Experimental Binding Energies in Supramolecular Complexes

Review pubs.acs.org/CR

Experimental Binding Energies in Supramolecular Complexes Frank Biedermann*,† and Hans-Jörg Schneider*,‡ †

Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz Platz 1, 76344 Eggenstein-Leopoldshafen, Germany ‡ FR Organische Chemie der Universität des Saarlandes, D-66041 Saarbrücken, Germany S Supporting Information *

ABSTRACT: On the basis of many literature measurements, a critical overview is given on essential noncovalent interactions in synthetic supramolecular complexes, accompanied by analyses with selected proteins. The methods, which can be applied to derive binding increments for single noncovalent interactions, start with the evaluation of consistency and additivity with a sufficiently large number of different host−guest complexes by applying linear free energy relations. Other strategies involve the use of double mutant cycles, of molecular balances, of dynamic combinatorial libraries, and of crystal structures. Promises and limitations of these strategies are discussed. Most of the analyses stem from solution studies, but a few also from gas phase. The empirically derived interactions are then presented on the basis of selected complexes with respect to ion pairing, hydrogen bonding, electrostatic contributions, halogen bonding, π−πstacking, dispersive forces, cation−π and anion−π interactions, and contributions from the hydrophobic effect. Cooperativity in host−guest complexes as well as in selfassembly, and entropy factors are briefly highlighted. Tables with typical values for single noncovalent free energies and polarity parameters are in the Supporting Information.

CONTENTS 1. Introduction 2. Strategies/Methods 2.1. Binding energies from a large variety of small molecules 2.2. Binding energies from supramolecular complexes with several noncovalent interactions 2.3. Binding energies from protein complexes 2.4. Binding energies from double mutant cycle (DMC) analysis 2.5. Binding energies from molecular balances 2.6. Binding energies from dynamic combinatorial libraries 2.7. Data from crystal structures 3. Selected Interaction Energies 3.1. Ion pairing/Salt bridges 3.2. Hydrogen bonds 3.3. Electrostatic contributions in ionophores 3.4. Halogen bonds and other polar/electrostatic interactions 3.5. Dispersive interactions, stacking, and C−H--π interactions 3.6. Cation−π and anion−π interactions 3.6.1. Cation−π interactions 3.6.2. Anion−π interactions 3.7. Hydrophobic interactions 3.7.1. Hydrophobic effects for convex solutes 3.7.2. Hydrophobic effects for concave hostcavities/high-energy water release © 2016 American Chemical Society

3.7.3. Binding-energy corrections for (de)solvation effects 3.7.4. Hydrophobic effects on account of kosmotropic and chaotropic solutes 3.8. Cooperativity in supramolecular complexes 3.8.1. Cooperativity in host−guest complexes 3.8.2. Cooperativity in self-assembled polymers 3.9. Entropic contributions 4. Overview and Outlook Associated Content Supporting Information Author Information Corresponding Authors Notes Biographies References

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1. INTRODUCTION After the early discoveries by Cramer, Pedersen, Cram, and Lehn, supramolecular chemistry has in the last decades gained an enormous momentum, with sometimes around 20,000 corresponding papers per year.1−12 Most of this fascinating development is fueled by the almost endless possible applications for, e.g.,

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Special Issue: Noncovalent Interactions Received: October 2, 2015 Published: May 3, 2016

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DOI: 10.1021/acs.chemrev.5b00583 Chem. Rev. 2016, 116, 5216−5300

Chemical Reviews

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Table 1. Typical Binding Free Energies for Important Noncovalent Interactions interaction type

−ΔG [kJ/mol]

system

section

salt bridges and ion pairs

inorganic salts in H2O organic ions in H2O ionic groups at protein surface ionic groups buried in protein core

5 to 6 5 to 8 0 to 7 12 to 20

3.1 & 2.4, 2.6

hydrogen bonds neutral

PhO-H···amide in CCl4 PhO-H···amide in CDCl3 amide−amide in CDCl3 amide−amide in protein core C-H···indole in CDCl3 p-F-PhO-H···F-CHR2 in CCl4 p-F-PhO-H···I-CHR2 in CCl4 Thr···Ser in protein core

11 6 to 8 5 to 8 2 to 10 4 6 4 3

3.2 & 2.1, 2.4,2.6, 3.5

with cations

+

N-H···O-CH2 (18-crown-6) in H2O +N-H···O-CH2 (18-crown-6) in MeOH

3 8

3.2

with anions

ureas···Cl¯ in DMSO ureas···COO¯ in DMSO pyrroloamides···Cl¯ in DMSO pyrroloamides···COO¯ in DMSO squaramides···F¯ in CH3CN squaramides···Cl¯ in CH3CN squaramide-cleft···Cl¯ in CHCl3 (per squaramide) C6H5O−H···¯OC6H4-p-NO2 in H2O Thr···Asp in protein core

9 20 13 21 46 35 31 to 39 17 7

3.2 & 2.1, 2.4,2.6

halogen bonds

C6F5I···Cl− > Br− > I− in acetone C8F17I···Cl− > Br− > I− in acetone Ph-F···OC-NR2 orthogonal in C6D6 Ph−Cl···OC-NR2 in protein pocket Ph-I···OC-NR2 in protein pocket

7 to 9 14 to 19 1 6 10

3.4 & 2.3

electrostatic

e-rich clip···C6H2(CN)4 in CDCl3/acetone pillar[5]arene···NC−CH2CH2−CN in o-xylene pillar[5]arene···NC−CH2CH2-CN in CH3CN “blue-box”···Phe in H2O

20 34 14 9

3.4

dispersive and stacking

porphyrin···pyridine in H2O porphyrin···quinoline in H2O H2O···Kr in gas phase cucurbit[5]uril···Xe in H2O cryptophane···Xe in H2O cucurbit[6]uril···CH2 − increment, in H2O

7 17 2.0 26a 30a ∼6a

3.5 & 2.5, 2.6, 3.72, 3.73

cation−π

indole···pyridinium in H2O phenyl···alkylammonium in H2O cyclophanes···quinolinium in H2O various association complexes in H2O

2 1 to 3 2 to 3 per contact 1.5 per contact

3.61 & 2.2

anion−π

RC6F5···Cl− in acetone 3,5(NO2)C6H4-···Cl− in C6D6 3,5(NO2)C6H4-···Cl− in MeCN phenyl···RSO3 ¯ in H2O

7 3 to 4 2 to 3 1 to 2

3.62

hydrophobic

alkane···flat surface in water various host−guest complexes in water

1 to 3 per CH2 ∼0 to 60

3.7

a

Corrected for ΔGsolvation. 5217


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of interest. In section 2, a variety of methods, including recently emerging techniques, is described that can be employed for dissecting the whole, measurable binding energies into the energetic contributions of individual interaction types. A particular advantage of supramolecular complexes is that they allow elucidation of the existence and the limitation of additivity of binding energies, which is inherently assumed in most applications, e.g., for rational drug design. Another advantage is that, in typical supramolecular complexes, several interactions contribute, and the loss of entropy of translation for any intermolecular association (see section 3.7) is already paid by a single association step. Computational descriptions of noncovalent interactions have seen enormous progress in recent years,30,31 but need for most real-life applications explicit consideration of solvent effects. In particular, hydrogen-bonding, dispersive, and polar interactions depend extremely on the medium; some, e.g., hydrophobic interactions are entirely solvent-driven, and ion pairing in aqueous medium is (counterintuitively at first glance) dominated by entropic contributions. Solvent parameters can be derived either with spectroscopic probes or, e.g., from hydrogen-bond measurements in solutions;32−37 it has been proposed that all kinds of noncovalent interaction can be treated as electrostatic interactions on the same polarity scale.38 The ensuing general H-bond scales were used to describe the hydrogen-bond properties of both solvents and solutes, or their functional groups. However, dispersive and hydrophobic interactions can fundamentally not be described with such polarity parameters. Our review addresses mostly affinity measurements of supramolecular complexes in solution, for which an overwhelming number of data is already available. Measurements in the gas phase, which have the advantage to be free of interfering medium effects, are becoming more frequent.39−41 The applied MS methods are technically more difficult than experiments in solution,42 but can now be applied even to proteins.43 Results from gas phase data will be mentioned only sparingly, also as most applications of supramolecular complexes are in solution. Thousands of supramolecular complexes have been described, often together with association constants; we will concentrate on representative studies that contributed to the development of a general frame of energies in noncovalent interactions.

sensing, separation, catalytic, and biomedical technologies. At the same time, supramolecular complexes open a highly promising way to analyze noncovalent interactions in detail.13−16 It is the aim of this review to provide the description of important noncovalent interactions types, in particular with respect to their energetic aspects, and to discuss the strategies used for their evaluation. Knowledge of the energetic contributions to binding is not only of fundamental interest but also key for the design and optimization of application-oriented supramolecular systems. Moreover, these results contribute to the understanding of biologically important associations and of technically used complexes, and in particular for the design of new drugs and of new artificial host structures. In addition, they shed light on the underlying binding mechanisms. Modern synthetic tools allow the construction of suitable host compounds, which can exert distinct interactions with complementary guests. Both the number and the kind of interactions can be implemented in these complexes, their structure can be identified quite accurately, and the thermodynamics of complex formation can be determined precisely. This is supported by systematic variations of the binding sites, by comparison of empirically derived binding parameters for different association types, and by investigations of medium effects. In that sense, we follow the traditional path of science: we ask questions or postulate hypotheses and then synthesize compounds and conduct suitable experiments to scrutinize our theories. The resulting data can serve to improve the basis for energy scoring functions as used, e.g., for rational drug design;17−22 such scoring functions are often calibrated with training sets containing known affinity values. Binding energies are also derived from fragment-based libraries used for drug design, which are based on the construction of potent smallmolecule ligands from low-molecular mass compounds.23−25 Several noncovalent forces, such as cation−π-, anion−π-, distinct dispersive interactions, or halogen binding, as well as more powerful variants of the hydrophobic effect were first identified in synthetic complexes, and after that were also discovered in protein−ligand interactions.13,26−29 The experimental elucidation of these interactions together with long recognized factors such as ion pairing, electrostatic forces, and hydrogen bonds is the focus of this review. New insights in the particular role of water in binding processes became available this way, and are also discussed. Energetics of noncovalent interactions can be highly sensitive to subtle structural or electronic changes of the interactions partners and to medium effects. For example, hydrogen-bonding energies of NH···OC interactions in the core of a protein were found to vary from 2 to 10 kJ/mol (Table 1); for example, they differed by a factor 5. Also the strong influence of solvent effects on noncovalent binding interactions is evident from the tabulated data. Table 1 should provide the reader a first overview of “typical” binding free energies for important noncovalent interactions types and refer him/her to the relevant sections in this review. It is not at all meant to provide a complete list, which on account of the subtlety of noncovalent interactions is out of scope (see also Table S1 in the Supporting Information). Binding increments for noncovalent interactions have to be treated with care, because (i) the system of interest should be as closely related as possible to reference systems for which the binding energies were determined, (ii) reported binding increments, e.g., that for a hydrogen-bond, may or may not be corrected for other, simultaneously occurring interactions and effects that were overlaying/masking the “pure” interaction type

2. STRATEGIES/METHODS In this review, we first give an overview on the available strategies to extract noncovalent interaction energy values from the study of mostly synthetic but also from protein- and peptide-based supramolecular complexes. Noteworthy, measurements with synthetic complexes suffer from fewer limitations in comparison to those with biopolymers, because they can be conducted at wide range of temperatures and in a large variety of solvents, usually without significant structural distortions. Moreover, complex formation of small synthetic systems is in most cases easier to characterize by spectroscopic techniques than that of proteins. Then, we describe the relevant values in the sequence of the underlying binding mechanisms, including long-known effects such as ion pairing, hydrogen bonding, and stacking/dispersive interactions, and more recently investigated interaction types such as halogen bonding, cation−π, anion−π, CH−π, and orthogonal interactions. The description of solvent and hydrophobic effects and of entropic contributions follows. Although those are not “simple” interaction types, they have important 5218


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shift of the nitrogen atoms of the NH binding centers; see section 3.2 and Figure 34. Notably, NMR titrations allow studying the binding of several guests with a selected host, vice versa, in the same solution, thereby minimizing possible errors.79 Knowledge of enthalpic and entropic contributions to binding can hold some surprises that would have gone unnoticed when simply comparing ΔG values.76 To exemplify, the guanidinium hosts 1 and 2 were designed to bind anions (Figure 1), for which

implications on receptor−ligand or host−guest complex formation. There are other strategies to exploit experimental data for the identification of noncovalent interactions, which are not in the scope of this review but should be mentioned. A promising “black box” strategy to extract descriptors from a number of experimental data as a learning set is the use of statistical analysis techniques such as principal component analysis (PCA) and discriminant analysis (DA); these methods have already gained great importance for differential sensing.44 Quantitative structure−property relations (QSPR, or SAR, structure activity relations45−47) have been used early,48,49 more recently including large-scale SAR analysis with an emphasis on data mining,50 and were supported by neural network techniques.51 A different approach, which is particularly popular in biocomputing and drug design, is to use training sets of binding affinities for a given receptor with many ligands, or for a ligand with many receptors, and then to obtain through a multiparameter equation the relevant descriptors that determine the complex stability. However, such parameters are often not independent of each other (not orthogonal), they may not have a significant physical meaning,52 and sometimes a large number is required for a for a given host−guest series; for example, for 70 cyclodextrin complexes five parameters were used.53 Recently, a multiple linear regression analysis of 218 different β-cyclodextrin complexes led, with a training set of 160 compounds, to acceptable correlations when a minimum of seven descriptors was used; however, most of them were physically not meaningful.54 The essential difference of the structure-based approach discussed in this review is that here one systematically varies host and guest structures, the number and the nature of interactions, or the medium, and measures the ensuing change of properties, usually of the complex stability, but often also enthalpic and entropic contributions of binding. The applied physical methods for the evaluation of the affinities and structures of supramolecular complexes are not in the scope of this review; they are dealt with in several monographs3,55−57 and reviews.58−64 In short, besides the traditional measuring methods (e.g., NMR and other spectroscopic titrations), there are several techniques that will likely find increasing use in the field. Surface plasmon resonance (SPR) has the advantage to measure not only affinities but also kinetics of complex formation. Additionally, it can be automatized for high throughput measurements, but needs special immobilization techniques for one partner.65−67 This is also the case for chemical force microscopy (CFM),68 which even allows direct measurement of noncovalent forces. A more recent development is the automated affinity screening of libraries obtained by combinatorial chemistry for optimal host structures (section 2.6). Isothermal titration calorimetry (ITC),69−71 including high throughput calorimetry,72 is of particular interest, as it can reveal striking features in the binding thermodynamics by giving direct access to ΔG, ΔH, and TΔS without having to rely on the questionable van’t Hoff method.73−77 Competition methods, where one measures binding dif ferences using two hosts with a guest, or vice versa, have distinct advantages regarding the accuracy and reproducibility of the affinity data.78 Thereby, calibration with respect to the absolute ΔG values can be achieved by reference to a particular ΔG determined independently by direct measurements. The same approach was applied to NMR titrations of many hydrogen-bond complexes, which allowed also a correlation of the 15N chemical

Figure 1. Example for the use of ITC measurements to unravel enthalpic and entropic contributions to binding. Reprinted with permission from ref 80. Copyright 2005 American Chemical Society.

the overall stronger binding (larger −ΔG value) of host 1 was “rationalizable” at first by its ability to form additional H-bonds with anions on account of its carboxamide moieties.80 However, closer investigation of the thermodynamic parameters revealed that the complexes of host 2 enjoy a stronger enthalpic driving force for binding. Conversely, the complexation of anions by host 1 is markedly favored by entropy. Both observations are unexplainable by a simple binding model.74,80 In this review, we will focus on ΔG binding energies (i) because much more experimental ΔG values than ΔH and ΔS values were reported, (ii) because estimating free energies has a large practical utility, e.g., for predicting the affinities of protein− drug complexes, and (iii) because, unlike ΔH and ΔS, the free energy ΔG is usually a “well-behaved”, additive quantity (see below). As pointed out early by Jencks, ΔG values can be additive in multivalent systems, but positive or negative cooperativity effects have to be taken into account (see section 3.8); the difference ΔGt between the sum of the intrinsic binding energies of A and B, ΔGA and ΔGB, and the measured total binding ΔGAB is a “connection Gibbs energy”, which in Jencks’s view is derived largely from changes in translational and rotational entropy, and not or only to a lower amount from enthalpic factors due to conformation changes.81 Entropic effects are discussed in section 3.9 in this review. As a note of caution, the reader should keep in mind that the interpretation of binding energies in supramolecular complexes must take into account that hydrophobic effects may significantly increase or decrease the binding strength in molecular cavities 5219


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Figure 2. Cooperativity in complexation of N-alkyl ammonium resorcinarene and diamides; X-ray structure (CCDC-1039550) of the host−guest 2:1 complex with R = Me instead of R = C6H13 in the host, and n = 4 in the diamide.86 Reprinted with permission from ref 86. Copyright 2015 Wiley VCH.

hydrogen bonds by Abraham89 and Raevsky90 et al.; they go back to measurements with small molecules and can be considered as forerunners of later investigations with truly supramolecular complexes. Unlike for contemporary supramolecular complexes with a relatively well-defined geometry, these early association complex studies have no control over the arrangements of the binding partners. Nevertheless, the very large number of underlying data points for simple donor and acceptor molecules compensates to some degree for this shortcoming. As will be shown, for example, in section 3.3, these descriptors can be transferred, for example, to the quantification of interactions between metal ions and oxygen in supramolecular ionophores (e.g., crown ether-type complexes), or of their solvent dependence. Thousands of binding constants between small molecules have been measured, most often spectroscopically in organic solvents such as carbon tetrachloride and chloroform. The interaction energies can for all kinds of acceptor A and donor D functions be described by a multiplicative combination of the factors CA and CD,90 or the acidity or basicity constants89 α2H and β2H (Table S2 in the Supporting Information), in form of eq 1a90 or eq 1b89:

(see section 3.7). In this instance, consideration of enthalpic and entropic contributions is essential for a better understanding (section 3.7). Another limitation, discovered by Collet et al.82,83 and generalized by Rebek et al.,84 is that there is an optimal filling factor for such cavities, which means a significant modification of the lock-and-key principle.85 Cooperativity between binding sites can be another complication in the extraction of single energy contributions from experimental complexation energies, as will be discussed in section 3.8. In addition, in complexes for which several close lying binding sites are active, and where more than one binding mode is possible, one can observe coexisting complexes with different association constants and positive or negative cooperativity. Such a case is illustrated with complexes of N-alkyl ammonium resorcinarenes salts and α,ω-diacetamides (Figure 2),86 for which a combination of hydrogen bonds between the carbonyl oxygen and the amide hydrogen of the guests, and additional CH···π interactions leads to formation of 1:1 complexes with short spacers (n = 1), but to stronger 1:2 complexes with longer spacers. The observed association constants amount in chloroform, e.g., for the host with R = C6H13 and the diamide with a spacer length of n = 4, to K1 = 425 M−1 and K2 = 4820 M−1. There is a cooperativity between the binding sites which was characterized by an interaction parameter α = 4K2/K1, and reaches, e.g., α = 45 for the above-mentioned case. Strain and repulsion are responsible for weaker binding with shorter spacers; lowering of binding for longer spacers was explained by their higher flexibility.

ΔG [kJ/mol] = 2.43CAC D + 5.70 (for CCl4) = 1.93CAC D + const (for CHCl3)

(1a)

or lg K (with K in M−1) = 7.354α2 Hβ2 H − 1.094 (for CCl4)

2.1. Binding energies from a large variety of small molecules

(1b)

(with n = 1312, R = 0.9956, and SD = 0.09 with eq 1b)

The most common and generally applicable access to empirically secured energy increments for noncovalent binding is to assemble many data points from a large variety of host and guest partners by systematic comparison of a given partner with many others. The strategy is related to Hammett-type linear free energy relations (LFER),87 which correlate the effect of substituents to reaction kinetics, reaction constants for equilibria, and various other properties. The validity of the so derived energy increments is usually characterized by linear correlation coefficients.87 However, the most interesting observations sometimes stem from outliers or deviations from linearity. For a limited number of reference compounds, different scales of electron accepting and donating power were derived early, such as Gutmann’s48 donor and acceptor numbers on the basis of Lewis-type complexes formation enthalpies and 31P NMR shift changes, or Drago’s49,88 E and C values. The best known and rather comprehensive binding energy factors are those for

2.2. Binding energies from supramolecular complexes with several noncovalent interactions

In contrast to associations between simple molecules, supramolecular complexes usually display several interaction types simultaneously. In a first approximation, one assumes that the single free energy contributions ΔΔG of interactions of type A, B, etc. are additive, so that the total binding energy ΔGt is ΔGt = n·ΔΔGA + m ·ΔΔG B

(2)

for which n and m designate the number of occurrences. The additivity of free energies is commonly assumed, also in most computational approaches of biopolymer associations, but can be violated, especially by a possible positive or negative cooperativity (section 3.9) or solvent effects; e.g., see Figure 13. Furthermore, the underlying enthalpic and entropic contributions can alter drastically, as is illustrated in Figure 1. 5220


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Figure 3. Cyclophane (CP66-NMe2+, with X = +NMe2) shows additive binding energies (−ΔG in kJ/mol, in water) for binding nucleotides and nucleosides.98 Graph: Additive ion-pair contributions in a variety of complexes with a number nC of salt bridges; from slope: average 5 ± 1 kJ/mol and salt bridge (A,B and C,C′, complexes of a tetraphenolate cyclophane (4−) with Me4N+ and an azoniacyclophane (4+) with mono- and dianionic naphthalene derivatives; D, anionic (sulfonate or carboxylate) with cationic (ammonium) triphenylmethane derivatives; E, organic dianions with organic dications; F, cationic azamacrocyle (6+ charges) with aliphatic dicarboxylates; G, cationic azacrowns with adenosine mono-, di-, and triphosphates). Reprinted with permission from ref 98. Copyright 1991 Wiley VCH.

Nevertheless, ΔG values are often “well-behaved”, i.e., show additivity, mainly because of compensation effects between ΔH and TΔS, which are, although often observed, experimentally often questionable91−93 and theoretically still being debated.94−97 For our purpose, it is sufficient to provide experimental tests for ΔG additivity. For instance, ΔGt is additive if a linear correlation with n is observed (eq 2), which usually is the case for systems with only one kind of interaction. Under this circumstances, the total binding energy relates to the individual binding increments as ΔGt = n·ΔΔGA. Alternatively, if the spread of n is not large enough for a correlation analysis one can also take the sum of all ΔΔGA values divided by n to obtain an average ΔΔGav. If the statistical deviation in ΔΔGav is then small with many structurally different host−guest complexes, one can assume additivity. Correlations with two and more parameters can easily be misleading, particularly if the parameters are not orthogonal to each other, i.e., if the interactions influence each other. Therefore, one usually uses a more reliable approach, in which each, or at least one of the two parameters, is determined independently. The strategy is illustrated in Figure 3. Other, more recently emerging approaches, such as the use of double mutant cycle analysis, molecular torsion balances, and measurements with dynamic combinatorial libraries, will be discussed in sections 2.3, 2.5, and 2.6. The cyclophane complex shown in Figure 3 illustrates how one kind of interaction, here ion pairing, can be distinguished from others, here van der Waals and hydrophobic contributions.98,99 The free-energy difference (ΔΔG) of complexes with nucleotides (containing a -PO32− residue) and parent nucleosides (the noncharged species) was found to be 10 ± 1 kJ/mol, a value representing a rather constant ion-pair contribution. At a given

time, one phosphate, bearing two negative charges, can form two salt bridges to one neighboring +NMe2 center of the cyclophane. NMR spectroscopy showed that binding occurred in an inclusion mode; that is, the nucleobase was immersed in the cyclophane cavity, while contacts between the cationic host center and the anionic phosphate nucleotide groups occur. The ion-pair value of 10/2 = 5 kJ/mol derived from Figure 3 is in agreement with independent measurements with about 100 ion pairs, which at the given ionic strength of the medium (see section 3.1) yielded a free energy increment of 5 ± 1 kJ/mol for a single salt bridge. The correlation shown in Figure 3 displays additivity: the observed total free binding energy is a linear function of the number of salt bridges involved in one complex. The slope of the correlation corresponds to approximately 5 ± 1 kJ/mol per single ion pair.98 As will be discussed in section 3.1 in connection with aminocyclodextrin complexes, the dissection between ion pairing and other noncovalent forces becomes more complicated if, other than in the cyclophane-nucleotide/nucleoside complexes above, one of the interactions is much stronger than the other, and if simultaneous optimal contact at different binding site locations cannot materialize. The same obstacle is also discussed in section 2.2, Figure 7, in the context of halogen bonding in protein−ligand complexes. Another approach to elucidate different binding contributions relies on modification of the host structure. This is illustrated with the cyclophane CP66 (Figure 3) in Scheme 1, where the + NMe2 group was replaced by a sulfonamide function, X = NSO2-C6H4-SO3−.100 A complexation free energy trend that is inverse to the one with X = +NMe2 was observed. The more hydrophobic host (X = N-SO2-C6H4-SO3−) binds naphthalene 5221


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be a significant factor that modulates the protein−ligand affinity.116 Following an established methodology, e.g., for hydrogenbonds,119 a survey of the available crystallographic data of protein−ligand complexes was conducted to extract typical distances and angles between the predicted R1-X Y-R2 interaction partners (X = Cl, Br, I; Y = donor atom, e.g., O, N, S; see section 3.4.).116 In brief, it was observed that a significant number of X··· Y contacts occur with distances smaller than the sum of the van der Waals radii (∑rvdW) of the halogen and a donor atom (Figure 4a); in addition, there is also a peculiar (dihedral) angle preference for t he R 1 -X ··· Y-R 2 interaction p artners.101,116,118,120−123 Both criteria are well accepted to provide structural evidence for a noncovalent bonding situation in protein−ligand complexes.101,119,122 To exemplify, Figure 4b shows the complex of the human thyroid hormone receptor with 3,5,3′-triiodothyroxine (T3), featuring two halogen bonds between iodine and oxygen atoms. The respective interaction distances of 3.1 and 3.5 Å are shorter than ∑rvdW = 3.6 Å,124 implying noncovalent bonding. However, in comparison with high-level computational results on halogen bonds (roptimum ∼ 3.1 Å),121,125 it is immediately clear that the shorter and colinear iodine−oxygen interaction provides more binding energy to the protein−ligand complex stability than the longer, tilted one.121,125,126 The main challenge, however, is to experimentally evaluate the halogen-bonding energies in protein complexes. According to the strategies described in section 2.2, a systematic alteration of a ligand that is structurally verified to undergo halogen bonding in a protein-binding pocket should be conducted, and after the affinities of the respective protein− ligand complexes were experimentally determined, one could hope to derive binding energy increments for the halogen bonding. Several studies on the halogen-bonding energies in protein complexes were reported to date.121,127−132 The experimental evaluation of halogen-bonding energies in protein−ligand complexes was pioneered by the group of Diederich with a systematic study on inhibitor binding to human cathepsin L (Figure 5) and MEK1 kinase.121,127 Use of a covalent inhibitor helped to establish nearly identical binding geometries, confirmed by X-ray analysis (Figure 5c), for each of the substituted inhibitors (X = F, H, CH3, Cl, Br, I), which is of crucial importance when attempting to dissect the large number of influencing factors on the protein−ligand interaction into individual contributions, e.g., that of a suspected halogen bond. Noticeably, the length of the X···OC distance of

Scheme 1. Modification of a Host for the Identification of Cation−π Interactions100,a

a

−ΔG values in kJ/mol.

less efficiently than the more hydrophilic one (X = +NMe2). With the latter, one observed a ΔG decrease for increasingly hydrophobic guests. These results pinpoint cation−π effects as the dominating interaction motif for the CP66-NMe2+ host (see section 3.6.1). 2.3. Binding energies from protein complexes

