Anions are intimately related to sustainable modern societies. Using synthetic receptors to monitor and manipulate ion concentrations provides the means to support power production, environmental remediation, and clean water supplies. Although designing a receptor to bind anions of different sizes and shapes is possible, accurately predicting their affinity and selectivity in solution remains difficult. This difficulty arises from the lack of quantitative knowledge and a limited understanding of how solvent affects ion recognition. Here, we show that anion binding depends on the solvent's dielectric constant. We see that the electrostatic contribution to binding drops so quickly with the dielectric constant that it no longer dominates solution stability, even in solvents of modest polarity. This finding will enable a paradigm shift of computer-aided design of receptors from gas to solutions, which matches real applications in food, energy, and water systems.

A fundamental understanding of anion binding by receptors is essential for managing salts during energy, water, and food production. However, the limited understanding of solvent effects in ion recognition leads to a persistent blind spot that prevents effective receptor design. We experimentally discovered an underlying 1/ɛ r dependence of anion affinity on solvent dielectric constant (ɛ r ). We found this relationship by measuring how chloride binds to macrocyclic triazolophane receptors across a wide range of solvents: ɛ r = 4.7–56.2. Solvent weakens affinity by screening electrostatics; electrostatics dominates when ɛ r < 4.7 (chloroform) and then transits a cross-over region (4.7 < ɛ r < 20.5; acetone), after which it no longer governs affinity (acetonitrile and DMSO). Density functional theory helped us understand this dependence. Our theory-backed model accurately predicts Cl – affinity in solvents used in liquid-liquid extractions in the nuclear fuel cycle. This model offers a general foundation for anion recognition and electrostatically driven complexation.

Introduction

1 Gale P.A.

Howe E.N.W.

Wu X. Anion receptor chemistry. 2 Crompton T.R. Determination of Anions in Natural and Treated Waters. 3 Smolders A.J.P.

Lucassen E.C.H.E.T.

Bobbink R.

Roelofs J.G.M.

Lamers L.P.M. How nitrate leaching from agricultural lands provokes phosphate eutrophication in groundwater fed wetlands: the sulphur bridge. 4 Greer M.A.

Goodman G.

Pleus R.C.

Greer S.E. Health effects assessment for environmental perchlorate contamination: the dose response for inhibition of thyroidal radioiodine uptake in humans. 5 Nordstrom D.K. Public health. Worldwide occurrences of arsenic in ground water. 6 Fahim M.A.

Al-Sahhaf T.A.

Lababidi H.M.S.

Elkilani A. Fundamentals of Petroleum Refining. 7 Lumetta G.J. The problem with anions in the DOE complex. 8 Hay B.P.

Firman T.K.

Moyer B.A. Structural design criteria for anion hosts: strategies for achieving anion shape recognition through the complementary placement of urea donor groups. , 9 Mascal M. Precedent and theory unite in the hypothesis of a highly selective fluoride receptor. , 10 Ramabhadran R.O.

Liu Y.

Hua Y.

Ciardi M.

Flood A.H.

Raghavachari K. An overlooked yet ubiquitous fluoride congenitor: binding bifluoride in triazolophanes using computer-aided design. 11 Pedersen C.J. Cyclic polyethers and their complexes with metal salts. 12 Hunter C.A. Quantifying intermolecular interactions: guidelines for the molecular recognition toolbox. 13 Solov'ev V.P.

Strakhova N.N.

Raevsky O.A.

Rüdiger V.

Schneider H.-J. Solvent effects on crown ether complexations. , 14 Rekharsky M.V.

Mori T.

Yang C.

Ko Y.H.

Selvapalam N.

Kim H.

Sobransingh D.

Kaifer A.E.

Liu S.

Isaacs L.

et al. A synthetic host-guest system achieves avidin-biotin affinity by overcoming enthalpy-entropy compensation. , 15 Gibb C.L.

Gibb B.C. Anion binding to hydrophobic concavity is central to the salting-in effects of Hofmeister chaotropes. , 16 Assaf K.I.

Ural M.S.

Pan F.

Georgiev T.

Simova S.

Rissanen K.

Gabel D.

Nau W.M. Water structure recovery in chaotropic anion recognition: high-affinity binding of dodecaborate clusters to gamma-cyclodextrin. , 17 Pike S.J.

Hutchinson J.J.

Hunter C.A. H-Bond acceptor parameters for anions. 18 Kundig W.

Ghosh S.

Roseman S. Phosphate bound to histidine in protein as intermediate in novel phosphate-transferase system. 19 Milo A.

