Guest Controlled Nonmonotonic Deep Cavity Cavitand Assembly

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Guest Controlled Non-Monotonic Deep Cavity Cavitand Assembly State Switching Du Tang, J. Wesley Barnett, Bruce C Gibb, and Henry S Ashbaugh J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b09021 • Publication Date (Web): 03 Nov 2017 Downloaded from http://pubs.acs.org on November 7, 2017

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The Journal of Physical Chemistry

Guest Controlled Non-monotonic Deep Cavity Cavitand Assembly State Switching Du Tang1, J. Wesley Barnett1, Bruce C. Gibb, 2 and Henry S. Ashbaugh1 1

Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, LA, 70118 2

Department of Chemistry, Tulane University, New Orleans, LA, 70118

Abstract Octa-acid (OA) and tetra-endo-methyl octa-acid (TEMOA) are water-soluble, deepcavity cavitands with nanometer-sized non-polar pockets that readily bind complementary guests, such as n-alkanes. Experimentally, OA exhibits a progression of 1:1 to 2:2 to 2:1 host/guest complexes (X:Y where X is the number of hosts and Y is the number of guests) with increasing alkane chain length from methane to tetradecane. Differing from OA only by the addition of four methyl groups ringing the portal of the pocket, TEMOA exhibits a nonmonotonic progression of assembly states from 1:1 to 2:2 to 1:1 to 2:1 with increasing guest length. Here we present a systematic molecular simulation study to parse the molecular and thermodynamic determinants that distinguish the succession of assembly stoichiometries observed for these similar hosts. Potentials of mean force between hosts and guests, determined via umbrella sampling, are used to characterize association free energies. These free energies are subsequently used in a reaction network model to predict the equilibrium distributions of assemblies. Our models accurately reproduce the experimentally observed trends, showing that TEMOA’s endo-methyl units constrict the opening of the binding pocket, limiting the conformations available to bound guests and disrupting the balance between monomeric complexes and dimeric capsules. The success of our simulations demonstrate their utility at interpreting the impact of even simple chemical modifications on supramolecular assembly and highlight their potential to aid bottom-up design.

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Introduction Manipulating self-assembly to form discrete, structurally well-defined supramolecular complexes1-4 offers an efficient way to engender compartmentalization and hence bring about novel approaches to controlling the spatial position of atoms. As a result, compartmentalization can be used to organize matter and broaden the utility of X-ray crystallography,5-6 control chemical reactivity and catalysis,3, 7-15 and bring about novel separation protocols.16-18 Of the varied strategies used for driving the assembly of molecular containers, utilizing the hydrophobic effect is arguably the least explored, yet offers a route not just to the formation of container complexes, but also to insight into the complex relationship between solute shape, solvation, and the hydrophobic effect writ large.19-20 With these ideas in mind, Gibb has explored the complexation and assembly of deepcavity cavitands such as octa-acid (OA)21-22 and tetra-endo-methyl octa-acid (TEMOA) (Figures 1 and 2a).23 These water-soluble, bowl-shaped hosts differ only by the presence of four methyl groups about the rim of the hydrophobic, guest-binding pocket, which narrows the portal of TEMOA while somewhat deepening the pocket. This seemingly minor structural modification drastically changes the binding and assembly properties of the host. Consider, for example, OA and TEMOA complexation with n-alkanes.22-24 For both hosts these hydrophobic guests can induce formation of container complexes where multiple cavitands assemble around guests, isolating them from water. In the case of OA, the relationship between guest size and assembly state is straightforward:24 methane (C1) does not bind to the host; ethane (C2) form 1:1 complexes (denoted X:Y, where X is the number of hosts and Y is the number of guests); the guests propane (C3) through n-octane (C8) form 2:2 host-guest capsular complexes; and larger guests still form 2:1 host-guest complexes. In the case of TEMOA this relationship is non-