Spurred by pharmaceutical research interests, a very large number of protein−ligand complexes were characterized, both structurally, e.g., by crystal structure analysis, and thermodynamically, e.g., by affinity screening (IC50 values). Comprehensive and inspiring reviews about this topic, discussing also implications on rational drug design, can be found elsewhere.13,101−106 Virtual screening of guest molecules that are complexed by a given host has recently been proposed, based on scoring functions with known guests as a training set.107 At first glance, this large data set appears to provide a superb starting point for fully describing noncovalent interactions in protein−ligand complexes by the methods described in section 2.2 for supramolecular complexes. However, the situation is much more complex. In the following, we describe exemplarily the common research approaches taken in protein chemistry, as they have been applied to the identification and characterization of halogen bonding in protein−ligand complexes. Halogenation of drugs is an often-applied strategy in pharmaceutical research to improve the pharmacokinetic properties (e.g., membrane permeability and stability) and to increase the affinity of drugs for their protein targets.108−110 The latter was mainly attributed to the higher hydrophobicity and better space filling of halogenated drugs, favoring their binding to lipophilic protein pockets. In addition, it was also clear that halogenation strengthens the dispersive interactions (section 3.5) of the drug with polarizable protein residues. After the identification of the halogen bond in small-molecule complexes,111−115 it was proposed that this interaction type can also

Figure 4. (a) Distribution of distances between X-bond donors and acceptors in 600 protein−ligand complexes as percentages of the sum of the van der Waals radii (%∑rvdW). (b) Recognition of 3,5,3′-triiodothyroxine (T3) by human thyroid hormone receptor. Halogen bonds are shown as dotted lines from the iodine atoms of T3 to the carbonyl oxygens of the peptide bonds (PDB-ID 2H79).117 Reprinted with permission from ref 118. Copyright 2013 Wiley-Blackwell. 5222


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Figure 5. (a) Binding pocket of human cathepsin L protein and a bound covalent inhibitor. Red dashed line: halogen bond, green dashed line: hydrogen bond between protein and inhibitor. (b) Correlation of experimentally determined binding increments of the Cl-, Br-, and I-substituted inhibitors with respect to the H-substituted analogue, with computed binding energies for small-molecule models. Data taken from ref 121. (c) Crystal structures of protein−inhibitor complexes. Left: Halogen bond between the iodine moiety of the inhibitor and the carbonyl oxygen of Gly61 in binding pocket S3. Right: Overlay of the binding geometries for the chloro- (magenta), bromo- (green), and iodo-substituted inhibitors. Figures (a) and (c): reprinted with permission from ref 127. Copyright 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Figure 6. (a) Relevant parts of the substituted inhibitors (X = H, F, Cl, Br, I) and of the protein-binding pocket of phosphodiesterase type 5 (PDE5), obtained from X-ray structures. A structural water molecule (for X ≠ F) is depicted as a sphere. (b) Binding free energy (ΔG), enthalpy (ΔH), and entropy (−TΔS) of the inhibitor−PDE5 complex in aqueous solution. (c) Correlation of experimental ΔGexp values of the Cl-, Br-, and I-substituted inhibitors with calculated binding energies (Ecalc) for small-molecule models. Data taken from ref 130. Figures (a) and (b): reprinted with permission from ref 130. Copyright 2014 American Chemical Society.

difference). A correlation (R2 = 0.99) of reported calculated stabilization energies of the halogen-bonding moieties Cl, Br, and I (evaluated for a small model system)121 and the experimentally found relative free energy differences (with respect to X = H) resulted in a perfectly linear behavior (Figure 5b), although only three data points were available. However, other contributing effects should also be considered. Inspection of the solvation

3.1 Å (X = Cl, Br, I) and the collinear arrangement was indicative for strong halogen bonds. At first glance, the agreement between expectation and experiment is very good. The binding affinity, reported as IC50 (μM), increases in the order F (0.34) < H (0.29) < CH3 (0.13) < Cl (0.022) < Br (0.012) < I (0.0065).121,127 The fluorine-substituted inhibitor is the weakest binder, whereas the iodine-substituted variant is the strongest (factor of 50× relative 5223


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Figure 7. (a) Structures of inhibitors for aldose reductase (AR) capable of halogen bonding (X = Br, I) or hydrogen bonding (X = NH2) to the Thr113 residue of the enzyme. (b) Alignment of the AR inhibitors and selected amino acids of the AR active site based on X-ray structures: blue, Br (4H); violet, Br (FH3); cyan, Br (F2H2); green, Br (F4); red, I (4H); gray, I (FH3); yellow, Br (F2H2). (c) Correlation of experimentally determined ΔGexp values of the inhibitors with calculated binding energies (Ecalc) for small-molecule models. (d) Correlation of experimentally determined ΔGexp values of the inhibitors with calculated binding energies (Ecalc), corrected for the computed desolvation energy of the inhibitor (ΔGsolv). Data taken from refs 129 and 131. Figure (b): reprinted with permission from ref 131. Copyright 2015 American Chemical Society.

(Figure 6b). In addition, the −ΔH value increased along the series H < Cl < Br < I, which follows the trend of the halogenbonding strength (see section 3.4) but excludes the classical hydrophobic effect (section 3.7) as the major driving force for binding. It is also noteworthy that, for X = Cl and Br, a strong halogen bond is formed with the Tyr residue and a weaker one with the cavity water, whereas for the iodinated ligand the situation is reversed (Figure 6a).130 Taking the reported energies of both the strong and weak halogen-bonding contact together, one observes again a linear correlation (R2 = 0.99, although only three data points were available) of the calculated halogen-bond strength with the experimentally determined ΔG value; see Figure 6c. Structural changes for the arrangement of peptide residues forming the binding pocket, or of cavity-water molecules, which are induced by subtle changes of the ligands, can have pronounced implications on the binding energies, in particular on ΔH and TΔS, but also on ΔG.13,122,131,132,136−140 Thus, reliable structural models are definitely needed if protein−ligand complexes should be used to quantify the binding strength of individual noncovalent binding motifs. This is not always a trivial task; for instance, it was recently crystallographically observed that even salts, common additives to enhance protein crystallization, caused the appearance of a halogen bond of a brominated ligand with a Tyr residue of CK2 kinase that was not present in the low-salt state.141 Even if the structure of protein−ligand complexes is highly conserved and if cavity solvation effects are similar for all ligands studied, there can be additional complications that hamper the

properties of the inhibitors, reported by their log P (logarithmic distribution or partition coefficient octanol/water at pH 7.4),133−135 shows that the hydrophobicity nearly uniformly also increases along the same series: F (2.36) < H (2.11) < CH3 (2.57) < Cl (2.73) < Br (2.96) < I (3.23).121,127 It is thus difficult to quantify how much of the corresponding overall affinity increase in the series X = F to I is due to halogen bonding, and how much is caused by the hydrophobic effect. Unlike synthetic supramolecular systems, proteins are (mostly) restricted to an aqueous environment so that a common strategy to dissect bonding energies from solvophobic effects (evaluation of the binding affinities in a range of apolar and polar solvents) cannot be applied. Furthermore, as will be discussed in section 3.7, the nonclassical hydrophobic and high-energy water effect cannot simply be characterized by lipophilicity numbers, but critically depends on the number of water molecules in cavities and their interaction energy. The individual thermodynamic parameters ΔH and TΔS can provide insight into rationalizing protein−ligand interactions, as was recently shown for the binding of halogenated inhibitors to phosphodiesterase type 5 (PDE5).130 In the systematic evaluation of inhibitor complexes (X = H, F, Cl, Br, I) a few surprising features emerged (Figure 6). First, X-ray crystallography showed that, in all complexes but for the fluorinated ligand, there is an additional water molecule in the binding pocket that forms together with the HO-moiety of Tyr612 of the protein a bifurcated halogen bond with the inhibitor (for X = Cl, Br, I); see Figure 6a. The complex formation was found to be enthalpically driven for (X = H, Cl, Br, I) but entropically driven for X = F 5224


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extraction of binding increments for a particular interaction type. Complexes of aldose reductase (AR) with halogenated inhibitors were investigated in depth by crystallography, calorimetric measurements, and computations.129,131,132 In Figure 7, a set of inhibitors are shown whose affinity for AR was experimentally determined, and which show nearly indistinguishable binding geometries.129,131 However, unlike the aforementioned examples for cathepsin L and phosphodiesterase type 5, no correlation can be observed between the computed binding energies (evaluated for small model systems) and the experimental free energy of binding (Figure 7b), indicative of the substantial contribution of additional interaction types but the halogen bonding to the relative complex stabilities within the inhibitor series. Again, because halogenation of organic compounds increases their hydrophobicity, an overlaying effect of differences in the desolvation cost for the inhibitor upon binding can occur. In fact, when the computed solvation free energies of the ligands were taken into account (see section 3.7), a meaningful correlation (R2 = 0.59) of computed and experimentally determined complex stabilities of the halogenated inhibitors appeared;129 see Figure 7d. However, it is clear that the relative stability trends between the complexes are not just due to halogen bonding (or hydrogen bonding in the case of X = NH2) of the inhibitor with the Thr113 residue. The presence of secondary effects is, of course, very common for protein−ligand complexes, because of the large number of spatially close potential interaction partners and potential interaction types (Coulombic, dispersive, etc.) in addition to the special noncovalent binding motif under study. The reason why these secondary effects (and the solvation effects) are prominent in the studies for aldose reductase is the unfavorable distance for halogen bonding in AR−inhibitor complexes, r(X··· O) = 2.9 Å ≠ roptimum = 3.1 Å, and the tilted, not collinear arrangement,131 whereas optimal halogen-bonding geometries were adopted for inhibitor complexes of cathepsin L and phosphodiesterase (see above). Thus, halogen bonding in AR complexes is energetically weak, and in competition with other secondary effects. A special methodology, the double mutant cycle, which was developed to reduce secondary effects in order to obtain the “pure” interaction energies for two binding partners X and Y is discussed in section 2.4. A deeper analysis protein−ligand complex is not only of pharmaceutical interest, but can also expose subtle but important effects, that would have gone unnoticed when focusing on the comparably small number and diversity of synthetic host−guest complexes. For instance, a survey through a large range of ligands and their monomethylated analogues with their corresponding proteins showed relative binding affinities centering around zero; that is, as intuitively expected, addition of a single methyl group has mostly not a strong effect (Figure 8).142 However, in 8% of the cases, the association constants increased by a factor of 10 (i.e., by −ΔΔG ca. 5 kJ/mol), and in 0.4% even by a factor of 100 (i.e., −ΔΔG ca. 11 kJ/mol), just on account of a single methyl group. When these special instances were analyzed more closely, it was found that, for instance, the freezing out of the motions of the ligand by steric bulk could markedly improve the binding affinity because the entropic cost of binding (see section 3.9) is reduced. This often-overlooked effect, and not only the higher hydrophobicity of -CH3 vs -H, should be kept in mind when rationalizing apparent binding differences between other host− guest pairs.

Figure 8. Distribution of free energy changes in activity for substitutions of a hydrogen atom by a methyl group in publications in the Journal of Medicinal Chemistry and Bioorganic Medicinal Chemistry Letters during 2006−2011. Modified figure reprinted with permission from ref 142. Copyright 2012 American Chemical Society.

2.4. Binding energies from double mutant cycle (DMC) analysis

The dissection of an experimentally determined binding energy into a sum of different contributions (e.g., hydrogen bonds, stacking and dispersive interactions, etc.) is, as said, a difficult undertaking because they usually do not occur separately. To exemplify, the contribution of a salt-bridge for the folding energy of a protein cannot be obtained by simply comparing the native proteinwith the salt-bridge forming amino acidswith a protein mutant containing different residues. This is because other, secondary interactions of the amino acid residues with the backbone occur at the same time and are different for native protein and the mutant. Fersht and co-workers overcame this hurdle by an elegant procedure, known as “double mutant cycles” (DMC), which eliminates the disturbing contribution of the secondary interactions.28,143−148 Thus, accurate binding increments (mostly ΔΔG, but the method can also be applied to ΔΔH and ΔΔS) for the X···Y interaction can be obtained through a DMC analysis; its principle is depicted in Figure 9. In essence, differences in the thermodynamic binding parameters (e.g., ΔGfold or ΔGa, if a protein−ligand interaction is being investigated, see below) are measured between the native protein containing the X···Y interaction of interest and three protein mutants: the mutated X′, a mutated Y′, and both mutated X′ and Y′ moieties. The Born−Haber cycle leads then to the equation for the DMC: ΔΔG = ΔGXY → X ′ Y − ΔGXY ′→ X ′ Y ′ =ΔGXY → XY ′ − ΔGX ′ Y → X ′ Y ′

(3)

By applying this method to the folding of the protein barnase, a stabilizing energy of 4−5 kJ/mol for a single Asp···Arg salt-bridge on the protein surface was experimentally determined,148 which is in good agreement with the average value of 5 ± 1 kJ/mol obtained independently for many salt bridges between small molecules in water (section 3.1). A buried Asp···Arg salt-bridge contributed much more, 14 kJ/mol:150 an increase which in principle is line with the solvent dependence of salt bridges. Hydrogen bonds, buried in the apolar protein core, were found to contribute on average 6 ± 4 kJ/mol to the folding by DMC studies,151 similar to that of amide H-bonds in small-molecule systems (5 kJ/mol in CHCl3; see section 3.2). Cation−π, NH···π, 5225


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Figure 9. (left) Schematic representation of a double mutant cycle for quantifying the strength of the noncovalent interaction between X and Y according to eq 3. (right) DMC approach utilized by the Fersht group to estimate the binding energy of a salt bridge in the barnase wild type.143,148,149

Figure 10. Determination of H-bonding stabilization between threonine and aspartic acid for the membrane protein bacteriorhodopsin. (left) Bifurcated H-bond between threonine (T90) and aspartic acid (D115) in the wild type (WT) of the protein, from XRD structures. (center) DMC for mutating each T90 and D115 into alanine (A) and corresponding ΔG changes on the folding stability; the resulting ΔGint = 7 kJ/mol denotes the stability of the T···D hydrogen bond. (right) Overlay of the XRD structures of the wild type (red), single mutant D115A (gray), and double mutant T90A/D115A (blue). Reprinted with permission from ref 159. Copyright 2008 Macmillan Publishers Limited.

and π−π interaction in proteins were also studied by the DMC method.146,152,153 Rigorous testing of the DMC method with several different mutants of ribosomal protein L9 has exposed rather large differences for the estimated stability of a particular surface-located salt bridge between the N-terminal amino group and Asp23, ranging from 3 to 7 kJ/mol, depending on the reference mutations X′ and Y′ chosen.149,154 Nevertheless, despite potential shortcomings, the DMC approach remains (one of) the best available option(s) for determining X···Y interaction energies between protein residues.155−158 Application of the DMC approach in a recent comprehensive study on hydrogen bonding in the membrane protein bacteriorhodopsin is shown in Figure 10.159 The crystal structure (left) of the nonmutated wild type protein shows an arrangement between a threonine (T) and an aspartic acid (D) residue that satisfies the structural criteria for a bifurcated H-bond. In order to evaluate the energetic contribution of this H-bond to the folding energy of the protein, both the T90 and the D115 were mutated into alanine (A), such that no significant A···A interaction (≡ X′···Y′ in Figure 9) occurs in the double mutant state T90D/ D115A. In comparison with the folding energies of the single mutants (D115A and T90A), the T···D hydrogen-bonding interaction in the wild type could thus be quantified by eq 3, being worth 7 kJ/mol, while many other hydrogen bonds in the same protein were found to be much weaker.159 Importantly, crystallographic analysis (right) verifies that the native protein (red), the double mutant (gray) and D155A mutant (blue) all show virtually identical conformations, which is an important criterion for obtaining realistic binding increments using the DMC method (see below).

Independent methods, e.g., assessing electrostatic effects by the pKa values of the ionizable protein residue changes involved in salt bridges,149,160 measurements of deuterium isotope effects,161 and crystallographic studies combined with computational approaches,162−165 can afford complementary information to the DMC method. These are important additional pieces of information because the DMC analysis is subject to three assumptions whose validity is difficult to judge a priori. First, meaningful binding increments for a X···Y interaction pair can only be derived if the X′,Y′ double mutant is a noninteracting reference state.149,166 Second, the secondary perturbations need to be additive functions of the mutations.149,166 Exception to the additivity principles in biochemical systems are well documented for spatially close residue pairs;167,168 long-range interactions or differential solvation effects can also be the cause of the nonadditivity of ΔG (and in particular for ΔH and TΔS).149,169−171 Studies about CH−π interactions illustrate the difficulties that can arise. It was reported that the interaction of three CH-bonds of cyclohexylalanine with Phe affords 8 kJ/ mol for the folding of the small model protein α2D,172 while a Phe−carbohydrate interaction pair (2 kJ/mol from 3 CH−π contacts)173 and a Trp−carbohydrate interaction pair (3 kJ/mol from 5 CH−π contacts)174 contributed much less in a β-hairpin peptide. It was speculated that either a repulsive interaction between the substituents in the X′,Y′ double mutant of protein α2D occurs, or that solvation differences between the protein and peptide systems could explain the apparent discrepancies.172 A third important prerequisite for the DMC method is that the conformation of the native state and the mutants should be essentially the same, or at least similar structural changes should 5226


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Figure 11. DMC analysis of a water-mediated hydrogen-bonding interaction between (S)-nicotine and Leu119 of the α4β2 neuronal nAChR protein. Reprinted with permission from ref 184. Copyright 2010 PNAS.

additional interactions should be much stronger than that of the X···Y pair, because all four states, XY, X′Y, XY′, and X′Y′, shall adopt the same folding structure/binding geometry. This fundamentally distinguishes DMC from measurement approaches with a large library of molecules or supramolecular complexes discussed in the preceding sections (2.1 and 2.2), which are also applicable to systems interacting by only a single interaction type. While usually being less problematic for protein folding studies because of the presence of the large number of nonmutated residues, these requirements should be kept in mind when studying folding of peptides, receptor−ligand complexes, or artificial host−guest complexes: Receptor−ligand and protein−drug complexes were evaluated by a DMC analysis, for instance to obtain an independent measure for the spatial proximity of certain amino acid residues of the receptor in the presence/absence of the ligand179 or to investigate the interaction distance between amino acid residues in the binding pocket of a protein and functional moieties on a ligand, drug, or antibody.145,157,180−183 Thereby, it is assumed that an interaction energy of a X···Y pair that is significantly different from zero indicates that X and Y are “in contact”. However, ΔΔG(X···Y) ∼ 0 does not imply spatial distance; see, for instance, refs 149 and 159. The DMC method was applied to the receptor−drug complex of α4β2 neuronal nAChR protein and (S)-nicotine to evaluate the energetic contribution of a proposed H2O-mediated hydrogen-bonding interaction between the sp2-nitrogen atom

occur for both related mutants (e.g., for both the X′Y and X′Y′, or for both the XY′ and X′Y′; see eq 3).149 The folding state of proteins is determined by a multitude of multiple weak interactions, such that mutations of a single noncovalent binding pair (e.g., a salt bridge) with similar sized moieties are believed not to cause significant conformational changes; preferably, this should be verified experimentally.159,165 The double mutant cycle method can also be applied to folding peptides,144,158,173,175−177 but a distinct difference is the higher accessibility of the X···Y interaction pair to solvent molecules compared to mutation studies with buried protein residues. A consequence of solvent-accessibility is that ΔG can lose its useful additivity character.171 This, and the higher conformational flexibility of peptides, somewhat complicates the direct comparison of the binding increments obtained with proteins and peptides.172 To illustrate, edge to face stacking of two Phe residues was determined to provide 4 kJ/mol stabilization in the hydrophobic core of protein α2D178 (5 kJ/mol for the edge-face stacking of two Tyr residues in barnase),146 while only 50% of this stabilization energy was reported for a β-hairpin peptide.175 Double mutant cycle analysis is subject to the condition that both the native and all three mutation states (X′Y, XY′, and X′Y′) show folding or binding. Because the reference mutation X′Y′ has to be noninteracting, it follows that other, additional interactions have to be present that serve as “anchors” to ensure that folding/complexation takes place. This was also schematically depicted in Figure 9a. Furthermore, the interplay of the 5227


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Figure 12. “Chemical” double mutant cycle analysis for HCV NS3 protease inhibitor complexes, where for convenience, only the drug is being mutated. Reprinted with permission from ref 185. Copyright 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Figure 13. Thermodynamic parameters for binding of structurally closely related inhibitors with thermolysin. The numbers shown give the relative differences between neighboring ligands in the diagram. Reprinted with permission from refs 187 and 170. Copyright 2012 and 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

co-workers, successive mutations of an inhibitor 1 for thermolys in protein via 2 (additional −CH3 moiety) or via 3 (additional −COOH moiety) into 4 (additional −CH3 and −COOH moiety) yielded trends in the experimental binding free energy that could not be rationalized by energy increments for a −CH3 or a −COOH group interacting with the protein-binding pocket;170,186 see Figure 13 (left). On the contrary, distinct structural differences, established by X-ray diffraction, in the cavity−water network that is in contact with the ligand are responsible for the observed complicated trends. Quantification of the ΔG, ΔH, and TΔS contributions of binding for eight structurally closely related inhibitors with thermolysin further exposed the complexity that arises when differential hydration effects of protein−inhibitor complexes occur (Figure 13 (right)).187 Even though the inhibitors structurally differ only by hydrocarbon tails, the effects on the complex-formation thermodynamics are dramatic and cannot be correlated by “simple” parameters such by the hydrophobicity of the ligand or

of nicotine and the -(CO)NH- group of the Leu119 residue (Figure 11).184 As a reference state (X′,Y′), the benzene analogue of nicotine and mutated protein (Leu119 → Lah119, with NH → O) were employed. The analysis revealed a coupling energy of approximately 11 kJ/mol, which could be attributed to two additional, H2O-mediated hydrogen bonds occurring in the native state that were missing the double mutant. On average, each H-bond is worth 5.5 kJ/mol, which is a reasonable value for such a NH···OH2···N interaction sequence (see section 3.2). Having to mutate protein residues, application of the conventional DMC method to the screening of protein−drug complexes is cumbersome. In order to obtain some of the desired information more rapidly, e.g., synergistic and antagonistic binding effects of functional groups of the drug, a DMC approach was developed that utilizes only chemical mutations of the drug (Figure 12).185 However, (even) the DMC method cannot always satisfactorily eliminate effects arising from differential solvation, in particular in aqueous media. In a systematic study by Klebe and 5228


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Figure 14. Double mutant cycle for the quantification of two terminal edge-to-face aromatic interactions in complex A (15·17). Reprinted with permission from ref 166. Copyright 2007 The Royal Society of Chemistry.

proteins, one can come up with a potential explanation. If the receptor−ligand system cannot simultaneously adopt the optimal interaction geometry both for the anchoring H-bonds and for the aromatic-rings, then one can expect that all interaction modes are somewhat weakened compared to a different receptor−ligand system that predominately interacts via only one X···Y pair. This argument would suggest that the X···Y binding increment obtained by a DMC method is, strictly speaking, only valid for the specific receptor−ligand combination. This hypothesis finds its counterpart in the protein systems: The energetic contribution of buried salt-bridges in proteins varies dramatically for different residues and proteins, ranging from overall stabilizing to destabilizing,149,150 whereas the interaction of opposite charges is always attractive for smallmolecule systems, in particular in apolar environments (Section 3.1). Similarly, H-bonds in proteins can also be substantially weaker (e.g., only 2.5 kJ/mol for the membrane protein bacteriorhodopsin)159 than that in small-molecule analogues. Binding increments obtained by a DMC analysis should therefore be treated as a lower limit for the maximal stabilization that a X···Y pair could in principle provide, unless it is confirmed that the X···Y pair has adopted its ideal binding geometry. To test this, a different receptor−ligand system should be utilized. Indeed, using two different rigid, well-defined receptor and ligands pairs, the OH···OC hydrogen-bonding interaction between phenol and an amide was quantified to contribute about 6 kJ/mol166,205,206 and 8 kJ/mol199 in CHCl3, which is now close to the expectation for a well arranged H-bond. It is even more challenging to obtain transferable binding increments if small changes in the binding geometry of the receptor−ligand complex compared to that of mutants have a strong impact on the energy values.200

by dispersion-energy increments. See section 3.7 for a detailed discussion of the hydrophobic effect. The double mutant cycle method was extended particularly by Hunter and co-workers to the investigation of noncovalent interactions in synthetic supramolecular systems.166,188 Given that all the aforementioned prerequisites are met, (i) absence of X′···Y′ interaction, (ii) additivity of energies, and (iii) identical conformations for the native guest-complex and its mutants, binding increments for the interaction of the functional groups X and Y can be obtained in the same manner by eq 3. Some notable examples are the determination of the stabilizing edge-face π−π stacking energy of two aromatic rings (Figure 14);188 an edge-face arrangement of a substituted aromatic ring with a pentafluorophenyl π-system was found to be mostly repulsive.189 Cation−π interactions of substituted aromatic rings were characterized this way,190 and the results were in accordance with an electrostatic π−π interaction model and additional DMC measurements for aromatic species.191−193 Other investigations, however, are in conflict with this interpretation and emphasize local (dispersive) interactions between the substituents194−196 (see section 3.5). The investigation of hydrogen bonds197−199 (see section 3.2), polar interactions of halogens and aromatic rings200,201 (see section 3.4), and CH−π interactions202 (see section 3.5) has also been possible through the DMC approach. In addition to its broad scope, useful features of the DMC approach are its applicability to the quantification of repulsive interactions166,189,200 and to characterize chelate effects.155,160,166,185,198,199 Despite this impressive success, a few words of caution are in order. For instance, it is surprising that the NH···OC hydrogen bonds between the amide units on the receptor and ligand were accounting for only 2.8 kJ/mol each in CHCl3,188 while about 5 kJ/mol would have been expected based on the large data set for small molecules and values used in scoring functions17 (section 3.2). The reason for the discrepancy remains unclear,203,204 but by analogy to results for DMC analysis with

2.5. Binding energies from molecular balances

The quantification of (weak) intermolecular interactions faces challenges that were hoped to be overcome by using molecular torsion balances instead of conventional host−guest pairs.207 5229


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Specifically, the complexation free energy ΔG is, with intermolecular complexation, reduced by the inherent entropic cost for bringing the binding partners together (see sections 2.2 and 3.9); as a result, a weaker or even no intermolecular complexation may occur. In this case, conventional binding studies, e.g., equilibrium measurements between “simple” ligands with only one binding interaction type, are hampered. The quantification of repulsive interactions is also not possible for conventional supramolecular complexes, unless other interaction types simultaneously drive the complex formation. Lastly, the control and knowledge of the exact geometric arrangement of the noncovalently bound partners is limited in the aforementioned measuring approaches. Molecular torsion balances are designed to “force” X and Y in an intramolecular arrangement (folded state) by a suitable molecular scaffold (Figure 15), where X and Y interact,

in the eq,eq conformer a free energy of 6.5 kJ/mol (see section 3.2). Later, 1,9-substituted trypticene derivatives served in the 1970s as a scaffold (O̅ ki and co-workers).210 The term “molecular torsion balance” was coined by Wilcox and coworkers in 1994,211 since when this tool for the quantification of noncovalent interactions gained popularity. Recent developments are directed toward the design of additional molecular balance scaffolds,212,213 such that different binding geometries between X and Y can be probed (see Figure 16). Although molecular balances are not supramolecular complexes, they can be viewed as covalent analogues and have provided valuable data for intermolecular forces because the equilibrium between the conformers depends on attractive or repulsive noncovalent interactions between the substituents (and the balance framework). The fundamental difference in the methods discussed in sections 2.2, 2.3, and 2.4 is that energies derived from measurements with molecular balances refer to intramolecular and not to intermolecular interactions. Important noncovalent interactions to which molecular torsion balance studies were applied include CH···π,214−218 OH···π,213,219,220 NH···π, 221 CH···O,210,222 and arene··· arene210−212,214,222,223 interactions as well as orthogonal dipolar224 and dispersive interactions,225,226 and solvophobic contributions.218,226,227 An example for the latter is shown in Figure 17. In the ideal case, molecular balance studies are combined with a double mutant analysis to take other secondary interactions and inherent conformational preferences of the balance into account.207,224 An illustrative example comes from the group of Diederich, who quantified the strength of the orthogonal interaction by Csp3-F and Csp2-F bonds and amide carbonyl groups in organic solvents, taking advantage of the well-defined orthogonal arrangement warranted by the balance, and the elimination of overlaying secondary interactions, e.g., π−π stacking effects, whose strengths depend on the substituents (Figure 18 and section 3.4). One of the advantages of the molecular balances approach is at the same time its weakness; the well-defined and fixed interaction geometry between two binding units X and Y that is governed by the backbone of the balance can cause fundamental problems in the interpretation of the results. In theory, the molecular balance is designed to provide the “optimal” binding energy between X and Y, similar to the optimal interaction geometry that would be adopted by the binding partners in the absence of the scaffold. In praxis, however, the interaction energy between X and Y for a particular binding geometry of X and Y, e.g., for a particular distance and angle, is probed. One can distinguish two scenarios: (a) For a rigid molecular-balance, the scaffold-determined interaction distance/angle of X and Y will most likely not coincide with that of the “ideal” equilibrium state between X and Y. Such a balance study will then rather probe an “unnatural” intermolecular binding geometry and, thus, provides a binding energy that is markedly different from that of the constraint-free ideal case. In fact, a recent study on arene−silver(I) interactions has provided binding free energies that differed by almost 100% (5.6 to 11.0 kJ/mol) for two different balances employed.228 Most other reported studies have only considered one balance for one interaction type. (b) The “ideal” binding geometry of X and Y may be reached when the molecular-balance scaffold is more flexible. Nevertheless, an additional issue is that this flexing of the scaffold into the ideal binding X···Y binding geometry may build up some strain, resulting in smaller apparent binding

Figure 15. Schematic operation principle of a molecular balance.207

attractively or repulsively. Importantly, the scaffold must also allow for at least one other conformation, where X and Y are a noninteracting distance from each other (the unfolded state), and an equilibrium must be established between the folded and unfolded states. In a first approximation, the free binding energy of the X···Y interaction can be quantitatively assessed by eq 4, after the ratio of folded and unfolded states were experimentally determined, for instance by NMR spectroscopy.207 ⎛ [folded] ⎞ ΔG = −RT ln⎜ ⎟ ⎝ [unfolded] ⎠

(4)

Historically, conformational studies for organic molecules, for instance of trans-1,2-disubstituted cyclohexanes, can be considered as prototypes for molecular balances, in which only in the diequatorial conformer do the substituents interact with each other (“folded” state), while diaxial substituents do not interact with each other (“unfolded” state).208 Scheme 2 shows an early example for an analysis based on measurements of conformational equilibria, here between eq,eqScheme 2. Conformational Equilibria in trans-2Fluorocyclohexanol for the Evaluation of ROH···F-R Hydrogen Bonds, which Stabilize the eq,eq Isomer209

and ax,ax-conformations of trans-2-fluorocyclohexanol.209 The energy differences vary from 6.5 kJ/mol in CCl4 to 5.0 kJ/mol in polar acetone, as only in the eq,eq conformer an OH···F hydrogen bonds can materialize. Comparison of the conformer energies with those obtained from the ΔG values for the monosubstituted cyclohexanes gives for the OH···F hydrogen-bonding attraction 5230


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Figure 16. Representative molecular balances: left, by Wilcox and co-workers; right, by Motherwell et al.