Neel A.J.

Toste F.D.

Sigman M.S. A data-intensive approach to mechanistic elucidation applied to chiral anion catalysis. 20 Li Y.

Flood A.H. Pure C-H hydrogen bonding to chloride ions: a preorganized and rigid macrocyclic receptor. Tz; Figure 1 Model System for Understanding Anion Binding in Solution Show full caption –. Top view: structures of the triazolophanes examined by theory (R 1 = R 2 = H) and experiment (R 1 = tert-butyl, R 2 = triethylene glycol mono-methyl ether). Side view: optimized geometries of the triazolophane (R 1,2 = H) and its 1:1 Cl− complex by M06-2X/6-31+G(d,p) level of theory. The replacement of phenylene substituents with hydrogens during computations has only a small impact on computed energies. 21 Hua Y.

Ramabhadran R.O.

Uduehi E.O.

Karty J.A.

Raghavachari K.

Flood A.H. Aromatic and aliphatic CH hydrogen bonds fight for chloride while competing alongside ion pairing within triazolophanes. (A) The 1:1 binding of shape-persistent triazolophane macrocycle with Cl. Top view: structures of the triazolophanes examined by theory (R= R= H) and experiment (R= tert-butyl, R= triethylene glycol mono-methyl ether). Side view: optimized geometries of the triazolophane (R= H) and its 1:1 Clcomplex by M06-2X/6-31+G(d,p) level of theory. The replacement of phenylene substituents with hydrogens during computations has only a small impact on computed energies.See Mendeley for the raw data here and here (B) The thermodynamic model of the 1:1 binding is pictured as a cycle. Downhill and uphill processes are represented by blue and red arrows, respectively. A fundamental understanding of anion binding in solution is essential for the design of synthetic receptorsto help manage anions related to sustainable modern societies. These anions include chloride and nitrate in water,nitrate and phosphate from agriculture-fed eutrophication,anthropogenic perchlorateand natural arsenatein public health concerns, and chlorideand sulfatein power production. This diversity of anions motivated studies that now allow us to create receptors by using computer-aided design.Although we can complement the shapes and sizes of anions by design, we do not know how solvation alters the complexation. Our understanding of how solvent affects recognition is incomplete and has barely moved beyond Pedersen's empirical observations with cation-crown ether binding that more competitive solvation of ions weakens binding.A more comprehensive understanding of binding in solution has emerged around Hunter's workon solute-solvent sorting of neutral guests. But ions are a completely different category of guest. Beyond a few isolated studies,knowledge in the field of anion recognition is limited to phenomenological listings of solvents ranging from noncompetitive to competitive. For example, although water is one of the most competitive for anion binding, we do not know why it does not impede anion binding by proteins.Solvent effects also have a broad impact on the chemical sciences where organic solvents dominate, such as recent advances using anion recognition in organocatalysis.The paucity of knowledge on how solvent affects anion recognition is a persistent blind spot. To address this shortcoming, we provide the first characterization and understanding of how solvents affect anion binding by exploiting the rigid shape persistence of macrocyclic triazolophanes Figure 1 A ).

22 Kamlet M.J.

Abboud J.L.M.

Abraham M.H.

Taft R.W. Linear solvation energy relationships. 23. A comprehensive collection of the solvatochromic parameters, π∗, α, and β, and some methods for simplifying the generalized solvatochromic equation. 13 Solov'ev V.P.

Strakhova N.N.

Raevsky O.A.

Rüdiger V.

Schneider H.-J. Solvent effects on crown ether complexations. 23 Kadam S.A.

Haav K.

Toom L.

Haljasorg T.

Leito I. NMR method for simultaneous host-guest binding constant measurement. 24 Beer P.D. Solvent dependent anion selectivity exhibited by neutral ferrocenoyl receptors. , 25 Juwarker H.

Lenhardt J.M.

Castillo J.C.

Zhao E.

Krishnamurthy S.

Jamiolkowski R.M.

Kim K.H.

Craig S.L. Anion binding of short, flexible aryl triazole oligomers. 25 Juwarker H.

Lenhardt J.M.

Castillo J.C.

Zhao E.

Krishnamurthy S.

Jamiolkowski R.M.

Kim K.H.

Craig S.L. Anion binding of short, flexible aryl triazole oligomers. , 26 Danil de Namor A.F.

Abbas I. Calixpyrrole-fluoride interactions: from fundamental research to applications in the environmental field. , 27 Sessler J.L.

Gross D.E.

Cho W.S.

Lynch V.M.

Schmidtchen F.P.

