Molecular Tweezers in Host−Guest Complexes: A ComputationalStudy through a DFT‑D ApproachJero me Graton,*,† Beatrice Legouin,‡ Francois Besseau,† Philippe Uriac,‡ Jean-Yves Le Questel,†Pierre van de Weghe,‡ and Denis Jacquemin*,†,§

†Chimie et Interdisciplinarite: Synthese, Analyse, Modelisation (CEISAM), UMR CNRS 6230, Universite de Nantes, 2 rue de laHoussiniere − BP 92208, 44322 Nantes Cedex 3, France‡Equipe Produits Naturels, Syntheses et Chimie Medicinale (PNSCM), UMR CNRS 6226, Universite de Rennes 1, 2, Avenue duProf. L. Bernard, 35043 Rennes Cedex, France§Institut Universitaire de France, 103, Boulevard Saint Michel, 75005 Paris Cedex 05, France

*S Supporting Information

ABSTRACT: The interactions of small organic molecules with arecently designed molecular tweezer have been modeled using densityfunctional theory approaches. The weak values of the complexationconstants of the different compounds make the computationsparticularly challenging. Nevertheless, the selected theoretical approachis shown to be able to detect several outliers that have been thenreexamined by experimental means. The autoassociation, as cyclicdimers, of two carboxylic acids is shown to significantly disturb the 1:1ligand@host equilibrium constants. Indeed, in CH2Cl2 solutions, thecomplexes mainly present a 2:1 ligand@host structure. Thisinvestigation is a further step toward the rational design of moleculartweezers.

1. INTRODUCTION

Molecular receptors based on noncovalent interactions havelong intrigued researchers. Among these weak interactions, theubiquitous noncovalent parallel aromatic interactions have beenfound to govern many molecular organizations particularly inmedicinal chemistry.1 During the past three decades,2,3 relyingon the pioneering work reported by Chen and Whitlock in1978,4 molecular tweezers, composed by two flat pincers (oftenaromatic moieties) and tethered by a rather flexible spacer,appeared as effective models to shed light on molecularassociations involving π−π-stacked aromatic interactions. Thepincer-to-pincer space between the two aromatic electron-rich(or electron-poor) pincers must be ca. 7 Å for an ideal insertionof an aromatic guest. Although the synthesis and study ofproperties of several molecular tweezers have been reported,their tedious preparations are a limitation for extensive studies.Recently, we synthesized a novel chiral molecular tweezer

TW (Scheme 1) by mixing of (+)-usnic acid to (1R,2R)-1,2-diaminocyclohexane, the electron-rich usnic acid moiety beingthe pincer and the diaminocylohexane corresponding to thespacer.5−7 TW presents the ability to form molecularassemblies via π−π-stacked aromatic interactions with variouselectron-poor aromatic compounds, and the associationconstants have been determined by 1H NMR and/or UV−visspectroscopies. These experiments are frequently used todetermine the thermodynamic stability of host−guest systems.However they suffer of some limitations, such as the solubility

of the species or, for weak association constants, a too weakvariation of the signal, using the graphical Benesi−Hildebrandmethod.8

Theoretical studies are therefore an important asset to obtaina more comprehensive picture of the complexation phenomena.In that framework, the dispersion-corrected density functionals(so-called DFT-D) that allow an accurate description ofsystems involving noncovalent interactions with strongdispersion effects are methods of choice thanks to theirmoderate computational cost. Consequently, a panel of DFT-Dschemes, such as the XDM method of Becke and Johnson,9,10

the DFT-D2/3 schemes of Grimme,11−13 the ωB97X-Dfunctional of Chai and Head-Gordon,14 the LRD correctionof Sato and Nakai,15,16 or the TS-vdW approach ofTkatchenko,17,18 have been developed to provide accuratethermodynamical parameters for molecular complexation. Anextra less parametrized alternative, the dDsC correction ofSteinmann and Corminboeuf,19−21 appears more effectivewhen investigating intramolecular phenomena but yieldsessentially the same results for intermolecular problems.In a preliminary work, we have performed a methodological

investigation of the interactions between TW and twomolecules for which experimental X-ray structures of the