Figure 17. Hydrophobic effects on folding were estimated by a comparative study in organic solvents and aqueous solution. The folding sate was found to be favored by approximately 1 kJ/mol in D2O vs CDCl3. Reprinted with permission from ref 218. Copyright 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

ΔΔG values between the parent compounds 1 and 2 with the increasing size of the stacking arms; for example, ΔΔG for the interaction of a phenanthrene shelf of 1 with a p-biphenyl arm was with 4.6 kJ/mol, only slightly larger than for the single benzene ring shelf of the control compound 1, with ΔΔG = 3.8 kJ/mol. No correlation was observed between ΔΔG and the calculated polarizabilities of the respective arms. It was concluded that dispersion forces contribute little, if anything, to stacking between arenes.225 However, the benzene ring in the shelf is in full contact only with an opposing benzene ring; all other extended arms which are used as test can only feel interaction at the edge, and not at the center, where the maximal polarizability is located. The conclusions are also at variance with data from complexations of porphyrins with arenes, for which the expected strong binding increase with increasing arene size was observed (see section 3.5). 2.6. Binding energies from dynamic combinatorial libraries

A recently emerging method for quantifying noncovalent interactions exploits beneficial features of dynamic combinatorial chemistry (DCC), developed mainly by Lehn and co-workers.230−236 First, DCC aims toward self-assembled components that are covalently bonded, such that they are sufficiently stable for purification and can be conveniently analyzed by a range of spectroscopic/structural methods. This is a significant advantage over the use of purely noncovalently bound systems whose kinetic instability often prevents their isolation. Second, DCC unlike conventional organic synthesisutilizes covalent bond formation that occurs reversibly under thermodynamic control. This means that the amount of each component found in a DCC library is proportional to its relative thermodynamic stability. Figure 19 illustrates how this operation principle can be utilized to quantify noncovalent interaction energies, for instance that of CH−π contacts:237 Protons in the vicinity of electronegative residues (e.g., oxygen) are positively charged, which in addition to dispersive effectscan result in an attractive interaction with electron-rich π systems. However, the binding strength of a typical CH−π donor (e.g., compound B in Figure 19) and a typical CH−π acceptor (e.g., compound 2) in aqueous media is too weak to allow for the formation of a significant amount of a B···2 complex and its isolation. When installing nearby functional groups on B and 2, capable of forming a strong (compared to the CH−π contact) intermolecular covalent bond,

Figure 18. Molecular balance combined with a double mutant cycle analysis to determine the R-F···CO interaction energies for Csp3-F (shown here) and Csp2-F bonds and amide carbonyl groups in organic solvents. Reprinted with permission from ref 224. Copyright 2007 Wiley-VCH.

energy for the interaction. In contrast, measurements with intermolecular complexes always reflect the energetic minima. It follows that it has to be taken into account that a torsion balance may only give a lower estimate for the binding energy for a X···Y pair, and that their interaction in a constraint-free environment can be significantly stronger. At the same time, the entropic cost inherent in intermolecular complexation can lead to smaller ΔΔG values than those seen in molecular balances (see above). How geometric constraints in molecular torsional balances can lead to questionable conclusions is illustrated with an example, for which the aim was to investigate stacking between a single benzene ring (Scheme 3) of 1, a “shelf”, and arenes of increasing size (“arms”)225 and therefore increasing polarizability.229 A control structure (2) without benzene at the shelf provided a measure of other factors influencing the folded−unfolded equilibria. The measurements showed a very small change of 5231


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Scheme 3. Molecular Balance with Stacking between a Single Benzene Ring (“Shelf”) and Arenes of Increasing Size (“Arm”, 1) or without Stacking (2)a

a

Solvent molecules are indicated as red spheres. Reprinted with permission from ref 225. Copyright 2015 The Royal Society of Chemistry.

Figure 19. Working principle and components of a dynamic combinatorial approach for estimating binding increments for CH−π interactions. Representative compounds used. 1−3: Aromatic CH−π acceptor systems (yellow/black rectangle). A−C: CH−π donor systems (red/rose rectangle). Modified figure reprinted with permission from ref 237. Copyright 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

that the covalent bond formation occurs reversibly (i.e., under thermodynamic control), any differences from the statistical expectation of the amount of covalently linked products are due to relative energy differences of the intramolecular noncovalent interaction motif. To exemplify, when competition experiments were conducted with A as a poor and C as good CH−π donor together with a substoichiometric amount of 1 as the CH−π acceptor, then a larger amount of the C-1 than of the A-1 product was observed by NMR experiments. (Note: the imine bond was permanently fixated by reduction to the amines in order to

then the occurrence of CH−π contact between B and 2 is simultaneously enforced upon covalent bond formation. In Figure 19, the reversible formation of an imine bond starting from an amine and aldehyde is utilized, but other weak covalent binding motifs, e.g., disulfide bonds, sugar-diol chelates, etc., are also suitable binding “synthons”.234−236 The key idea of the DCC approach for quantification of weak noncovalent interaction is to let the system equilibrate in the presence of stoichiometric amounts of other potential interaction partners, e.g., stronger and weaker CH−π donors or acceptors.237 Under the prerequisite 5232


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compounds could also be isolated because the formation of a covalent disulfide bond enforced the macrocyclization. When salts were added, the screening of the charges caused a lowering of the charge-selectivity but heterocharged dimer remained the predominately formed species. By equilibrating a stoichiometric mixture of two different monomers and quantification of the amount of homodimers (A− A and B−B) and hetereodimers (A−B) formed in the dynamic combinatorial library in water, the equilibrium constant of the binary mixture could be determined via:

facilitate the NMR studies.) The relative stability differences of complexes between CH−π donors C and A with CH−π acceptor 1 can then be directly obtained via eq 5, which yielded 3.8 kJ/ mol. ΔΔG = −RT ·ln[molar ratio of products]

(5)

“Absolute” interaction energies for CH−π contacts were estimated by competitive binding experiments of CH−π acceptors 1, 2, or 3 with a “non-interacting” reference acceptor and yielded energies between 2 and 8 kJ/mol; Table 2 shows Table 2. Net Interaction Free Energies (kJ/mol) for the CH−π Complexes Established between CH-Donors A−C and the Aromatic Rings as CH-Acceptors of 1−3a

1 2 3 a

A

B

C

0 polarized CH−π

1 polarized CH−π

2 polarized CH−π

4.1 2.6 2.4

5.2 3.7 2.7

8.1 5.4 3.5

Kaq(A, B) =

[A−B][A−B] [A−A][B−B]

(6)

When the same procedure was applied to the dynamic combinatorial library in the presence of 1 M NaCl, the equilibrium constant Ksaline(A,B) was obtained (Table 3). The trends are intuitive: Binary mixtures of oppositely charged peptides, e.g., (Lys2,Glu2), result in an equilibrium in water that lies far on the side of the heterocharged dimers (2+,2−), while binary mixtures of noncharged peptides (Asn2,Ser2) or of equally charged peptides, e.g., (Asp2,Glu2) or (Lys2,Orn2), do not favor the heteroproduct side (A,B) markedly beyond statistical reasons. However, the charge repulsion in homocharged (2+,2+) or (2−,2−) dimers in a mixture with noncharged peptide lead to a shift of the equilibrium to the A,B dimers. Expectedly, in a saline solution of high ionic strength, all mixtures behaved similar.238 Free energy values for the equilibria of the binary mixtures can be obtained via ΔGaq(A,B) = −RT ln Kaq, but these do not directly relate to the strength of individual interactions, e.g., ion pairs of a heterocharged (2+,2−) dimer, because the homodimers contribute to the overall free energy of the equilibrium, e.g., by charge repulsion of the homocharged (2−,2−) and (2+,2+) species. Applying a double mutant cycle analysis (see section 2.4) to the reported ΔGaq(A,B) values, we have derived the desired binding increments, assuming that the noncharged heterodimer (Asn2, Ser2) is a noninteracting reference state (X′Y′). In a first approximation, this appears plausible because hydrogen bonding between the solvent-exposed side chains is likely much reduced in water. To exemplify, the strength of one ion-pair between Lys and Glu side chains can be calculated in analogy to eq 3 in section 2.4 by eq 7.

Values from ref 237.

energy contributions in agreement with expectations, e.g., CH−π donor strength C > B > A and CH−π acceptor strength 1 > 2 > 3 (see section 3.5); solvophobic contributions are reflected in the weak interaction with A. The resulting C−H--π interaction energies are listed in Table 2 and are generally in line with the literature values in section 3.2. It should be kept in mind that the derived values can be larger than those measured between partners in noncovalent complexes, as the latter can suffer from an adverse entropy of translation disadvantage. The same precaution holds for energy values derived from measurements with molecular balances. The DCC method for estimating the pair-interaction energies is, much like the double mutant cycle methodology (section 2.4) and the molecular balance approach (section 2.5.), also amenable to the quantification of repulsive noncovalent interactions because the formation of the covalent bond (the “anchor”) more than compensates for any repulsive contact. This was exploited in a study on Coulombic effects between positive, negative, and noncharged building blocks for macrocyclization (Figure 20) in water and saline solution, in which the high ionic strength weakens the salt bridges (see section 3.1). As expected with Coulombic forces, in a dynamic combinatorial library obtained in water, macrocycles with a balanced charge (2+,2−) were much more present than those composed of equally charged species (2+,2+ or 2−,2−); nevertheless, the latter

Figure 20. (a) Dynamic combinatorial library of macrocycles composed of positive, negative, and noncharged pseudopeptidic building blocks. Reprinted with permission from ref 238. Copyright 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. 5233


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Table 3. Representative Equilibrium Constants for DCC Libraries of Binary Mixtures of Peptides in Water, and in Saline Solution, and Associated Free Energy Differencea

a

residues on A

residues on B

Kaq(A,B)

−ΔGaq(A,B) (kJ/mol)

Ksaline(A,B)

−ΔGsaline(A,B) (kJ/mol)

Lys (+) Asn (o) Lys (+) Asn (o) Lys (+) Asn (o) Asp (−) Ser (o) Orn (+) Orn (+) Asn (o)

Glu (−) Glu (−) Asp (−) Ser (o) Ser (o) Asp (−) Glu (−) Glu (−) Lys (+) Ser (o) Lys (+)

500.0 10.8 500.0 4.2 10.8 23.3 5.6 10.8 3.8 12.3 5.3

15.4 5.9 15.4 3.5 5.9 7.8 4.2 5.9 3.3 6.2 4.1

7.1 3.7 4.5 4.2 4.2 5.6 5.3 5.0 3.4 4.5 2.2

4.9 3.2 3.8 3.5 3.5 4.2 4.1 4.0 3.1 3.8 1.9

Values taken from ref 238.

Table 4. Energy Increments from a Double Mutant Cycle Analysis of the Interactions between Charged Peptide Side Chains (per contact pair) for the Dynamic Combinatorial Library of Macrocycles and Data Shown in Figure 2a

a

residue X

residue Y

charge

−ΔGaq(X···Y) kJ/mol

−ΔGsaline(X···Y) kJ/mol

Orn, R(CH2)3NH3+ Orn, R(CH2)3NH3+ Lys, R(CH2)4NH3+ Lys, R(CH2)4NH3+ Asp, RCH2COO− Orn, R(CH2)3NH3+

Asp, RCH2COO− Glu, R(CH2)2COO− Asp, RCH2COO− Glu, R(CH2)2COO− Glu, R(CH2)2COO− Lys, R(CH2)4NH3+

+− +− +− +− −− ++

>2.0 >2.2 1.3−1.8 1.8−2.0 −(1.5−1.6) −(0.9−1.0)

0.0−0.3 0.5−0.6 ≤0.2 0.4−1.6 0.0 0.1

ΔGaq in 40 mM Tris-buffer (pH 6.5), ΔGsaline in the same buffer, containing also 1.0 M NaCl.

The trends are reasonable; the strongest attractive interaction are observed for heterocharges side chains of a similar side-chain length, Orn···Glu, while the weakest are found for the sizedissimilar Lys···Asp couple. Repulsive forces between Asp···Glu are significantly stronger than between Orn···Lys, likely because the charged groups of the latter can more efficiently move out of each other’s way. In saline solution, all attractive and repulsive charge-mediated interactions are much lower in magnitude. A final consistency check can be done by using the individual ΔGaq(X···Y) values for predicting the ΔGaq values of the dynamic equilibrium composition of A,A + B,B ⇄ 2 A,B. For instance, for a mixture of (Lys2,Lys2) = (A,A) and (Glu2,Glu2) = (B,B) equilibrating with (Lys2,Glu2) = (A,B), one expects the heteroproduct formation to be favored by

4ΔGaq (Lys···Glu) = [ΔGaq (Lys2 , Glu 2) − ΔGaq (Asn2 , Glu 2)] − [ΔGaq (Lys2 , Ser2) − ΔGaq (Asn2 , Ser2)]

(7)

where X = Lys, Y = Glu, X′ = Asn, and Y′ = Ser. The factor “4” results from the occurrence of two ion pairs per (Lys2,Glu2) that are formed during macrocyclization, and it also considers the stoichiometry factor “2” of the (A,B) dimer in the Kaq definition (see eq 6). Because of symmetry, the noninteracting reference state can be alternatively chosen as (Ser2,Asn2), such that X = Lys, Y = Glu, X′ = Ser, and Y′ = Asn, which leads to

ΔGaq = 2·2·ΔGaq (Lys···Glu) − [2 ·ΔGaq (Lys ···Lys)

4ΔGaq (Lys···Glu) = [ΔGaq (Lys2 , Glu 2)

+ 2·ΔGaq (Glu···Glu)]]

− ΔGaq (Ser2, Glu 2)]

When the unknown repulsive energies between Lys···Lys and Glu···Glu are approximated by that between Orn···Lys and Asp··· Glu, respectively, one obtains ΔGaq ∼ 13 kJ/mol, which is in good agreement with the experimental value of 15 kJ/mol. Dynamic combinatorial libraries can also be used to determine effective molarities (EM) in ring−chain equilibria, from which information about the enthalpy (e.g., strain in a cyclic product) and entropy (freezing of rotors) of the system can be derived.239−243 In the field of polymer chemistry, related research questions are of major importance for describing macrocyclization reactions under thermodynamic control,244,245 for which extensive mathematical models date back to the 1950s.246 In short, theory predicts that for every bifunctional monomer that has a sufficiently high association with other monomers of its kind (i.e., a high association constant Kinter) and which reacts to near completion, there is a critical concentration (CC) above

− [ΔGaq (Lys2 , Asn2) − ΔGaq (Ser2, Asn2)]

(9)

(8)

The resulting stabilizing interaction energies per Lys···Glu ion pair of 1.8 kJ/mol (Lys → Asn mutation) and 2.0 kJ/mol (Lys → Ser mutation) are in good agreement. They also fall well within the range of binding increments for solvent exposed salt bridges in proteins (see section 2.4), which were also determined by DMC analysis. Notably, the Lys···Glu ion pair is weaker in energy compared to optimally arranged ion pairs in supramolecular associations and complexes (5 kJ/mol, section 3.1), which can be rationalized by the nonideal interaction geometry between Lys and Glu in the shape-fixed peptidic macrocycles. The values of other attractive and repulsive interaction energies obtained from similar DMC analyses are tabulated in Table 4. 5234


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Figure 21. Hydrogen-bond energies E as a function of D···A distances; OHB, ordinary H-bond, marked as (●); CAHB, negative or positive chargeassisted H-bond marked, marked as (−) or (+); colored horizontal lines on the bottom show the ranges of variation of the D···A distances for each type of bond from dD···A(vdW) to the shortest value dD. Reprinted with permission from ref 265. Copyright 2009 American Chemical Society.

remain also desirable in order to provide a platform for quantitatively dissecting the energetic contributions of the driving forces for self-assembly.

which only the amount of linear species and not of cyclic oligomers rises, when the monomer concentration is increased. For the synthesis of polymers, this CC sets a practical limit below which no polymerization occurs under thermodynamic control. In other words, small effective molarities, defined as EM(n): = K intra(cyclic‐ring of size n)/ K inter

2.7. Data from crystal structures

X-ray analysis of crystal structures has been the most valuable source to define geometric conditions for a large variety of intermolecular interactions, in particular for hydrogen bonds.258−261 Although structural data themselves can, of course, not directly provide information on energies, statistically meaningful search results from the Cambridge Structural Database (CSD)262 or the Protein Data Bank (PDB)263 can help elucidate the dependence of structural data on the strength of interactions. Thus, histograms indicate that hydrogen-bond X−H···A angles are mostly close to 180° for O−H···OC interactions, still dominate at 180 with CC−H···OC cases, but show also values down to 120°. Very weak alkane−alkane bridges are characterized by almost equal angle distribution from 180 to 100°, indicating rather van der Waals-type of interactions than hydrogen bonding. Stronger interactions mostly display shorter distances between acceptor and donor, but correlations with X−H···A distances are usually considerably scattered; this is also observed for angles with hydrogen bonds in spite of their directional character.264 Figure 21 documents that there is an approximate correlation between hydrogen-bond strength and D···A distance as found in crystals, accompanied, however, by a large variation.265 Leading crystallographers have pointed out that crystals need not reflect a minimal free energy structure, and that the choice of relevant intermolecular bonds can be arbitrary.266 In particular, weak noncovalent forces will be difficult to locate in crystals, where many other and stronger interactions determine the lattice structure. For this reason, the frequency or the absence of a critical distance in a large structure data set (e.g., from CSD), which would indicate or contradict a weak interaction, e.g., with fluorine as hydrogen-bond acceptor, is not a reliable indicator for the presence or absence of such interactions (see section 3.2 for an example). Databases such as PDB contain mostly systems, e.g., protein−drug complexes, for which a specific interactionmotif (e.g., a fluorine-H-bond) was deliberately set up, such as a

(10)

which are indicative of a high ring strain of the usually undesirable cyclic oligomers, are desired. For the use of ring−chain equilibria to investigate binding forces with supramolecular model systems, the EM (thus CC) should be in a convenient concentration range such that both cyclic and linear species can be observed. However, usually a rather high concentration of monomer would be required, which poses practical issues (solubility, availability, etc.). The use of monofunctional chain-stoppers (which also purposely or unavoidably play a role for industrial polymerization reactions) was recently proposed as an alternative for applying the DCC method to the determination of EM values also under dilute concentrations.247 The double mutant cycle (DMC) analysis of fully noncovalent protein−ligand or supramolecular complexes was described, section 2.4, and their strengths and shortcoming were discussed. It was especially noted that “the anchor” should be strong enough to enforce a similar complex geometry in all cases but it should not influence the energy differences between the mutants. This is not always guaranteed when the anchor is of the noncovalent type. Combining the DMC method with dynamic covalent chemistry appears to be a promising approach toward this goal. Dynamic covalent chemistry has already found use in proteinchemistry, mostly for identification of new ligands/drugs,248,249 but its use to covalently fixate a ligand into a protein-binding pocket seems underexplored. Section 2.3 shows for the representative example, cathepsin L, how useful the covalent anchoring strategy can be to elucidate simultaneously occurring weak noncovalent interactions in protein complexes. Several other landmark studies in dynamic combinatorial chemistry with synthetic systems were directed toward the assembly of fascinating structures, showing selective-binding of templates, cooperativity, self-replication, chemical evolution, and stimuliresponsiveness.230,231,233,250−257 However, less complex systems 5235


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zero ionic strength (I) for alkali and earth alkali salts a stability decrease in the order Ca2+ > Mg2+ ≫ Li+ > Na+ > K+; the stabilities of the alkali-ion pairs were described as a function of the anion charge z by

drug-substituent capable of H-bonding with the protein, in order to cause a desired biological effect. Therefore, the likelihood to find specific interactions such as weak hydrogen-bonds is larger for PDB than in related CSD structures. The latter contains, for instance, all kinds of fluorine compounds, with no deliberate bias to certain interaction motifs. Crystal structures have been used to improve force field potential functions on the basis of high resolution test structures.267 In polymorphs268 and in cocrystals,269 one finds several coexisting structures, mainly if energy differences between molecular conformers and crystal lattice energies are similar. Comparison to spectroscopically analyzed structures, e.g., by NMR, do often show similar geometries of host−guest complexes both in the crystals and in solution, as demonstrated, e.g., for donor−acceptor distances in peptide dimers.270 One reason for the difference between the solid state and solution structure of host−guest associations is that host cavities are usually occupied also by solvent molecules (see section 3.7). One observes with relatively stable complexes that the cavity volume is in solution only partially occupied,82,83 on average by 55 ± 9%.84 Larger packing coefficients are observed if the complex is particularly stabilized by stronger noncovalent forces between the cavity and the guest, or also with some globular proteins.84 With cyclic host compounds, in particular with shallow cavities (e.g., calixarenes), solid state structures with the guest residing outside the cavity are more the rule than the exception, in contrast to association in solution or in the gas phase.85

lg K = 0.5z + A/z, with A = −0.24 for Li+, − 0.30 for Na +, −0.43 for K+

(11)

For Li+, Na+, and K+ salts, the same linear dependence on the charge z of the anion was found. Calorimetry shows a dominating entropic driving force with an average of −TΔS = −8 ± 2 kJ/mol for all alkali salts, which in the absence of significant ΔH contributions agrees with the value of ΔG = −8 kJ/mol at I = 0 found for some organic ion-pair complexes by extrapolation to I = 0; see below. As discussed above and in section 2.1, there are rather constant free energy ΔΔG contributions for ion pairing in water. It is noteworthy that the observed value of ΔΔG = −5 ± 1 kJ/mol for a single salt bridge is rather independent of the nature of the cation and the anion.98 In nonpolar solvents, however, binding constants of ion pairs depend not only on the interaction between the host and encapsulated guest molecule, but also on the gegenion. Thus, association constants (in M−1 units) of some calix crown ethers with tetraethylammonium salts in chloroform with tosylate as gegenion amounted to K = 30, with chloride amounting to K = 100, with trifluoroacetate amounting to K = 390, and with picrate amounting to K = 2200.285 Such changes are typical for aprotic solvents; in water, solvation secures a dominant separation of the (gegen)ions. The situation is also more complex if both cation and anion find a place within a host cavity, see also Scheme 31 in Section 3.8.1. The charge density distribution between the ions286 as well as between the ligand and the ions287 can then have a significant influence on the affinities. The correlation in Figure 2 comprises both relatively hard ions such alkali metal ions or sulfate anions, as well as of soft ions, such as phenolates or thiolates. The correlation is in line with the Bjerrum or the Fuoss equation, which also describes ionpair association essentially as a function of the ion charges zA and zB and the dielectric constant ε of the medium; a corresponding plot of the stability ΔG vs zAzB shows for over 200 ion pairs the expected linear correlation (Figure 22).3 The DMC experiments discussed in section 2.6 have shown with a range of charged peptides an ion-pairing free energy contribution of − ΔΔG = 1.5 to 2 kJ/mol; the smaller value

3. SELECTED INTERACTION ENERGIES 3.1. Ion pairing/Salt bridges

Ion pairing is the basis of countless supramolecular complexes, in particular with anions,271−278 apart from those relying on hydrogen bonding (section 3.2). In water, formation of salt bridges is mostly driven by entropy, usually accompanied by unfavorable ΔH contributions on account of desolvation of the interacting ions upon association.279 In complexes between amino compounds and acids, only the ion pair formed by complete protonation of the amine and deprotonation of the acid is dominated by entropy. For a comprehensive discussion of the very effective complexation with polyammonium receptors and, e.g., phosphate or pyrophosphate, the reader is referred to the literature.280 There, it is shown that, even in water, hydrogen bonds can play a significant role, where both anions and amines can act as acceptors or donors. In these specific complexes, not all partners can at a given pH be fully protonated and fully deprotonated at the same time. With hydrogen-bond contributions, enthalpy can become the significant driving force so that the free energy is only partially determined by electrostatic forces between the receptors and anions. The general entropic driving force for ion pairing in water (in the absence of significant H-bonding contributions) is also found in methanol as solvent, e.g., with complexes of phenylamidinium ion-containing receptors for carboxylates.281 Similarly, the selfassociation between oppositely charged complementary building blocks for capsules (see Scheme 5 further below), such as tetraamidinium calix[4]arene and tetrasulfonatocalix[4]arene, is driven by large entropic contributions in MeOH/H2O.282 Inorganic salts as well as ammonium carboxylate salts regularly display similar ΔΔG values around 5 to 6 kJ/mol per ion pair, and the lg K values are approximately a linear function of the charges.283 More recent measurements284 showed, however, at

Figure 22. Ion-pair association constants at zero ionic strength as a function of charge product, calculated for 203 ion pairs. Reprinted with permission from ref 3. Copyright 2000 Wiley VCH. 5236


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Figure 23. Debye−Hückel-correlation of the association constants (as lg K) of the ion pairs CP and CP2 and the ionic strength measure √I(1 + √I) of the aqueous medium. Reprinted with permission from ref 289. Copyright 1999 Wiley VCH.

Figure 24. Complexation lg K values of anions 1-− with a macrocyclic amine as a function of the protonation degree nH of the amine. Reprinted with permission from ref 291. Copyright 2008 Wiley VCH.