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monotonic:24 C1 and C2 form 1:1 complexes, C3 through C6 form 2:2 capsular complexes; C7 and C8 form 1:1 complexes, and; C9 or larger form 2:1 host guest capsules. Moreover, whereas OA only ever forms monomeric and dimeric complexes, TEMOA has been observed to form larger tetrameric 4:2 and hexameric 6:3 complexes for guests longer than C17.23 Finally, and intimately tied to these facts, the binding motif of guests inside the capsular complexes formed from each hosts differs. Thus, as we discuss below, in the case of OA four distinct guest motifs have been observed, whereas only one binding motif has been observed within TEMOA. Molecular simulations have proven invaluable in rationalizing the experimentally inferred conformations of guests encapsulated within OA dimers, connecting bound guest motifs that are largely unobserved in solution with their packing under confinement. For instance, short phenyl-substituted hydrocarbons (alkanes, alkenes, and alkynes) were generally found to exhibit linear conformations, while longer chains tend to adopt folded structures.25 In a systematic experimental study of n-alkanes as a function of guest length, Gibb and coworkers22, 26 inferred these flexible guests adopt a succession of conformational motifs, from extended, to helical, to hairpin, to spinning top structures, with increasing length. Barnett, Gibb, and Ashbaugh27 subsequently used simulations to relate the encapsulated alkane motifs with the conformational strain inferred from guest packing free energies, providing a thermodynamically nuanced picture of the forces stabilizing distinct guest conformations. Simulations have additionally been used to examine the structural determinants that induce conformational changes in alkanes28 and polyethylene glycol oligomers29 bound within carbon nanotubes, as well as to examine the binding of non-polar guests30 and water31 within the binding pocket of OA. These studies point to the potential utility of molecular simulations to guide the design of cavitand/guest assemblies from the bottom-up.

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Here we present a systematic molecular simulation and thermodynamic analysis of the assembly of OA and TEMOA with alkanes to assemble into a range of monomeric and dimeric (capsular) host/guest complexes in water. We consider n-alkane guests C1 to C16 encapsulated within deep-cavity cavitand hosts to form 1:1, 2:1, and 2:2 complexes. We characterize the free energies of assembling cavitands and alkanes by evaluating the potentials of mean force (PMFs) between the complex constituents along designated trajectories. These PMFs are subsequently used within the context of a reaction network model to deduce the relative populations of complex species as a function of the guest chain length in order to elucidate the distinct experimentally determined assembly trends for OA versus TEMOA. We subsequently characterize guest packing within dimers to rationalize the predicted complexation patterns observed from our simulations.

Methods Molecular dynamics simulations of n-alkanes complexed with OA and TEMOA in water were performed using GROMACS 5.1.32 The alkanes were modeled using the L-OPLS all-atom force field,33 which accurately reproduces the thermodynamic and conformational properties of long alkanes. The series of n-alkane guests from methane (C1) to hexadecane (C16) were considered. OA and TEMOA were simulated using the Generalized Amber Force Field (GAFF)34 with partial charges obtained from the AM1-BCC calculations.35 The net charge of the each cavitand was set to -6e to match the expected protonation state at pH 7.31 This charge state was obtained by deprotonating the four benzoic acid groups around the rim of the cavitand and two of the four groups at the base of the hosts (Figure 1). Six sodium cations per host, modeled using GAFF,34 were included to neutralize the host charge. Water was modeled using the TIP4P-

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EW potential.36 Non-bonded Lennard-Jones interactions were truncated beyond a separation of 9 Å with a mean-field dispersion correction for longer-range contributions to the energy and pressure. Electrostatic interactions were evaluated using the particle mesh Ewald Summation method with a real space cutoff of 9 Å.37 Simulations were conducted in the isothermal-isobaric ensemble at 25 ˚C and 1 bar, where the temperature and pressure were controlled using the NoséHoover thermostat38-39 and Parrinello-Rahman barostat,40 respectively. Bonds involving hydrogens for the hosts and guests were constrained using the LINCS algorithm,41 while water was held rigid using SETTLE.42 The equations of motion were integrated using a time step of 2 fs. We characterize the stability of the alkane/cavitand complexes using PMFs between the assembly constituents. A PMF quantifies the interaction free energy between components along a designated reaction trajectory, which here is collinear with the host’s four-fold (C4) rotational axis of symmetry (Figure 2a). We consider three separate PMFs in this study (Figure 2b): the interaction between a single alkane and cavitand to form a 1:1 complex; the interaction between an empty cavitand and a 1:1 alkane/cavitand complex to form a 2:1 complex; and the interaction between two 1:1 alkane/cavitand complexes to form the corresponding 2:2 complex. In the first set of simulations, we determined the PMF between a cavitand (OA or TEMOA) and a single alkane (C1 to C16) from bulk water into the host pocket along the C4-axis. In these simulations the cavitand and guest were solvated by 2600 water molecules in a cubic simulation box. To align the cavitand along the z-axis of the simulation box, restraint potentials were applied to two dummy atoms along the C4-axis of each host. The first “bottom” dummy atom was determined by the average position of the four atoms connecting the four charged feet of the cavitand to the bottom row of aromatic rings, while the second “top” dummy atom was determined by the