Received: July 20, 2012Revised: September 24, 2012Published: October 9, 2012

Article

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complexes were available.22 It turned out that DFT-Dcalculations could provide values in semiquantitative agreementwith experimental measurements (NMR, UV, complexationconstants, etc.), provided that a very large atomic basis set(def2-QZVP) was applied so to avoid significant basis setsuperposition errors (BSSE).22 More specifically, Grimme’sB97-D functional13 has been found to be very effective,especially when the dispersion term was refined thanks to thelatest D323 and D3BJ 9,10,24 schemes, which are moresophisticated than the original (D2) method.12 However, ourfirst study was limited to the consideration of two host−guestcomplexes, making investigations of the correlation betweenexperimental and theoretical values out of reach.Recently, in a throughout study, Grimme computed the

equilibrium association of 13 selected host−guest systems usinghis own DFT-D3 method.25 He reached an impressiveagreement with experimental complexation energies usingboth the COSMO-RS26 solvation model and a correction tothe vibrational entropies. Kessler et al.27 also investigated theperformance of DFT-D for the study of five molecular tweezers,using tetracyanobenzene (TCNB) as aromatic guest. Theyconcluded that the B3LYP functional, when corrected fordispersion interactions, provided realistic relative complexstabilities, although the TCNB@tweezer binding energieswere significantly overestimated, contrary to Grimme’s study.In the present study, we conversely consider a constant

molecular tweezer with a larger set of guest compounds(Scheme 2) with the aim of reaching an accurate ranking. Thisallows a refined assessment of the methodology proposed inour first work in terms of chemical ranking. A specific challengecompared to previous studies relies on the small absolute valuesof the complexation constants, which are in addition distributedin a tiny range (1.5 kcal mol−1). The structures presenting acarboxylic acid function, revealed as outliers by the theoreticalmodel, have been reinvestigated in the light of their infrared

spectra in CH2Cl2 solutions, showing that despite its limitationsthe previously proposed protocol is helpful to bring chemicallymeaningful information. Indeed, we intend to provide acomputational procedure reasonably describing the relativeevolution of the binding energy observed experimentally. Thismethodology is expected to be able to detect problematicexperimental values but also to be reasonably fast in order toallow scanning new hosts and/or guests and to select thesystems of interest before chemical synthesis.

2. METHODS2.1. Theoretical Methods. The structural optimizations of

host, guests, and host−guest complexes were performed usingGaussian 09.28 The binding energies of TW with 2,4,7-trinitrofluorenone (TNF) and 7-chloro-4-nitrobenzoxadiazole(NBD) have been investigated previously.22,25 According to ref22, the B97-D12 functional and the 6-31G(d) basis set havebeen employed to optimize all geometries. The consideredguests are picric acid (PA), 2,5,7-trinitro-9-oxo-9H-fluorene-4-carboxylic acid (CTNF), 3,5-dinitrobenzoic acid (DNBA),methyl 3,5-dinitrobenzoate (DNBA-Me), methyl 2,5,7-trinitro-9-oxo-9H-fluorene-4-carboxylate (CTNF-Me), TCNB, andtetracyanoquinodimethane (TCNQ). As shown in thefollowing, the dimerization of carboxylic acids, DNBA andCTNF, occurs in CH2Cl2 solution, and the 2:1 complexationmode between TW and the corresponding dimers has beeninvestigated. The trimer association has not been considered,the acids being already present in their dimeric form insolution. Consequently, the 1:2 complexes with TW arecertainly established from these dimers rather than from twoseparated monomers. For most structures, no experimental X-ray data are available as starting points. For starting ourgeometry optimizations, several (ca. 10) relative host/guestpositions have been obtained by rotating and translating theguest inside the host, keeping in mind that the two pincers ofTW compel the aromatic ligand to remain parallel to itsaromatic arms. In the following, we report only the structuresyielding the minimal energies. The harmonic frequencies werecomputed analytically at the same level of theory in order tocharacterize the stationary points, to allow comparisons withthe experimental νCO stretching frequencies and to determinethe entropic contributions to the Gibbs free complexationenergies. The basis set superposition errors (BSSE) were

Scheme 1. General Representation of a Molecular Tweezer(top) and Sketch of the Chiral Molecular Tweezer, NamelyTW, Considered in This Work Which Features Two(+)-Usnic Acid Moieties as Tethered Pincers and (1R,2R)-1,2-Diaminocyclohexane as Spacer