Scheme 4. Ion Pairing with Some Representative Complexes: lg K Values in Water with nH Estimated Number of Salt Bridges

charged amino acids to neutral acids and the reverse exhibits a very large variation range of resulting energies, reaching from, e.g., 0.5 to 2 kJ/mol for salt bridges on the surface of barnase to 15 kJ/mol and more in buried salt bridges, as determined also by DMC methods.149 Structural studies are necessary to understand these variations, due to changes of several other interaction, such as hydrogen bonds upon salt-bridge formation. Also, entropy costs, e.g., due to water localization at the protein surface, can diminish the energy gain by a salt bridge significantly, by up to 8 kJ/mol for a relatively strong binding of a water molecule.288 Figure 23 shows how the ΔG values depend as predicted by the Debye−Hückel equation on the ionic strength of the solution,289 somewhat unexpectedly even for strongly anisotropic ionic host−guest structures. Extrapolation to infinitely diluted solution with I = 0 yields for one salt bridge 8 kJ/mol

compared to the about 5 kJ/mol derived from free moving saltbridge complexes can be due to conformational restriction for an ideal anion−cation contact and to accompanying differences in solvation. Interestingly, the repulsive interaction between equally charged amino acids, which can only be accessed with, e.g., the DMC method, is with 1 to 1.6 kJ/mol on the same order as the attraction between anionic and cationic charges acids, which points to the common electrostatic nature of these interactions. In proteins the investigation of ion-pair energies is usually based on the energy differences between folding and unfolding caused by mutation of charged amino acids, or/and by observation of protonation pK changes of charged amino acids upon folding.150 A direct determination of the salt bridge is very difficult in view of the conformational changes accompanying the presence or absence of salt bridges. Thus, the mutation of 5237


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heptaamino α-CD and subtracts the −ΔG = 8.8 kJ/mol observed for the corresponding noncharged nucleosides, the remaining 19 to 20 kJ/mol would account for the ion-pair contributions. Force field simulations indicated that about 6 to 7 salt bridges are possible with sufficient contact between the ammonium and phosphate centers. The resulting average value of about 3 kJ/mol per single salt bridge, which agrees with the value for complexes with inorganic phosphate, is smaller than the 5 kJ/mol observed with many other associations (see above). This can be ascribed to the limitation of achieving an optimal contact simultaneously between all interacting sites. This is particularly so, if one contribution is much stronger, so that the second one cannot or can only partially materialize, exposing an obvious limitation of the additivity principle. More recent investigations with a series of β-CD and tert-butyl phenyl guest compounds with ionic or neutral substituents X in the p-position highlighted this problem more clearly.302 Thus, the monoamino β-CD binds, e.g., the electroneutral guest with X = N(O)Me2 with an affinity of −ΔG = 22 kJ/mol, and the one with X = guanidinium+ and X = SO3− almost equally well with −ΔG = 20 kJ/mol, even though there are opposite charges. A distinct ion-pair contribution is seen only if complexes such as with the heptaamino-CD become much stronger; there the values are −ΔG = 11 kJ/mol for X = N(O)Me2, 23 kJ/mol for X = SO3−, and 9 kJ/mol for X = guanidinium+. Nevertheless, the ion-pair contributions ΔΔGpolar calculated for a large number of complexes by subtracting the ΔG value of a complex with charge from the same without charge could be correlated with Coulomb energies Ecoul calculated based on a simplified Debye−Hückel−Onsager equation as a function of an effective length reff within which ion shielding occurs (Figure 25). However, reff was adjusted for a best fit. Upon adding

instead of the 5 kJ/mol which is observed usually for 0.1 M buffer solutions. The slope of the correlation line is, as in other cases290 with m = 4 ± 0.6, close to the value expected for a 2 + 2 combination of dianion + dication, although the Debye−Hückel equation is based on the assumption of spherical ions. As mentioned above, ΔG = −8 kJ/mol at I = 0 is in line with −TΔS = −8 kJ/mol found for alkali salts in view of the negligible ΔH contributions in such ion pairs. With amines as receptor for anions, the binding energy is a function of the amine protonation degree, as is shown in Figure 24 with a series of tricarboxylates and the macrocyclic amine host aneN7.291 The stability of the ion pairs at a given pH depends on the geometric matching between cation and anion, which is maximized with tricarboxylate 3, whereas the more flexible citrate 5 binds less strongly. Scheme 4 illustrates with several representative complexes292 that lg K values in water correspond roughly to the number n of salt bridges, in line with an average value of 5 kJ/mol for each bridge. It should be noted that, for closely positioned anions and cations, n is counted according to the possible number of bridges, e.g., n = 2 for the interaction of one RPO32− anion with one R2NH2+ cation. Possible hydrogen-bond contributions to the stability of ion pairs can be examined by comparison of stabilities of protonated amines with quaternary amines, which in water usually shows negligible difference. Therefore, hydrogen bonding appears as a rule in water to be not an important contributor, unless partially protonated polyamines are involved (see above). The affinity of linear, fully protonated oligoamines such as spermine, spermidine, putrecine, etc. for ds-DNA shows a linear dependence on the number of charge centers.293 If one takes the number of possible salt bridges between a DNA-phosphate and an ammonium group into account, one arrives for the binding constants of the biogenic amines294 again at 5 ± 1 kJ/mol for a single bridge.295 For complexes with guanidinium salts, it has been emphasized in several reviews296−298 that it is difficult to separate ion pairing and hydrogen bonding in water. However, it is unlikely that the situation for guanidinium ions should be very different from ammonium ions in 55 M water as a strongly competing hydrogen-bond acceptor. The experimentally maximum value of a phosphate−guanidinium interaction of 7.5 kJ/ mol in water299 is actually close to the one to expect for two salt bridges. Only if there are additional hydrogen-bond acceptors close to the guanidinium group, is there clear evidence for their binding contribution (see section 3.2). On the other hand, results from infrared-spectroscopy measurements of ion pairs between methylguanidinium (MeGd+) and trifluoroacetate (TFA) in D2O and dimethyl sulfoxide do indicate that hydrogen bonds, formed between the bifurcate TFA carboxylate group and the two +NH2 groups of MeGd+, contribute significantly.300 Cyclodextrins (CDs) bearing ionic substituents bind charged organic guest molecules by ion pairing as well as by other forces, including polar, dispersive, and hydrogen-bonding interactions, which are not easy to separate from each other. β-CD with a monoamino substituent at the outer rim 6-position complexes mononucleotides with −ΔG values between 15 and 24 kJ/mol, β-CD with seven amino substituents exhibits affinities of 25 to 33 kJ/mol with mononucleotides, and, e.g., 37 kJ/mol with ATP.301 Comparison of various nucleotides and corresponding inorganic phosphates, ribose phosphates, ribose, and nucleosides allowed for distinguishing the relevant binding contributions, similar to the strategy described in section 2.2 with cyclophane- nucleotide complexes. If one takes, for example, the average −ΔG value of 27.5 kJ/mol for the mononucleotide complex with the

Figure 25. Coulombic energy contribution, Ecoul, calculated with a simplified Debye−Hückel−Onsager equation vs experimental ΔΔG values obtained by subtracting the ΔG value of a charged complex from the same without charge. Reprinted with permission from ref 291. Copyright 2008 Wiley VCH.

salts, the change of ΔΔGpolar could be correlated with the Debye−Hückel equation for complexes with anionic guest (X = SO3¯) and heptaamino β-CD, which is in line with the dependence of ion pairing free energy on the ionic strength observed with cation−anion associations289 (see above, Figure 23). As said, formation of ion pairs can also be accompanied by a predominant enthalpy gain, if other noncovalent forces play a significant role. Such a case is evident in the complexation of methyl viologen (M2V) by sulfonated calix[n]arenes, CX4, and CX5 (see Figure 26) with ΔH = − 32.0 and −31.5 kJ/mol, 5238


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Figure 26. Tetrameric p-sulfonatocalix[4]arene (CX4) complexes methyl viologen (M2V) in water with a vertical arrangement of the guest. The larger homologue CX5 binds M2V in a vertical fashion, as evidenced by NMR spectroscopy. Multiple ion pairs can form in each complex. Reprinted with permission from ref 303. Copyright 2007 American Chemical Society.

Scheme 5. Supramolecular Structures or Capsules that Self-assemble from Complementary Anionic and Cationic Partners (see text)

respectively, at pH 7.2 in 100 mM phosphate buffer.303 Associated entropic contributions were small and unfavorable, −TΔS = 3.6 and 0.7 kJ/mol, respectively. Hydrophobic effects are small for this host (see section 3.7) so that Coulomb attraction and dispersive interactions are the main driving forces for binding. When the dicationic methyl viologen was electrochemically reduced to the monocation radical, the ΔΔG values of binding dropped by 5.2 and 6.9 kJ/mol, respectively,303 close to the usual value for ion pairing. Expectedly, the energy loss for CX5 is larger than for CX4 because of a closer contact between the charges of the host and guest (see Figure 26). The association between complementary anionic and cationic partners can lead to interesting supramolecular structures,304 and follows the rules of salt-bridge formation. CX4-derivative capped porphyrins (Scheme 5, I) show in methanol lg K = 7.1, and in MeOH/water (55:45) lg K = 5.4.305,306 In methanol, the complexation was entirely driven by entropy. Also in the aqueous

medium, there is a dominating entropic contribution to binding, in line with common observation with ion pairs. Capsule IV (Scheme 5), which is based on calix[4]arene and decorated at the upper rim either with L-alanine moieties or positively charged amidinium groups, self-assembles in water with lg K = 4.5, and ΔH° = −14 kJ/mol with a large entropic contribution of − TΔS° = −12 kJ/mol.307 The capsule IV complexes N-methylquinuclidinium cations, as shown by NMR and mass spectrometry. A similar capsule III derived from calix[4]arenes bearing phosphonate anions at the rim and calixes with anilinium groups is formed in water with lg K ≈ 3 and in methanol with lg K ≈ 6.308 A phosphonate trisubstituted mesitylene forms with a complementary mesitylene triammonium derivative capsule II (Scheme 5).309 The −ΔG = 20 kJ/mol measured in D2O reflects that more than three salt bridges with 5 kJ/mol for each are formed, as visualized in Scheme 5. The affinity in methanol amounts to −ΔG = 30 kJ/mol (lg K = 5.3). 5239


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Solvent effects on ion pairs are experimentally not well documented; theoretical descriptions need special solvation parameters and are particularly complicated for complexation of salts in low dielectric media.310 As is demonstrated in Figure 27

Figure 28. Distance dependence of binding free energy ΔG, measured in water with complexes of a tetraphenolate host and tetraalkylammonium ions R4N+ (R = Me, Et, n-propyl, n-butyl). Reprinted with permission from ref 314, Copyright 1988 American Chemical Society.

reviews.258−261,264,315 Nevertheless, the criteria for defining hydrogen bonds and their strength continues to be debated.316,317 In proteins, the evaluation of hydrogen-bond strength faces the same problems already discussed above for salt-bridge analyses.318,319 In particular, the strength of hydrogen bonds is larger in a hydrophobic core of a protein than at the outside; in the core, it can reach values close to those measured with supramolecular complexes. For instance, amide-to-ester backbone mutagenesis was used to quantify the energetic contribution of backbone peptides to protein folding; the derived value of around 5.5 kJ/mol agrees quite well with typical interactions for an amide−amide bond in chloroform320−322 (see below). Direct measurements of hydrogen-bond energies are only possible in the gas phase.323 We discuss here only selected cases in supramolecular complexes in solution, preferentially those that provide quantitative binding energy data of general value. Similar to ion pairs, one usually finds additive free energy contributions also with hydrogen-bonded complexes. As discussed in section 2.1, many free energy increments ΔΔG for hydrogen bond, and partially also the underlying enthalpy contributions ΔΔH, were first derived from measurements with a large variety of complexes between simple donors and acceptors, mostly in chloroform or carbon tetrachloride as solvent; corresponding increments α and β, or CA and CD are tabulated in the literature3 and in the Supporting Information. That the strength of a D−H···A bond increases with decreasing ΔpKa = pKa(D−H) − pKa(A−H+) (the difference of acidity of the H-bond donor and acceptor) has been verified experimentally,265 and this implies that the strength reaches a maximum when ΔpKa approaches zero. An empirical pKa slide rule, which contains separate scales of the pKa’s of the proton donors (D−H) and proton acceptors (A) allows bringing selected donor and acceptor molecules into coincidence with ΔpKa ≈ 0, and thus permits realistic prediction of binding constants.265 A particularly large set of complexation constants has been measured with 4-fluorophenol as donor and provides hydrogen-bonding ΔΔG values for a thousand bases.324

Figure 27. Solvent effect on ion pairs; association free energy ΔG (kJ/ mol) of Et4NBr as a function of 1/ε. Reprinted with permission from ref 14. Copyright 2009 Wiley VCH.

for an alkylammonium salt, there is, as expected, a roughly linear dependence of the association energy on the dielectric constant with 1/εr, at least for protic media.14 Several solvents exhibit special interaction with ions and are not expected to show straight correlations, as witnessed from Figure 27. For example, the highly polar dimethyl sulfoxide can strongly coordinate cations.311 Binary mixtures of water−DMSO are known to exhibit unique physicochemical properties and pronounced nonideal behavior.312 Bjerrum theory predicts for contact ion pairs, in which the van der Waals radii are in contact, a strong falloff of the ion-pair stability with an increasing distance between cation and anion. Associations between tetramethylammonium or methylguanidinium ion and a series of dianions, in which the carboxylates were separated with varying distance, showed such a distinct distance dependence; see Scheme 6. For the narrow distances, one expects contact ion-pair formation, whereas, for larger distances, solvent separated ion pairs are forming. Calculations of the relative binding constants based on the Bjerrum−Fuoss equation were in general agreement with the experimental constants.313 Figure 28 displays complexes between a cyclic tetraphenolate and tetraalkylammonium ions, in which the length of the alkyl group determines the cation−anion distance r. A correlation of the binding energy with r−1 was experimentally found, which is in agreement with a purely electrostatic model.314 3.2. Hydrogen bonds

Hydrogen bonding is probably the most important noncovalent binding motif in supramolecular systems as well as in biopolymers, and has been aptly discussed in many books and

Scheme 6. Dicarboxylates with Varying Distances d between the Anionic Groups and Corresponding Association ΔG in Methanol, with (a) Tetramethylammonium or (b) Methylguanidinium Ions

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Host−guest complexes are often characterized by simultaneous occurrence of several hydrogen bonds; this is a common problem with many organic compounds, drugs, and proteins and has been recently addressed with the help of IR techniques. A shift of Δν(OH) in the IR to lower wavenumbers of the OH band reflects the strength of a hydrogen bond, and an assignment of an individual pK value to each binding site of, e.g., bases with multiple interactions sites is possible.324 We begin the survey with supramolecular complexes that are characterized by relatively strong donors or acceptors, such as protonated amines as donor. Additivity is seen here in the stability of complexes between, e.g., the 18-crown-6 ether and protonated amines. There is a correlation of the binding energy with the number of available +N−H bonds; the data indicate in water a ΔG value of 2.7 kJ/mol for a single +N−H bond with two oxygen atoms.325 The influence of solvents such as water, 2propanol, tert-butyl alcohol, n-octanol, DMF, DMSO, and pyridine, which lead to 1000-fold changes of the binding constants, is a rather linear function of the related Ca or β* value for a given solvent (Figure 29). These results demonstrate once more the predictive power of simple polarity factors; correlations with other solvent parameters showed more scatter.325

Figure 30. Logarithms of stability constants of hydrogen-bonded complexes of 3,4-dinitrophenolate anion with substituted phenols in THF vs differences of pKa values of donor and acceptor molecules. Reprinted with permission from ref 326. Copyright 1996 American Association for the Advancement of Science.

RCONH···bromide.331 The affinities decrease in the order F > Cl > Br > I, in line with the decreasing charge densities and corresponding gas-phase acidities.332 As mentioned before, the hydrogen-bond donor capacity strongly increases with the acidity of the N−H function; e.g., N,N′-dinitrophenyl urea binds in acetonitrile anions such as acetate with lg K = 6.6, chloride with lg K = 4.5, and fluoride with lg K = 7.4. Proton transfer occurs with formation of the HF2− anion; the observed affinities correlate with ab initio-calculated charges at anion oxygen atoms (Figure 31), which verifies the electrostatic nature of these hydrogen bonds.333 On the other hand, N−H···S hydrogen-bonded complexes between, e.g., indole and dimethyl sulfide were found to be stronger than the N−H···O hydrogen bonds;334,335 this was ascribed to dispersive interactions similar to those between C−H or N−H bonds with arene, in line with the large polarizability of sulfur. Complexation energies can depend sensitively on conformational arrangements of participating binding sites, as illustrated in Scheme 9.336 The 1,3-dialanylcalix[4]arenes A bind carboxylates in the competitive solvent acetone with association constants K of about 500 M−1, yet fixation of the conformation by introduction of a bridge in host B leads to a very large increase by almost 2 orders of magnitude, e.g., K = 44.000 M−1 for benzoate. The weak affinity with the open receptor A is partially due to intramolecular hydrogen bonds between binding sites and by possible self-associtation of the host compound. In the coformational fixed receptor B, the binding sites are kept apart by the bridge so that competitive intramolecular hydrogen bonding is effectively prevented. The affinities are larger with benzoate than with acetate due to a larger dispersive stabilization energy for a phenyl than for a methyl moiety (section 3.5). Squaramides (see Figure 32) bear more acidic N−H groups than, e.g., dinitrophenyl urea. The affinities in acetonitrile with oxyanions such as MeCOO¯, HSO3 ¯, or NO3¯ are similar as with urea, but those with halide anions are up to 4.4 kJ/mol higher (Figure 32).327 Spectacular association constants of up to K = 1014 M−1 for ammonium salts in chloroform were reported with several hosts bearing two squaramide functions placed in a convergent way in axial positions on a steroidal framework; here the free energy difference ΔΔG between squaramides and urea hosts amounts to (6.5 ± 1) kJ/mol (Scheme 10).337 The binding increment for Cl− per squaramide residue in CHCl3 (water saturated) ranged from 31 to 41 kJ/mol depending on the substituent residues, which is similar to that of the dinitrophenyl

Figure 29. Solvent effect on lg K values of the complex between 18crown-6 and benzylammonium chloride against the solvent basicity parameter β of the solvent. Reprinted with permission from ref 325. Copyright 1999 Wiley VCH.

With strong donors and acceptors, there is a simple correlation between the complexation free energies and pKa values of hydrogen-bond donors and acceptors, in line with the polar nature of these relatively strong hydrogen bonds.326 In Figure 30, this is exemplified for anionic phenolate as acceptor. Several reviews and books describe the use of amides, ureas, and pyrroles for anion complexation.272−274,278,327,328 Scheme 7 shows some typical examples and the preference for carboxylate binding due to the ideal matching with urea, and of pyrrole units as donor part.329 Enhanced NH acidity as in hosts C and D lead to a significant affinity increase. Thioureas330 are particularly suited as donors; the acidity of thioureido-NH protons is, e.g., in DMSO with pKa of 21.1 much higher than for urea with a pKa of 26.9. The data in Scheme 8 show that the energy contributions for amide-halide-anion complexes, measured in chloroform, are roughly additive and amount to about − ΔΔG = 5 ± 1.5 kJ/mol for RCONH···chloride and to − ΔΔG = 3.5 ± 1.5 kJ/mol for 5241


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Scheme 7. Anion Complexation (free energies in DMSO with 0.5% water), with Amide, Ureas, and Pyrrole Units as Donor329

Scheme 8. Complexation of Halide Anions with Open Chain Amide-type Host Compounds, Measured in Chloroform331

a

nH, number of possible hydrogen bonds.

host and the guest forms upon acidification of the amides through strongly electron-withdrawing groups (e.g., X = CN, NO2). Measurements with a large series of hydrogen-bonded complexes in DMSO:H2O (99.5:0.5) with several carboxylic acids and receptor molecules based on indolocarbazole, carbazole, indole, urea, etc. showed that the strength of the anionic receptors was primarily determined by the basicity of the anion, in the order lactate < benzoate < acetate < trimethyl acetate.343 Carboxylate anions with their planar structures can form two bifurcated hydrogen bonds with tetradentate receptors, resulting in high stabilities. Other factors such as size and geometric fit of the anion and the receptors, and steric demands as well as hydrophobic interactions need also to be accounted for. Complexations with 28 hydrogen-bond receptors including differently substituted indolocarbazoles, diphenylureas, and diphenylthioureas (Scheme 12) were measured in acetonitrile (+0.5% water) with acetate as the guest,78 using the more accurate method mentioned in section 1, which relies on measurements of relative binding differences. Notably, a possible deprotonation of acidic receptors by acetate was checked by measuring their acidities (ΔpKa values) relative to acetic acid in the same solvent. Bulky substituents such as chloro- or trifluoromethyl groups located next to the binding sites show the expected free-energy decrease due to steric hindrance. Complex stabilizing effects of electron-withdrawing chloro and nitro groups in the phenyl rings were seen as usual. With methoxy substituents, the cancellation of inductive and resonance effects led to only small affinity changes. Thus, the acetate-carbazole I complex showed for X = Y = H, lg K = 4.46; for X = H, Y = 2-NO2, lg K = 5.09, but for X = H, Y= 2-MeO, lg K = 4.5. Similarly, one observed for the diphenylurea II with X = Y = H, lg K = 4.2 and for X = Y = 4NO2, lg K = 6.04. The position of the substituents had little influence on the binding affinity, in line with predominant

Figure 31. Correlation between the binding lg K values of anion complexation by N,N′-dinitrophenyl urea in acetonitrile and charges at the oxygen atoms of the anions. Reprinted with permission from ref 333. Copyright 2004 American Chemical Society.

squaramide host (Figure 32), providing ΔG = 35 kJ/mol in acetonitrile. Pyrrole units such as in calixpyrroles are an extremely versatile part of many hosts for anions; they can be made particularly selective for fluoride binding and are discussed in several reviews.338−341 Scheme 11 shows some examples for large affinity and selectivity differences with pyrrole-derived host compounds. Instead of pKa or α and β values, one can attempt to use also Hammett-substituent constants for the prediction of hydrogenbonded complexes with phenyl derivatives. However, measurements of complexes between diethyl barbital and 2,6diamidopyridine derivatives bearing substituents X at the pposition in chloroform revealed with a Hammett plot a break between the different electronic substituents (Figure 33).342 It was suggested that a much shorter hydrogen bond between the 5242


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Scheme 9. Association Free Energies between 1,3-Dialanylcalix[4]arenes and Carboxylate Anions in Acetone336

Figure 32. Comparison of the halide-anion affinity in acetonitrile between a squaramide and a urea as host. Reprinted with permission from ref 327. Copyright 2010 Royal Society of Chemistry.

Scheme 10. Steroidal Squaramide and Steroidal Urea Receptors for Halide Ions, Featuring a Convergent Arrangement of the NHDonors To Form a Cleft for Anion-Binding337

the hydrogen-bonding strength decreases with increasing polarity of the solvent. Hydrogen-bond complexes between electro-neutral amide- or urea-type donors and acceptors are of importance in many biological systems, and also their use in new materials. In a first approximation, many complexes of this type can be described with additive free energy increments of 5 ± 1 kJ/mol per bond in chloroform.344 Closer inspection of complexes between nucleobases, however, revealed that the sole use of this energy increment is often not sufficient. Thus, the Watson−Crick base pairing between the nucleobases G and C has three hydrogen bonds, and the one between A and T has two. By simple additivity, one would therefore expect for a GC pair a free energy that is 50% larger than for an AT pair (Scheme 14).

inductive effects, apart from steric hindrance effects at positions close to the N−H donor. Although thioureas are stronger acids than ureas, they showed a lower binding affinity toward acetate due to lower hydrogen-bond donating ability. NMR titrations of such hydrogen-bond complexes in DMSO-d6:H2O (99.5%:0.5% m/m) gave similar results.79,343 The 15N chemical shift of the nitrogen atoms of the NH binding centers could be correlated with the measured affinity (Figure 34). Complexation studies with phenol-type hydrogen-bond donors and pyridine-type or amide-type H-bond acceptors were carried out in detail with a DMC approach (Scheme 13).199 The results indicate that the contributions per hydrogen bond are fairly additive, close to the experimental error margin (±0.5 kJ/mol), and noticeably so in four different solvents. As expected, 5243


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which donor D and acceptor A are on the same side, forming a combination AD with DA, these charges are repulsive. In the GC case, which bears a DAA interacting with an opposite ADD combination, they are overall attractive. As discussed in section 2.2, it can be attempted to describe the total interaction with two parameters, one standing for the hydrogen bond (ΔGp), the other one for the electrostatic secondary interaction, which is either attractive (ΔGAA or ΔGDD), or repulsive (ΔGAD), each multiplied by the numbers m, n or o of occurrence:347

Scheme 11. Pyrrole Derivatives as Anion Host: Complexation for A (R = CH2-o-Pyr) in MeCN, and for B (R = propyl) in DMSO (with 0.5% H2O)339

ΔG = mΔG P + nΔGAA − oΔGAD

(12)

Analysis of 58 complexes of the kind illustrated in Scheme 15 in chloroform showed that the total ΔG can be calculated within ±1.8 kJ/mol based on ΔGp = −7.9 kJ/mol for the primary and 2.9 kJ/mol for all secondary ΔGAA-, ΔGDD-, and ΔGADincrements. The same value of 2.9 kJ/mol for both attractive and repulsive interactions is in line with Coulombic forces playing an essential role. Complexes which do not conform to the above-mentioned equation are either those with particularly strong or weak hydrogen bonds or, in particular, those where steric hindrance prohibits simultaneous contacts between all binding sites. Thus, the DAADADDA combination of complex IV in Scheme 15 gives an experimental binding free energy close to the calculated interaction energy only for the substituent R2 = n-butyl, but not for the bulky R2 = tert-butyl. Later studies showed that aside from steric factors and the possible presence of tautomeric structures, other parameters are necessary for an improved stability description, such as potentially occurring interactions with C−H bonds.352 A larger data set containing related hydrogen-bonded complexes in chloroform has been the basis for the development of a multiparameter equation

Figure 33. Complexes between diethyl barbital and 2,6-diamidopyridine derivatives (X = H, Cl, CN, NO2, Me, OMe; and R = CH2-CMe3) and correlation with Hammett σ constants and reaction constants ρ. Reprinted with permission from ref 342. Copyright 2014 American Chemical Society.

ΔG = 5.6 + 3.2n intra − 3.5nNH···N

Scheme 12. Hydrogen-Bond Receptors: Indolocarbazoles, Diphenylureas, and Thioureas78

− 4.1nNH···O − 0.7nsec − 2.2nCH···O

(13)

in which nNH···O stands for N−H···OC bonds, nNH···N for N− H···NC bonds, nCH···O for C−H···OC bonds, nintra for intramolecular H-bonds broken before complexation, and nsec for secondary electrostatic interactions (attractive minus repulsive). The intercept of 5.6 reflects the loss in translational and rotational entropy for the association of two partner molecules (all kcal/mol). As Figure 35 shows, the resulting correlation for a set of 86 complexes in chloroform is quite linear, however, with a standard deviation between predicted and observed ΔG of ±2.7 kJ/mol. In line with ab initio calculations, the empirical correlation indicates that the A·T base-pair does have enhanced stability relative to complexes with only N−H···N and N−H···O hydrogen bonds, due to a Hoogsteen geometry in the A·T base pair, favored by ca. 4 kJ/mol over the conventional Watson− Crick structure.352 Hydrogen bonds between a phenolic hydroxyl group and phosphonate diester, carboxylic ester,353 or ether functions354,355 were evaluated using zinc−porphyrin complexes of the kind shown in Scheme 16. The strong coordination between zinc and the pyridine units allows one to regard the hydrogen bonds as the intramolecular interaction, and secures a uniform basic geometry rather than one independent from the substituents at the pyridine. For a total of 120 zinc complexes, substituents on both the porphyrin derivatives and, in particular, the pyridine ligands were varied in order to study the influence of geometrical complementarity and conformational flexibility in the recognition process. The effective molarities (EMs) for two different

Figure 34. Correlation between acetate binding constants (lg Kass) of symmetrical indolocarbazole receptors and the15N chemical shifts of the ring nitrogen atoms in DMSO-d6:H2O (99.5%:0.5% m/m); receptors 25 and 26 are outliers due to steric hindrance of the substituents close to the NH binding center. Reprinted with permission from ref 79. Copyright 2014 American Chemical Society.

Experimentally, a much higher value for GC is found (+190%), which was explained by comparing the partial charge patterns, obtained from ab initio calculations.345,346 In the AT case, for 5244


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Scheme 13. Association between Phenol-type Compounds with OH Hydrogen-Bond Donor Moieties and Pyridine-type or Amidetype Hydrogen-Bond Acceptors199

Scheme 14. Watson−Crick Base Pairs with Primary and Secondary Interactionsa

Experimental association energies −ΔG in CDCl3, and −ΔG values calculated with primary and secondary increments; see text.