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average positions of the four carbon atoms on the second row of aromatic rings closest to the cavitand portal. The dummy atom at the bottom of the binding pocket was spatially restrained with a harmonic force constant of 100000 kJ/(mol nm2), while the vector connecting the bottom atom to the top was fixed along the z-axis using a harmonic angular constraint of 50000 kJ/(mol). The PMF was determined over a series of overlapping windows spanning from bulk water into the host pocket using umbrella sampling. The guest center was restrained to the C4-axis of the host using a harmonic potential acting normal to the symmetry axis with a force constant of 100000 kJ/(mol nm2). In the case of guests with an odd number of carbon atoms, the center was taken as the middle carbon along the chain backbone (i.e., carbon number (n+1)/2). For guests with an even number of carbons, a dummy atom was placed between the n/2 and n/2+1 carbons to serve as the restraint center. Sample windows were simulated from 5 Å deep-inside the cavitand pocket, measured from the center of the top plane defined by the four carbon atoms on the second row of aromatic rings closest to the cavitand mouth, to 15 Å out into bulk solvent. Forty overlapping windows were used along the z-axis of box with the harmonic umbrella potential minimum separated in 0.5 Å increments and a force constant of 15000 kJ/(mol nm2).43 Each simulation window was equilibrated for 1 ns, followed by a 15 ns production run. System configurations were saved every 0.2 ps for post-simulation analysis. The PMF for forming the 1:1 complex was reconstructed from the overlapping windows using the weighted histogram analysis method.44 In the second set of simulations, we determined the PMF between two cavitands (OA or TEMOA) with one of the hosts in a 1:1 complex with a single guest (C1 to C16) in water. The two cavitands were turned to face one another with their C4-axes in mutual alignment to ultimately form a dimeric 2:1 host/guest assembly (Figure 2). Both hosts were aligned with the simulation

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box’s z-axis, using the same restraints as in the 1:1 complexation simulations. No restraint was applied to the guest, however, which was held within the cavitand pocket via the hydrophobic effect. Sample windows were simulated from distances ranging from the center of the two cavitand faces, which established a separation of zero, to 13 Å into the bulk water. Twenty-five overlapping windows were simulated here, with the harmonic umbrella potential minimum separated in 0.5 Å increments and a force constant of 15000 kJ/ (mol nm2). The same simulation procedures and PMF reconstruction methods were used here as for the 1:1 complexation study. In addition, we considered the PMF between two empty hosts devoid of guests to form a 2:0 dimer. 2600 to 3000 TIP4P-EW water molecules were used to solvate these complexes. In the third set of simulations, we determined the PMF between two cavitands (OA or TEMOA) with both hosts in a 1:1 complex with a single guest in water. As in the 2:1 complexation study, the two cavitands were turned to face one another with their C4-axes in mutual alignment to ultimately form a 2:2 host-guest assembly (Figure 2). In the case of OA we considered guests from C1 to C11, while in the case of TEMOA we considered guests from C1 to C9. Longer guests were found to result in increasingly repulsive interactions that destabilize the complexes. As above, no restraints were placed on the guests. The same simulation procedures, PMF reconstruction methods, and numbers of hydration waters were used here as for the 2:1 complexation study.

Results and Discussion Alkane/Cavitand Assembly Forces. Driven by the hydrophobic effect, the interaction between the alkanes and the cavitands in water is attractive. For example, Figure 3 illustrates the PMF between C9 and OA from bulk water into the host pocket along the C4-axis to form a 1:1

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complex. The minimum of the host/guest attraction sits at the face of the OA portal (z = 0 Å) and extends ~5 Å into the bulk solvent. The depth of the attractive well (-70 kJ/mol) is sufficient to overcome the unfavorable hydration free energy of C9 in water (17 kJ/mol), such that C9 complexation with a single host engenders solubilization. The depth of the 2:1 OA/C9 attractive well is significantly deeper than that for formation of the 1:1 complex, suggesting the capsular complex is more stable than the monomeric complex. The increased depth of the 2:1 complex formation reflects not only the free energy gain associated with burying the portion of C9 that extends from the 1:1 complex into bulk water, but also the free energy gain arising from the desolvation and association of the aromatic groups ringing the portal of each cavitand. The equilibrium contact minimum between cavitands at z = 3.5 Å corresponds roughly to the diameter of a carbon atom. The depth of the 2:2 OA/C9 attractive well lies between that of the 1:1 and 2:1 complexes. This reflects the fact that while the burial of the non-polar cavitand faces to form the dimer is strongly favorable, the packing of two C9 chains within the dimer confines is more frustrated than compared to a single chain. This packing frustration is also reflected in the observation that the minimum in the 2:2 complex PMF lies ~0.4 Å further to the right than that for the 2:1 complex. We note that the extent of the 2:2 complex interaction has a longer range than that of the 2:1 capsule. This added attraction range is attributable to the ends of the two C9 guests that extend out from the 1:1 complexes into bulk water. The relative stability of the cavitand/Cn complexes can be compared by their free energy of association, which we quantify by the minima in the complex associations PMFs. The association free energy minima for the 1:1 (: ), 2:1 (: ), and 2:2 (: ) complexes as a function of the guest chain length are plotted in Figure 4 (Full PMFs for complex formation for