Scheme 2. Chemical Structures of the Guest Molecules

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accounted for on the gas phase structures using thecounterpoise procedure (CP),29,30 and the solvent effectswere included through single-point polarizable continuummodel (PCM) calculations.31 The CPCM32,33 and SMD34

solvent models were also tested to check whether they yield torefined thermodynamics of the binding energies. Single-pointdef2-QZVP calculations performed on the optimized structureswith both B97-D and M06-2X35 functionals have beenperformed to estimate the interaction energies. The dispersioncontribution to the complexation energies was eventuallystudied with the default D2 procedure as well as with both theD3 and the D3BJ models. These latter calculations wereperformed using Grimme’s code.36

2.2. FTIR Spectroscopy. Infrared spectra of DNBA andCTNF were recorded using a Fourier transform spectrometerBruker Tensor 27 at a resolution of 1 cm−1. The CaF2 cells of0.5 cm path lengths were thermostat-controlled by a Peltiereffect regulation from −5 to +35 °C. The structures of DNBAand CTNF in CH2Cl2 solution were characterized in the regionof the νCO stretching bands, based on the concentration andtemperature variations.2.3. Job’s Method. UV data were recorded at 440 nm on a

UVIKON 931 spectrophotometer. A Job’s plot analysis,37 alsocalled the method of continuous variation, was performed todetermine the stoichiometry of the CTNF@TW complex.Solutions of CTNF and TW at 10 mM were prepared inMeOH 4% in CH2Cl2 for solubility reasons. Aliquots ofsolution were varied alternatively from 0.25 to 1.75 mL forguest and host solutions to keep constant the total volume (2mL), each containing the same total number of moles of CTNFand TW. The plot of the solution absorbance against the molarfraction of CTNF shows a maximum corresponding to therelative stoichiometry of the complex.

3. RESULTS AND DISCUSSION

For sake of clarity, only the equilibrium constants determinedpreviously through NMR measurements6 will be compared toour theoretical results. Indeed, it is our opinion that the UVdata lead to K values that are globally in the line of the NMRdata but suffer from larger uncertainties.3.1. Host−Guest Complexes. As noted previously, the

experimental (X-ray) geometries of complexes with TW areonly available for TNF and NBD, and we have performed B97-D/6-31G(d) geometry optimization for all complexes. Asillustrated in Figure 1, the distance between the two arms of thetweezer is found to be rather independent of the incorporated

ligands (it ranges from 6.2 to 6.7 Å), and the aromatic cores areperfectly superimposed with the others. For the complexesstudied here, with trifling differences of interaction energies,geometrical parameters cannot be used to discriminate thesystems.The binding energies (E and G) computed for the series of

nine ligand@TW complexes are listed in Table 1 for theselected B97-D3BJ/def2-QZVP//B97-D/6-31G(d) level oftheory. Since the only available experimental value for TCNQhas been obtained through UV spectroscopy, this value was notincluded in our training set but will be considered as an externaltest. Using the suggested TBE level (theoretical best estimateslisted in the rightmost column in Table 1)22 for comparisonswith the experimental binding energies, the resulting linearcorrelation presents a regression coefficient not larger than r2 =0.327 and a standard deviation not smaller than s = 2.2 kcalmol−1 (Figure 2). At first sight, these (very) poor statisticalresults suggest that the selected theoretical model is not onlyvery inaccurate but also fails to properly describe theexperimental variation of the binding energies. Nevertheless,we show below that a series of amendments of the experimentalanalysis efficiently yield improved theoretical versus exper-imental agreement.

3.2. Assessing the Reliability of the ExperimentalValues. Clearly, DNBA is the most significant outlier with astrong deviation, around 4 kcal mol−1, from the regression line(see Figure 2). The behavior of this carboxylic acid hastherefore been reconsidered in light of its IR spectra recordedin CH2Cl2 at 25 °C, following the very same experimentalconditions used to determine the complexation constants.6

