-Ea /kBT
2.34
Ea is the activation energy of translational diffusion in the bulk solution. In
water, for instance, Ea is associated with the energy needed for breaking the
hydrogen bonds.
There are two main ways in NMR by which diffusion coefficients can be
obtained. The first one is the analysis of T1 relaxation data to obtain the
correlation time of the molecule which, as discussed previously, is related to
the diffusion coefficient of the molecule56, 57. There are some limitations in
41
using the first approach, such as assumptions considered in relaxation data
analysis and the need for an exact value of the hydrodynamic radius, all of
which makes the second approch a better choice.
The second approach is the pulsed-field gradient (PFG) method, which
directly measures translational diffusion56, 57. If in addition to the static
magnetic field, there is a spatially dependent magnetic field gradient, the
Larmor frequency becomes spatially dependent too. The basis of the
diffusion measurement is that a well-defined field-gradient can label the
position of the spin. The simplest form of the “Stejskal and Tanner” or PFG
sequence is depicted in figure 2.10. The first π/2 r.f. pulse rotates the
equilibrium magnetization into the x-y plane. A gradient pulse of duration δ
and strength g is introduced in the middle of period τ. At the end of τ, spins
experience a phase shift originating both from the main field and the
gradient.
τ
τ
π
( )
2 x
πy
S
g
G
δ
∆
Figure 2.10 The Stejskal–Tanner pulsed-field gradient sequence.
The following π pulse at the end of the first τ period reverses the precession
sign. During the second τ period, another gradient is applied, of equal
magnitude and duration as the first one. If the spins have not experienced
any translational motion the two gradients cancel each other and all spins are
refocused. In the presence of diffusion, the phases are distributed and the
echo signal is weakened. Faster diffusion results in a weaker echo signal. In
this sequence, the signal is attenuated by both T2 relaxation and diffusion.
Normalization of the signal with respect to the signal obtained in the absence
of the applied gradients gives the attenuated signal as56:
E(2τ) = exp(- γ2g2Dδ2(∆ – δ/3))
42
2.35
where γ is the gyromagnetic ratio, and ∆ is the separation between the
gradient pulses. Typically, δ is defined to be in the range of 0–10 ms, ∆ in
the range of milliseconds to seconds, and g can go up to 20 T.m-1. To
measure diffusion, keeping τ constant, a series of experiments are performed
with varying δ or ∆.
43
3- Dynamics of cyclodextrins and
cryptophanes studied by NMR
On account of inclusion phenomena some of the physical and chemical
properties of the constituting components are modified or new
characterizations emerge. In the first place the guest molecule confronts a
new environment where its motional freedom is restricted. Molecules can
behave quite differently when restrained within a molecular container with a
defined shape, volume, and chemical environment. Among different
methods and techniques that are used to elucidate inclusion complexes,
NMR plays a key role in determination of stoichiometry, association
constants and conformations covering both domains of structure and
dynamics26, 58. A host-guest system is a dynamic entity. Commonly the host
is considered as the frame of reference and guest movement with respect to
the frame is studied. Consequence of translational motions of the guest is the
association and dissociation processes. Even though NMR is sensitive to a
broad range of dynamic processes frequencies, it is necessary to have a
definition of NMR time scale. Fast molecular motions tend to average out
some of the NMR parameters. For example if the life times of free and
bound states in a complex is in order of 10-3 or shorter the chemical shifts of
two species are averaged by the exchange process26, 59. Rates of association
and dissociation in cavitands such as cyclodextrins are normally fast in NMR
time scale60, 61. In contrast, owing to their cage-shape cavities, cryptophanes
exhibit slow exchange12.
3.1 Stoichiometry and binding constant
A primary task in studying the host-guest systems in solution is to define the
stoichiometry of the complex. For cyclodextrins the most commonly
observed ratios are H:G = 1:1 and 2:1. Camphor:α-CD is an example of 2:1
ratio62 while metoprolol makes an 1:1 complex with α-CD63. However some
parameters such as concentration and temperature can change the
stoichiometry31. In the case of having a single stoichiometry for a complex,
the common method employed in NMR is the Job’s method64, 65. The
44
approach is based on the continuous variation of the host and guest
proportions in a series of samples with constant total concentration of host
plus guest. The sample preparation should be done in a way to cover the
whole range of zero to one ratio(X) of each species concentration to the total
concentration. A plot of XGuest.∆p, where p is most commonly the chemical
shift, versus XHost reveals the stoichiometry.
Quantification of binding constant, K, is the next step of investigating the
complexes in solution. For a 1:1 stoichiometry complex, one can estimate K
providing that the equilibrium concentration (in the case of neutral moieties)
of each species in equation 1.1 is in hand. When the rates of formation and
decomposition are fast some of the observed NMR parameters are
population weighted average. The most common observed NMR parameter
for estimation of binding constant is the chemical shift. There are two main
methods, graphical and curve fitting. In graphical methods a linear
relationship between the chemical shift and K is sought. For example 1:1
stoichiometry is described by rectangular hyperbola and there are some
proposed solutions for that66, 67. In curve fitting methods binding isotherms
are calculated using the known stoichiometry and compared to the
experimental data using fitting procedures68, 69.