Figure 35. Correlation for a set of 86 complexes with multiple hydrogen bonds according to eq 13; standard deviation ΔG of ±2.7 kJ/mol. Reprinted with permission from ref 352. Copyright 2007 American Chemical Society.

types of H-bond acceptor were found to be linearly correlated; it was suggested that EM is a property of the supramolecular architecture, with an interplay between K and EM. The effective

molarities (EMs) for the intramolecular ether−phenol values were found to be practically identical to the EMs for the interactions in toluene; correlations of lg K of log EM, and of

a

Scheme 15. Typical Hydrogen-Bonded Complexes with Secondary Interactions, with Binding Constants in Chloroforma

Complexes I,348 II,349 and III350 show high binding constants. Complex IV351 exhibits, for (a) R2 = n-butyl, K = 2000 M−1 and, for R2 = t-butyl (steric hindrance), K = 47 M−1; ΔG [kJ/mol], for n-butyl, 18.6 (calc. 17.9) and, for t-butyl, 9.4.

a

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Scheme 16. Zinc−Porphyrin Complexes with the Type of Pyridine Ligand, which Exhibit the Most Efficient Geometry for Binding, Either with One or Two Interaction Sites354,355

Scheme 17. Hydroxyl Group and C−H--π Hydrogen Bonding in Carbohydrate Complexesa

a Complexation ΔGexp measured in CHCl3; ΔGt calculated with (a, left) −ΔΔGOH = 2.0 and −ΔΔGCH = 1.5, or (b, right) −ΔΔGOH = 3.0 and −ΔΔGCH = 1.0; see text (all values in kJ/mol).357,358

Figure 36. Molecular balances for the evaluation of OH···π interactions, and the free-energy difference ΔG = − RT ln(pD/pU) versus the solvent hydrogen-bond acceptor parameter β. Y = Me, Z = OH; see text.219

ΔΔG between TCE and toluene showed, however, a large scatter. As expected, the bonds between phenolic hydroxyl groups and phosphonate diesters were found to be the strongest. Ligands with R = CH2P(OEt)2O instead of R = CH2CH2OEt exhibited, e.g., −ΔΔG 7 to 8 kJ/mol if there is one bond (one residue), or 13 to 17 kJ/mol if there are two bonds (2 residues, all in toluene as solvent). The doubling of ΔΔG with two bonds shows the usual additivity, and is within the error also seen with carboxylesters (R = CH2CH2COOEt) as acceptor: 3 kJ/mol with one bond, 5 kJ/mol for two bonds. Independent equilibrium

measurements with p-cresol showed for association with CH3COOEt and Et2O the same small −ΔG = 2.5 kJ/mol in both TCE and toluene. Only the strong acceptor EtP(OEt)2O showed a large solvent effect, with −ΔG = 6.3 kJ/mol in TCE and 12 kJ/mol in toluene. The −ΔG values are in line with the general donor capacity scale described in section 2.1, with CA increments of 1.62 for ROR, of 1.78 for RCCOR, and of 2.50 (PhO)3PO, or of 3.1 for (EtO)3PO. Artificial receptors for carbohydrates rely mostly on weak hydrogen bonds of the hydroxyl groups with different host 5246


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elements and C−H bonds with arenes, as secured also by structural analyses (Scheme 17).356−358 Due to the weak interactions, one often uses solvents such as chloroform, which are not strongly competitive for hydrogen bonds. A multitude of different donors and acceptors are operating in these complexes, which can be grouped into either those with OH substituents and those involving arenes. Tentatively, one can ascribe a binding energy increment −ΔΔGOH ≈ 2.0 kJ/mol to the first group, and −ΔΔGCH ≈ 1.5 kJ/mol to the second. These ΔΔGOH values are taken as average from corresponding literature hydrogen-bond factors CA and CD, which also go back to measurements in chloroform (see above). The total free binding energy ΔGt can in analogy to eq 12 then be described by ΔGt = nΔΔGOH + mΔΔGCH

Figure 37. Hammett-correlations of hydrogen-bond equilibria with para-substituted tetrafluorobenzenes or phenylacetonitriles and hexamethylphosphoramide (HMPA) as acceptor.365

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,where n and m denote, as usual, the number of occurrences. With the above-mentioned ΔΔG increments from CA/CD values in chloroform, the calculated ΔGt values for the hydrogen bonds are about 15% smaller than the observed ones, which indicates that other, e.g., dispersive interactions also contribute. If for a better matching −ΔΔGOH = 3 kJ/mol and −ΔΔGCH = 1 kJ/mol are used, the calculated ΔG values deviate on the average by only ±2 kJ/mol from the observed ones. Preliminary analyses indicate that similar predictions can be made for other carbohydrate complexes in chloroform.359 Hydrogen bonds with aryl and other unsaturated moieties as acceptor were investigated with a series of molecular balances shown in Figure 36.219 With tertiary alcohols (Y = Me, Et, CH CH2, CCH), the conformer with the hydroxyl group facing downward, forming a hydrogen bond with the aryl group (1, 3), was more abundant than the conformer with an OH···π bridge toward the alkene (2, 4). Based on a triple mutant cycle analysis, it was concluded that the OH···π−arene interaction is stronger than the OH···π−alkene interaction by approximately −1.2 kJ/ mol. The influence of the solvent on the free folding energy (ΔG = −RT ln(pD/pU), where pD and pD are the relative abundances of the conformers with the OH group facing downward or upward, respectively (see also eq 4 in section 2.5), correlated well with the acceptor strength factor β (Figure 36). The difference observed with the Y-substituents also shed light on the electrostatic interactions of these (see section 3.4). Weak hydrogen bonds such as those with C−H as a donor, which have been reviewed several times,360−364 are difficult to measure in competing protic solvents and often are accompanied by the formation of different species, such as in the case of benzene dimers by edge-to-face besides face-to face orientations. In the gas phase, C−H hydrogen bonds show characteristic variations; for example, the association between benzene and methane is only worth 4.5 kJ/mol, as compared to that of a benzene−water interaction with 14 kJ/mol;361 here, water can also act as acceptor for arene−C-H bonds. C−H--π bonds are known to bear also the landmark of dispersive interactions, but their strength can nevertheless be modeled with free energy increments derived for polar interactions. Thus, C−H bonds can be described with the donor−acceptor increments cited above, with an acidity value of α = 0.20, indicating a very weak hydrogen bond. Similarly, equilibria of para-substituted phenylacetonitriles with the strong acceptor hexamethylphosphoramide (HMPA), and of 3-substituted 1,2,4,5-tetrafluorobenzenes with HMPA exhibit linear correlations with σp substituent constants (Figure 37).365 Complexes between a chiral pyridine−crown ether derivative and ammonium salts of α-amino acid methyl esters in chloroform showed discrimination between the enantiomers,

which reached a maximum value of −ΔΔG = 5.0 kJ/mol for tryptophan, compared to only −ΔΔG = 1.5 kJ/mol for alanine; the absolute affinities also increased significantly from Ala to Trp.202 This was explained by interaction between a C−H bond of the crown ether and the aryl residue of the amino acid, which was supported by structural evidence from NMR and crystal structure data. Through DMC analysis (section 2.4), utilizing the mutation of a CH2 group into a CF2 group at the host, and the mutation of the key amino acid of the guest, e.g., D-Trp-OMe → D-Leu-OMe, the authors derived a relatively large value for the CH−indole interaction of −ΔΔG = 4.1 kJ/mol. Pillarenes, first reported in 2008, are macrocycles composed of hydroquinone units (5 to 10) linked in the para position (Scheme 18).366−368 They are symmetric and possess two Scheme 18. Pillar[5]arene (R = alkyl or OH) Forms in Chloroform Strong Complexes with Bis(imidazoles) with Varying Spacers X (α,ω-alkyl, 1,4-phenyl)

identical gates that are typically flanked by hydroxyl or alkoxylresidues. The cavity walls of pillarenes are electron-rich; thus, electron-poor species, e.g., alkyl ammonium or imidazolium salts, are particularly good guests,369−371 but also noncharged species can be strongly bound. For example, pillarenes form stable intracavity complexes with neutral bis(imidazole) in chloroform (Scheme 18), with ΔG values of up to 24 kJ/mol, essentially driven by enthalpy and a relatively modest entropic disadvantage. The complexations were ascribed to C−H···O(N) and C−H···π interactions; in line with competitive solvents such as DMSO or acetone suppressing the complexations.372 As will be discussed in section 3.4, electrostatic interactions also play a great role in the tight fit with these pillarenes. Aromatic capsules can complex n-alkanes with sizable affinities, which are at maximum for long chains like that of ntetradecane adopting a helical conformation because this maximizes the number of CH−π interactions with the aromatic walls of the cavity.373 Possible deformations of host and guest, as 5247


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Scheme 19. Anion Receptors That Utilize C−H Hydrogen Bonds

Scheme 20. Hydrogen-Bonded Complexes in Watera

a

I, aryl-extended calix[4]pyrroles (R = H, Ph, or COOH). II, a carbohydrate receptor for cellobiose (“synthetic lectins”).

Figure 38. (a) Thermodynamic parameters for the complexation of galactosamine (1) and glucosamine (2) by CB7 in water. (b) Model for CB7·2 inclusion complex, based on NMR data. Modified figure: reprinted with permission from ref 383. Copyright 2012 Wiley VCH.

receptors. Here, the external water-solubilizing groups are far away from the binding site. The deep, aromatic cavity with four converging pyrrole NHs allows complexation of pyridine Noxides, which are very effective H-acceptors, with −ΔG = 25 to 35 kJ/mol, dominated by ΔH as shown by ITC measurements. Of particular importance in carbohydrate recognition356,378 are interactions between the axial sugar C−H bonds and arenes, which amount in water to about 6 kJ/mol.379 Calorimetry with various pyranosides and a benzene solution has shown enthalpies ΔH of up to −130 kJ/mol.380 The DCC experiments discussed in section 3.6 were leading to the C−H--π free energy contributions listed in Table 2;237 the data reflect the significant binding-free-energy increase with increase of the C−H acidity, and with increase of the electron-donating power of the aromatic acceptor. The values derived for C−H bonds, which are facing the naphthol site and which are activated by the nearby oxygen atoms of pyranose, reach, e.g., 1.9 kJ/mol for the three axial C−H bonds. While these data point to significant electrostatic forces in such C−H--π associations, the importance of dispersive interactions cannot be excluded, as the arenes also exhibit a sizable polarizability.

well as competition with solvents, make it difficult to derive energy values for a single C−H--π interaction. Anions as particularly strong hydrogen-bond acceptors can also use moderately acidic C−H bonds as donors,374 e.g., in the form of a pentacyano-macrocycle (Scheme 19, left), which in methanol/DCM = 4:6 showed −ΔG of up to 70 kJ mol−1 with large anions such as BF4−, ClO4−, and PF6−.375 A pyrrolo triazoliumcyclophane (Scheme 19, right) binds anions by both NH and CH hydrogen bonds;376 it displays a high solventdependent selectivity for tetrahedral oxyanions in comparison to monoanions and trigonal planar anions; e.g., −ΔG = 40 kJ/mol for HSO4−, and 36 kJ/mol for chloride binding in acetonitrile. The complexation energy of HSO4− is reduced to 31 kJ/mol in the more competitive acetone/water (2:3) solvent mixture, while chloride binding was no longer detectable. Hydrogen bonding in an aqueous medium is one of the big challenges for supramolecular chemistry; on account of the strong competition by 55 M bulk water, the aryl-extended calix[4]pyrroles I shown in Scheme 20 illustrate a way to minimize this problem by at least partial protection of strong donor sites from external water,377 in analogy to protein 5248


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interaction energy of 2.0 to 3.2 kJ/mol, or 0.7 to 1.0 kJ/mol per single C−H--π interaction, depending on the nature of both the aromatic ring and the carbohydrate.173 Replacement of an interacting aromatic ring in the peptide chain by an aliphatic group resulted in a decrease in interaction energy by 0.4 kJ/mol, which shows that hydrophobic contributions are small in comparison to the C−H--π interaction. Favorable interactions were only observed when the hydroxyl groups of the carbohydrate were protected using either acetyl groups or methyl groups, which implies a significant cost for desolvation of the sugar. For the interaction of an amide N−H group with a aryl surface, a value of 4.5 kJ/mol was derived from measurements with a double mutant cycle197 (section 2.3). As mentioned in section 2.4, some other DMC folding studies were also leading to a rather wide range of C−H--aryl interaction energies.173,237 Folding measurements with a large range of glycosylated and nonglycosylated arene-rich protein β-sheets showed no dependence on aryl substituents, which would have been typical for electrostatic interactions. Thus, it was concluded that the major driving forces for C−H--aryl interactions are, besides hydrophobic effects, of dispersive nature.384 Weak hydrogen-bond acceptors such as organic halogens can also be characterized with binding-energy increments. Complexes with 4-fluorophenol as donor and 1-haloadamantane, halocyclohexane, and halopentane in CCl4 show a consistent affinity increase from primary over secondary to tertiary substitution (Figure 39).385 In contrast to conclusions drawn from crystallographic surveys,386−388 organic fluorine is a relatively good acceptor, in line with the halogen-electronegativity scale.389 To date, the hydrogen-bond donor and acceptor strength has not been systematically evaluated for many supramolecular complexes in different solvents. Figure 40 shows one example for association of hydroxyl groups with various acceptor functions, as measured in chloroform;390 in view of their importance for carbohydrate complexation, the chosen donors were trans-1,2cyclocyclohexandiol (A), n-dodecyl-α-D-glucopyranoside (B), and n-dodecyl-α-D-galactopyranoside (C). The data illustrate (a) that the affinities are quite parallel for the ligands A, B, and C, increasing as a function of the number of available OH groups, (b) that they increase for the anions in the sequence I < Br < Cl, according to the charge density, and (c) that bifurcated oxoanions, e.g., carboxylates, are best suited, particularly for vicinal diols due to the ideal geometry matching. As mentioned before, hydrogen bonds are usually so weak in water that they only materialize in the presence of additional interactions. Complexes between acyl-guanidinium receptors and dipeptides (Figure 41) showed, for example, a strong affinity increase upon introduction of hydrogen-bonding functions. A systematic comparison of the affinities indicated a value of 10 kJ/ mol for the primary double salt-bridge effect, in agreement with the increments derived in section 2.1, and an increment of 4 kJ/ mol for a hydrogen bond.391,392 See also Table SI in the Supporting Information. Solvent effects on hydrogen bonds may be derived from donor and acceptor parameters such as α and β in eq 1 (section 2.1), which by themselves were obtained from hydrogen-bonded complexes.393 A linear correlation for the prediction of the solvent influence on hydrogen bonds was obtained by reference to measurements with perfluoro-tert-butyl alcohol as very strong donor and tri-n-butyl phosphine oxide as very strong acceptor, which provide a scale of α and β values for different solvents. On the basis of an equilibrium A·S + D·S = A·D + S·S, in which the

Carbohydrate receptors such as II in Scheme 20 (“synthetic lectins”) exhibit, e.g., for the disaccharide cellobiose in water an association constant of 650 M−1, dominated by a change in enthalpy of ΔH = −13 kJ/mol, with a remarkably small entropy disadvantage of −TΔS = −2.5 kJ/mol.381 Much of the complexation strength stems from interaction between the axial cellobiose C−H bonds and the arene sidewalls, although hydrophobic forces certainly also contribute. The orientation of the C−H bonds toward the arenes was secured by NMR spectroscopy, and the selectivity among different saccharides is dominated by the number of available axial C−H bonds. Dendrimer receptors similar to the one in Scheme 20 were shown to rather selectively complex D-glucose in water with association constants of up to K ≈ 70 M−1.382 For comparison, only K ≈ 3 M−1 was found for D-galactose. Glucosamine was bound with up to K = 7 × 103 M−1; with 20 mM NaCl the constant decreased to 1.6 × 103, in line with ion-pairing character in the complex (see above). As expected, the association constants increase with total negative charge of the side chains. It is noteworthy that a structurally much simpler, noncharged host−cucurbit[7]uril (CB7) also complexes amino sugars with high affinity (Ka up to 104 M−1) in water (Figure 38).383 Even though C−H--π bonds and ion pairs do not occur in CB7· aminosugar complexes, the observed binding enthalpy of about −14 kJ/mol is strikingly close to that of synthetic lectin II for cellobiose (see above), but unusually small for typical CB7 complexes (ΔH up to −90 kJ/mol; see section 3.7). For CB7, high-energy water release in combination with ion-dipole interactions between the ammonium group and the carbonylfringed portal of the host are the main driving forces for binding. High-energy cavity water may also occur in the rather wellshielded, hydrophobic cavity of the receptor II, further supported by comparison to the structurally similar CP1 and CP2 in section 3.7. Furthermore, the complexation of amino sugars by CB7 is strongly entropically favored (−TΔS from −2.8 to −10 kJ/ mol),383 which resembles the findings for receptor II, but which is very uncommon for CB7 complexes (see section 3.7). By comparison, it can be concluded that the desolvation of the sugar contributes a favorable entropic component to binding, but at the same time reduces the binding enthalpy in water. Measurements with complexes as shown in Scheme 21 reveal −ΔG values for the attraction between anthracene and sugars in Scheme 21. Zipper Complex Used for the Measurement of Carbohydrate−π Interaction

chloroform of up to 1.4 kJ/mol (error below 1 kJ/mol), if, as with glucose and galactose derivatives, the pyranose oxygen is pointing away from the aromatic face. With other sugars, for which the ring oxygen is pointing toward the arene, one finds repulsion.166 Folding studies with peptide hairpins including double mutant cycles indicated for a pyranose and an aromatic ring an 5249


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Figure 39. Free energies (ΔG in kJ/mol) of haloalkane binding with 4-fluorophenol in CCl4; first column, 1-haloadamantane; second, halocyclohexane; third, 1-halopentane; data from ref 385. Reprinted with permission from ref 389. Copyright 2012 Wiley VCH.

Figure 40. Association of hydroxyl compounds with anions. The interaction of A, trans-1,2-cyclocyclohexanediol; B, n-dodecyl-α-D-glucopyranoside; and C, n-dodecyl-α-D-galactopyranoside with oxoanions (1−3, hexadecyltrimethylammonium countercation), and with halide anions (4−6, tetrabutylammonium counteraction) was investigated in CHCl3. Data from ref 390.

3.3. Electrostatic contributions in ionophores

The attraction between ions and lone pairs of nitrogen or oxygen is the basis of most ionophores, and can be related to electrostatic interaction as well as to polarization effects. Consequently, the stability of, e.g., metal ion complexes can for suitable aromatic host compounds be correlated and predicted with Hammettsubstituent constants (Figure 42).395 Similarly, the affinity between p-substituted aniline crown ethers and bis(4fluorobenzyl)ammonium ions exhibits linear correlations with Hammett σ values.396 The donor and acceptor increments89,90 α and β, or CA and CD discussed in section 2.2, reflect not only the strength of hydrogen bonds, but as illustrated in Figure 43, also in an additive way the partial charge differences at the lone pairs of crown ether and cryptand-oxygen atoms; this allows straightforward predictions for the design of ionophores and related receptors.397 Solvent effects on such ionophore affinities can best be predicted by Gibbs transfer energies ΔGtransfer of the metal ion from water to the given solvent, as was shown for complexes of potassium salts with 18-crown-6 in 14 different solvents. The observed binding constants decrease from the propylene carbonate as medium to water by a factor of 104; the correlation with ΔGtransfer (Figure 44) shows that the cation desolvation free energies dominate the medium effects; correlations with other solvent parameters such as β values or Gutman’s donor numbers showed more scatter.398

Figure 41. Association of acyl guanidinium hosts with Ac-Ala-O− and with a dipeptide D (Ala-Ala, R1 = R2 = Me, K = 30,600 M−1; binding constants K [M−1] in 40:60 water/d6-DMSO (v/v).391,392

solvent competes with the solute (A and D are the hydrogenbond acceptor and donor, respectively, and S is the solvent), one can describe the total interaction by the equation ΔG = −(α − αS)(β − βS) + 6 [kJ/mol]

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3.4. Halogen bonds and other polar/electrostatic interactions

,in which α and β, and αS and βS are the hydrogen-bond donor and acceptor parameters for the solute and solvent, respectively. The constant value of 6 kJ/mol is introduced as the assumed cost of bringing two molecules together in a bimolecular complex (see section 3.9).394

Interactions between halogen atoms, which can be considered as Lewis acids and neutral or anionic acceptors (e.g., Lewis bases) bear, as also do most hydrogen bonds, the landmark of essentially 5250


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Figure 42. Complex of p-tert-butylcalix[4]arene-esters with potassium picrate and Hammett-correlation with extraction constants (as lg K) from H2O to CH2Cl2. Reprinted with permission from ref 395. Copyright 2006 Wiley VCH.

electrostatic forces. Although they have been aptly reviewed,399−402 there are until now limited data available on binding energies in solution,403,404 and most studies were conducted in the crystalline state.405 Interaction free energies for complexes between CBr4 and the halide anions Cl−, Br−, and I− showed in CH2Cl2 only small differences (2.7 to 2.9 kJ/mol),406 which is also the case for interaction between C6F5I and those anions in acetone, for which −ΔG varied between 9.5 and 12 kJ/ mol.403 Nevertheless, the observed sequence Cl− > Br− > I− is in line with charge-density differences and consistent with the importance of the electrostatic component. The same conclusion emerges from associations with heavily fluorinated ligands such as C8F17I, for which the −ΔG values [kJ/mol] in acetone are 19 for Cl−, 17 for Br−, and 14 for I−, respectively.403 The perfluorosubstituted receptors in Scheme 22 exhibit association free energies ΔG, which come relatively close to those relying on hydrogen bonds (see section 3.2), and which are fairly additive if one goes from one to three binding sites, with an average value of −ΔΔG = 7 kJ/mol for a single C6F5···Cl¯ interaction.407 The affinities follow again the order Cl− > Br− > I− ≫ TsO−, NO3−, HSO4−, different from the order observed with hydrogen-bondbased anion complexes. Several other studies also speak for a dominant electrostatic character of halogen bonding, but it has been shown for associations between bis(haloimidazolium) donors and Cl, Br and I anions, that here entropic terms account for more than 50% of the overall free energy (association constants of up to 3 × 106 M−1), showing small differences between acetone, dichloromethane and THF as the solvent.408 In line with electrostatic interactions, complexes between para-substituted (iodoethynyl)-benzenes and quinuclidine as acceptor in C6D6 showed a linear correlation with Hammett parameters σp (Figure 45). Other receptors are weaker, with association constants K [M−1] of 1.5 with amides, of 1.9 with Et3N, of 3.0 with (n-Bu)2SO, and of 8.4 with (n-Bu)3PO, compared to K = 16 with quinuclidine.409 The thermodynamics of halogen bonds were investigated in cyclohexane with a series of para-substituted iodotetrafluoroarenes XC6F4I as donors and tri-n-butylphosphine oxide as the acceptor.410 Fairly linear correlations of lg K were found with σm Hammett substituent constants (Figure 46a), less so with σp constants, in line with a predominant inductive effect of the

Figure 43. Binding affinities ΔG (in methanol) for potassium (K+) with crown ethers and cryptands versus the sum of group electron donor parameters (ED = ∑ of CA increments, see section 2.1) in a given crown ether and cryptand modification. Reprinted with permission from ref 397. Copyright 1993 American Chemical Society.

Figure 44. Solvent effect on lg K of complexes between 18-crown-6 and KSCN as a function of Gibbs transfer energies ΔGtransfer (kJ/mol) of the metal ion from water to the given solvent. (DMF: N,N-dimethylformamide, HMPT: hexamethylphosphoric triamide, DMSO: dimethyl sulfoxide, PC: propylene carbonate). Reprinted with permission from ref 398. Copyright 1996 American Chemical Society.

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Scheme 22. Additivity in Halogen Binding Receptors for Chloride, Measured in Acetone407

Similarly, the solvent effect on the stabilities of complexes involving a single hydrogen bond or halogen bond (X-bond) has been quantified. Association constants for binary complexes of 4(phenylazo)phenol, molecular iodine, and tetramethylurea were measured in 15 different solvents by UV/vis absorption and 1H NMR titration experiments. The stabilities of the H-bonded complexes decrease by more than 3 orders of magnitude with increasing solvent polarity. In contrast, the X-bonded complex of molecular iodine with tetramethylthiourea is remarkably insensitive to the nature of the solvent (association constants measured in alkanes and alcohols are similar). It was suggested that charge-transfer (CT) interactions make a major contribution to the stability of these X-bonded complexes, rendering them resistant to increases in solvent polarity, which is in contrast to H-bonds, where electrostatic forces determine their thermodynamic stability.412 That halogens can act as CT acceptors with nitrogen- and oxygen-containing or unsaturated donors has long been proposed based on structural and spectroscopic studies.112,113,413 However, recent computational results favor a purely electrostatic and dispersive mechanism;414 the latter interaction type is rather solvent-independent, which reconciles the aforementioned differences between hydrogenand halogen-bonding. CT is now assumed to play energetically a minor role in halogen bonding, albeit different views may prevail. Halogen bonding was also used for the design capsules (Figure 47);415 in benzene/acetone/methanol (70:30:1); the formation free energies were for the substituent X = I, ΔG = −20.0 kJ/mol, enthalpically favored by ΔH = − 53 kJ/mol, with an entropic disadvantage of − TΔS = 32 kJ/mol; with X = Br, ΔG was reduced to −3.5 kJ/mol, with X = Cl or X = F no association was detectable. These results are all in agreement with findings for typical halogen bonds. The capsule with X = I showed for 1,4dioxane as guest ΔG = −31 kJ/mol and, for 1,4-dithiane, ΔG = −48 kJ/mol (in mesitylene +2% of 3,5-dimethylbenzyl alcohol), pointing to particular dispersive interactions with the sulfur compound. Similar differences were observed with binding to the separate cavitands as part of the capsule. The self-assembled cage shown in Figure 48 binds lipophilic guest by hydrophobic interactions and anions by electrostatic interactions. Iodoperfluorocarbons as halogen-bond donors associate inside the cavity with NO3¯ anions and/or H2O as acceptor molecules. Competition experiments in water with pentafluoroaryl halides showed binding in the preference I > Br > Cl ≫ F in the order of increasing halogen-bond donor strength.416

Figure 45. Hammett correlation for complexes between parasubstituted (iodoethynyl)benzenes and quinuclidine. Reprinted with permission from ref 409. Copyright 2014 American Chemical Society.

substituents. The electrostatic nature of the halogen bond was also supported by correlations with the molecular electrostatic potential surface at the iodine atom, calculated at the AM1 level (Figure 46b) or with a DFT (B3LYP/6-31+G**-LANLdp) method (Figure 46d), while comparison with a model of Hunter based on pairwise electrostatic effects15 (see below) showed more scatter (Figure 46c). Medium effects were studied with the iodoperfluorooctane−triethylamine complex in 10 different solvents; no significant correlation was observed with polarity parameters; in particular, 2-propanol, tert-butyl alcohol, and chloroform reduced the association constants by up to a factor of 10 in comparison to cyclohexane, indicating hydrogen-bond contributions. Complexation of iodoperfluorohexane as halogen-bond donor with several amines as hydrogen-bond acceptors was compared to affinity values based on eq 15 mentioned above, which was successfully applied to many hydrogen-bonded systems, and is assumed to reflect electrostatic interactions.411 With tributylphosphine oxide and some primary amines, there was an acceptable correlation, but not so for piperidine and similar cyclic amines. It was concluded that, in these sterically more hindered complexes, electrostatic interactions do not prevail. That polar effects play a smaller role in halogen bonding than in hydrogen bonds was also shown by comparing solvent effects on related complexes. The hydrogen bond between tetramethylurea and a phenol exhibited in octane an association constant of K = 2,440 M−1, whereas in methanol no binding was detectable. In contrast, the halogen-bond association between tetramethylthiourea and iodine falls from K = 8,800 M−1 in octane to a respectable K = 2,700 M−1 in methanol.412 5252


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Figure 46. Linear free energy correlations of the binding strength of complexes between iodotetrafluoroarenes XC6F4I as donors and tri-(nbutyl)phosphine oxide as the acceptor with different parameters that reflect electrostatic interactions; see text. Reprinted with permission from ref 410. Copyright 2010 with permission American Chemical Society.