As illustrated in Figure 3, the IR spectrum of DNBA stronglydepends on both concentration and temperature. Despite thepresence of only one carbonyl group in DNBA, two absorptionbands are observed in the νCO stretching region at 1753 and1715 cm−1, their intensity ratio being strongly affected by bothconcentration and temperature. Therefore, these two absorp-tion bands can be safely attributed to the existence of anautoassociation equilibrium of DNBA in CH2Cl2 solution. Thehigh-frequency band is characteristic of the νCO stretchingmode of the DNBA monomer whereas its low-frequencycounterpart is the signature of the νCO···HO stretching mode inthe DNBA dimer. This interpretation is further substantiated aslow concentrations and high temperatures (Figure 3) favor theνCO band at the expense of the νCO···HO signature.Furthermore, our theoretical results at the B97-D/6-31G(d)level are also fully consistent with these attributions since theνCO (monomer) and νCO···HO (dimer) bands are calculatedto absorb at 1773 and 1719 cm−1 (no scaling factor wasapplied), respectively. Consequently, the concentration ofDNBA dimer is significant in the experimental conditions (2× 10−3 M in CH2Cl2 at 25 °C). Following the νCOabsorbance, ACO, as a function of the variation of DNBAconcentration, CCO, we have determined the self-associationconstant of DNBA, K = 64 dm3 mol−1, thanks to eq 138

ε ε= +

CA

Kl

Al

2 1C O

C O C O2 2 C O

C O (1)

where l is the cell path length and εCO is the molar absorptioncoefficient of the carbonyl stretching band of DNBA. Thecorresponding Gibbs energy of self-association is ΔG° = −2.5kcal mol−1, in reasonable agreement with the theoretical

Figure 1. Superposition of the optimized structures of ligands@TWcomplexes showing the invariable distance between the two arms ofTW and the constant position of the aromatic ring of the ligands.

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dimerization value of −3.8 kcal mol−1 [B97-D/def2-QZVP//B97-D/6-31G(d)].39

According to these results, DNBA exists in CH2Cl2 solutionunder both monomeric and dimeric forms. Moreover, the 1:2complex, computed for the (DNBA)2@TW structure (Figure4), is found to be significantly more stable than the 1:1 complex(Table 1). Consequently, the simultaneous equilibria takingplace in solution prevent an accurate determination of thecomplexation constant of DNBA in TW, and this system hastherefore been removed from our panel.Owing to the observed behavior of DNBA, the structure of

the second carboxylic acid, namely CTNF, has also beenrevisited in CH2Cl2 though it is not a clear-cut outlier in Figure2. The structure of CTNF involves two different carbonylgroups, corresponding to the carboxylic function and thefluorenone moiety, and two absorption bands are located in theνCO region at 1742 and 1712 cm−1 (Figure 5). Contrary toDNBA, these bands do not show any significant dependence onconcentration or on temperature. As a result, no autoassoci-ation equilibrium is established in solution for CTNF, the onlystructure found being either the monomer or the dimer.Theoretical calculations show that the CTNF dimer is morestabilized (−4.8 kcal mol−1)39 than the corresponding DNBAentity (−3.8 kcal mol−1, see above), despite the foreseen steric

Table 1. Ligand@TW Experimental (ΔGNMR) and Theoretical (B97-D3BJ/def2-QZVP) Complexation Energies (E in kcalmol−1) and Gibbs Energies (G in kcal mol−1), Taking into Account the Solvent Effects (E(PCM) and G(PCM)); Values Correctedfor Both Solvent and Basis Set Superposition Effects (E(CP,PCM) and G(CP,PCM))

ΔGNMR E E(PCM) E(CP,PCM) G G(PCM) G(CP,PCM)a

TNF −2.35 −29.0 −25.0 −24.0 −15.0 −10.9 −9.9NBD −1.30 −20.9 −16.7 −15.8 −8.4 −4.2 −3.3CTNF −1.93 −25.4 −21.8 −20.9 −11.0 −7.5 −6.6CTNF-Me −1.64 −25.7 −22.0 −21.1 −11.6 −7.9 −6.9PA −1.61 −21.8 −17.8 −16.7 −8.4 −4.8 −3.7DNBA −1.83 −20.5 −17.2 −16.2 −7.2 −3.9 −2.8DNBA-Me −1.02b −21.7 −19.3 −18.4 −7.3 −5.0 −4.0TCNB −1.37 −23.8 −18.9 −18.2 −12.8 −8.1 −7.4TCNQ −1.88c −26.0 −23.2 −22.5 −14.8 −12.2 −11.6(CTNF)2 −1.92d −25.8 −21.6 −20.6 −9.5 −5.4 −4.3(DNBA)2 −1.81d −26.2 −21.7 −20.5 −8.1 −4.8 −3.7

aThe TBE (theoretical best estimates) in ref 22. bK = 5.7 (NMR) and 5.6 (UV), values refined owing to the inhomogeneous values publishedpreviously.6 cUV value. dCalculated from the experimental data,6 with a guest concentration divided by a factor of 2.