Direct measurement of diffusion coefficient, D, is another NMR method
that can be used to estimate K. It was first applied to the field of host-guest
chemistry in the work of Stilbs70 in 1983 on the systems of alcohols in α- and
β-cyclodextrins. It is now widely used even for large biological inclusion
systems as well71, 72. Being related to the molecular size, the diffusion
coefficient is a direct reporter of phenomena such as associations and
aggregations. The advantage of measuring D over chemical shift is that all D
parameters may be known for the system. Since the host molecule is usually
much bigger than the guest it is assumed that D of host is not greatly
changed due to complexation and the complexed guest has the same D as the
host molecule.
When the host–guest complexation equilibrium has a slow exchange rate
compared to the NMR time scale, the signals of the host and guest nuclei in
the complex and free species appear at different chemical shifts. A typical
approach of calculating the association constant is to extract the intensities of
the signals from different species in the solution. A more precise method to
extract the association constant is to measure the rates of the guest
complexation and decomposition. Huber et al.73 obtained the binding
constant of xenon in the cavities of two cryptophane derivatives using signal
line width measurements. Brotin et al.74 studied a number of similar
complexes using variable-temperature one dimensional magnetization
transfer (1D-EXSY). Besides the binding constants interesting
thermodynamics information is obtained 75.
45
3.2 Nuclear magnetic relaxation
As discussed in the previous chapter, relaxation parameters can provide
valuable information on the structure and dynamics of a system under study.
Measuring the relaxation rates due to the dipolar mechanism gives us the
rotational correlation time, which characterizes overall molecular tumbling
and intramolecular motions. In supramolecular complexes, the rotational
correlation times of guest compounds are usually so increased that one can
obtain equilibrium constants using the corresponding change of the
relaxation rates32. This method was used with 81Br relaxation in
cyclodextrins complexes76. 13C relaxation rates were used since 1976 to
obtain correlation times for guest and host molecules in complexes by CDs.
Behr discussed in his paper that, besides the thermodynamic stability and
formation and dissociation kinetics, motional parameters of the species,
composing a host guest system can give a wealth of information on the
dynamic properties of the system77. Spin-label-induced 13C nuclear
relaxation rates were used to determine guest molecule positions in α-CD
with di-tert-butyl nitroxide complexes78. Proton longitudinal and transverse
relaxation rates were used to determine the motion of (±)camphor guest
molecules in both diastereometric complexes with α-CD 79.
Dynamics of small organic molecules complexing cryptophanes were
studied in solid-state and solution using 13C and 2H80-82. In these studies
effect of the cavity size on the efficiency of the complexation were
investigated by calculating the motional parameters of the guest, host and the
complex. Complexes of cryptophane-E with chloroform and
dichloromethane in solution were investigated and the difference between
the order parameter obtained for the guest molecule in each complex was
discussed. It was found that these two guest molecules experience different
degrees of restriction inside the same type of cavity. Moreover, they gave an
estimate of the strength of dipolar coupling between the 13C and bonded
protons in the guest molecules, directly using solid-state NMR methods. The
2
H line shape analysis and nuclear spin relaxation studies of the same
complexes were accomplished in solid-state. In the solid state, guest
molecules are considered to be either encaged within the cavity or in the
interstitial position, i.e. between the host molecules. It was observed that 2H
spectra of encaged chloroform is broad and its correlation time is relatively
long whereas the encaged dichloromethane showed a narrow line and a fast
correlation time was calculated for it.
Relaxation studies were performed on other nuclei such as 129Xe. The
cross relaxation effect between the proton and 129Xe nuclei was studied in
complexes of Xe@cryptophanes 83. Although the relaxation time of 129Xe is
hundreds of seconds, it is shortened to tens of seconds in complexing to
cryptophanes or cyclodextrins.
46
NOEs bear structural information about interatomic distances in
molecules and thus provide information about the molecular conformation.
In supramolecular chemistry they can be used to probe the distances and
relative orientation of the host and guest molecules in a complex.
Particularly in CDs complexes, NOEs occurring between the H3 and H5
protons of the host molecule and guest protons indicates that the inclusion
complex has formed32. NOE magnitude depends as well on the rotational
correlation times, which characterizes overall molecular tumbling and
intramolecular motions.
47
4- Discussion of the papers
This work is based on 5 papers in which the main focus of the work is on the
study of the motional properties of small organic molecules complexed to
larger host molecules using 13C spin relaxation measurements. Versatility of
13
C relaxation measurements makes it possible to monitor even weak
molecular interactions such as solvation effects. Binding to a larger moiety
slows down the motion of the small molecule so that its motion falls out of
the extreme narrowing regime. This allows us to collect more relaxation data
by doing the measurements at different magnetic fields. The procedure is
that one should adopt suitable spectral density functions that best model the
motion of the molecules. Using defined spectral densities one can calculate
the relaxation parameters. This is done by minimizing a chi-square function
by least-square analysis. This function represents the difference between the
calculated and experimental relaxation data. The calculations are performed
using MATLAB 7.4.0 software. The motional parameters for the host
molecule were also investigated. In all the papers it was assumed that the
effect of the complexation on the motion of the host molecule is negligible.
