Collective Effects of Multiple Chiral Selectors on Enantioselective

Jul 7, 2009 - Molecular simulations were performed to predict the adsorption of racemic mixtures of (R,S)-1,3-dimethylallene (DMA) in three homochiral...
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Collective Effects of Multiple Chiral Selectors on Enantioselective Adsorption Xiaoying Bao, Randall Q. Snurr,* and Linda J. Broadbelt* Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208 Received April 7, 2009. Revised Manuscript Received June 15, 2009 Molecular simulations were performed to predict the adsorption of racemic mixtures of (R,S)-1,3-dimethylallene (DMA) in three homochiral metal-organic frameworks (HMOFs). All three HMOFs include the same chiral linker, (R)-6,60 -dichloro-2,20 -dihydroxy-1,10 -binaphthyl-4,40 -bipyridine (L), but have different topologies. While a single linker L shows very little enantioselectivity between the DMA enantiomers, the three HMOFs with closely packed linkers L have enantiomeric excesses of 6%, 28%, and 45%, showing that closely situated chiral selectors function synergistically to enhance the enantioselectivity. Both the confinement created by the linkers and the number of chiral linkers that form the confinement are important in enhancing the enantioselectivity. In addition, the simulations show that the enantioselectivity of the three HMOFs may be further enhanced by modifying the composition of the linker L.

Introduction Studies of chiral separation mechanisms often focus on analyzing the diastereomeric complexes formed between one chiral selector molecule and the two selectand enantiomers.1-6 A commonly employed strategy to improve enantioselectivity is to adjust the molecular structure or composition of the selector to maximize the potential energy differences between the two diastereomeric complexes.4,7 However, the collective effects of an array of closely spaced chiral selectors on chiral stationary phases (CSPs) are usually not studied, although it has been suggested that such effects may be significant for chiral discrimination.4,5,8-10 Unfortunately, these collective effects are often difficult to take into account because of the irregular, noncrystalline nature of conventional CSPs.4 In this work, it is demonstrated computationally that both the chiral selector and the collective effect of the closely spaced chiral selectors in/on the chiral stationary phase are important factors to be considered to maximize the energy differences between the diastereomeric complexes. The enantioselectivity of a chiral stationary phase may be enhanced drastically if multiple chiral selectors are packed together to function synergistically for enantioselective separation. In turn, the enantioselectivity of these packed structures is dependent on the molecular composition of the individual chiral selectors. Homochiral metal-organic frameworks (HMOFs) are used here to demonstrate these concepts. Homochiral MOFs are *Corresponding author. E-mail: [email protected] (R.Q.S.); [email protected] (L.J.B.). (1) Bentley, R. Arch. Biochem. Biophys. 2003, 414, 1–12. (2) Lipkowitz, K. B. J. Chromatogr., A 2001, 906, 417–442. (3) Abel, C.; Juza, M. Chiral Separation Techniques, 3rd ed.; Wiley-VCH Verlag, GmbH & Co. KGaA: Weinheim, 2007. (4) Ahuja, S. Chiral Separations by Chromatography; Oxford University Press: New York, 2000. (5) Davankov, V. A. Chirality 1997, 9, 99–102. (6) Radhakrishnan, T. P.; Topiol, S.; Biedermann, P. U.; Garten, S.; Agranat, I. Chem. Commun. 2002, 2664. (7) Lipkowitz, K. B.; Demeter, D. A.; Zegarra, R.; Larter, R.; Darden, T. J. Am. Chem. Soc. 1988, 110, 3446–3452. (8) Bao, X. Y.; Broadbelt, L. J.; Snurr, R. Q. Mol. Simul. 2009, 35, 50–59. (9) Davankov, V. A.; Meyer, V. R.; Rais, M. Chirality 1990, 2, 208–210. (10) Okamoto, Y.; Yashima, E. Angew. Chem., Int. Ed. 1998, 37, 1020–1043.