Figure 2. Correlation between the ligand@TW experimental(ΔGNMR) and theoretical (G(CP,PCM)(B97‑D3BJ/def2‑QZVP)) binding en-ergies. The estimated experimental error bars6 are indicated.

Figure 3. Evolution of the IR spectra of CH2Cl2 solutions of 3,5-dinitrobenzoic acid (DNBA) obtained by varying the concentration(A) or the temperature (B). The spectra have been normalized toequivalent concentration for inset A.

Figure 4. Side view (left) and front view (right) of the optimizedgeometry of (DNBA)2@TW.

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hindrance induced by the vicinal nitro group in the former.Second, while the calculated νCO stretching frequency of thefluorenone moiety appears insensitive to the association (1754and 1755 cm−1 in monomer and dimer, respectively), theabsorption band of the carboxylic νCO is computed at 1781cm−1 in the monomer and at 1711 cm−1 in the dimer.Therefore, the IR experimental data and the theoretical resultsclearly hint that the only structure found for CTNF in CH2Cl2solution is the cyclic dimer. This result is corroborated by thecorresponding Job’s plot (Figure 6) which exhibits a maximumat a molar fraction of 0.67 when CTNF is considered as amonomer but close to 0.5 when considering a dimeric guest.Consequently, the experimental complexation constant6 withTW corresponds to the (CTNF)2@TW complex rather thanthe CTNF@TW complex, and the theoretical model should beadapted accordingly.The optimized (CTNF)2@TW structure (Figure 7) reveals

that only one moiety of the dimer is between the two arms ofTW, and the corresponding binding energy (Table 1) is foundto be equivalent or only slightly less stabilized than the 1:1complex. This is in contrast with the (DNBA)2@TW structure,which is significantly more stable than the corresponding(DNBA)@TW complex, a difference related to the geometriesof the 2:1 complexes. Indeed, the DNBA molecule that is notenclosed in TW’s arms is folded back over the spacer with anitro group close to the CH groups of the cyclohexyl group(Figure 4). On the contrary, the second molecule of the CTNFdimer is free of any (stabilizing) interaction with TW (Figure7). Nevertheless, since no equilibrium is found between themonomer and dimer of CTNF, one can safely consider the 1:2complexation as the only possible in CH2Cl2 solution.

Subsequently, only this complexation mode is considered inthe following simulations. Additionally, the experimentalconcentration of (CTNF)2 is half of the CTNF concentrationintroduced in solution, and the previously published exper-imental equilibrium constant6 has been corrected (K = 25.5rather than K = 26).

3.3. Binding Energies Prediction. Removing the DNBAdata and considering the corrected CTNF values, theexperimental and theoretical binding energies of sevenguest@TW systems can be compared (see Tables 2 and 3).The dispersion contribution calculated with Becke andJohnson’s dispersion term (DFT-D3BJ) appears as the mostreliable one for the simulation of the ligand@TW complexationwith (generally) the largest correlation coefficients and the

Figure 5. Concentration (A) and temperature (B) effects on the IRspectra of CH2Cl2 solutions of CTNF. See caption of Figure 3 formore details.

Figure 6. Job’s plot for a solution of CTNF and TW ([CTNF] +[TW] = 10 mM) at 440 nm. The used solvent is CH2Cl2 with 4%MeOH.

Figure 7. Optimized geometry of (CTNF)2@TW.

Table 2. Regression Coefficients, r2, and StandardDeviations, s, Obtained from the Linear CorrelationsEstablished between Experimental and Theoretical 6-31G(d)Complexation Energies for Ligand@TW

B97-D/6-31G(d) B97-D3/6-31G(d)B97-D3BJ/6-31G(d)

methoda r2 s r2 s r2 s

E 0.582 0.31 0.555 0.32 0.673 0.28E(PCM) 0.474 0.35 0.456 0.35 0.556 0.32G 0.712 0.26 0.716 0.26 0.767 0.23G(PCM) 0.569 0.32 0.557 0.32 0.670 0.28

aCTNF@TW substituted by (CTNF)2@TW.