The overall correlation time of the host molecule is of special interest when
compared to that of the complexed guest. Behr and Lehn77 concluded that,
for supramolecualr system, in addition to thermodynamic association
constants, one can define dynamic coupling coefficients. Taken as the ratio
of host correlation time to that of the guest, this parameter reflects the
dynamic rigidity of the system, composed of the two entities.
However, as discussed in previous chapters, the relaxation parameters are
affected by the exchange going on in the systems. The stoichiometries of the
systems that we chose were already studied in other research groups to be
1:1. In those cases where the data were not consistent with this stoichiometry
higher ratios were examined as well, especially in the cases where the
experimental conditions were somewhat different from those reported in the
literatures.
Depending on the timescale of the exchange one should exclude the effect
of the exchange in different ways. In fast exchange, where the exchange
rates are much faster than the relaxation rates, the observed relaxation data,
which are population averaged, can be resolved into the free and bound
contributions if one has the information of the molar fraction of each species.
A common approach is to extract the association constant of the reaction.
Among several approaches, in present works, it was made use of
48
translational diffusion measurements using PFG NMR spectroscopy. In the
slow exchange, the rates of the exchange are comparable to the relaxation
parameters. In this regime one obtains separate relaxation data for the signals
from the bound and free guest molecules but the rate contributes to the
relaxation rates. This is evident by observing bi-exponential curves in the
inversion recovery experiments. In this case the exact values of the forward
and backward exchange rates are needed. By introducing them into modified
Bloch equations one obtains the pure relaxation data in the absence of the
exchange.
4.1 Papers I-II
These two papers deal with complexes of cryptophanes with
dichloromethane and chloroform molecules. In the first paper complexes of
dichloromethane with cryptophane-A, -223 and -233 are studied. These three
molecules basically have the same structural shape with the difference that
the cavity size increases from cryptophane-A to -233 by having different
length of the linkers. This, on the other hand, results in a decreased
symmetry of the cavity area. Despite the exchange is slow in the chemical
shift timescale it turned out that it is still comparable to the scale of the
relaxation time. Thus the measurement conditions were changed in the
direction where the relaxation rates were dominant over the effect of the
magnetization transfer due to exchange.
Relaxation parameters of dichloromethane were measured at different
magnetic fields in solution for the first two hosts and in solid for the largest
molecule. For the solution part, dipolar interaction was considered as the
dominant relaxation mechanism for the guest whereas the host relaxation
parameters show some evidence of CSA for aromatic carbons. Measuring
the dipolar coupling constant using solid-state method complements the
study of the three cryptophane complexes.
In Table 4.1 the order parameters obtained for dichloromethane in
different cryptophanes is summarized. In this table some results from
previous studies on cryptophane-E81 are also included. The order parameters
of dichloromethane in different cryptophanes imply that it can gain lower
motional restriction in the larger cavities. The outcome of this study was that
in this series of cryptophanes the cavity size plays a central role in the
complexation. Result of the solid-state study also confirms this conclusion.
49
Table 4.1 Order parameters and dipolar coupling constants for the bound
dichloroemthane to cryptophanes.
Host/temperature
S2
Motionally-averaged Cavity volume
DCC, kHz
pm3·10-6
Solution Solid-state
Cryptophane-A/223K 0.46±0.06
14.2±0.9
95
Cryptophane-223/233K 0.20±0.03
9.4±0.7
102
Cryptophane-233/283K
8.2±1.0
117
Cryptophane-E/273K 0.02±0.003
3.2±0.3
3.3
121
The thermodynamic parameters of the complexes of dichloromethane
with cryptophane-A and -223 are presented in Table 4.2 Both complexes are
enthalpy-favoured and enthropy-unfavoured, which is in fact the case in
most of the inclusion complexes.
In order to involve the thermodynamic information on the complexes of
cryptophane-E in the conclusion above we performed some variable
temperature studies on chloroform and dichloromethane complexing
cryptophane-E. In this way one can also compare the results of two different
guests with different sizes and symmetry properties that interact with the
same cavity. The thermodynamic quantities for all the complexes are
summarized in Table 4.2.
Table 4.2 Thermodynamic parameters for the cryptophane comeplexes.
Complexes
∆H0, kJ.mol-1
∆S0, kJmol-1
CH2Cl2@ cryptophane-A
-16
-24
CH2Cl2@cryptophane-223
-24
-52
CH2Cl2@cryptophane-E
-26
-56
CHCl3@cryptophane-E
-71
-192
A higher gain in the enthalpy of the larger guest in the largest cavity can be
attributed to a better ratio of the guest to host volume.