CCH and Y = CN as compared to the Y = CHCH2, ascribed to the charge at Cα of the CX groups.219 Clips and tweezers containing electron-rich sidewalls complex electron-poor ligands with sizable affinities.419 For instance, water-soluble derivatives are efficient receptors, in particular for positively charged ligands such as NAD+, but also for nucleosides. Hydrophobic contributions are also of importance;420 see section 3.7 for more details. The examples in Scheme 23 illustrate the binding energy increase with the electronwithdrawing nature of the substituents, which can be quantified by electron-density calculations.421 Complexes of electron-rich cyclophanes are also examples for important electrostatic binding contributions; particularly, high affinities were observed for aromatic guests that carry electronwithdrawing substituents (Scheme 24).103,422 In pillarenes (a.k.a. pillararenes), the accumulation of πelectron-rich arenes in a narrow space leads, much like in clips and tweezers, to a strong negative electrostatic potential in the cavity (Figure 49). Thus, these hosts bind efficiently cationic371,423 and electron-deficient424 guest molecules. With 1,4-dibromobutane (BrC4Br), dicyanoethane (CNC2CN), and 1,3-dicyanopropane (CNC3CN) as guest molecules, the affinities correspond to calculated charge density distributions. The free energies of binding measured in a variety of solvents follow the order BrC4Br < CNC3CN < CNC2CN, as expected from the calculations.425

Multipolar interactions, for example those between C-Hal and CO dipoles, were recently found to occur more frequently than thought before.417 Until now, there are few affinity measurements with related supramolecular complexes, although they have been thoroughly characterized in solid-state structures. With a molecular balance shown already in section 2.5 (Figure 18), the interaction free energy between a C−F dipole and an amide CO group, which are typically in an orthogonal orientation, was determined to amount to 0.8 to 1.2 kJ/mol.224 Replacing the C−F by a CO group yielded for the orthogonal CO···CO interaction in benzene a value of 2.1 kJ/mol,418 which is in the range of aromatic stacking or edge-to-face interactions (see section 3.5). The polar interaction of C-Hal groups with arene surfaces was inferred with a double mutant cycle using phenyl rings with substituents Y = H, NMe2, or NO2, and CX3 groups with X = F, Cl, or Br.200 As expected from the negative partial charges at the π-cloud and at the halogens, one observed repulsive interactions on the order of 2 to 3 kJ/mol, with higher value for the most electronegative fluorine. However, the differences were unfortunately close to the experimental accuracy. The benzobicyclo[3.2.2]nonanes used for the investigation of OH···π hydrogen bonds (Figure 36) show also the electrostatic nature of interactions between Y = CCH and CN groups with π-systems. In line with ab initio calculations, an increase in the pU value in molecular balances 1−4 was observed for Y = 5253


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Figure 47. Halogen bonding in newly designed capsules (with X = I or Br; R = C6H13 for the upper, and R = C11H23 for the lower part). Reprinted with permission from ref 415. Copyright 2015 Wiley VCH.

water. Usually, one can expect that solvent effects on hosts and guests do not show differences originating in steric effects, but this is obviously not so with narrow cavities. The use of solvents that for steric reasons cannot enter a cavity has been introduced early for complexations with cavitands.426−430 Other well-known electrostatically controlled complexes, which are very successfully used mainly by the group of Stoddart for the design of molecular motors,431−433 are based on, e.g., cyclobis(paraquat-p-phenylene) (“blue box”, Scheme 25) as πaccepting tetracationic cyclophanes and hydroquinone, 1,5dioxynaphthalene, or tetrathiafulvalene units as donor. These complexes exhibit strong charge transfer (CT) bands in the visible region but the observed affinities, reaching up to 25 kJ/ mol,434,435 are attributed to electrostatic attraction between donor and acceptor.436 The binding selectivities for aromatic amino acids in water are, −ΔG = 17.1 for Trp, >15.9 for Tyr, and ≫8.7 kJ/mol for Phe, which is in agreement with electrostatic binding contributions while binding driven by the hydrophobicity of the amino acid guest437 would have shown the ranking Trp > Phe > Tyr. An extended tetracationic cyclophane “ExBox” (see Scheme 25) complexes polycyclic aromatic hydrocarbons (PAHs), ranging from two to seven fused rings, with ΔG values in acetonitrile from 14 to 22 kJ/mol, with a moderate binding energy increase with their size. The complexation is essentially driven by enthalpy, usually with adverse TΔS values around ±4 kJ/mol or less.438 A related macrobicyclic cyclophane composed of six pyridinium rings fused with two central triazines and bridged by three para-xylene units (“BlueCage”)439 also complexes efficiently polycyclic aromatic hydrocarbons in acetonitrile; however, it was found that the six PF6− counterions can occupy

Figure 48. Self-assembled cage that binds pentafluoroaryl halides. The binding preference follows the series X = I > Br > Cl ≫ F. Reprinted with permission from ref 416. Copyright 2015 Wiley VCH.

The pill[5]arene complexes exhibit an association constant dependence on the used solvent over several order of magnitudes, in the order o-xylene > toluene > p-xylene > DMSO ≈ acetone > acetonitrile, which is not a simple function of their dielectric constant ε (Figure 50). For instance, toluene, oxylene, and p-xylene have very similar ε values, but the ΔG and ΔH values of guest binding differed strongly. This was explained, and supported with MD and QM calculations, by the different capacities of the solvent molecules to enter the cavity; while toluene and p-xylene were partially included, the two ortho methyl groups in o-xylene make this impossible, so that solvent competition in the cavity is minimized. Similar effects are described in section 3.7 for the binding to “dry” host cavities in 5254


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Scheme 23. Electrostatic Interactions of Clips (R = OH) with Electron-Poor Ligands421,a

a

Complexation −ΔG in kJ/mol, in CDCl3/Me2CO = 1:1. Right: crystal structure of p-dicyanobenzene with the anthracene clip.

Scheme 24. Complexation Free Energies ΔG (in water, kJ/ mol) with an Electron-Rich Cyclophane and Substituted Phenyl Derivatives422

geometry (e.g., see the crystal structure in Figure 51a) and that also weak donors and acceptors can be studied because the complexation is in all cases assisted by high-energy water release from the host cavity,447 a special variant of the hydrophobic effect (section 3.7). There is a good correlation (R2 = 0.89) between the HOMO energy level of the donor and the inverse wavelength of the resulting CT absorption band across a wide spectral range, Figure 51b, in full agreement with the Mulliken CT model.448,449 Likewise, tuning of the LUMO energy level of the acceptor leads to an equally good correlation (R2 = 0.90) with λCT−1. However, no correlation at all was observed for the binding strength of the donor or acceptor with respect to HOMO or LUMO energy levels, even when solvation effects were taken into account (Figure 51b), according to a procedure described in section 3.7, and even not when only the subsets of strong donors and acceptors were investigated.445 3.5. Dispersive interactions, stacking, and C−H--π interactions

Stacking and other interactions with aromatic systems are the subject of countless papers and many reviews102,103,450−453 that outline the underlying principles. In the present section, we discuss therefore only affinity data measured in solution, which at least to some degree can be applied on a broader scale. As it has become clear that dispersive contributions are the major driving force for stacking and also edge-to-face attractions,454−456 in contrast to earlier assumptions,166,192,193 we discuss such van der Waals effects in this section. Measurements with a molecular balance (Figure 52) showed, for stacking, additive effects of the substituents such as CH3, H, OCH3, Cl, CN, and NO2.194 In order to correct for solvent and repulsive oxygen lone pair−π interactions in the folded state, a separate balance (b) was used in which the substituted phenyl ring cannot interact. The so corrected values of ΔG1 − ΔG2 exhibit a linear Hammett correlation with σm values (Figure 53), which was taken as evidence for dominating electrostatic effects within the π-system, although direct interaction with the substituents was not excluded. The torsional balance shown in Figure 52 was used to evaluate not only polar effects by different substituents, but also their sensitivity toward the solvent.457 In apolar organic solvents, good correlations were found with σm Hammett substituent constants, which was attributed to interactions between the formyl group

Figure 49. Pill[5]arene with methoxy groups (R = Me) at the rim; calculated electrostatic potentials show a significant negative potential in the cavity and a positive potential at the rim. Reprinted with permission from ref 425. Copyright 2015 American Chemical Society.

the cavity as a consequence of anion−π interactions and compete with the PAH guests for binding to the host. Other than sometimes assumed,440−442 CT interactions as such play energetically usually a minor role; for example, even a strong acceptor such as 1,3,5-trinitrobenzene shows with a strong donor such as hexamethylbenzene in CCl4 only ΔG = 4.5 kJ/ mol.443 This is not significantly more than what is expected based on dispersive/stacking interactions alone (section 3.5). With toluene, there is no measurable association any longer.443 The large macrocycle cucurbit[8]uril can tie aromatic donor and acceptors in a face-to-face stacking motif together (Figure 51a), which allows for systematic investigation of the influence of the electronic properties of the donor and acceptor on the spectroscopic properties and binding strength.442,444−446 The advantage of this system lies in the well-defined complex 5255


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Figure 50. Solvent effects on stability of pill[5]arene-complexes; see text. Reprinted with permission from ref 425. Copyright 2015 American Chemical Society.

Scheme 25. Stacking Combined with Electrostatic Interactions: (a) Tetracationic Cyclophanes A (“blue box”) That Complex (strongly) Electron-Rich Guests;431,435 (b) Tetracationic Extended Cyclophanes B (“ExBox”) That Bind Polyaromatic Hydrocarbons (PACs)438a

a

Binding constants for complexation in acetonitrile are given. For discussion of their binding features in water, see section 3.7.

and the meta positions on each side of the balance. There was a preference for the formyl oxygen over the least electron-rich Xsubstituted ring when X = NO2, while the other conformer is preferred when X = NEt2. Change of the solvent had large effects on the Hammett correlations, which was rationalized by calculated electrostatic potentials, demonstrating the role of the solvation around the substituents. Another torsional balance, which was used to demonstrate the electrostatic influence on stacking interactions by correlation of conformational freeenergy differences and calculated charges, was already shown above in the context of hydrogen bonding.219 As mentioned in section 2.3, double mutant measurements have indicated for phenyl rings stacking stabilization,188 and destabilization (repulsion) with pentafluorophenyl rings,189 both speaking for dominating electrostatic effects for stacking. Hammett correlations with substituted phenyl derivatives in a molecular balance have been taken as evidence also for electrostatic C−H--π interaction, amounting to 1.4 kJ/mol in CHCl3 (see section 2.3),458 but recent experiments with other torsion balances have shown that binding changes in these systems are essentially due to direct local interactions between the substituent and the arenes,194,195 in line with computational results.196 Early experiments that used a strategy related to the dynamic combinatorial chemistry (DCC, section 2.6) approach

were also in favor of local interactions between the substituents.459 One observes a significant electrostatic binding contribution only if the aromatic partners bear partial charges of opposite sign, as was illustrated above with corresponding clips and tweezers as host (Scheme 23).421 A prototype for the association of chargecomplementary aryl species is the interaction of benzene with perfluorinated benzene. Experimentally, a binding enthalpy of 6 kJ/mol was observed in liquid krypton, which was converted to a binding energy of 12 kJ/mol in the gas phase, taking solvent effects into account.460 Considering the typical entropic cost of complexation of 6 kJ/mol (section 3.9), it is clear that the degree of complexation is very low in solution, while stacking interactions between aryl and perfluorinated aryls are commonly observed in the solid state. Stacking of heterosubstituted arenes with the large surface or with porphyrins was shown to be an additive function of the substituent increment and the phenyl part (see below). In water, the association free energy ΔG with different arenes is, at the first approximation, a function of the contact size, as visible in the ΔG values with porphyrin complexes (Scheme 26). The data also show that the presence of heteroatoms within the ring has little influence on the stacking energy.461 Importantly, hydrophobic contributions would lead to the same size dependence, but can be 5256


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Figure 51. (a) Ternary complexes are formed of the macrocycle cucurbit[8]uril (CB8) with aromatic donors and acceptors. The structure of the CB8ternary complex with 2,7-dihydroxynaphthalene and p-NO2-phenyl-substituted 4,4′-bipyridinium is shown. (b) Correlation of the HOMO and LUMO energy level of the donor and acceptor, respectively, with the inverse wavelength of the observed CT band.445 The plot of EHOMO vs the desolvationcorrected binding strength is shown; see text.

Figure 52. (a) Molecular torsional balance for measuring electrostatic substituent effects (SEs) in stacking, and (b) a control balance for measuring the solvent and repulsive oxygen lone pair to π interactions of the linker. Reprinted with permission from ref 194. Copyright 2014 American Chemical Society.

increment for the nitro group in nitromethane, nitropropanoic acid, and various nitrophenyl derivatives. This allowed construction of a scale for dispersion-energy contributions for many functional groups (Table 5).463 Notably, alkyl substituents gave, as is the case for fluorine, almost negligible binding, with the exception of cyclopropane, which is known to exhibit more sp2 than sp3 character. Quite similar affinity changes with various halogen derivatives have been seen in complexes of cyclodextrins with halobenzenes, and of pillarenes with 1,4-dihalobutanes (Figure 54).463 Similar to the observations with porphyrin complexes, the affinity increases in the order F < Cl < Br < I, as does the polarizability α. This excludes a binding mechanism via induced dipoles instead of dispersive forces, as the electronegativity of the halogens follows the opposite trend. The data show that, in contrast to

excluded by comparison with saturated ligands; the latter show negligible binding, although they are more hydrophobic than arenes.462,463 As discussed above, substituents on the aryl rings were believed to generate differences mainly by changes of the electron density distribution in the π-system,193,457,458 opposite to new experimental195 and computational196 results, which indicate that often direct interactions with the substituents play a decisive role. Systematic exploration of complexes with porphyrins, which offer a π-surface sizable enough to accommodate also large ligands (see Scheme 26), showed that substituents on phenyl rings can greatly enhance the affinity by direct interaction with the π-surface.461,462 The corresponding ΔΔG values for each substituent have been found to be additive with 56 different compounds, exhibiting, e.g., the same ΔΔG 5257


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Table 5. Binding Free Energy Increments ΔΔG (kJ/mol) of Different Groups R and Molecular Polarizability α of Corresponding Methyl Derivatives CH3-R461−463,a Substituent R -CH3 -CH(CH3)2 -CHCH2 -CC-cyclopropyl -phenyl -pyridyl -F -Cl -Br -I -NH2 -OCH3 -COOCH3 -COCH3 -SCH3 -CN -NO2 -CONH2

Figure 53. Hammett σm plot of ΔG1 − ΔG2 for the monosubstituted balances (in Figure 52) with substituents in the meta- (blue) or parasubstituents (red); substituents from left to right: CH3, H, OCH3, Cl, CN, and NO2. Reprinted with permission from ref 194. Copyright 2014 American Chemical Society.

Scheme 26. Free Energies ΔG of Associations of a Cationic Water-Soluble Porphyrin with Aromatic Guest Molecules of Increasing Size in Watera

α CH3-R 4.47 6.26 6.18 12.3 2.97 4.72 5.7 7.97 4.0−4.7 5.16 6.94 6.35 4.45 7.37 5.67

ΔΔG (kJ/mol)

n

Na+ > K+ ≫ NMe4+.474 Complexes with several cyclophanes show distinct differences between 5258


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Figure 55. A container with imidazole units and its complex with CHCl3. Reprinted with permission from ref 430. Copyright 2015 American Chemical Society.

Scheme 27. Cyclophanes I−III Exhibit Typical +N−π Interactionsa

a

Association free energies ΔG in kJ/mol.100,469,470,476,477 For cyclophane CP66, see Figure 3 and Scheme 1.

Scheme 28. (a) Rebek-Type Imide Receptors Bearing a Neutral (A) or a Positively Charged (B) Quinoline Ring. Thermodynamic Parameters for the Binding of 9-Ethyladenine (1) through H-Bonding and Stacking Interactions, Obtained in (CDCl2)2 by NMR Titrations and van’t Hoff Analysis. (b) Crystal Structure of the B·1 Complex, Which Adopts a Favorable Stacking Geometry Including Cation−π Interactiona

a

Reprinted with permission from ref 480. Copyright 2004 with permission Royal Society of Chemistry.

isoquinolinium over noncharged isoquinoline for II and III was linked to a strong enthalpic advantage (e.g., ΔΔH = 15.9 kJ/mol for II), which was partially counteracted by entropy. These hosts are discussed again in section 3.7 with respect to the influence of high-energy water release on the binding features; e.g., see Figure 66. For CP66, there are four arenes, so that the single value would be 10/4 = 2.5 kJ/mol to a first approximation. However,

the oxygen atoms in I and hydrophobic effects (section 3.7) may also influence the complexation energies. The replacement of the two p-xylene side walls of the cyclophane I (Scheme 27) by saturated cyclohexyl moieties lowered the binding of the N-methyl quinolinium guest in water as solvent by ΔΔG ∼ 5 kJ/mol. This finding suggests a relative contribution of 2.5 kJ/mol per aromatic ring toward the binding 5259


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Scheme 29. Binding Affinities Were Obtained for Several Binary Cation−Anion Mixturesa

a The strength of a single cation−π interaction was obtained by correlating ΔΔG (after subtraction of 5 kJ/mol for each salt bridge) with the number of m of phenyl rings. Outliers (open gray circles) are likely due to conformational mismatch. Reprinted with permission from ref 482. Copyright 1992 American Chemical Society.

of a cation, as compared to the contribution of the saturated ring.478 Evaluation of a large range of synthetic complexes with hosts of the type I included also sulfonium and guanidinium ions and substituted aryl parts of the host as well as, e.g., furan and thiophene units. From the comparison of binding free energy ΔG with either the neutral 3-methyl quinoline (ΔG = −25 kJ/mol) or the charged N-methyl quinuclidinium salt (ΔG = −35 kJ/ mol), it was concluded that a typical value for the cation−π interaction is about 10 kJ/mol in total.479 Taking into account that the quinuclidinium ion can interact with four to six phenyl rings, the increment for the interaction with a single aryl unit would again be on the order of 2−3 kJ/mol. The assumption of a simultaneous interaction with several phenyl rings is reasonable in view of the charge distribution, which even in simple organic ions such as tetramethylammonium resides not at the center, but at the peripheral C−H parts. Methoxy and bromo substituents in the macrocycle were found to promote conformation changes. It was emphasized that the observed affinities are the result of an interplay of hydrophobic, electrostatic, conformational, and solvation effects.479 A similar binding energy difference of ΔΔG = 2.4 kJ/mol, indicative of one cation−π interaction, is also seen in the 9ethyladenine complex with a receptor bearing alternatively a neutral or a positively charged quinoline ring (Scheme 28).480 Surprisingly, entropic and not enthalpic factors cause the higher affinity of the cationic receptor for the aromatic guest in 1,1,2,2tetrachloroethane; however, the analysis has invoked the potentially problematic van’t Hoff method and nonlinear plots. With a benzylic bisphosphonate-arginine binder, a single benzene−guanidinium interaction was reported to be worth 2.5 kJ/mol, again in line with aforementioned values.481 Similar cation−π energies emerged from the analysis of several ion pairs, which bear a different number of phenyl rings (Scheme 29).482 After subtracting 5 kJ/mol for each salt bridge present in an ion pair (cf. section 3.1), one observes a linear correlation amounting to a contribution of 1.5 kJ/mol for a single +N−π interaction. Many artificial host compounds were reported that bind cationic organic species in water, e.g., choline and acetylcholine with Ka of up to 8 × 104 M−1. A tetraphenolate resorcinarene with four negative charges at the rim (see Figure 28) binds choline with ΔG = −23 kJ/mol.314 If one subtracts 4 × 5 kJ/mol for the four salt bridges from the overall free binding energy, one obtains a reasonable value of 2 to 3 kJ/mol for each cation−π interaction pair. Sulfonated calixarenes (Scheme 30) are also strongly binding to cationic species.483,484 For instance, CX4 (see Figure 26) complexes cationic amino acids and peptides with favorable ΔH = −14 to −20 kJ/mol and small entropies of TΔS = +2 to −2 kJ/mol, as evident from calorimetric measurements.485,486

Scheme 30. Synthetic Trimethyllysine and Acetylcholine Receptor Exhibiting Cation−π Interactions

Efforts to develop mimics of the so-called “aromatic box” in enzymes for complexation of methylated lysine lead to structures such as I (Scheme 30), which binds in water trimethyllysine with 16 mM and acetylcholine with 24 mM affinity.487 Measurements with tetraalkylammonium compounds showed increasing affinity with the length of the alkyl chain, with 42 mM for Bu4N+. This and the observed solvent effects led to the conclusion that hydrophobic contributions (section 3.7) play a dominant role, and the cation−π effect is a minor contributor.488 As mentioned in section 2.4, double mutant cycles were also used to measure cation−π interactions. A cycle similar to that shown in Figure 14, in which a pyridinium unit was interacting with phenyl rings bearing substituents such as NO2, H, and NMe2, showed ΔΔG = −8 kJ/mol for the NMe2 derivative. For the p-NO2 compound, a repulsive interaction of +2 kJ/mol was deduced.190 The resulting energy value of 8 kJ/mol, however, is not necessarily reflecting the typical interaction between a single cationic center and an arene, because the pyridinium model encompasses also stacking contributions. The influence of the substituents at the arene on the cation−π strength depends on the resulting change in electron density. Fluorination of arenes is known to alter both stacking, edge-toface, and cation−π interaction. Interactions with benzene are favored, as perfluorination reverses the quadrupole of benzene, so that there is attraction instead of repulsion in parallel stacking. Conversely, fluorination on the aryl side walls of host I lead to a decreased binding of cationic guests by approximately 4 to 8 kJ/ mol.489 A uranyl-salophen receptor with substituted phenyl side arms (Figure 56) complexes tetramethylammonium chloride (TMACl) in CDCl3 with association constants of up to K = 1.7 × 104 5260


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increments (Scheme 28; see ref 482). Stronger anion−π interactions occur if the negative partial charge at arene centers is inverted by electron-withdrawing substituents, for instance by fluorine.506 Several studies highlighted below have quantified the correlation between anion binding strength and the calculated electrostatic surface potential at the arenes; for that reason, anion−π interactions could have been discussed as well in section 3.4 under polar interactions. Besides appropriately substituted phenyl rings, many electron-deficient heterocycles, such as pyridine, pyrazine, triazines, tetrazines, or cyanuric acids, bear the same signature of an electrostatic attraction with anions.503 Complexation of halides with substituted 1.3.5-triphenyl receptors shown in Figure 57 showed with the 3.5-dinitrophenyl

Figure 56. Uranyl-salophen receptor with substituted phenyl-side arms for complexation of tetramethylammonium cation, and Hammett correlation with σp constants of substituent X. Reprinted with permission from ref 490. Copyright 2012 Royal Society of Chemistry.

M−1 if the substituent is X = OCH3; other substituents such as CH3, H, Br, and NO2 led to weaker affinities.490 There is a good Hammett correlation with substituent constant σp that reflects the electron-donating influence of the substituents. Gegenions compete with complexation of cations, particularly in nonprotic solvents. Thus, the small cavity of a calix[4]arene macrocycle can complex n-BuNH3+·salts in CDCl3 with a large association constant of 2.7 × 105 M−1, only in the presence of a superweak or weakly coordinating anion such tetrakis[3,5-bis (trifluoromethyl)phenyl]borate.491 The significant contributions of cation−π interactions in proteins have been mentioned above (see also section 2.3) and have been frequently reviewed178,492−494 also, e.g., in the context of interaction with arenes103 and with respect to nucleic acids.495 We therefore mention here only some corresponding ΔG values. Based on DMC measurements with, e.g., barnase or apoflavodoxin mutants, the interactions between phenylalanine rings and protonated and nonprotonated histidine were reported to vary between 1.2 and 3.6 kJ/mol.152 In an extensive evaluation with the Protein Data Bank, the cation−π interaction motif was frequently found, one for every 77 residues of protein length, which stresses the importance of such interactions in proteins. In ligand-gated ion-channel proteins, a large number of cation−π interactions have been recently identified, with up to 16 kJ/mol in total interaction strength due to these interactions;496 the dissection of single cation−π energies in the multiple interactions within “aromatic boxes” of proteins is, however, far from straightforward. Systematic methylation of an enzyme−inhibitor alkylamino group resulted in binding changes that amount to approximately 2.8 kJ/mol per aromatic ring.497 Analyses of parameters in folding of several peptide hairpins were leading to similar energy contributions for the cation−π interaction, such as 4 ± 0.4 kJ/ mol498 or, in other cases,499 2.4 ± 0.4 kJ/mol. Hydrophobic effects also play a role, as do entropic contributions.498,499 Cation−π effects are weakened by diminishing the electron density of the π-surface, which has been demonstrated in detail also with proteins.492,493 In summary, most studies indicate a value of 2 ± 1 kJ/mol for an ammonium ion interaction with an undistorted phenyl ring. 3.6.2. Anion−π interactions. Anion−π interactions have been aptly reviewed;500−504 they are weak with unsubstituted arenes, as demonstrated early with complexes between, e.g., bisaryl compounds bearing anionic groups that were in contact with the π-moiety of electroneutral bisaryl counterparts.505 In water, the observed ΔG values were about 2 kJ/mol, which partially can also be due to stacking. Similar ΔΔG values were derived from a series of ion pairs, for which both cation and anion interactions are evaluated together with the known salt-bridge

Figure 57. Complexation of halides (as tetrabutylammonium salts) with substituted 1.3.5-triphenyl receptors. (a) Binding free energies by NMR titrations. (b) Rendering of complexes; receptor 1 engages in C−H anion interactions while receptor 2 can, for steric reasons, only adopt a weak σ binding mode with the halides. Reprinted with permission from ref 507. Copyright 2008 American Chemical Society.

substituent stronger binding with halide anions than with the 2.4dinitrophenyl substituent that can mostly interact with the acidified aryl C−H bonds.507 From the regular difference in the ΔG values with the two receptors, one can conclude that about 2 kJ/mol reflect the C−H-anion contributions. The differences between the halides, also seen in other studies with anion receptors, are in line with their Lewis basicity and electrondonating ability. Stronger binding occurs with more electron-poor arene parts, as illustrated with calixpyrroles bearing substituted arenes (Figure 58).508 With unsubstituted phenyl groups, the nitrate anion is essentially only bound by hydrogen bonds with the pyrroles, with a total −ΔG = 8.5 kJ/mol for R = C6H5 and 10 kJ/ mol for R = Me as substituent. With, e.g., the 3.5-dinitro derivative, the affinity increases to 16.5 kJ/mol, in line with the calculated electrostatic surface potential (ESP), and similar to the results with cleft complexes discussed above. The enlargement of anion−π interactions with increasing electrostatic surface potentials of the arenes was also quantified with complexes between halide anions and calix[4]pyrrole receptors bearing two substituted phenyl rings (Figure 59).509 The large contribution of hydrogen bonding of the anions with the pyrrole units was subtracted by comparison to the phenylfree systems. Both repulsive and attractive interactions between +4 and −4 kJ/mol were observed in acetonitrile solution. The major difference between the complexes is surprisingly not correlated to enthalpy but to entropy changes. In the less polar 5261


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Figure 58. (a) Nitrate association energies in phenyl-substituted calixpyrroles as a function of the electrostatic surface potential ESP in the arene. (b) Complex geometry for the most strongly nitrate-binding calixpyrrole with 3,5-dinitrophenyl substituents. Reprinted with permission from ref 508. Copyright 2013 with permission American Chemical Society.

Figure 59. Complexation of halide anions with calix[4]pyrrole receptors bearing two substituted phenyl rings; dependence of thermodynamics electrostatic surface potentials (ESP) at the aryl parts. Reprinted with permission from ref 509. Copyright 2014 American Chemical Society.