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smallest standard deviations. The best statistics are found withthe complexation energies (E) computed at the B97-D3BJ/def2-QZVP//B97-D/6-31G(d) level that significantly improve theinitial results (Table 1).Although BSSE corrections and the inclusion of solvent

effects are helpful to obtain absolute binding energies, theydeteriorate the quality of the relative chemical ranking (smallercorrelation coefficients and larger standard deviations). Besidesthe inherent approximation of the selected DFT model, weattribute this finding, on the one hand, to the limits andnumerical stability of the CP correction when very large basissets are used and, on the other hand, to the use of a continuumapproach in the PCM model that cannot model all solvationeffects. It is therefore preferable (and faster) to use E or Gwithout solvent models and CP corrections to reach a valuableprediction of the ordering of the complexation energies, but atthe price of poor absolute values. The def2-QZVP basis setyields larger correlation coefficients with the binding energies(E), for which it significantly outperforms 6-31G(d), than withthe Gibbs binding energies (G). This might be related to therather crude model used to determine the entropic correction,which does not allow a consistent improvement for alreadyaccurate def2-QZVP binding energies (see below for possiblecorrections similar to Grimme’s method).25 The absolutecomplexation energies obtained with the 6-31G(d) basis set aretoo large, by up to 10 kcal mol−1. For example, the Gibbsbinding energy of (CTNF)2@TW corrected from the solventeffects is −16.0 kcal mol−1 with 6-31G(d) and −5.4 kcal mol−1

(def2-QZVP), while the experimental ΔGNMR value is −1.9 kcalmol−1. In addition, the M06-2X meta-GGA hybrid that doesnot include an explicit dispersion term but was previouslyshown to provide accurate complexation energies seems notefficient for the present systems. This is substantiated by thelarge standard deviation (not less than 0.77 kcal mol−1),although the r2 value (0.800) is the highest of the series. Thisoutcome is related to the very small interaction energies understudy that can only be recovered with an empirical correction.In short, the NMR experimental results are better predicted

(eq 2, Figure 8) from the complexation energies (E) computedat the B97-D3BJ/def2-QZVP//B97-D/6-31G(d) level orsimilarly at the B97-D3/def2-QZVP//B97-D/6-31G(d) level.

Δ = +‐ ‐G E0.131 1.562NMR (B97 D3BJ/def2 QZVP) (2)

= = = −n r s7; 0.771; 0.23 kcal mol2 1

Though we do not advocate the application of a systematiclinear correction to improve theoretical estimates, this equation

might be useful to rapidly estimate the experimental complex-ation energies of guest@TW systems.

3.4. Further Methodological Discussion. In their recentstudy of complexation of TCNB in several tweezers,27 Kessleret al. concluded that their DFT calculations correctly describethe trends in complex stability but that they failed to producerealistic magnitudes of complexation energies. This is consistentwith our findings for the complementary ligands@TW series.Our binding energies are indeed significantly overestimated byDFT by comparison with experiment but a correct chemicalranking is found even if it is distributed over a tiny energyrange. Considering a much larger energetic range (21 kcalmol−1), Grimme succeeded in describing the bindingassociations of supramolecular complexes with an unprece-dented accuracy25 and attributed the quality of his results tothree factors: the DFT-D3 correction, the vibrational entropyscaling, and the solvation model used. In order to assess howthe two latter corrections could improve our simulations, wehave first scaled the vibration entropy following the proposedprocedure, in which the low-frequency contribution isinterpolated between the harmonic vibrational entropy and apure rotational entropy (see ref 25 for further details). Thiscorrection contributes to 1.7−2.9 kcal mol−1 to the free

Table 3. Regression Coefficients, r2, and Standard Deviations, s, Calculated for the Correlations Established betweenExperimental and Theoretical def2-QZVP Complexation Energies