4.2 Papers III-V
In this group of papers, container type molecules were studied as host
molecules. Complexes of α-cyclodextrin with quinuclidine and 1,7heptanediol, and β-cyclodextrin with adamantanecarboxylic acid were
investigated. The interior of the cyclodextrins is hydrophobic32 and the
solvent in which the complexation occurs is a mixture of deuterated water
and DMSO. The first distinction between these systems and those mentioned
in 4.1 is the fast kinetic of the exchange between the host cavity and the
50
solvent medium. This indicates that the complexes are less kinetically stable.
One of the reasons might be the truncated cone-shape of the cyclodextrins
that compared to cage-like cavity of the cryptophanes less hinders the
complexation–decomposition of the guest molecule. Furthermore, depending
on the interactions between guest-host, guest-solvent and guest-guest, guest
molecule can penetrate with different depth into the host cavity. This is
qualitatively studied by NOESY and ROESY methods. Having hydrophilic
groups such as carboxylic acid group in adamantanecarboxylic acid or the
hydroxyl group in diol leaves the chance of being in contact with the solvent
molecules through hydrogen bonding.
Since the exchange was fast in all three complexes, translational diffusion
coefficient measurements were used to estimate the association constants.
Stoichiometries of all complexes were adopted from the literatures. In the
case where the diffusion data did not fit to the assumed stoichiometry, other
ratios of host to guest were examined. The binding constant obtained for the
AdCA@β-CD complex were high at 25° and 0° C, indicating the high
thermodynamic stability of this complex. In contrast, very low association
constant was calculated for the quinuclidine@α-CD, and an intermediate
value for the association constant of the diol@α-CD was obtained at 15° C.
13
C longitudinal relaxation times and NOE enhancements were measured
using conventional methods at several magnetic fields. Using the association
constants, one can estimate the population of the free and bound guest
molecules and the pure relaxation parameters for each group of the
molecules is obtained. Reorientation of adamantanecarboxylic acid, bound to
the host cavity, at 25° C is described using model-free approach, using a
fixed value for overall correlation time, equal to that of host, and axially
symmetric model. Comparing the rotational diffusion coefficients of AdCA
in the bound and free forms shows that, due to the complexation, anisotropy
of its motion is increased to a high degree, implying that, despite high
association constant of the complex, the guest molecule freely rotates inside
the cavity of the host molecule around its symmetry axis that coincides with
that of the host. At lower temperature of 0°C it is no longer possible to
model the reorientation of the bound guest using model–free formalism, and
thus the Clore model, which is an extension to the model-free, is used to
account for one more local motion for AdCA. It is assumed that, besides
rotating around the symmetry axis, molecule is rocking to sides inside the
cavity.
Owing to the low association constant of the quinuclidine@α-CD, the
complex solution was prepared with a higher concentration of the host
compound. Thus we decided to account for the effect of the increased
viscosity compared to the sample with zero concentration of the host.
Analysis of the data after viscosity correction revealed that 13C spins in
quinuclidine are sensitive to the solution composition whereas the
composition effect on the host spins was negligible. Therefore each sample
51
was treated separately when analysing the relaxation data. In a similar
fashion, data were analysed using Lipari-Szabo and axially symmetric
models, and the latter model showed that the motional anisotropy of
quinuclidine is increased upon complexation with α-CD. Again, the guest
molecule is free to rotate around its symmetry axis inside the cavity. Another
interesting feature of the application of the axially symmetric model in both
studies was that, using the perpendicular rotational correlation time of the
bound guest, one can obtain an overall correlation time which is quite similar
to that of the host. This is an approval of the assumption of using the overall
correlation time as a fixed parameter in Lipari-Szabo analysis. This, as well,
provides an estimate of the coupling effect of the complexation on the
motion of the components.
In the last study a guest molecule with different geometry and flexibility
features than the former guest molecules was studied in complex with α-CD.
This study was accomplished semi-quantitatively since the motion of the
guest molecule was rather complicated to be simply studied using common
methods, explained above. The Lipari-Szabo analysis of the data showed
that fixing the overall correlation time of the bound diol at the value of the
host does not produce a correct trend for the calculated relaxation
parameters, in comparison to the experimental ones. Thus, in a next attempt,
an unconstrained Lipari-Szabo study is accomplished that yields a global
correlation time much shorter than that of the host. However the trend of the
calculated relaxation parameters is in agreement with the experimental data.
The best fit, however, was obtained using the Clore model (see equation
2.20).
52
Acknowledgment
During the last few years, I have derived enormous personal and scientific
benefit from my time spent at FOOS, specifically at physical chemistry, both
from the people who work here and the environment that they have created.
First and foremost, I would like to thank Jozef for his patience, continuous
support and help, and the science he taught me throughout the whole period
of my PhD.