Bates G.W.

Light M.E.

Gale P.A. Calix[4]pyrrole as a chloride anion receptor: solvent and countercation effects. , 28 Howe E.N.

Bhadbhade M.

Thordarson P. Cooperativity and complexity in the binding of anions and cations to a tetratopic ion-pair host. 29 Tresca B.W.

Hansen R.J.

Chau C.V.

Hay B.P.

Zakharov L.N.

Haley M.M.

Johnson D.W. Substituent effects in CH hydrogen bond interactions: linear free energy relationships and influence of anions. Solvent parameters have long been investigated through linear free-energy relationships (LFERs).The expectation is that the solvent parameter found to correlate with affinity will lead to physical insights into the solvation processes ( Figure 1 B) that have the most impact on binding.However, existing studies on anion recognition have several shortcomings that significantly impede understanding. These include narrow solvent ranges,incomplete and/or inaccurate binding models,and flexible receptors with solvent-driven geometriesthat might reflect solvent-dependent conformations rather than binding. A general, experimentally verified and physically meaningful model of the intrinsic solvent dependence of anion recognition is missing. One long-standing belief is that anion binding is driven by electrostatics. However, this appears to be rooted in gas-phase studies,and it is not clear whether this expectation should hold when the host is uncharged. If anion binding is electrostatically driven, then the solvent dependence should reflect dielectric screening; this intuitive idea stands untested.

12 Hunter C.A. Quantifying intermolecular interactions: guidelines for the molecular recognition toolbox. , 22 Kamlet M.J.

Abboud J.L.M.

Abraham M.H.

Taft R.W. Linear solvation energy relationships. 23. A comprehensive collection of the solvatochromic parameters, π∗, α, and β, and some methods for simplifying the generalized solvatochromic equation. 30 Tomasi J.

Mennucci B.

Cammi R. Quantum mechanical continuum solvation models. 31 Gilson M.K.

Given J.A.

Bush B.L.

McCammon J.A. The statistical-thermodynamic basis for computation of binding affinities: a critical review. , 32 Kovalenko A.

Hirata F. Self-consistent description of a metal–water interface by the Kohn–Sham density functional theory and the three-dimensional reference interaction site model. 33 Langton M.J.

Robinson S.W.

Marques I.

Felix V.

Beer P.D. Halogen bonding in water results in enhanced anion recognition in acyclic and rotaxane hosts. , 34 Hostas J.

Sigwalt D.

Sekutor M.

Ajani H.

Dubecky M.

Rezac J.

Zavalij P.Y.

Cao L.

Wohlschlager C.

Mlinaric-Majerski K.

et al. A nexus between theory and experiment: non-empirical quantum mechanical computational methodology applied to cucurbit[n]urilguest binding interactions. 35 Wu Y.-D.

Wang D.-F.

Sessler J.L. Conformational features and anion-binding properties of calix[4]pyrrole: a theoretical study. , 36 Sure R.

Grimme S. Comprehensive benchmark of association (free) energies of realistic host-guest complexes. , 37 von Krbek L.K.

Achazi A.J.

Solleder M.

Weber M.

Paulus B.

Schalley C.A. Allosteric and chelate cooperativity in divalent crown ether/ammonium complexes with strong binding enhancement. , 38 Howe E.N.

Busschaert N.

Wu X.

Berry S.N.

Ho J.

Light M.E.

Czech D.D.

Klein H.A.

Kitchen J.A.

Gale P.A. pH-Regulated nonelectrogenic anion transport by phenylthiosemicarbazones. , 39 Liu Y.

Singharoy A.

Mayne C.G.

Sengupta A.

Raghavachari K.

Schulten K.

Flood A.H. Flexibility coexists with shape-persistence in cyanostar macrocycles. , 40 Ho J.

Coote M.L. A universal approach for continuum solvent pK a calculations: are we there yet?. As a complement to experiment, theory uses a variety of solvation models, e.g., empirical,quantum mechanical,and statistical mechanical,to help understand solvent effects. Solvents are represented either as a dielectric continuum, also known as implicit solvation, or instead as explicit solvent molecules. Use of explicit solvation is yet to have rigorous benchmarking beyond water.Implicit models are most prevalent and could be most relevant when solvent molecules do not bind specifically to receptor or anion. Solvent is represented as a smoothly varying continuum supporting fluctuating polarizations, i.e., dipoles, in response to the charge distribution of solutes. Despite the wide use of implicit models,their utility for enabling a physical understanding of anion recognition is limited by the fact that global agreement between experiment and computation across solvents has never been achieved.