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all the cases considered are reported in the Supporting Information). The formation free energies for 1:1 complexation is a strongly decreasing function of the chain length for guests up to C6, beyond which the association free energy surface is comparatively flat. We ascribe the initial drop in the 1:1 association free energy to increasing attractive van der Waals interactions between the host and guest. The depth of the binding pocket is comparable in depth to the length of C6. We then expect longer chains to extend beyond the pocket into water with diminishing contributions to the overall guest binding free energy. The 1:1 association free energies are slightly more attractive for TEMOA compared to OA. This is attributable to the increased van der Waals interactions between the guest and TEMOA’s four endo-methyl units. The 2:1 capsular assembly free energies display richer behavior than that for the 1:1 complex (Figure 4b). Starting from the favorable formation free energy of an empty 2:0 cavitand complex (i.e., n = 0), the 2:1 association free energy is a linear, weakly decreasing function of the alkane length up to C8. Up to this guest length, OA and TEMOA 2:1 association is essentially indistinguishable within the simulation uncertainty. Beginning with C9, the association free energies for both hosts take a sharp down turn, becoming markedly more attractive. It is interesting to note that experimentally C9 corresponds to the guest length for which 2:1 complexes become stable for both hosts.22, 24 In the case of OA, the free energy drops to a broad minimum for alkanes ranging from C12 to C15. The 2:1 association free energy for C16 in OA dimers ticks up slight, although the difference between the C15 and C16 free energies is comparable to the simulation uncertainty. We interpret the drop in the free energy starting with C9 to the guest being able to span the interiors of the two encapsulating cavitands, gaining significant van der Waals interactions with both hosts. Previously we established that the end-toend interior length of an OA dimer is comparable to C11,27 with the guest bound in a trans-

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enriched extended conformational motif. Starting with C12 the alkane methyl ends collide with the opposing ends of the OA dimer interior, forcing the guest to adopt a helical motif to be accommodated within the complex. We attribute the minimum from C12 to C15 to competition between the guest gaining favorable van der Waals interactions while having to adopt unfavorable gauche conformations to fit within the host dimer. Starting with C17, we previously found alkanes adopt a hairpin like motif that may account for the slight uptick in : for C16 in OA dimers. In difference to OA, the endo-methyl substituents of TEMOA are found to restrict alkane conformations around the equatorial region of the capsule, ultimately favoring extended guest motifs. As a result, the 2:1 association free energies in TEMOA display a comparatively narrow minimum centered about C12. The dramatic increase in the association free energy beyond C12 reflects the inability of TEMOA to accommodate more compact guest conformations. This, in turn, contributes to the destabilization of TEMOA dimers and the experimental observation of tetrameric TEMOA 4:2 complexes for guests longer than tetradecane.23 While beyond the scope of the present work, we are actively examining the stability of multimeric TEMOA assemblies. Starting with the empty dimer, the complex formation free energies for the 2:2 assemblies are weakly decreasing functions of the length of the bound pair of guests (Figure 4c). Up to C4 the free energies of the 2:2 complexes of OA and TEMOA is essentially the same. In the case of TEMOA, : displays a minimum from C3 to C5, after which the association free energy becomes markedly repulsive for C6 and longer chains. This guest length corresponds to that where TEMOA experimentally reverts back from a 2:2 to a 1:1 complex.24 In contrast to TEMOA, the 2:2 OA association free energy continues to drop with increasing alkane length before reaching a minimum at C7, after which the free energy sharply rises. This compares

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qualitatively with the experimental observation that 2:2 complexes are stable over a broader range of guest lengths in OA compared to TEMOA, suggesting distinct assembly patterns between these hosts. Cavitand/Guest Assembly Model. The competitive equilibrium between the hosts and guests to assemble into distinct complexes can be rationalized via a reaction network model. The set of four reactions that describe assembly equilibrium between alkane guests () and distinct complexes (1:0, 1:1, 2:0, 2:1, and 2:2 assemblies) are 1:0 + ⇌ 1:1,

(1a)

1:0 + 1:0 ⇌ 2:0,

(1b)

1:1 + 1:0 ⇌ 2:1,

(1c)

1:1 + 1:1 ⇌ 2:2.