I am especially grateful to Arnold, Mattias, Dick, Sasha, Atto, Lena,
Magnus, Zdenek, Jüri, Piotr, Peter Damberg, Leila, Torbjörn, Kristina
Romare, Ann-Britt, Per-Erik and Eva for all that I have learned from them
and the whole lot of help they have given me.
Special thanks to Fatemeh, Katja, Andy, Zoltan, Dmytro, Alireza, Vasco,
Isabel, Martin, Johan, Jonas, Ken, Adolfo, Shahriar, Emiliana, Danuta,
Sasha, and rest of the friends for their friendship, help and the great times we
had together.
I also would like to acknowledge Jöran Karlsson and Vladislav Orekhov at
the Swedish NMR center in Göteborg University, and Thierry Brotin and
Jean-Pierre Dutasta at ENS Lyon for their help during the time I spent there
to use their facilities.
At last I would like to express my thankfulness to Shahram and my parents
and siblings in Iran without whom none of this work would have been
possible.
53
References
(1) Hoeben, F. J. M.; Jonkheijm, P.; Meijer, E. W.; Schenning, A. P. H. J.
About Supramolecular Assemblies of Pi-Conjugated Systems.
Chem.Rev. 2005, 105, 1491-1546.
(2) Cram, D. J.; Cram, J. M. Host-Guest Chemistry. Science 1974, 183, 803809.
(3) Lehn, J.-M. Supramolecular Chemistry: Concepts and Perspectives.
(Weinheim, VHC), 1995.
(4) Pons, M.; Millet, O. Dynamic NMR Studies of Supramolecular
Complexes. Prog. Nucl. Magn. Reson. Spectrosc. 2001, 38, 267-324.
(5) Houk, K. N.; Leach, A. G.; Kim, S. P.; Zhang, X. Binding Affinities of
Host-Guest, Protein-Ligand, and Protein-Transition-State Complexes.
Angew. Chem. Int. Ed. 2003, 42, 4872-4897.
(6) Cramer, F. D. Inclusion Compounds. Revs. Pure Appl. Chem. 1955, 5,
143-164.
(7) Cram, D. J.; Cram, J. M.; Container Molecules and their Guests
(Cambridge, Royal Soc. Chem.), 1997.
(8) Fyfe, M. C. T.; Stoddart, J. F. Synthetic Supramolecular Chemistry. Acc.
Chem. Res. 1997, 30, 393-401.
(9) Collet, A. Cyclotriveratrylenes and Cryptophanes. Tetrahedron 1987, 43,
5725-5759.
(10) Cram, D. J. Cavitands: Organic Hosts with Enforced Cavities. Science
1983, 219, 1177-1183.
(11) Jasat, A.; Sherman, J. C. Carceplexes and Hemicarceplexes. Chem. Rev.
1999, 99, 931-967.
54
(12) Collet, A.; Dutasta, J. -P.; Lozach, B.; Canceill, J. Cyclotriveratrylenes
and Cryptophanes: Their Synthesis and Applications to Host-Guest
Chemistry and to Design of New Materials. Top. Curr. Chem. 1993,
165, 103-129.
(13) Warmuth, R. Inner-Phase Stabilization of Reactive Intermediates.
Eur.J.Org.Chem. 2001, 423-437.
(14) Weber, E.; Josel, H. P. A Proposal for the Classification and
Nomenclature of Host-Guest-Type Compounds. J.Inclusion Phenom.
1983, 1, 79-85.
(15) Davies, J. E. D. Species in Layers, Cavities and Channels (Or Trapped
Species). J. Chem. Educ. 1977, 54, 536-539.
(16) Goshe, A. J.; Steele, I. M.; Ceccarelli, C.; Rheingold, A. L.; Bosnich, B.
Supramolecular Recognition: On the Kinetic Lability of
Thermodynamically Stable Host-Guest Association Complexes. Proc.
Nal. Acad. Sci. U. S. A. 2002, 99, 4823-4829.
(17) Steed, J. W.; Atwood, J. L. Supramolecular Chemistry: A Concise
Introduction. (Chichester, Wiley), 2000.
(18) Beer, P. D.; Gale, P. A.; Smith, D. K. Supramolecular Chemistry
(Oxford, Oxford University), 1999.
(19) Ma, J. C.; Dougherty, D. A. The Cation-Pi Interaction. Chem.Rev. 1997,
97, 1303-1324.
(20) Sussman, J. L.; Harel, M.; Frolow, F.; Oefner, C.; Goldman, A.; Toker,
L.; Silman, I. Atomic Structure of Acetylcholinesterase from Torpedo
Californica: A Prototypic Acetylcholine-Binding Protein. Science
1991, 253, 872-879.
(21) Lehn, J. Supramolecular Chemistry - Scope and Perspectives
Molecules, Supermolecules, and Molecular Devices (Nobel Lecture).
Angew. Chem. Int. Ed. 1988, 27, 89-112.
(22) Pedersen, C. J. The Discovery of Crown Ethers (Nobel Address).
Angew. Chem. 1988, 100, 1053-1059.