Figure 60. Simultaneous anion−π and cation−π interactions combined with ion pairing. Reprinted with permission from ref 510. Copyright 2015 American Chemical Society.

experimentally and computationally clear that the solvation shell, e.g. the hydrogen-bond count, local density, orientation, mobility of water molecules, etc., around a solute depends critically on the molecular properties of a solute (polarity, shape, size) but also on the temperature of the system.511−521 The formation of a large cavity accommodating two lipophilic particles, which requires a smaller number of solvating water molecules than their individual solvation in two smaller, separate cavities, is the origin of the hydrophobic driving force for the aggregation of nonpolar species in aqueous media. For instance, the formation of micelles, biomembranes, and aggregated structures,511,522−525 protein folding526−537 and macroscopic observations, such as the immiscibly of water and oil, are frequently explained by the reduction in solvent-accessible surface area or volume through hydrophobic aggregation.533,538 Solvophobic effects are not restricted to water.425,539−541 Experiments with a molecular balance in a large range of solvents have shown that cohesive solvent−solvent interactions can be a significant driving force for the association of apolar partners.541 The folding energies of the balance correlate well with the cohesive energy density (ced) of many solvents that were

solvent chloroform, however, enthalpic contributions were found to be much stronger than in acetonitrile. The perfluoro-substituted receptors, already presented in Scheme 22 in section 3.4, exhibit association free energies ΔG that come relatively close to those relying on hydrogen bonds (see section 3.2), and which are fairly additive if one goes from one to three binding sites, with an average value of ΔΔG = 7 kJ/ mol for a single C6F5 interaction.407 The affinities follow again the order Cl− > Br− > I− ≫ TsO−, NO3−, HSO4−, different from the order observed with hydrogen-bond-based anion complexes. Figure 60 shows a system in which anion−π and cation−π interactions can occur on the same aromatic surface, together with ion pairing.510 Such ion-pair−π interactions lead to interesting spectroscopic changes, with a solvent- and pHindependent red shift of absorption and emission of push−pull fluorophores originating in antiparallel ion-pair−π attraction to a polarized excited state. 3.7. Hydrophobic interactions

3.7.1. Hydrophobic effects for convex solutes. The structural arrangement of water molecules around solutes has always beenand remainscontroversially discussed. It is 5262


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Figure 61. (a) Hydration free energy per surface area for a spherical cavity in water as a function of the solute radius. The proportionality ΔGhydr /A ∼ R at small sizes implies ΔGhydr ∼ volume. Only for larger solutes is the macroscopic relation ΔGhydr = γA reached, implying ΔGHP = γΔA (see eq 16a,b). (b) Hydrophobic driving force per surface area for aggregation of hydrophobic particles into clusters. Modified figure: reprinted with permission from ref 511. Copyright 2005 Nature Publishing Group.

liquid−liquid transfer data resulted in higher values, const = 120−200 J/(mol Å2), than that of a gas−liquid transfer, const.= 20−100 J/(mol Å2). A free energy estimate of 1−3 kJ/mol for the hydrophobic interaction of a CH2 group with a flat surface can be made, assuming that 1/4 to 1/2 of the solvent accessible area of the CH2 group is buried in the complex. However, linear alkanes (up to 20 carbons) adopt their chain-extended, not coiled up conformation in water, implying that the ΔGHP ∼ volume relation, and not the ΔGHP ∼ surface area relation would be more appropriate.511 Experimental studies for the interaction of flat surfaces (watersoluble porphyrins) with hydrophobic or polarizable compounds showed that hydrophobic effects contribute less than 1 kJ/mol per CH2 group, whereas dispersive interactions can lead to sizable contributions (section 3.5).462 In line with this, micelle formationleading to a larger desolvation of the alkyl chainsis characterized also by only small free energies, which, even for long-chain surfactants such as hexadecyltrimethylammonium bromide (CTAB), amount only to approximately 17 kJ/mol in total (i.e., ∼ 1 kJ/mol per CH2).551 For protein complexes, the hydrophobic contributions are usually quantified by a similar equation (eq 1b), using empirically derived constants, which, however, vary significantly, from 200 to 500 J/(mol Å2).3,552 For instance, mutation of protein α-helix residues for Glu or Ala in barnase protein (see also section 2.3) gave an empirical relation of − ΔΔGfolding = 0.23 kJ/(mol Å2) ΔA + 7.7 kJ/mol.553 Transfer energies for amino acids have also been determined, but the energy values can show significant spreads. For instance, the hydration-energy differences between isoleucine and alanine lie between 0.9 and 20 kJ/mol depending on the model system and method used.437 Mutation of Ile in barnase protein to Ala reduces the protein-fold stability by about 3 kJ/mol, which may be at first attributed to the hydration energy differences of their unfolded states.531 However, computations have suggested that this difference originates primarily from noncovalent interactions in the folded state (e.g., differences in dispersion interactions and degrees of freedom), and not from differences of the hydration energies, which cast doubts over the importance of the hydrophobic effect for the folding of proteins.531 Sizeable enthalpic contribution (ΔΔH ∼ 2ΔΔG) were found for mutant studies with ubiquitin, (e.g., ΔΔH folding = 26 kJ/mol, Δ(−TΔS)folding = 13 kJ/mol) for the substitution of valine for alanine,554 in conflict with an entropic view of the hydrophobic

found to be a better descriptor than others, e.g., surface tension.540 Water has, with ced = 550 cal cm−3, by far the largest value, compared, e.g., to methanol with 209, chloroform with 85, perfluorobenzene with 69, and n-hexane with 52 cal cm−3. Solvent cohesiveness, in addition to internal pressure, plays also the decisive role for the dissolution of apolar solutes.542 Traditionally, the hydrophobic effect was correlated with the liberation of water molecules from lipophilic surfaces upon association of particles, with a resulting entropic advantage (the classical hydrophobic effect),526,543,544 or/and an enthalpic gain by materialization of more hydrogen bonds in the bulk phase (the so-called nonclassical effect).81 The latter effect is visible in the cohesion force that, for water, is much larger than for other solvents (see above); in Sinanoglu’s equation (eq 16a,b), the water−air surface tension, γ = 72 dyn/cm ≡ 434 J/(mol Å2), is multiplied with the microscopic difference in surface (ΔA) between the interacting particles before and after association to obtain a measure for the hydrophobic driving force.545,546 It should be noted that the same equation is usually applied also if classical entropic contributions are assumed to prevail, however with different constraints (see below). ΔG hp = γ ΔA

ΔG hp = const ΔA

(16a,b)

Contemporary models reconcile the conflicting interpretations; for small solutes (R < 1 nm), the water molecules in the solvent cage around the solute are optimally hydrogen-bonded but restricted in their mobility, leading to a predominately entropic “classical” hydrophobic driving force for aggregation of solutes in water with ΔGHP ∼ volume (Figure 61). For large solutes (R > 1 nm), the “non-classical” effect predominates, where ΔGHP ∼ surface area.511 Computer-aided simulations with ellipsoidal plates (length 2 nm) have suggested a similar, but smaller proportionality-constant value than γ.547 Recent aggregation studies with polymers and Raman-MCR measurements also support the solute-size-dependent model.512,548 Near the crossover point, both effects can be equally important and the interpretation is complex. Correlation of experimental alkane transfer energies with computed solvent accessible surface areas resulted in proportionality constants between 20 and 200 J/(mol Å2), depending on the reference system chosen (alkane in its own liquid or as its gas), on the calculation method for the surface area and on the consideration of volume-entropy effects.437,549,550 Use of 5263


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shell upon binding, which allows for utilizing experimentally determined hydration free energies (or transfer energies) to quantify the hydrophobic impact of the guest on binding, without having to detour to potentially troublesome solvent-accessible surface relations. (ii) The solvent cages around a rigid and wellshielding host and around its host−guest complex are structurally similar to each other, in particular for noncharged guests. Thus, these solvation effects may cancel each other in a first, approximate binding-energy analysis. (iii) The free host may contain cavity-water molecules whose release upon guest inclusion strongly contributes to the overall binding energy (“high-energy water” release; see further below). When relative binding differences of structurally similar guests with the same host are compared, then this cavity-solvation effect also cancels in the analysis if each guest displaces all, or at least the same number of, water molecules. Water molecules do not occupy small, hydrophobic cavities of hosts, because the entropic gain of filling the void of the host cannot compensate for breaking hydrogen bonds of H2O. Computations have suggested that spherical host cavities with R ≤ 1 nm are “dry”, unless there is a stabilizing H2O−cavity−wall interaction.556,557 Recent experimental data support these predictions. The perfluorinated metal−organic-framework material FMOF-1, a potent methane adsorbent, contains channels with the size of 1.2 × 0.8 nm, for which adsorption studies did not find measurable uptake of water vapor.558 However, detailed IR spectroscopy investigations confirmed the presence of a small amount of H2O, which predominately formed self-stabilizing pentameric water clusters, while no interaction with the cavity wall was detectable.559 Notably, upon coadsorption of alcohols, the water uptake increased because hydrogen bonding to the alcohol can stabilize the cavity-water molecules. In contrast, similarly wide channels (dmax 1.1 nm) in zeolite LTL are not dry but contain clusters of water molecules that can engage in Hbonding with the Si−O oxygen atoms of the channel wall.560 Nanotubes formed by nonpolar peptides contain inside water molecules in a linear wire-like arrangement.561 Besides, it was proposed that water molecules between the sheets mackinawite FeS minerals are poorly hydrogen-bonded on account of geometric constraints.562 The cavity of the small, rigid, and well-shielded macrocyclic host cucurbit[5]uril (CB5), Figure 63, is hydrophobic and too small to allow for water-cluster formation. Thus, it is likely dry, in analogy to other small, nonpolar cavities.557 The hydrophobic, H-bond donor- and acceptor-free cavity of cucurbiturils has a similarly low polarizability as that of perfluorinated groups,563,564

effect, but in line with the nonclassical hydrophobic effect. The results were interpreted in terms of loss of dispersion interactions and increase in residue mobility upon the substitution of large to small side-chain residues.554 Correlations of the free energy of complex formation/folding with the surface area according to eq 16a,b were usually not corrected for other, simultaneously occurring effects (e.g., dispersion interactions, electrostatics, entropy etc.). For instance, the comparably high proportionality constant of 430 J/(mol Å2),555 determined from aromatic stacking complexes, is certainly not purely reflecting hydrophobic binding contributions (see section 3.5). The overall hydrophobic contribution for the aggregation or folding of compounds in water depends critically on the solute sizes; if both the uncomplexed/unfolded and complexed/folded species are fully solvent-accessible, then the overlay of the individual entropic and enthalpic effects can be difficult to unravel. 3.7.2. Hydrophobic effects for concave host-cavities/ high-energy water release. For host−guest complexes, for which the guest is buried in the cavity of the host and well shielded from bulk solvent, the effects can be more readily dissected (Figure 62): (i) The guest can shed its entire solvation

Figure 62. Host−guest binding in the absence and presence of water as solvent differs by the individual hydrophobic contributions to binding. ΔGwater = ΔGintrinic + ΔGhydr(H·G) − [ΔGhydr(H) + ΔGhydr(G)]. The hydrated host may contain enthalpically frustrated cavity-water molecules, giving rise to a nonclassical hydrophobic effect for binding (high-energy water release), or the cavity can be dry; see below. Convex guests are typically surrounded by structured water molecules (“iceberg” model), whose release contributes to the classical hydrophobic driving force for binding; see section 3.7.1.

Figure 63. Small cavity hosts CB5, cryptophanes Cryp1 and Cryp2, and α-CD. While the cavity of CB5 is likely dry, both cryptophanes and α-CD (are believed to) contain cavity water. The rendering shows three water molecules in the cavity of α-CD that are partially stabilized by H-bonding with the host.26 5264


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Table 6. Results from Water-Box Simulations and Comparison to Literature Data for Water Molecules inside Molecular Host Cavities26 and Channel Materials Systema hosts with a predominately “dry” cavity

hosts with cavity water

Nb

Nexpc

bulk water pillar[5]arene tweezer FMOF-1 CB5

0.5 0.7 − −

− − low558 0) for the complex formation in cohesive solvents, overpowering other noncovalent interaction modes such as π−π stacking. Cyclophanes CP3 and CP4, obtained by dynamic combinatorial approaches (see section 2.6), differ in the size of one linker and, thus, the size of their cavity.477,606 Binding of aliphatic and aromatic guests, and of charged or not-charged guests by the cyclophanes in water shows surprising but consistent trends: The smaller CP3 binds all guests more exothermic than CP4, by about 7 kJ/mol. At the same time, the entropic contribution to binding is by a similar value less favorable for CP3 than for CP4.477,606 Size-matching arguments cannot explain the trends, given the widely different sizes of the guests (13 different were studied) and the rather high shape-flexibilities of the hosts. However, the data can be rationalized when recalling the systematic differences between the small host CB7 and the larger host CB8, which both have, in a first approximation, comparable cavity diameters to that of CP3 and CP4, respectively. It is plausible that the energetic frustration of the cavity water in CP3 is higher than in CP4, thus guest binding to CP3 is more exothermic. At the same time, the high-energy water model predicts a more unfavorable entropy for CP3-complexation, which was experimentally observed.

Other cyclophanes (e.g., CP66, Figure 67a) also contain highenergy cavity water, as shown early with MD simulations;98,607 new simulations show a low hydrogen-bond count (e.g., N = 5, m = 2.9, or Z = 3.4).26 The electron-poor tetracationic viologen-based cyclophane608 bipyCP4+ (Figure 67b) strongly complexes electron-rich aromatic molecules mediated by electrostatic attraction.434,609,610 For instance, 1,5-dihydroxynaphthalene (1,5Np) (Ka = 9 × 105 M−1), indole (7100 M−1), and catechol (3900 M−1) are strongly bound in water.447,609 A PEGylated 1,5Np derivative was found to be complexed >10 more strongly in water than in acetonitrile.435 In addition, its complexation by bipyCP in water was strongly exothermic (ΔH = −65.7 kJ/mol) with an associated large unfavorable entropic contribution (30.5 kJ/mol);611 thus, involvement of high-energy cavity-water release in the host−guest complex formation is implied. MD simulations show the presence of 3.2 water molecules inside the cavity, which on average are involved in 2.7 hydrogen bonds,447 resulting in a Z value of 2.9. The width-extended (14.6 Å × 6.9 Å)438 analogue ExBox4+ (for structure, see Scheme 25 in section 3.5) binds the 5-MeO-indole derivative melatonin in water similarly strongly (Ka = 1 × 105 M−1) but with very different enthalpic (−30.0 kJ/mol) and entropic contributions (1.3 kJ/ mol).612 Similar thermodynamic values are found for complexation of aromatic polycyclic hydrocarbons in organic solvents.438,613 Generally, cavity water in short cavities with large openings can be stabilized by cluster formation and H-bonding with the bulk. For pillar[5]arene,366,368 a small-cavity host based on substituted hydroquinones, MD simulations suggested that the cavity contains on average no or very few water molecules, similar to the finding for the small clip (Table 6). It is therefore unlikely that there is a significant complexation driving force from highenergy water. Most reported examples are limited to the binding 5268


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Figure 69. Water-soluble clip and tweezers.626,627 (a) Cavity water inside a noncharged clip analogue.26 (b) The cavity of a structurally similar tweezer is predominately “dry”. (c) Crystal structure of acyclic glycouril tweezer. Modified figure: reprinted with permission from ref 627. Copyright 2012 Macmillan Publishers Limited.

through H2O···π interactions with the cage. It was suggested that guest binding to the host would be favored by entropy resulting from “melting of the ice”;589 nevertheless, the liberation of water molecules from the cage contributes energetically much less to guest binding than high-energy cavity water release, e.g., from cucurbiturils. Simple resorcinarenes, which are structurally also closely related to calixarenes, possess an even flatter cavity;621 thus, highenergy water release contributions to binding cannot be expected. Better shielded, deep, water-soluble cavitands (e.g., see Figure 73) were prepared in order to exploit the hydrophobic effect for binding more efficiently. Indeed, stronger guest binding in water was observed with those. However, compared to the cucurbit[n]uril host with a similar sized cavity, also the cavitands fall short in binding affinity,622 with some noteworthy exceptions,623 in particular for the recognition of charged guests by charged cavitands.624 Nevertheless, the high-energy water release effect for cavitands is smaller than for CBn, as becomes clear from the comparison of the binding enthalpies, ΔH = −36 kJ/mol for the cavitand-adamantane host−guest pair625 shown in Figure 73, and ca. − 80 kJ/mol for adamantane derivatives with CB7 (see Figure 64). The H-bond acceptor in the cavity wall of resorcinol-based cavitands can stabilize cavity-water molecules, so that contributions from high-energy water release are reduced. Computationally, on average 4.3 cavity-water molecules were found with a hydrogen-bond count of 3.15, given a slightly different water model.585 This means that the Z-value for the cavitand is Zmax = 4.3·(4.00−3.15) = 3.7 at its maximum, which is much lower than those of CB6, CB7, and CB8 (see Table 6). A further cavity-water stabilization can be expected through the aromatic panels of the host, as was discussed above. Large hydrophobic binding contributions can also occur in the absence of closed cavities, as can be seen for some molecular clips and tweezers.30,419,626,628−631 For instance, the affinity of a negatively charged clip (Figure 69a) for the cationic aromatic guest N-methyl nicotinamide (NMNA) is higher in water (K = 9 × 104 M−1) than in methanol (1700 M−1),626 although the electrostatic attraction between oppositely charged species is weaker in the more polar medium. For NAD+ as a guest (K = 8800 M−1), ΔH = −30.5 kJ/mol and −TΔS = 8.0 kJ/mol were obtained in water,30 which is consistent with the high-energy water release model. The Z-value of 3.6 for a noncharged clip is comparable to that of cyclodextrins. In contrast, MD simulations

of positively charged or electron-deficient guests in organic solvents through electrostatic interaction (see also section 3.4).369,370 In fact, binding constants for both charged and noncharged guests were found to decrease with increasing solvent polarity.372,615 Simple calix[4]arenes are not well suited for shielding the cavity water from hydrogen bonding with the bulk because their shallow “bowl” is exposed to the solvent (Figure 68a). The Z value of the simplest calix[4]arene unit is very small (Table 6), excluding significant high-energy water release effects on binding. Potential guests also do not benefit from a “dry cavity”. Indeed, host−guest complexes with small lipophilic guests are almost exclusively reported for solid calixarene derivatives that bind gaseous small molecules such as CH4, CO2, CF3Br, C2F6, CF4, etc.616 through dispersive forces. The largest binding constants observed for neutral guest molecules reach only 103 M−1.617 Binding of small neutral molecules such as alcohols with this host have afforded much lower Ka values, CB8·MV·indole, no matter which ionization conditions were chosen.649 This discrepancy was reconciled by noting that the electron-richness of the second guests follows the order 2,6-Np > 2-Np > indole (which explains the gas phase stabilities), but the hydrophobicity of the guests follows the trend indole > 2-Np ≫ 2,6-Np, as can be judged by the computed hydration free energies650−652 (ΔGhydr) of = −19.6, − 26.0, and −43.9 kJ/mol, respectively.649 The apparent coinciding stabilities of the ternary complexes in solution are therefore the result of two opposing effects: the direct noncovalent host−guest interactions and the hydrophobicity of the guests. The binding free energies in solution and relative gas-phase stabilities of the ternary complexes relative to 1,3,5-trihydroxybenzene (THB) were determined for a large range of second guests with CB8·MV as the host.649 No direct correlation between the gas-phase and

solution phase stability was found (Figure 72). For instance, THB and 2,6-Np show similar intensities of their ternary complexes in ESI-MS experiments; however, their binding free energy in solution differs by almost 20 kJ/mol. However, if the data are corrected for the hydrophobicity of the guests (i.e., by its ΔGhydr value), a satisfactory correlation (R2 = 0.89) between the predicted gas-phase stability (ΔGwater + ΔGhydr) and the measured logarithmic complex-intensity ratios is found. For complexes of the host CB7 with aromatic amino acids (Trp, Phe, Tyr, His) and the positively charged Lys and Arg, analogous discrepancies between solution and gas-phase behavior were observed.653 Specifically, the binding strength follows the series Phe > Tyr > Trp > Lys ≫ Arg, His in water at pH 7, and Phe > Lys ≈ Tyr ≈ Arg > Trp > His at pH 2. Conversely, the stability of the CB7·(amino acid) complexes in the gas phase, probed by their relative abundance and by collision-induced dissociation experiments, yielded a lower stability of the CB7·Phe complex than that of, for instance, the CB7·His complex. The trends were rationalized by the solvation energy differences, i.e., the hydrophobicity, of the amino acids.653 These results for structurally simple and well-defined supramolecular complexes highlight that ESI-MS experiments, albeit frequently tested,654−657 should also be used with caution for the screening of protein−ligand binding affinitiesunless the solvation energies of the ligands are taken into account. Similar conclusions were made for comparative stability studies of protein−ligand complexes under ESI-MS conditions and in solution.658 3.7.4. Hydrophobic effects on account of kosmotropic and chaotropic solutes. The impact of a hydration shell around (mostly but not exclusively) ionic guest molecules on protein folding or the host−guest complexation has long been known.659−661 Originally, anions and cations were grouped according to their effect on salting-out or salting-in proteins (Hofmeister series),662 but the implications were later found to be more general.663,664 Kosmotropic anions (e.g., fluoride, sulfate) are thought to “increase water structure“ and, thus, to emphasize the classical hydrophobic effect, while chaotropic anions (e.g. iodide, thiocyanate, perchlorate) are thought to “decrease water structure“ and, thus, to favor a nonclassical hydrophobic driving force for complexation.665 These effects can be seen for the host−guest complexes of “octaacid” (Octa) with the hydrophobic guest adamantane carboxylic acid (ADC; Figure 62).625 Addition of kosmotropic anions (e.g., fluoride) to the aqueous solution raised the complexation free energy for the 5272


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Figure 74. (a) Chemical representation of cylocextrins (CD) and of dianionic borate clusters. (b) Crystal structure of a 2:1 complex of γ-CD with B12Br122−. (c) Binding constants for γ-CD complexes with borate clusters. Reprinted with permission from ref 670. Coyright 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Figure 75. Water-soluble bambus[6]uril BU6 and crystal structure of the 1:1 BU6−chloride complex (R = -CH2C6H5).674 Similar complex geometries were crystallographically observed for other BU derivatives.672 Reprinted with permission from refs 674 and 675. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 2015. (b) Crystal struture of BU6 (R = −CH2C6H5) showing a cavity-water molecule that is H-bonded to two benzoate anions residing at the portals of the host. Reprinted with permission from ref 673. The Royal Society of Chemistry. (c) Water-soluble biotin[6]uril and crystal structure of its 1:1 complex with iodide.677 (d) Crystal structure of biotin[6]uril with two cavity-water molecules.587 Reprinted with permission from refs 587 and 677. Copyright 2015 and 2014 The Royal Society of Chemistry.

Octa·ADC by about 2 kJ/mol, while chaotropic anions (e.g., perchlorate) more strongly decreased ΔG by about 6 kJ/mol. However, the comparably strong decrease in ΔG upon addition of perchlorate is not only a Hofmeister type effect on the water structure, but also contains contributions of the competitive binding of the anion (Octa·ClO4−: Ka = 95 M−1).625

Through recent extension of the analysis by the same authors, there is now evidence that the Hofmeister effect observed for their Octa host is predominately (up to 90% at below 150 mM salt concentration) related to the direct interaction of anions with the host cavity and of the counter cations with the exterior carboxylates, while at higher salt concentrations the interactions 5273


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Figure 76. Simplified structure of a neutral bis(cyclopeptide) receptor for sulfate and ioide and 3D rendering of its 1:1 complex with iodide. Reprinted with permission from ref 679. Copyright 2014 The Royal Society of Chemistry.

kosmotropic and chaotropic desolvation effects on anion binding. Preorganization effects of the host−anion complexes are rather similar for each halide, as can be judged from the almost uniform − TΔS values for BU6-anion binding in chloroform; 0.9, 5.8, 5.6, and 5.6 for F−, Cl−, Br−, and I−, respectively.676 Final conclusive evidence for the involvement of high-energy water release in the binding of anions by BU6 in water comes from comparison of the aforementioned ΔH values in water to that obtained in the poorly anion-stabilizing solvent chloroform; e.g., − 56.0 and −63.9 kJ/mol for Br− and I−, respectively.676 Findings for the structural closely related biotin[6]uril (Figure 75c)587,677 resemble the BU6 binding features; halogen anions are bound in water by biotin[6]uril with selectivities following along the Hofmeister series (Cl < Br < I). The binding of all anions tested is strongly exothermic, e.g. Cl− (−30.7), Br− (−37.5), and I− (−42.8 kJ/mol), and entropically unfavorable. However, unlike for BU6, the latter does not differ markedly for the halides (−TΔS = 22 ± 1 kJ/mol).587 Two cavity-water molecules that are hydrogen-bonded to each other were observed by X-ray diffraction (Figure 75d).587 Their individual H-bond count is low; the water molecules are high in energy. Neutral bis(cyclopeptide) receptors (Figure 76) with multiple N−H hydrogen-bond donors were shown to bind anions in water solvent mixtures, e.g. Ka = 5 × 103 M−1 for sulfate and Ka = 9 × 103 M−1 for iodide in water/methanol (95:5).678,679 In complete contrast to the behavior of the BU6 host, anion binding for the bis(cyclopeptide) receptor becomes significantly less exothermic with a high water content, (e.g., ΔH(SO42−) = −11.7 kJ/mol in 30% water, +4.1 kJ/mol in 95% water; ΔH (I−) = −9.8 kJ/mol in 30% water, −6.6 kJ/mol in 95% water). The entropic contribution to binding is strongly favorable, −TΔS = −25.2 kJ/ mol for SO42− and 16.0 kJ/mol for I− in 95% water.679 The relative trend between sulfate and iodide fully agrees with the expectation for the binding of kosmotropic and chaotropic anions. It is noteworthy that anion binding to the peptidic receptors does not likely benefit from high-energy water release, because of the flexible structure and multiple H-bonding donor (N−H) and acceptor (CO and sp2-N) units present in the host, all of which will assist to energetically stabilize potential cavity water molecules. The receptors rather exploit the preorganization effect, dispersion (for iodide), and the classical, entropy-driven hydrophobic effect for binding. CBn macrocycles form stronger complexes with positively charged than with noncharged guests, giving binding increments of ΔΔG = 13−20 kJ/mol per positive charge, which is nearly exclusively due to entropy and not enthalpy, reminiscent of ion pairing (section 3, section 1). The liberation of solvent molecules from the positively charged moiety of the guest upon binding is a

of added cations with the anionic guests (e.g., ACD) may also play a role.666 The studies with well-defined and structurally rather simple systems expose the persisting difficulties in understanding the hydrophobic effect, specifically the influence of salts on the water structure. A water-structure centered rationale was also used to explain the salting-out and salting-in effects of salt addition to protein solutions, but other explanations, e.g. specific interactions between the salts and the solutes surface, were also put forward.661,663,664,667 It is noteworthy that when the “waterstructure-maker” or “breaker” acts itself as the guest for the host, then the opposite trends are observed. For instance, several cyclodextrins display higher affinities for the chaotropic ClO4− than for the kosmotropic HPO42−;668−671 the higher dehydration energy for the double-charged HPO42− compared to the monoanion ClO4− can readily explain this trend. In addition, dianionic borate clusters were recently reported to show astonishingly high binding constants with γ-cyclodextrin (Figure 74), which was rationalized by a “super-chaotropic” behavior and the energetically unfavorable water solvation shell around the anions.670 Indeed, the binding of the borate clusters to γ-CD is characterized by a larger enthalpic driving force for complexation than previously observed for that host, which was counterbalanced by a higher entropic cost. Release of poorly hydrogenbonded and disordered water molecules from the surface of the chaotropic guests upon binding can explain these trends. As shown in section 3.2, strong anion binding in water by noncharged macrocycles has also been achieved by hydrogenbonding, via N−H or C−H donors, but optionally, high-energy water release contributes here: For instance, the recently discovered bambus[6]uril (BU6; see Figure 75) shows remarkably high binding affinities for halogen anions (F− to I−) and perchlorate, both in organic solvents (e.g., Ka = 2 × 1010 M−1 for iodide) and in water (e.g., Ka = 2 × 106 M−1 for iodide).672−676 The complexation is always strongly exothermic and entropically unfavorable, even for the binding of kosmotropic fluoride in water (ΔH = −18.5 kJ/mol and − TΔS = 12 kJ/mol).675 This observation cannot be explained by C−H···F− bonding or dispersive interactions alone, but neatly fits the high-energy water release thermodynamic signature. Structural evidence comes from X-ray diffraction; a single cavitywater molecule that is hydrogen-bonded (m = 2) to two benzoate or tosylate anions located at the portal of the host was reported (Figure 75b).673 Binding enthalpies for BU6-anion binding in water strongly increase in magnitude along the series F− (−18.5), Cl− (−45.4), Br− (−68.0), to I− (−81.0 kJ/mol), while at the same time the entropic cost also drastically increases, (12.0, 30.3, 41.8, to 47.5 kJ/mol).675 The trends in the thermodynamic binding parameters fully agree with the above-discussed 5274


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Scheme 31. Cooperativity in Ditopic Receptorsa

a

See text. Representative binding cooperativity values are given.

nation of transferable X···Y interaction increments (e.g., for Hbonding, halogen-bonding, dispersive interactions, etc.) can be complicated or obscured by the cavity-water effect.