(1d)

and

For completeness we consider the formation of 2:0 complexes, eq. (1b), despite the fact empty dimers are not observed experimentally. The corresponding equilibrium reaction quotients are [:] [:][ ] [:] [:]

= :,

(2a)

= : ,

(2b)

[:] [:][:]

= :,

(2c)

and [:] [:]

= : .

(2d)

The equilibrium constants for the reaction network can be related to multi-dimensional integrals over all separations and orientations of the PMF between interacting guests and host cavitands.4547

The PMFs evaluated here, however, only consider a slice along a single reaction coordinate,

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omitting a significant fraction of the total integration domain. Nevertheless, headway towards rationalizing the observed assemblies can be made by assuming the equilibrium constants are proportional to the Boltzmann weighting of the PMF minima (Figure 4). The equilibrium constants in eq. (2) subsequently can be approximated as47 : = exp (−:/)

(3a)

for the formation of a 1:1 complex, and : = exp (−: /)

(3b)

for the formation of dimeric host complexes (x = 0, 1, or 2 encapsulated guests). Here the monomeric, α, and dimeric, β, pre-factors are adjustable parameters that account for the missing contributions from the equilibrium constant integral, including contributions from the myriad of non-complex forming reaction paths and the loss of host orientational degrees-of-freedom when forming a dimer. To minimize biasing of the distribution of assembly states, we make the reasonable assumptions that α and β are the same for both hosts and that β does not depend on the number of encapsulated guests. To fit α and β, we adjusted their values to reproduce the experimental assembly behavior to alkanes with OA, which only displays monotonic changes from monomeric to dimeric host assemblies with increasing guest length. These parameters were subsequently applied to predict the assembly behavior of TEMOA. The total concentration of cavitand hosts, [1] , in this reaction network is [1] = [1: 0] + [1: 1] + 2([2: 0] + [2: 1] + [2: 2]).

(4)

We assume [1] = 3 mM, corresponding to a typical experimental host concentration. The bulk alkane guest concentration in solution was determined from the relationship48-49 [] =

"#

%$exp (−& ' /),

12


(5)

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where ( is the gas phase guest partial pressure, RT is the product of the gas constant and temperature, and & ' is the excess chemical potential of the guest in water. The guest partial pressures were assumed to adopt the vapor pressure of the pure alkane liquids at 25°C, except in the case of those guests with normal boiling points below this temperature (i.e., C1 through C4). In this case, the guest pressure was assumed to be 1 atm. Alkane partial pressures at 25 °C, determined from Wagner correlation fits to experiment,50 used here are reported in the Supporting Information. The alkane guest excess chemical potentials at infinite dilution in water were determined from simulations using standard free energy perturbation techniques for the L-OPLS alkanes in TIP4P/EW water. Simulation details, guest excess chemical potentials, and saturated guest concentrations are reported in the Supporting Information. The reaction network model can be expressed as a quadratic equation in [1:0] [] )[1: 2(: + : : [] + : : 0] + (1 + : [])[1: 0] − [1] = 0,

(6)

whose analytical solution determines the concentrations of all the assemblies. The distribution of 1:0, 1:1, 2:1, and 2:2 complexes between OA and alkanes as a function of the guest length are reported in Figure 5a. The values of α and β used were 2 × 10-4 M-1 and 8 × 10-11 M-1, respectively. The progression of dominant (i.e., most populous) OA complexes with increasing guest chain length is: empty 1:0 OA monomers for no guest and C1; 1:1 OA/Cn complexes for C2 and C3, 2:2 OA/Cn complexes from C4 to C8; and 2:1 OA/Cn complexes for alkanes longer than C9. The population of empty dimer (2:0) complexes is negligible for all guest sizes, falling significantly below 0.1%, and therefore is not reported in Figure 5. While C3 preferentially stabilizes dimers experimentally, the predicted succession of OA/Cn complexes follows experiment.22, 24

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The predicted distribution of TEMOA/Cn complexes is reported in Figure 5b. The progression of dominant TEMOA assembly morphologies is: empty 1:0 TEMOA monomers for no added guest; 1:1 TEMOA/Cn complexes for C1 and C2; 2:2 TEMOA/alkane complexes for guests ranging in length from C3 to C5; 1:1 TEMOA/Cn complexes reemerge as dominant from C6 to C8; and finally 2:1 TEMOA/Cn complexes dominate for C9 and longer. This progression of assemblies is clearly non-monotonic, with the monomeric 1:1 complexes reemergent between the dimeric 2:2 and 2:1 complexes, clearly capturing the experimental differences between alkane assembly with OA versus TEMOA.22,