(23) Menon, S. K.; Hirpara, S. V.; Harikrishnan, U. Synthesis and
Applications of Cryptands. Rev. Anal. Chem. 2004, 23, 233-267.
55
(24) Cram, D. J. The Design of Molecular Hosts, Guests, and their
Complexes. J. Inclusion Phenom. 1988, 6, 397-413.
(25) Meier, W. M. Zeolites and Zeolite-Like Materials. Pure Appl. Chem.
1986, 58, 1323-1328.
(26) Dodziuk, H. Cyclodextrins and their Complexes. (Weinheim, Wiley),
2008.
(27) Dodziuk, H. Introduction to supramolecular chemistry. ( Boston,
Kluwer Academic Publishers), 2001.
(28) Saenger, W. Cyclodextrin Inclusion Compounds in Research and
Industry. Angew. Chem. 1980, 92, 343-361.
(29) Zabel, V.; Saenger, W.; Mason, S. A. Topography of Cyclodextrin
Inclusion Complexes. Part 23. Neutron Diffraction Study of the
Hydrogen Bonding in Beta -Cyclodextrin Undecahydrate at 120 K:
From Dynamic Flip-Flops to Static Homodromic Chains. J. Am. Chem.
Soc. 1986, 108, 3664-3673.
(30) Dodziuk, H.; Nowinski, K. Structure of Cyclodextrins and their
Complexes. Part 2. do Cyclodextrins have a Rigid Truncated-Cone
Structure? Theochem 1994, 110, 61-68.
(31) Rekharsky, M. V.; Inoue, Y. Complexation Thermodynamics of
Cyclodextrins. Chem. Rev. 1998, 98, 1875-1917.
(32) Schneider, H.; Hacket, F.; Ruediger, V.; Ikeda, H. NMR Studies of
Cyclodextrins and Cyclodextrin Complexes. Chem. Rev. 1998, 98,
1755-1785.
(33) Szejtli, J. Introduction and General Overview of Cyclodextrin
Chemistry. Chem. Rev. 1998, 98, 1743-1754.
(34) Gabard, J.; Collet, A. Synthesis of (D3)-Bis(Cyclotriveratrylenyl)
Macrocage by Stereospecific Replication of a (C3)-Subunit. J. Chem.
Soc., Chem. Comm. 1981, 1137-1139.
(35) Holman, K. T. Cryptophanes; Molecular Containers. Encyclopedia of
Supramolecular Chemistry 2004, 340-348.
(36) Garel, L.; Dutasta, J.; Collet, A. Complexation of Methane and
Chlorofluorocarbons by Cryptophane-A in Organic Solution. Angew.
Chem. Int. Ed. 1993, 32, 1169-1171.
56
(37) Mecozzi, S.; Rebek, J.,Jr The 55% Solution: A Formula for Molecular
Recognition in the Liquid State. Chem. Eur. J. 1998, 4, 1016-1022.
(38) Canceill, J.; Lacombe, L.; Collet, A. Analytical Optical Resolution of
Bromochlorofluoromethane by Enantioselective Inclusion into a Tailormade Cryptophane and Determination of its Maximum Rotation. J. Am.
Chem. Soc. 1985, 107, 6993-6996.
(39) Slichter, C. P. Principles of Magnetic Resonance, with Examples from
Solid State Physics. (New York, Harper & Row), 1963.
(40) Levitt, M. H. Spin Dynamics Basics of Nuclear Magnetic Resonance.
(Chichester, Wiley), 2002.
(41) Smith, S. A.; Palke, W. E.; Gerig, J. T. The Hamiltonians of NMR. I.
Concepts Magn. Reson. 1992, 4, 107-144.
(42) Cavanagh, J.; Fairbrother, W.; Palmer, I.,Arthur G.; Skelton, N. Protein
NMR Spectroscopy: Principles and Practice. (San Diego, Academic
Press), 1995.
(43) Lippens, G.; Jeener, J. The Dipolar Interaction Under all Angles.
Concepts Magn. Reson. 2001, 13, 8-18.
(44) Kowalewski, J.; Mäler, L. Nuclear Spin Relaxation in Liquids: Theory,
Experiments, and Applications. (New York, Taylor & Francis), 2006.
(45) Smith, S. A.; Palke, W. E.; Gerig, J. T. The Hamiltonians of NMR. Part
IV: NMR Relaxation. Concepts Magn. Reson. 1994, 6, 137-162.
(46) Lipari, G.; Szabo, A. Model-Free Approach to the Interpretation of
Nuclear Magnetic Resonance Relaxation in Macromolecules. 1. Theory
and Range of Validity. J. Am. Chem. Soc. 1982, 104, 4546-4559.
(47) Lipari, G.; Szabo, A. Model-Free Approach to the Interpretation of
Nuclear Magnetic Resonance Relaxation in Macromolecules. 2.
Analysis of Experimental Results. J. Am. Chem. Soc. 1982, 104, 45594570.