B97-D/def2-QZVP B97-D3/def2-QZVP B97-D3BJ/def2-QZVP M06-2X/def2-QZVP

methoda r2 s r2 s r2 s r2 s

E 0.751 0.24 0.777 0.23 0.771 0.23 0.782 0.89E(PCM) 0.562 0.32 0.558 0.32 0.641 0.29 0.510 1.50E(CP) 0.737 1.68 0.747 1.23 0.743 1.62 0.800 0.77E(CP+PCM) 0.551 2.24 0.538 1.66 0.617 1.91 0.518 1.39G 0.563 0.32 0.357 0.39 0.468 0.35 0.227 1.62G(PCM) 0.453 0.36 0.276 0.41 0.432 0.36 0.141 1.51G(CP) 0.519 1.99 0.308 2.05 0.424 2.35 0.109 1.56G(CP+PCM) 0.416 2.07 0.229 1.87 0.387 2.11 0.051 1.38

aCTNF@TW substituted by (CTNF)2@TW.

Figure 8. Correlation between the ligand@TW experimental(ΔGNMR) and theoretical (E(B97‑D3BJ/def2‑QZVP)) binding energies. Thepredicted values for TCNQ@TW and (DNBA)2@TW are displayedin red, and the uncorrected DNBA@TW and CTNF@TW values arein blue.

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enthalpies of association. In a second step, the CPCM32,33 andthe SMD34 models of solvation have been applied instead ofthe PCM procedure. The solvent effects have a contributionaround 2−5 kcal mol−1 with the CPCM model, as well as withthe PCM one, while the SMD scheme yields to largercontributions (3−7 kcal mol−1). Unfortunately, appliedseparately or together, these amendments do not improvesignificantly our statistics, and the selected method (B97-D3BJ/def2-QZVP//B97-D/6-31G(d) level) remains the mosteffective in our case. Nevertheless, using the SMD model, animprovement of the absolute complexation energy is found (3kcal mol−1) for the three fluorenone derivatives, remainingalthough significantly overestimated. If our results are not asaccurate as Grimme’s ones, it should rather result from thegeometry optimization model, since the TPSS-D3/def2-TZVPlevel probably yields more refined geometries than B97-D/6-31G(d) structures. Nevertheless, one must keep in mind thatthe energetic range studied in this work is very tiny, and theseresults therefore appear really satisfying and useful for theprediction of host−guest association.3.5. Structure−Property Relationship. The experimental

determinations attribute to TNF the highest equilibriumconstant with TW. In the theoretical calculations, thiscompound is also predicted to provide the largest complexationenergy (E) as shown in Table 1, despite being surpassed byTCNQ on the basis of G(PCM) and G(CP,PCM) parameters. NoNMR equilibrium constant is available for this lattercompound, but an UV estimate corresponding to ΔG =−1.88 kcal mol−1 has been previously published.6 As shown inFigure 8, this data is in excellent (and probably partly lucky)agreement with the theory-based estimate of −1.84 kcal mol−1

calculated through eq 2. This result confirms that the relativetrends given by the binding energies (E) with the def2-QZVPbasis set are more robust. Comparing the two cyano derivatives,our theoretical results corroborate that the TCNQ@TWcomplex is more stable than its TCNB@TW counterpart.This contrasts with previous results obtained for strongercomplexes using a trimethylene-bridged40 and benzene-spaced41 molecular clips that bind TCNB more strongly thanTCNQ.In the fluorenone series, the NMR experimental equilibrium

constant of CTNF is just slightly higher than the CTNF-Mevalue but is significantly weaker than TNF’s.6 This behaviorpreviously appeared rather surprising since the H-bond donorability of the carboxylic acid moiety was expected to improvethe affinity with the electron-rich aromatic tweezer. We haveshown above that CTNF remains fully associated as a cyclicdimer (at least in CH2Cl2) and that the complexation with TWsubsequently occurs as a (CTNF)2@TW structure. As aconsequence, the CTNF structure completely loses its H-bonddonor propensity, explaining that the CTNF-Me and CTNFbehave similarly.In contrast with CTNF, a significant difference is predicted in

the binding energy of DNBA and (DNBA)2 with TW, thecomplexation of the dimer being strongly favored. Thecomputed energy has been introduced in eq 2 in order tocheck the correlation with experimental data. As illustrated inFigure 8, the predicted ΔG, −1.87 kcal mol−1, is very close tothe experimental value corrected for dimerization, −1.81 kcalmol−1 (Table 1). This agreement confirms that, in CH2Cl2solution, DNBA is mainly complexed with TW in a (DNBA)2@TW structure.