24

Our predicted population distributions capture other

assembly subtleties as well. For instance, experimentally it was observed that C1 forms a stronger 1:1 complex with TEMOA than with OA. It was postulated that this results from enhanced van der Waals interactions between the guest and the endo-methyl substituents of TEMOA. In agreement with experiment, our model predicts the 1:1 TEMOA complex is dominant for C1 (Figure 5b) while the 1:0 complex dominates for OA (Figure 5a), reflecting the enhanced attractions observed with TEMOA compared to OA (Figure 4a). In addition we observe for the longest guest considered, C16, the 2:1 complex with TEMOA is destabilized relative to that for OA. Experimentally, OA makes 2:1 complexes with alkanes ranging in length from C9 to C25.26 In the case of TEMOA, however, for guests longer than C14, the dimeric assemblies experimentally are destabilized in favor of 4:2 tetrameric and 6:3 hexameric assemblies.23 We attribute the destabilization of the TEMOA 2:1 dimers with the increasingly repulsive PMF minima for 2:1 complex formation beyond alkanes longer than C12 in TEMOA (Figure 4b). We note that the destabilization of the TEMOA 2:1 complex for C16 is accompanied by the growth in the empty 1:0 TEMOA host to 26% of the host population, while the 1:1 complex only increases marginally to 1% (Figure 5b). The preferential growth of the empty host

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population compared to the 1:1 complex is a direct result of the diminishing solubility of the alkanes with increasing length. The solubility of C16 with based on eq. (5) is on the order of 2 pM. When substituted in eq. (2a), the model predicts a larger population of empty hosts over 1:1 complexes. The comparative growth of the 1:0 versus 1:1 assemblies actually begins around C13, but the population of TEMOA dimers is too significant for the monomeric host complexes to register in Figure 5. The mean complex aggregation numbers (i.e., the mean number of complexed hosts averaged over all assembly states) can be evaluated from the distribution of cavitand/alkane assembly states (Figure 6). The OA aggregation number steadily increases from one to two over the range of guest lengths from no guest to C6, after which all the hosts exists as a dimer. Barring a slight hump for the OA/C2 complexes, the complex aggregation number increase is monotonic. The size of the C2 hump, however, is smaller than the error bars from C1 to C3, suggesting this minor feature is potentially an artifact. The aggregation numbers of the TEMOA complexes, however, are distinctly non-monotonic, initially growing from 1 to ~1.6 from no guest to C5, before dropping back down to monomeric aggregation for C6 through C8. For C9 and longer, TEMOA reassembles into dimers, although these dimers start to become unstable for C16. These observed trends for the assembly of OA and TEMOA are in excellent agreement with the variation in the cavitand/alkane complex volumes with alkane chain length inferred from NMR diffusion experiments.22, 24 We hypothesize that the non-monotonic assembly profile of TEMOA arises from differences in the 2:2 association free energies for OA and TEMOA (Figure 4c). While : for both hosts exhibit a minimum with chain length, this minimum occurs for shorter chain lengths in TEMOA than in OA. To test the hypothesis that : controls the reemergence of the 1:1

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complex, we substituted our : results for OA into the equilibrium network model for TEMOA. In this case, the non-monotonic aggregation behavior of TEMOA is suppressed, with the complexes monotonically switching between the monomeric to dimeric aggregation states (Figure 6 inset). The TEMOA/C16 complexes are still predicted to be destabilized compared to C15, since this results from the increasingly more repulsive values of : for TEMOA. Similarly, if : for TEMOA is substituted into the reaction network model for OA, OA is found to exhibit non-monotonic assembly patterns like TEMOA (not shown). These results support our hypothesis that the dimerization of 1:1 cavitand/alkane complexes to form 2:2 assemblies controls the distinct assembly patterns observed between the host species. Structural Differences Between OA and TEMOA Dimers. In addition to the PMF minima, we may also consider the inter-cavitand separations at which those minima occur to characterize the dimer structures and gain further insights into their relative stability. The equilibrium separation of the 2:1 OA complexes is ~3.5 Å, largely independent of chain length up to C16 (Figure 7a). The equilibrium separations of the 2:1 TEMOA complexes, on the other hand, display a more varied dependence on the guest size. Up to C12 the TEMOA host separation is ~4.2 Å. The comparatively greater separation for the TEMOA dimer reflects the protrusion of the endo-methyl substituents of TEMOA above the cavitand rim (Figure 2a). For guests longer than C12, the equilibrium TEMOA dimer separation increases with chain length as the guest pries the dimer open. The increasing separation is reflected in the corresponding increase in : for guests longer than C12 (Figure 4b), that ultimately destabilize the 2:1 TEMOA dimer. We attribute the increase in the 2:1 TEMOA equilibrium separation to the observation that n-alkanes encapsulated within this host adopt predominantly extended conformations, while a succession of conformational motifs can be packed within OA dimers with increasing chain length.26-27 The