(48) Clore, G. M.; Szabo, A.; Bax, A.; Kay, L. E.; Driscoll, P. C.;
Gronenborn, A. M. Deviations from the Simple Two-Parameter ModelFree Approach to the Interpretation of Nitrogen-15 Nuclear Magnetic
Relaxation of Proteins. J. Am. Chem. Soc. 1990, 112, 4989-4991.
57
(49) Kowalewski, J.; Ericsson, A.; Vestin, R. Determination of NOE
[Nuclear Overhauser Enhancement] Factors using the Dynamic
Overhauser Enhancement Technique Combined with a Nonlinear LeastSquares-Fitting Procedure. J. Magn. Reson. 1978, 31, 165-169.
(50) Bothner-By, A. A.; Stephens, R. L.; Lee, J.; Warren, C. D.; Jeanloz, R.
W. Structure Determination of a Tetrasaccharide: Transient Nuclear
Overhauser Effects in the Rotating Frame. J. Am. Chem. Soc. 1984,
106, 811-813.
(51) Bax, A.; Davis, D. G. Practical Aspects of Two-Dimensional
Transverse NOE Spectroscopy. J. Magn. Reson. 1985, 63, 207-213.
(52) Peng, J. W.; Thanabal, V.; Wagner, G. Improved Accuracy of
Heteronuclear Transverse Relaxation Time Measurements in
Macromolecules: Elimination of Antiphase Contributions. J. Magn.
Reson. 1991, 95, 421-427.
(53) Bain, A. D. Chemical Exchange. Mod. Magn. Reson. 2006, 1, 417-423.
(54) Zimmerman, J. R.; Brittin, W. E. Nuclear-Magnetic-Resonance Studies
in Multiple-Phase Systems: Lifetime of a Water Molecule in an
Adsorbing Phase on Silica Gel. J. Phys. Chem. 1957, 61, 1328-1333.
(55) Nicolay, K.; Braun, K. P. J.; de Graaf, R. A.; Dijkhuizen, R. M.;
Kruiskamp, M. J. Diffusion NMR Spectroscopy. NMR Biomed. 2001,
14, 94-111.
(56) Price, W. S. Pulsed-Field Gradient Nuclear Magnetic Resonance as a
Tool for Studying Translational Diffusion: Part 1. Basic Theory.
Concepts Magn. Reson. 1997, 9, 299-336.
(57) Stejskal, E. O.; Tanner, J. E. Spin Diffusion Measurements: Spin
Echoes in the Presence of a Time-Dependent Field Gradient. J. Chem.
Phys. 1965, 42, 288-292.
(58) Fielding, L. Determination of Association Constants (Ka) from Solution
NMR Data. Tetrahedron 2000, 56, 6151-6170.
(59) Sandström, J. Dynamic NMR Spectroscopy. (New York, Academic
Press), 1982.
(60) Yonemura, H.; Kasahara, M.; Saito, H.; Nakamura, H.; Matsuo, T.
Spectroscopic Studies on Exchange Properties in through-Ring
58
Cyclodextrin Complexes of Carbazole-Viologen Linked Compounds:
Effects of Spacer Chain Length. J. Phys. Chem. 1992, 96, 5765-5770.
(61) Berg, U.; Gustavsson, M.; Åström, N. Direct Observation and Rate of
Interconversion of the 1:2 Complex between 1,4Dimethylbicyclo[2.2.2]Octane and Alpha -Cyclodextrin by NMR. J.
Am. Chem. Soc. 1995, 117, 2114-2115.
(62) Dodziuk, H.; Ejchart, A.; Lukin, O.; Vysotsky, M. O. 1H and 13C NMR
and Molecular Dynamics Study of Chiral Recognition of Camphor
Enantiomers by Alpha -Cyclodextrin. J. Org. Chem. 1999, 64, 15031507.
(63) Ikeda, Y.; Hirayama, F.; Arima, H.; Uekama, K.; Yoshitake, Y.;
Harano, K. NMR Spectroscopic Characterization of
metoprolol/cyclodextrin Complexes in Aqueous Solution: Cavity Size
Dependency. J. Pharm. Sci. 2004, 93, 1659-1671.
(64) Job, P. Formation and Stability of Inorganic Complexes in Solution.
Ann. Chim. Appl. 1928, 9, 113-203.
(65) Sahai, R.; Loper, G. L.; Lin, S. H.; Eyring, H. Composition and
Formation Constant of Molecular Complexes. Proc. Nat. Acad. Sci.
U.S.A. 1974, 71, 1499-1503.
(66) Mathur, R.; Becker, E. D.; Bradley, R. B.; Li, N. C. Proton Magnetic
Resonance (P.M.R.) Studies of Hydrogen Bonding of Benzenethiol
with several Hydrogen Acceptors. J. Phys. Chem. 1963, 67, 2190-2194.
(67) Hanna, M. W.; Ashbaugh, A. L. Nuclear Magnetic Resonance (N.M.R.)