possible explanation. However, methylated ammonium species, CH3NH3+ and (CH3)4N+, are known water-structure breakers (chaotrops);680 thus, the situation is more complex. In addition, the charged groups on the CB binding guests rest outside the cavity and stay in contact with the bulk solvent (see Figure 64b). The observed entropic advantage of binding charged guests may be related to the unique properties of the CBn portals, which were shown to create a more polar microenvironment than that of bulk water.681 In contrast, when the charged group is buried in the CB6 cavity, thus fully shedding its water shell, there is a dominating enthalpic binding contribution, as can be seen by comparing the CB6-binding thermodynamic of the guests + NH3(CH2CH2CH2)3NH2+(CH2)4NH3+ (ΔH = −35.0 kJ/ mol, TΔS = −14.2 kJ/mol) and NH3(CH2CH2CH2)3CH2(CH2)4NH3+ (ΔH = −25.5 kJ/mol, TΔS = −8.9 kJ/mol).595 Displacement of water molecules from protein-binding pockets by a ligand is an important contributor for the protein−ligand binding process136,137,139,140,170,187,682−686 and may even overpower the energetic contribution due to the direct noncovalent interactions between the protein and ligand, which are described by the lock-and-key principle. The situation is generally very complex because some water molecules may be strongly bound by polar amino acid side chains while others are readily displaced (high-energy water). Some water molecules may remain inside the binding pocket in proximity to certain ligands, while being displaced by others. In addition, water molecules can serve as bridge or “glue” between donor and acceptor and thus stabilize a structure.184 Because of the complexity of the systems, the energy contribution of cavitywater release from proteins cannot be accurately experimentally determined to date. The reader is referred to some recent, excellent reviews on this topic.13,138,186 Likewise, the determi-

3.8. Cooperativity in supramolecular complexes

3.8.1. Cooperativity in host−guest complexes. Cooperative binding means that the occupation of one binding site influences another site, either enhancing or weakening the affinity (positive or negative cooperativity, respectively).160,687−689 Although semantically tempting, cooperativity should not be confused with simultaneous association at several sites, which is the basis of the chelate or multivalency effect, and is characterized by additive binding contributions. Cooperativity can, but must not be the result of conformational change induced by occupation of one binding site in the form of allosteric systems;690−692 one ligand (or effector) can also influence the binding at another site by, e.g., electrostatic effects. Such a behavior is seen in many ditopic synthetic receptors,693 which have been developed often with the aim of a larger affinity, or positive cooperativity, and of selectivity for, e.g., specific ion pairs.694 Receptors that offer, e.g., one binding site for cations and another one for anions can bind ion pairs, by which the electrostatic attraction between the ions will enhance the affinity, in particular if the ions are close enough to form contact ion pairs.695,696 This is illustrated with ditopic hosts in Scheme 31, which provide binding sites such as ethylene glycol units or crown ether elements for metal binding, and, e.g., ureas for anion binding.697 The metal free host A binds, e.g., bromide in CDCl3/CD3CN (2:1) with only K = 20 M−1, but in the presence of Na+, the constant increases to 620 M−1.696 With the crown ether derivative B, association constants of chloride in DMSO/ MeCN (3:1) increase from K = 50 M−1 (metal free host) again by 5275


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Scheme 32. Cyclopeptide-Related Receptors Exhibiting Cooperativity between the Binding of Anions and Cations

order of magnitude to K = 470 M−1 in the presence of Na+. However, for bromide, only a small increase from K = 9 M−1 to K = 27 M−1 was observed in the presence of Na+.698 Host C represents a case for binding of ions in a rather large distance, and displays even a solvent-dependent cooperativity:699 Cooperative binding of fluoride together with cesium occurs in CDCl3/ CD3OD (9:1), whereas, in MeCN, no fluoride was bound, likely due to the stronger solvation of fluoride ions in acetonitrile. The system D shows in an intriguing way both positive and negative cooperativity:700 the binding of chloride, benzoate, and dihydrogen phosphate anions to the amide groups was in CD3CN/DMSO (1:1) enhanced by a factor of up to ten in the presence of potassium ions. In contrast, the smaller sodium ions occupy the two crown ether moieties in a 1:1 manner, and thus prevent the conformational change favoring anion binding, which is brought about only by the larger potassium ion. From the association constant increase by a factor of 50 in CDCl3/ CD3CN, the free energy by electrostatic attraction between the cation and anion in complex with A can be estimated to amount to 9.5 kJ/mol. For D, measured in CD3CN/DMSO, the factor is 10, corresponding to 5.5 kJ/mol. Other examples of positive cooperativity, in which also conformational changes play a role, involve cyclopeptides such as those displayed in Scheme 32.701,702 With host A, the association constant with BuNMe3X salts was in chloroform K = 300 M−1 with iodide (X = I), but 104 times larger with tosylate (X = OTs) as the anion. This was explained by a conformational change of the host structure induced by tosylate that binds more strongly than iodide. The encapsulated tosylate then stabilized the binding of the BuNMe3+ cation by electrostatic cation−anion attraction. The host B complexes ammonium iodides as their ion pair in chloroform with large affinities, e.g., N-methylquinuclidinium iodide with K = 8.3 × 104 M−1.703 Structural studies with NMR and X-ray diffraction indicate that cation−π interactions also contribute significantly to the association. A very large cooperativity was seen with host C,704 with +H3NCH(Bn)CO2Me as the cation and nitrate as anion; a 257-fold increase was observed to K = 1.8 × 104 M−1. Conversely, tetraalkylammonium salts bind weakly due to the steric hindrance of the tetraalkyl residue, e.g., K = 70 M−1 with nitrate as the anion. Large allosteric effects are seen with receptors, for which an open conformation is closed by an effector, and binding of a second ligand occurs only in the closed form. Conformational coupling in synthetic receptors such as those in Scheme 33 can be much stronger than in proteins that are more flexible. In other words, higher Krel values, that are the ratio of association constants in the presence and absence of the effector, are reached. Such allosteric systems can work as logical AND gates. In receptors such as A,705 B,706 C,707 and D708 (Scheme 33), the

Scheme 33. Cooperativity with Allosteric Ditopic Receptor Complexes (see text)

binding of the second ligand is, in the absence of the effector, often unmeasurably small, which means that the binding of the other ligand alone is not strong enough to overcome the enthalpic strain and entropic cost to close the cavity. This cost for A can be compared to the association constants in structurally related host compounds with covalently closed cavities, such as CP66 in Figure 3. This host binds the fluorescent dye dansylamide with ΔG = 4.7 kJ/mol,709 a value which may well reflect the cavity closure cost.705 In comparison, the coordination energy of metal ions such as Zn2+ with ethylene diamine is by far large enough to compensate for the cost of the conformation change of the host. The same energetic arguments hold for complex B, in which contraction of the macrocycle by coordination with zinc ions leads by stacking to binding of dansylamide, with a large cooperativity value of Krel > 100. The capsule C presents a case of positive allosteric cooperativity in the presence of Li+ ions, and negative cooperativity with Na+;707 in the absence of metal ions the host includes [60]fullerene with K = 39 M−1. By addition of Li+, the association constant increased to K = 2.1 × 103 M−1, so that Krelpos = 54. In contrast, addition of Na+ leads to the absence of a detectable fullerene binding, so that Krelneg < 10. The difference was ascribed to conformational changes of the host induced by the metal ion binding. In complex D,708 binding of chloride and 5276


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Scheme 34. Allosteric Cooperativity in Cyclophane−Ferrocene Complexes through Host−preorganization by PdCl2 Complexation

Figure 77. Macrocyclic receptor relying on C−H bonds with the indole moiety of tryptophan, showing enhanced affinity and enantioselectivity in the presence of an intramolecular hydrogen bond with a phenolic OH group. Reprinted with permission from ref 711. Copyright 2011 Wiley VCH.

Figure 78. (a) Cooperatively enhanced receptor CER with steroidal arms, the parent receptor R, and tricationic guest G3+. (b) Hydrophobic association between the lipophilic arms of CER preorganizes the CER for binding of guest G3+. Reprinted with permission from ref 715. Copyright 2015 American Chemical Society.

to a limitation in dynamics and therefore can decrease the entropy cost of complex formation.712 A reinforced molecular recognition is thus possible for guest binding by noncovalent interactions within the receptor, which materialize only in the presence of a guest as effector molecule.713 The receptor in Figure 77, which exploits the formation of C−H hydrogen bonds to the indole moiety of tryptophan (see section 3.2), exhibits a large difference in affinity and enantioselectivity depending on the presence or absence of an intrareceptor hydrogen bond with a phenolic OH group at the periphery. If the hydrogen bond is removed by methylation of the OH group, the association constant drops by a factor of 12, and the enantioselectivity KD/KL by a factor of 6.3.711 Within a family of not preorganized hosts,

bromide anions at the amides is induced by complexation with cesium ions, which closes the conformation by interaction with the crown ether units. A similar type of positive allosteric cooperativity due to conformational changes was observed for the cyclophanes H1 and H2, binding ferrocene (FC) in acetonitrile (Scheme 34).710 While host H1 showed an affinity of 36 M−1, the more rigidified H2 had an affinity of 60 M−1. Crystal structures were utilized to confirm the allosteric host-preorganization through PdCl2 complexation. A special type of positive cooperativity that is frequently used in biopolymers but until now only occasionally in synthetic complexes relies on activation of noncovalent bonds within receptor parts upon binding of a guest compound. This also leads 5277


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Figure 79. (a) Cooperative binding of fluorinated aliphatic guests to Fujita’s cage in water. (b) Crystal structure for a 4:1 inclusion of C5H3F7. Modified figure: reprinted with permission from ref 716. Copyright 2014 American Chemical Society.

Figure 80. Cooperative binding of guest to the host cucurbit[8]uril, resulting in 2:1 homoternary complexes in water; see text. The 1:1 CB8·G complex is energetically destabilized by residual, energetically frustrated cavity water.447

surely also operate. As was discussed in section 3.7, water molecules in Fujita’s cage form an ice-like cluster that is energetically stable. If now only one, two, or three guests bind at a time, then the residual cavity-water molecules are high in energy because their hydrogen-bonding opportunities are largely reduced. Full solvent displacement upon simultaneous binding of four fluorinated guests is thus energetically preferred and cooperative binding is observed. Analogous findings were made for the stepwise 2:1 complexation of aromatic molecules by the large macrocycle CB8. Often, it is difficult dissect the stepwise binding constants Ka(1) and Ka(2);719 nevertheless, for a positively charged anthracene guest AntNMe3 (Figure 80), the step-wise binding constants resulted as lg Ka(1) ∼ 4 and lg Ka(2) ∼ 7. Thus, Krelpos ∼ 100−1000 (ΔΔG = 11−17 kJ/mol) could be obtained with good confidence.720 Spectroscopic findings underline this; formation of the homoternary CB8·(AntNMe3)2 complex can be selectively monitored by the emerging excimer emission of the closely arranged anthracene moieties. Indeed, saturation of the excimer emission occurs near 0.5 equiv of CB8, verifying that predominately the homoternary 1:2 and only very little of the 1:1 CB8·AntNMe3 intermediate is formed.720 Similar findings were made for other dyes, e.g. for cationic acridizinium dyes,721 and for the “famous”, dual-emitting, neutral dye p-dimethylaminobenzonitrile (DMAB), that showed the hitherto elusive excimer emission as its 1:2 CB8 complex (Figure 80).722 Similarly, viologen-radical cations (Figure 80) were shown to be 80% dimerized in the presence of 0.5 equiv of CB8, while, in the absence of the host, the monomer was predominant (>95%).723 High cooperativities are implied in these systems. They are at least in part due to the hydrophobic effect, as is clear from homoternary CB8 complexes that show lower or no cooperativity, but for which the individual enthalpic and entropic binding contributions could be obtained.447,719,724−726 It is generally found that the second binding step is much more enthalpically favored, ΔH(2) < ΔH(1), while entropically more disfavored,

the largest affinity and also enantioselectivity was observed if there were many folded conformations.714 Figure 78 illustrates the principle of reinforced binding by noncovalent interactions within the receptor with a recently described artificial receptor CER, which bears anionic binding groups attached at the end of cholic acid arms.715 Upon ion pairing of the carboxylate termini with 1,3,5-tris(amino methyl) benzene as guest, the lipophilic steroid arms fold together, mediated by hydrophobic forces, and support in this way the saltbridge formation. The association constant is K = 138 M−1 in water, in comparison to only 24 M−1 with a parent receptor R, which lacks the interacting steroidal arms. The complexation with the steroidal arms was entropically driven, with − TΔS = −70 kJ/mol, in line with hydrophobic and ion-pairing contributions, while the parent host exhibits a large favorable enthalpy of ΔH = −144 kJ/mol with an adverse entropic term of −TΔS = 125 kJ/mol. The bis(cyclopeptide) receptors discussed in section 3.7 also exhibit enforced complexations by hydrophobic interactions within the receptor that do not directly involve the guest.678 Cooperative binding of fluorinated aliphatic and aromatic species in “Fujita’s” cage (see Figure 68 in section 3.7) was observed in water, where titration experiments with CF3CH(OH)CF3 showed a binding stoichiometry of 4:1 guest−host and yielded a Hill coefficient of 3.2 (Figure 79),716 indicating strong cooperativity.717 For comparison, oxygen binding by hemoglobin shows a Hill coefficient of 1.7 to 3.2.718 The reported apparent association constant is K = 130 M−1 for CF3CH(OH)CF3. Crystallographic analysis confirmed the 4:1 binding stoichiometry for the similarly sized fluorinated cyclopentane (C5H3F7), Figure 79b. Noteworthy, the less hydrophobic CH groups point toward the opening of the cage, which helps the fluorine residues both to pack closely and to minimize the unfavorable exposure of the fluorine groups to water. The cooperativity was explained by the “fluorophilic interaction” as the driving force for binding;716 however, hydrophobic forces 5278


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Usually, the inverse, σ = Krel−1, is used, but we report here Krel for better comparison to aforementioned examples of cooperativity in supramolecular complexes. Cooperatively aggregating monomers contain usually hydrogen-bonding motifs.729,730,732,741−743 For those, K2 is usually smaller than K, because H-bond donors and acceptors of two monomers are spatially oriented in the nucleation process, which is energetically costly. Subsequent monomer addition to the preorganized nucleus is then energetically more favorable.733 For instance, polymerization of disk-like monomers (1; see Scheme 35) yielded Krel ∼ 300.743 Similarly, Krel values were also reported for the aggregation of some bis-urea monomers.732 The more general model to assess cooperative supramolecular aggregation is the thermally activated self-assembly model,729,734 which is equivalent to the K2−K model for strongly cooperative systems.730 This analysis yields the dimensionless activation constant Ka = σ = Krel−1, the elongation enthalpy ΔHelong, and the polymerization temperature Tp, below which aggregation can occur (i.e., ΔHelong = TpΔS). For monomer 1 (Scheme 35), a large value of ΔHelong = −182 kJ/mol accompanied by sizable unfavorable entropic contributions, ΔSelong = −437 J/(K mol), was obtained in methylcyclohexane (MCH) as the solvent, which corresponds to ΔGelong = −40 kJ/ mol at 293 K.743 For the smaller monomer (2; see Scheme 35), which also contains three H-bond acceptor and -donor units, the elongation enthalpies (−86 kJ/mol) and entropy (−165 J/(K mol)) were much smaller, but ΔGelong = −39 kJ/mol is very similar to that of monomer 1,743 indicating strong enthalpy− entropy compensation. The cooperativity is 10× higher for monomer 1 (Krel = 300) than for 2 (Krel = 30). For the 1,3,5-trisamido-benzenes monomer 3a(Scheme 35), ΔHelong = −54 kJ/mol and ΔSelong = −159 J/(K mol) are found in MCH, which corresponds to a comparably low ΔGelong value of −8 kJ/mol at 293 K.741 Nevertheless, the cooperativity Krel = 4500 is markedly higher than for 1 and 2. Comparison of ΔGelong values for supramolecular aggregates of structurally related monomers could provide access to binding increments, e.g., if the monomers differ in the number of hydrogen-bonding or π−π

−TΔS(2) > −TΔS(1).447 Both the ΔΔH values and Δ(−TΔS) reached up to 50 kJ/mol,724 which cannot be explained by π−π stacking effects alone. In fact, cavity-water molecules in the restricted environment of the 1:1 binary complexes are much higher in energy than those inside the larger CB8 cavity (Figure 80),447 for which some self-stabilization through cluster formation occurs, resembling the above given reasoning for cooperative binding behavior in Fujita’s cage. 3.8.2. Cooperativity in self-assembled polymers. Assembly of supramolecular oligomers and polymers can show cooperative behavior that often proceeds through a nucleation− elongation mechanism (Figure 81).239,727−735 Previously, such

Figure 81. Aggregation can occur via a cooperative nucleation− elongation mechanism, or via an isodesmic mechanism. Drawing style adopted from ref 734.

systems were analyzed with Scatchard736 or Hill plots,718,737−739 but it was suggested that this method may not be adequate for describing systems with intra- and intermolecular interactions.740 One popular model for cooperative supramolecular polymerization is the “K2−K” model, for which the ratio of the dimerization constant (K2, describing the nucleation process) and the elongation constant K (assumed to be independent of the degree of polymerization for n ≥ 3) is taken as a measure for the cooperativity:727,728

K rel = K /K 2

(17)

Scheme 35. Monomers That Form Supramolecular Aggregates

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Figure 82. Self-assembly of a luminescent platinum complex has led to different supramolecular aggregates, kinetically trapped states, and the thermodynamic state, which all showed pronounced differences in their emission colors. Reprinted with permission from ref 745. Copyright 2016 Macmillan Publishers Limited.

kJ/mol was made for neat water. The associated enthalpic and entropic values are even more strongly affected by the solvent composition: ΔH = −80 kJ/mol to −144 kJ/mol, and from −TΔS = 49 to 101 kJ/mol, going from 40:60 to 30:70 THF/ water ratio.744 The relative trend is in line with the enthalpic, nonclassical hydrophobic effect for aggregation of large solutes in water (see section 3.7). It is noteworthy that cooperative behavior was not observed for monomer 6b, possessing a hydrocarbon tail, and also its aggregation tendency is lower (e.g., ΔG = −33 kJ/mol and ΔH = −133 kJ/mol, for 30:70 THF/ water).744 It was attempted to explain the estimated binding energy difference between 6a and 6b in neat water, ΔΔG = 18 ± 6 kJ/mol, by two surface-energy relationships (ΔGhp = const ΔA; see section 3.7), but the analysis remained somewhat inconclusive. Nevertheless, involvement of special “fluorophilic” interactions was disregarded, and the differences were attributed to the hydrophobic effect. It is worth pointing out again that the hydrophobic/solvophobic effect is solute-size dependent (see Figure 61 in section 3.7) and thus can lead to a relative destabilization of small aggregates of monomers (2 < Nnucleus < N) in comparison to that of the monomer (N = 1) or elongated stacks (N > Nnucleus); for monomer 6a, Nnucleus = 7 at 30:70 THF:water ratio.744 Consequently, a nucleation-elongation growth mechanism and cooperativity can be found for aggregation in aqueous media, even for monomers that form nondirectional intermolecular interactions. Recently, it has been demonstrated how the nucleation− aggregation process can be monitored in real time, and how kinetically trapped states can be visually observed, when taking self-aggregating luminescent platinum complexes as the monomers (Figure 82).745 The nucleation and elongation enthalpies were reported to be ΔHnucl = −18 kJ/mol and ΔHelong = −103 kJ/mol, respectively, in 60:40 dioxane water, which is comparable to that of monomers 1 and 2 shown in Scheme 35. Most importantly, this study demonstrated that kinetically trapped states with markedly different intermolecular arrangements may be visited during the dynamic self-aggregation

stacking units. However, subtle structural changes can result in significant energetic changes, as can be seen by comparing 3a and 3b, that differ mainly in the position of one methyl group in one of the three side chains.741 ΔΔGelong = 1 kJ/mol and ΔΔHelong = 3 kJ/mol in MCH at 293 K were measured, favoring the aggregation of 3a. (The cooperativities of 3a and 3b differ even by a factor of >10.)741 Similar complications have been discussed for the use of chemical DMC methods; see section 2.4, where slightly different binding geometries may result in apparent binding increments. In isooctane, the elongation enthalpy differed even by ΔΔHelong = 7 kJ/mol for the isomeric 3a and 3b; nevertheless, enthalpy-energy compensation resulted in ΔΔGelong ≤ 1 kJ/mol for all solvents tested.741 In other words, cooperatively binding monomers may be suitable systems for determining (even small) binding free energy increments of noncovalent interactions. Importantly, in the absence of hydrogen-bonding motifs, an isodesmic (i.e., K2 = K3 = Kn) and not a cooperative polymerization behavior was observed in organic solvents, e.g., for monomer 4, ΔG = −34 kJ/mol at 293 K in MCH.730 Intuitively, π−π stacking or dispersive interactions do not require significant monomer reorganization. On the other hand, the structurally related monomer 5 (Scheme 35), which contains hydrogen-bonding motifs, shows highly cooperative polymerization behavior (Krel = 104), even though its free energy for aggregation is, with ΔG = −39 kJ/mol, similar.730 Cooperativity is observed when the dimers/short oligomers are higher in energy than the larger aggregates; thus, the dimers/short oligomers act as a nucleus or seed for the growth of the aggregates. Interestingly, cooperative behavior was observed with the perfluoro-alkyl-substituted monomer 6a (see Scheme 35) in THF−water mixtures, where a combination of π−π stacking and hydrophobic forces becomes dominant (Krel up to 300 in 40:60 THF/water; ΔGelong = −31 kJ/mol).744 For higher water contents (>35%), isodesmic behavior was observed. The ΔG value markedly changes with increasing water content, e.g., to −43 kJ/mol for 30:70 THF/water. An estimate of ΔGelong = −87 5280


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Figure 83. Free energies of complex formation between α,ω-amides and carboxylates in CHCl3 as a function of the number of rotatable single bonds (nrot) between the terminal amide and carboxylate functions. Representative complexes with nrot = 5 and nrot = 9 are shown schematically. Modified figure: reprinted with permission from ref 758. Copyright 1998 Wiley VCH.

association process. Another factor responsible for the observed linear correlation between number of binding sites and the total binding free energy ΔG t can be the above-mentioned compensation between ΔH and TΔS. Vibrational entropies can be reduced by complex formation, but also enhanced due to the formation of new noncovalent bonds. A significant loss of rotatory degrees of freedom in complex formation is expected, in particular, for single bonds; the corresponding energetic disadvantage was estimated to reach 1.5 to 6 kJ/mol753−756 or, depending on the barrier nature, 0 to 15 e.u.757 Experimental data from supramolecular complexes indicate smaller disadvantages: free energies of complex formation between α,ω-amides in chloroform decrease as expected with the increasing number n of rotatable single bonds between the terminal amide (Figure 83), but the slope of the correlation indicates a loss of only ΔΔG = 0.5−1.3 kJ/mol per single bond.758 Similar small entropy values were observed in ion-pair complexes with a varied number of single bonds between the charged functions (see Figure 23 in section 3.1),289 and also with peptide sheets759 and with calcium−EDTA complexes.760 In line with these observations, nickel or copper complexes with trans-1,2-diaminocyclohexane and the more flexible ethylene diamine exhibit within the error the same stability.761 There are examples that show that that preorganization of a linker in host molecules has no effect on chelate cooperativity.762 Recent findings confirm that, for an optimal affinity, the advantage of an induced fit with more flexible host components can outweigh the disadvantage of conformational restriction in the host.763 Other observations with some host−guest complexes, however, suggested that freezing of a rotor in supramolecular complexes can cost about 5 kJ/mol in ΔG.764

process depending on the solvent composition or exposure to light. This serves as a reminder that even slight changes may lead to strong effects in supramolecular systems, such that structural and thermodynamics investigations should always go hand in hand. 3.9. Entropic contributions

Several binding forces are by themselves entropy driven, in particular ion pairing in water (see section 3.1). In addition, the association of molecules is accompanied by mostly adverse entropy contributions.687 It has been emphasized early that formation of an enthalpically strong complex involves a greater reduction of configurational freedom;94,746,747 this seems to be supported by often-observed linear correlations between ΔH and TΔS (enthalpy−entropy compensation). Several supramolecular complexes, however, teach us the opposite: some of the strongest known complexes owe their high stability also to negligible entropic disadvantages. Thus, a cucurbituril−ferrocene association was shown by calorimetry to exhibit a ΔH value of −90 ± 1 kJ/mol, accompanied by TΔS close to zero.600 The latter is a result of the rigid, spherical shape of the guest and its positively charged moiety, which binds to the portal region of the host and causes restructuring of the solvent molecules. This point was discussed in more detail in section 3.7. It has been stated: “few concepts in chemistry have reached a state of such confusion as the enthalpy−entropy compensation”.748,749 Several recent investigations demonstrate that indeed enthalpy−entropy compensation is not a general feature of intermolecular associations,95,750−752 but nevertheless, it is frequently observed. Entropy contributions are difficult to partition, also as ΔS values depend on the choice of the standard concentration.31 The problems to quantify configurational entropy, which refers to solute motions, and solvent entropy, which involves changes in solvent motions, have been aptly discussed.31,687 Experimental values for the loss of translatory degrees of freedom vary considerably and depend very much on the medium, as has been demonstrated mostly with associations between small molecules.14,199 In the study of several complex measurements in solution, a TΔS penalty of 3 to 9 kJ/mol, most often of 6 kJ/mol, was assumed for the complex formation. In complexes with multivalent ligands, translational entropy costs are paid to a large degree already by a first association step, similar to that between single small molecules. The usually observed additivity of single ΔΔG binding contributions in supramolecular complexes clearly indicated minor and rather constant TΔS contributions in the

4. OVERVIEW AND OUTLOOK It is hoped that the overview on experimentally derived energies of supramolecular complex formation contributes to further applications in many fields, including the design of new drugs, of sensors, or of new materials for separation, storage, drug delivery, and other applications. The binding energy of the single noncovalent interaction used in typical supramolecular complexes reaches in solution from 1 kJ/mol to over 25 kJ/mol. The association data in the literature evaluated for a large variety of host−guest complexes lead to generally applicable free energy increments. For these, we give an overview in Table 1 and Table S1 in the Supporting Information, which in view of the very 5281


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different donor and acceptor capacities of the many participating organic functions can only represent some typical examples. The large dependence of the binding energies on the medium could only be illustrated for a few complexes, and would deserve a separate review. Systematically planned variations of host−guest structures and of the experimental conditions of complex formation can provide a basis for a better understanding of supramolecular association in natural and synthetic systems, and for the theoretical prediction of noncovalent interactions. Correlation of binding data with empirically or computationally derived factors, such as pK values, Hammett-type substituent constants, or electrostatic potentials, can help to characterize the nature of the underlying noncovalent interactions. The analysis of well-defined supramolecular systems also allows testing of suggested binding mechanisms, including those which have until now still been under debate, such as the stacking between arenes, and the importance of dispersive interactions in solution, or of hydrophobic contributions.

including receptor and enzyme mimics and DNA interactions; in recent years, he has also studied molecular recognition in chemomechanical polymers. He is the author of over 280 publications, including many reviews, book contributions, and monographs, as well editor of books on supramolecular chemistry and of the RSC book series Smart Materials.

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ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemrev.5b00583. Table S1. Overview on single noncovalent interaction free energies (detailed version of Table 1, with literature references). Table S2. Factor values for hydrogen bonds and other polar interactions (PDF)

AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest. Biographies Frank Biedermann graduated from the Universität Leipzig in 2007, followed by his Part III and doctorial studies in supramolecular and polymer chemistry under the supervision of Dr. Oren A. Scherman at the University of Cambridge (UK). In 2012, he returned to Germany as a postdoctoral researcher in the group of Prof. Werner M. Nau at the Jacobs University Bremen. In 2013, he joined the group of Prof. Luisa De Cola at the Institut de Science et d’Ingénierie Supramoléculaires (ISIS) in Strasbourg, France, and then moved in 2015 to the Institute of Nanotechnology (INT) at the Karlsruhe Institute of Technology (KIT), Germany. In mid-2016, he will be appointed as an Emmy-Noether junior research group leader at the INT. His research interests include supramolecular and materials chemistry with a focus on the design of functional chemosensors and receptors by exploitation of the nonclassical hydrophobic effect. Hans-Jörg Schneider studied in Munich, Berlin, and Tübingen, where he obtained his Ph.D. degree in 1967 in the group of Michael Hanack. After two years as a postdoctoral researcher with Robert Fahey at the University of California, San Diego, he worked in the laboratory of the late Professor Walter Hückel on his habilitation. Since 1972, he has been Professor of organic chemistry at the Universität des Saarlandes. His research concerned first stereochemistry, mechanisms of organic reactions, and NMR-spectroscopy, and later supramolecular chemistry, 5282


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