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limited flexibility of the guest within TEMOA ultimately pries the dimers open for guests longer than can be accommodated within the internalized complex volume. In the case of the 2:2 OA complex, the dimer separation is independent of the guest chain length up to C8 (Figure 7a) with the same equilibrium separation as the 2:1 complex. For alkanes longer than C8, however, the equilibrium separation of the dimer systematically increases with the guest size. The increase in the OA dimer separation for guests longer than C8 is in reasonable coincidence with the minimum in : at C7 for OA (Figure 4c). In contrast to OA, the rise in the equilibrium 2:2 TEMOA dimer separations begins with alkanes longer than C5 in concordance with the narrower window of stability for this complex. If the host dimer separations are plotted as a function of the total van der Waals volume of the encapsulated guests rather than against the individual guest chain lengths, the results for the 2:1 and 2:2 capsular complexes can be brought into harmony (Figure 7b). For example, the 2:1 and 2:2 OA dimer equilibrium separations are the same up to an encapsulated guest volume of ~300 Å3, corresponding to 16 encapsulated carbons (one C16 or two C8’s). We might anticipate that the 2:1 OA complex will begin to open for C18 based on the fact that the 2:2 complex separation begins to increase with C9. Experimentally, however, 2:1 OA complexes with C18 and longer chains are stable. These experiments26 and our previously reported simulations,27 find that C18 is packed within the capsule interior in a hairpin motif, which is not observed for guests in the 2:2 complexes. Even longer alkanes adopt a spinning top motif in 2:1 OA complexes, which is only available for sufficiently long chains to incorporate the requisite number of turns along the guest backbone. In the case of the TEMOA dimers, we observe similarly excellent agreement between the 2:1 and 2:2 equilibrium separations over the full range of simulated guest volumes. In particular, the 2:2 results predict the host separation will start to

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increase when total guest volume is greater than ~220 Å3. This volume lies between that of an individual C12, corresponding to the guest size before the 2:1 TEMOA complex cracks, and two C6 chains, corresponding to the guest length for which the 2:2 TEMOA complex first opens. Beyond this guest volume the equilibrium separations for the 2:1 and 2:2 complexes match quantitatively. Our results implicate alkane guest packing as a primary determinant of the interhost separation, although the specific encapsulated guest volumes that begin to crack open and destabilize the complexes are host dependent, likely reflecting the differing shapes of the internalized spaces. In principal, the narrowing of TEMOA’s portal accounts for the differing assembly patterns of the two hosts, limiting the packing motifs available to the encapsulated guests. To quantify the width of the host portals we examine the lateral displacement of guest carbons at the seam between cavitand dimers in 2:1 complexes (Figure 8 inset). Specifically, we identify the guest carbon closest to the midpoint between the two hosts and measure the distance of the carbon from the line drawn through the midpoints of the two host portals. The root mean square displacements as a function of the alkane length are plotted in Figure 8. This figure shows that the side-to-side displacement of the guests is significantly restricted in TEMOA compared to OA over the entire range of alkanes simulated. Lateral displacements in both hosts are greatest for C1, as this guest is free to explore both the dimer seam as well as the depths of the host pockets. The lateral displacement decreases with increasing guest length as portions of the guests are forced to reside in the equatorial region of the capsule. Interestingly the displacement passes though a minimum with increasing guest chain length in both the OA and TEMOA dimer. In the former, we attribute the increase in the displacement for chains longer than ~C11 to conformational changes in the guest from a trans-enriched extended motif to a helical motif

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starting with C12.27 The helical motif is not been observed in 2:1 TEMOA complexes, however, as a result of the constriction of the host portal. The increase in the mean lateral displacement for alkanes longer than C12 largely results from the increase in the inter-host separation as the complex cracks open (Figure 7).

Conclusions In conclusion, we have advanced a molecular rationale for the surprising non-monotonic switching between monomeric and dimeric assembly states of deep cavity cavitand TEMOA with alkanes of increasing length. Molecular simulations of cavitand assembly with alkanes in water show that while the free energies of forming monomeric 1:1 complexes are qualitatively similar for OA and TEMOA, significant differences between hosts forming dimeric 2:1 and 2:2 complexes are observed. The endo-methyl substituents distinguishing TEMOA from OA tend to crowd alkanes within dimers, destabilizing TEMOA complexes with 12 or more carbons. Resultantly, the relative conformational freedom of guests within OA dimers is severely limited within TEMOA capsules. This constriction, in turn, manifests as increasingly repulsive contributions to the TEMOA 2:2 and 2:1 complex dimerization free energies for shorter alkanes than observed for OA. When the complexation free energies determined from our simulations are utilized within a reaction network model for the formation of monomeric and dimeric complexes, we find that our simulations accurately reproduce OA’s monotonic and TEMOA’s nonmonotonic assembly patterns, giving us confidence that our simulations capture the essential underlying physics. Moreover, our simulations suggests TEMOA 2:1 complexes to become destabilized for guests longer than C15, hinting at the experimental observation that multimeric complexes are stabilized for guests longer than those investigated here.23