Study of Molecular Complexes of 7,7,8,8-Tetracyanoquinodimethane
and Aromatic Donors. J. Phys. Chem. 1964, 68, 811-816.
(68) Hynes, M. J. EQNMR: A Computer Program for the Calculation of
Stability Constants from Nuclear Magnetic Resonance Chemical Shift
Data. J.Chem.Soc., Dalton Trans. 1993, 311-312.
(69) Salvatierra, D.; Diez, C.; Jaime, C. Host/guest Interactions and NMR
Spectroscopy. a Computer Program for Association Constant
Determination. J.Inclusion Phenom. Mol. Recognit. Chem. 1997, 27,
215-231.
(70) Rymden, R.; Carlfors, J.; Stilbs, P. Substrate Binding to Cyclodextrins
in Aqueous Solution: A Multicomponent Self-Diffusion Study.
J.Inclusion Phenom. 1983, 1, 159-167.
59
(71) Chien, W.; Cheng, S.; Chang, D. Determination of the Binding Constant
of a Protein Kinase C Substrate, NG(28-43), to Sodium Dodecyl Sulfate
Via the Diffusion Coefficient Measured by Pulsed Field Gradient
Nuclear Magnetic Resonance. Anal. Biochem. 1998, 264, 211-215.
(72) Orfi, L.; Lin, M.; Larive, C. K. Measurement of SDS Micelle-Peptide
Association using 1H NMR Chemical Shift Analysis and Pulsed-Field
Gradient NMR Spectroscopy. Anal. Chem. 1998, 70, 1339-1345.
(73) Huber, J. G.; Dubois, L.; Desvaux, H.; Dutasta, J.; Brotin, T.; Berthault,
P. NMR Study of Optically Active Monosubstituted Cryptophanes and
their Interaction with Xenon. J. Phys. Chem. A 2004, 108, 9608-9615.
(74) Brotin, T.; Devic, T.; Lesage, A.; Emsley, L.; Collet, A. Synthesis of
Deuterium-Labeled Cryptophane-A and Investigation of XeCryptophane Complexation Dynamics by 1D-EXSY NMR
Experiments. Chem. Eur. J. 2001, 7, 1561-1573.
(75) Hill, P. A.; Wei, Q.; Eckenhoff, R. G.; Dmochowski, I. J.
Thermodynamics of Xenon Binding to Cryptophane in Water and
Human Plasma. J. Am. Chem. Soc. 2007, 129, 9262-9263.
(76) Yamashoji, Y.; Fujiwara, M.; Matsushita, T.; Tanaka, M. Evaluation of
Association between Cyclodextrins and various Inorganic Anions in
Aqueous Solutions by Bromine-81 NMR Spectroscopy. Chem. Lett.
1993, 1029-1032.
(77) Behr, J. P.; Lehn, J. M. Molecular Dynamics of a-Cyclodextrin
Inclusion Complexes. J. Am. Chem. Soc. 1976, 98, 1743-1747.
(78) Eastman, M. P.; Brainard, J. R.; Stewart, D.; Anderson, G.; Lloyd, W.
D. Spin-Label-Induced Selective Carbon-13 Nuclear Relaxation:
Structures of the Gamma -Cyclodextrin-Tempone and Alpha Cyclodextrin-Di-Tert-Butyl Nitroxide Inclusion Complexes in Solution.
Macromolecules 1989, 22, 3888-3892.
(79) Anczewski, W.; Dodziuk, H.; Ejchart, A. Manifestation of Chiral
Recognition of Camphor Enantiomers by Alpha -Cyclodextrin in
Longitudinal and Transverse Relaxation Rates of the Corresponding 1:2
Complexes and Determination of the Orientation of the Guest Inside the
Host Capsule. Chirality 2003, 15, 654-659.
(80) Petrov, O.; Tosner, Z.; Csoeregh, I.; Kowalewski, J.; Sandström, D.
Dynamics of Chloromethanes in Cryptophane-E Inclusion Complexes:
60
A 2H Solid-State NMR and X-Ray Diffraction Study. J. Phys. Chem. A
2005, 109, 4442-4451.
(81) Tosner, Z.; Lang, J.; Sandström, D.; Petrov, O.; Kowalewski, J.
Dynamics of an Inclusion Complex of Dichloromethane and
Cryptophane-E. J. Phys. Chem. A 2002, 106, 8870-8875.
(82) Lang, J.; Dechter, J. J.; Effemey, M.; Kowalewski, J. Dynamics of an
Inclusion Complex of Chloroform and Cryptophane-E: Evidence for a
Strongly Anisotropic Van Der Waals Bond. J. Am. Chem. Soc. 2001,
123, 7852-7858.
(83) Luhmer, M.; Goodson, B. M.; Song, Y.; Laws, D. D.; Kaiser, L.;
Cyrier, M. C.; Pines, A. Study of Xenon Binding in Cryptophane-A
using Laser-Induced NMR Polarization Enhancement. J. Am. Chem.
Soc. 1999, 121, 3502-3512.
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