In our calculations, the NBD@TW complex is predicted tobe the weakest of the series, and this is rather consistent withexperiment. Indeed, the equilibrium constant measured byNMR is the second smallest (only DNBA-Me has a smallercomplexation interaction). Eventually, among the ligandsselected as guests during the measurements of the complex-ation constants, those having H-bond donors do not improvethe affinity toward TW as indicated by CTNF and DNBA (seeabove).6 Likewise, picric acid (PA) is also an H-bond donor forwhich the equilibrium constant with TW is not particularlylarge. As illustrated in Figure 8 for the optimized structure ofthe PA@TW complex, the hydroxyl moiety of PA is alreadyinvolved in an intramolecular interaction with one of its twovicinal nitro groups and presents therefore a very lowaccessibility to further intermolecular H-bonding. Conse-quently, its H-bond donating capacity is not expected to playa significant role in the complexation with TW. In addition,considering its structure in Figure 9, all carbonyl functions are

already involved in intramolecular H-bonds with either aminoor hydroxyl moieties, decreasing their ability to interact with theligand, whereas the furyl oxygen atoms are significantlycrowded by the acetyl groups, subsequently prevented to actas H-bond acceptors. In short, the intramolecular interactionsfound in TW prevent the guest to bind to its host through H-bond interactions.

4. CONCLUSIONS AND OUTLOOKWe have performed a systematic examination of a series ofcomplexes between a molecular tweezer showing electron-richaromatic moieties and nine ligands with an electron-pooraromatic core through a dispersion-corrected density functionaltheory approach. From the present results and analysis, we havefound a reasonable agreement between the experimental NMRequilibrium constants and theoretical estimates, despite the factthat the interaction energies of weak complexes range only over1.3 kcal mol−1. A special attention was paid to the experimentalstructure of the carboxylic ligands in solution, an IR analysisdemonstrating that autoassociation equilibria occurred, andcompelled us to consider their cyclic dimer during oursimulations. These amendments allowed improving the agree-ment between experimental and theoretical results and hencereaching an accurate chemical ranking of the ligand@TWcomplexation energies. Consequently, the present contributionclearly shows how relevant theoretical investigations of weaklyinteracting molecules might provide new chemical insights.Selecting the B97-D3BJ/def2-QZVP or the B97-D3/def2-QZVPcomplexation energies (E) computed on the B97-D/6-31G(d)geometry, the ligand@TW experimental binding energies are

Figure 9. Optimized geometry of PA@TW, showing the intra-molecular H-bonds (displayed as ∗) occurring on the PA and TWstructures.

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described with a reasonable accuracy (standard deviation s =0.23 kcal mol−1). This procedure therefore appears as a cost-effective method for calculations of host−guest complexation oftweezers presenting a significant contribution of dispersioneffects.In the future, the improvement of the ligand@host binding is

planned, investigating how the modifications of the tweezer’sstructure could improve the complexation constants. Ascreening through the present computational protocol followedby measurements of the equilibrium complexation constants ofthe best candidates indeed appears as a cost-effective approach.

■ ASSOCIATED CONTENT

*S Supporting InformationBinding energies (E) and Gibbs binding energies (G) of thenine guest@host complexes using several levels of theory. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*Tel 33 2 76 64 51 68 (J.G.), 33 2 51 12 55 64 (D.J.); Fax 33 251 12 54 02; e-mail Jerome.Graton@univ-nantes.fr (J.G.),Denis.Jacquemin@univ-nantes.fr (D.J.).

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

D.J. is indebted to Prof. S. Grimme for useful suggestionsregarding the computation of complexation energies with DFT-D. D.J. acknowledges the European Research Council (ERC)and the Region des Pays de la Loire for financial support in theframework of a Starting Grant (Marches -278845) and arecrutement sur poste strategique, respectively. This researchused resources of (1) the GENCI-CINES/IDRIS (Grantsc2011085117 and c2012085117), (2) CCIPL (Centre deCalcul Intensif des Pays de Loire), and (3) the local TROY

cluster acquired thanks to regional support.

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