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Our work highlights the fact that small chemical modifications to constituents of a supramolecular assembly can dramatically impact on their structure and properties. Moreover, the computational strategy utilized here demonstrates the role molecular simulations can play in interpreting the impact of chemical modification on the assemblies observed to aid in their bottom-up design. The guest packing-controlled assembly between distinct supramolecular structures is reminiscent of the elaborate switching properties of many proteins, promising a potential route to enable biomimetic functions within synthetic materials.

Supporting Information Full alkane/cavitand potential of mean force profiles and the thermodynamic properties used to evaluate n-alkane solubilities in aqueous solution are provided in the supporting information.

Acknowledgements We gratefully acknowledge financial support from the NSF (CBET-1403167). We also thank the Louisiana Optical Network Initiative who provided computational support.

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Figure Captions Figure 1. Chemical structures of hosts OA and TEMOA.

Figure 2. Illustrations of the host and host/guest complex structures. a) Top (face) views of OA and TEMOA hosts and side view of TEMOA. The main body of the cavitand host (OA) is shown as a wire frame view. The additional four endo-methyls of TAMOA are highlighted as bronze van der Waals surfaces. The cavitand host C4-axis of symmetry is pictured in the TEMOA side view. b) 1:1, 2:1, and 2:2 complexes between OA and C8. The cavitand host is illustrated as the red and blue surfaces, while the octane guests are depicted by the van der Waals surfaces. The side of the complexes has been peeled back to show the guests within.

Figure 3. Potentials of mean force determined from simulation for formation of 1:1, 2:1, and 2:2 complexes between nonane and OA. In this figure z = 0 Å corresponds to the face of one of the cavitands held on the left-hand side of this diagram with the pocket facing right. Symbols for the 1:1, 2:1, and 2:2 interactions are defined in the figure legend. Error bars are omitted for clarity.

Figure 4. Potential of mean force minima determined for cavitand/alkane complex formation as a function of the alkane chain length. Figures a, b, and c report minima for 1:1, 2:1, and 2:2 complex formation, respectively. Symbols for complex formation with OA and TEMOA are defined in the figure legend in a. Error bars indicate one standard deviation.

Figure 5. Predicted distribution of cavitand/alkane complex morphologies between 1:0, 1:1, 2:1, and 2:2 assembly states as a function of alkane chain length. Results for OA and TEMOA are

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reported in a and b, respectively. Symbols for the 1:0, 1:1, 2:1, and 2:2 assemblies are defined by figure legend. The population of 2:0 complexes was found to be negligible, falling below 0.1%, and subsequently are not reported in this figure. The total cavitand concentration in solution is 3 mM. The values of α and β used in the equilibrium constants for OA and TEMOA in eq. (4) were 2×10-4 M-1 and 8×10-11 M-1, respectively. Error bars are not reported here for clarity.

Figure 6. Average cavitand aggregation number in cavitand/alkane complexes as a function of the alkane guest length. Results for OA and TEMOA are defined by figure legend. Error bars indicate one standard deviation. The inset figure illustrates the predicted TEMOA aggregation numbers obtained using the : results for OA reported in Figure 3c.

Figure 7. Equilibrium 2:1 and 2:2 inter-host separation as a function of the encapsulated guest length (a) and total encapsulated guest van der Waals volume (b). The equilibrium separation is determined by the position of the minimum in the dimerization PMFs. Symbols are defined in the legend in a.

Figure 8. Root mean square lateral displacement from the complex centerline for the guest carbon closest to the seam in 2:1 assemblies as a function of the guest length. Figure symbols are defined in the legend. Error bars indicate one standard deviation. The lateral displacement, ∆r, is illustrated in the inset figure. The centerline (dashed) is determined by the line connecting the center points of the mouth of each cavitand. The distance is measured distance is relative to the carbon atom closest to the seam between the two hosts, identified by the open circle.

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Figure 1.

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Figure 3.

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Figure 4.

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Figure 5.

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Figure 6.

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Figure 7.

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Figure 8.

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Table of Contents Figure.

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Guest Controlled Nonmonotonic Deep Cavity Cavitand Assembly

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