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metal-organic frameworks11-16 with a single sense of chirality throughout the framework.17-20 Most of the HMOFs reported so far are synthesized by using metal or metal oxide nodes connected by homochiral linkers.20 Unlike conventional CSPs, the structures of HMOFs are regular, and they can be determined accurately from X-ray diffraction, which makes it possible to investigate the collective effect of closely spaced chiral linkers. Three HMOFs (HMOFs 1-3), made from the same chiral linker, (R)-6,60 -dichloro-2,20 -dihydroxy-1,10 -binaphthyl-4,40 -bipyridine (L), and the same metal center, Cd, but different counterions and auxiliary ligands were chosen for this study.21,22 The chemical formulas of HMOFs 1-3 are [CdL2(H2O)2][ClO4]2,21 Cd3Cl6L3,22 and Cd3L4(NO3)6.21 The structures of HMOFs 13 are shown in Figure 1. HMOFs 1-3 are thermally stable, and they retain their structural integrity upon solvent removal.21,22 HMOFs 1-3 possess pores with sizes ranging from 0.5 to 1.8 nm, ideal for enantioselective adsorption.8 Linker L packs differently in the three structures, as shown by the different space groups of HMOFs 1-3 (P43212, P1, and P4122). This makes HMOFs 1-3 perfect candidates for elucidating the effect of linker packing on enantioselectivity. (R,S)-1,3-Dimethyl-1,2-propadiene, commonly known as (R,S)-1,3-dimethylallene (DMA), was studied as a simple sorbate. (11) Eddaoudi, M.; Moler, D. B.; Li, H. L.; Chen, B. L.; Reineke, T. M.; O0 Keeffe, M.; Yaghi, O. M. Acc. Chem. Res. 2001, 34, 319–330. (12) Kitagawa, S.; Kitaura, R.; Noro, S. Angew. Chem., Int. Ed. 2004, 43, 2334– 2375. (13) Rowsell, J. L. C.; Yaghi, O. M. Microporous Mesoporous Mater. 2004, 73, 3–14. (14) Snurr, R. Q.; Hupp, J. T.; Nguyen, S. T. AIChE J. 2004, 50, 1090–1095. (15) Maspoch, D.; Ruiz-Molina, D.; Veciana, J. Chem. Soc. Rev. 2007, 36, 770– 818. (16) Ferey, G. Chem. Soc. Rev. 2008, 37, 191–214. (17) Bradshaw, D.; Claridge, J. B.; Cussen, E. J.; Prior, T. J.; Rosseinsky, M. J. Acc. Chem. Res. 2005, 38, 273–282. (18) Kesanli, B.; Lin, W. B. Coord. Chem. Rev. 2003, 246, 305–326. (19) Lee, S.; Mallik, A. B.; Xu, Z. T.; Lobkovsky, E. B.; Tran, L. Acc. Chem. Res. 2005, 38, 251–261. (20) Lin, W. B. MRS Bull. 2007, 32, 544–548. (21) Wu, C. D.; Lin, W. B. Angew. Chem., Int. Ed. 2007, 46, 1075–1078. (22) Wu, C. D.; Hu, A.; Zhang, L.; Lin, W. B. J. Am. Chem. Soc. 2005, 127, 8940–8941.

Published on Web 07/07/2009

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Figure 1. Crystal structures of HMOFs 1-3. the LJ parameters were taken from related studies.8,28-30 The Lorentz-Berthelot mixing rules were used to obtain the HMOFsorbate interaction parameters, and the LJ cutoff was 8.98 A˚. Monte Carlo (MC) simulations in the NVT ensemble were used to estimate the average potential energy ÆΔEæ of a single DMA enantiomer molecule with the periodic HMOF frameworks or nonperiodic structures formed by several linkers. Random translation/rotation and reinsertion moves were employed. In the periodic HMOFs, the average potential energy was estimated as R ÆΔEæ ¼

Methods The adsorption isotherms of DMA racemic mixtures in HMOFs 1-3 were predicted with the Music code23 using grand canonical Monte Carlo (GCMC) simulation in the μVT ensemble at 300 K. To speed up convergence, energy-biased insertions of the sorbate molecules were employed. Acceptance ratios for insertions and deletions were above 1% (slightly lower at the higher loadings) to ensure good equilibration in GCMC simulations.24 A total of 240-480 million GCMC moves were attempted during each GCMC simulation. The crystallographic information of the HMOFs 1-3 frameworks was taken from the literature.21,22 To speed up computation, the HMOF frameworks and the sorbate molecules were taken to be rigid during the GCMC simulation. The rigid framework assumption is based on the fact that there are no long, dangling groups in the HMOF structures. Also, previous work has shown that framework flexibility has only a limited effect on adsorption of hydrocarbons in zeolites.25 The rigid sorbate molecule assumption is based on the rigidity of the allene backbone in the DMA enantiomers. The geometries of the sorbate molecules were obtained by optimizing them using density functional theory with the B3LYP functional26 and the 6-31G basis set. Due to the lack of strongly charged groups in the sorbate molecules, Coulombic interactions between the sorbate-sorbate and sorbate-sorbent atom pairs were neglected. van der Waals interactions were modeled using Lennard-Jones (LJ) sites on the sorbate and HMOF atoms. To further simplify the calculations, the CH3 groups in the sorbates were modeled as united atoms. Table S1 in the Supporting Information lists the LJ parameters used for this study. For the HMOFs, the LJ parameters were taken from the universal force field (UFF),27 while for the sorbates (23) Gupta, A.; Chempath, S.; Sanborn, M. J.; Clark, L. A.; Snurr, R. Q. Mol. Simul. 2003, 29, 29–46. (24) Snurr, R. Q.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1993, 97, 13742– 13752. (25) Vlugt, T. J. H.; Schenk, M. J. Phys. Chem. B 2002, 106, 12757–13763. (26) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (27) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024–10035. (28) Clark, L. A.; Chempath, S.; Snurr, R. Q. Langmuir 2005, 21, 2267–2272.

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h i ΔEðrB, ψB Þ exp -βΔEðrB, ψB Þ drB d ψ B   R B B exp -βΔEðrB, ψ Þ drBd ψ

where B r and ψB stand for the position and orientation, respectively, of the center of mass of the sorbate enantiomer molecule. B r can be any position in the unit cell. β is 1/kT with k representing Boltzmann’s constant. For nonperiodic structures, the following formula was used to estimate the average potential energy: R ÆΔEæ ¼

  ΔEðrB, ψB Þ exp -βΔEðrB, ψB Þ H drB d ψB   R exp -βΔEðrB, ψB Þ H drB d ψB

where B r , ψB, and β are as defined above and H is a step function specifying that if any atom in the sorbate molecule is not interacting with at least one atom in the nonperiodic structure, then H = 0; otherwise, H = 1. This is to prevent the sorbate molecule from escaping from the nonperiodic structure during simulation. A pseudocode describing the algorithm is given in the Supporting Information (Figure S1). The average potential energy difference between the two DMA enantiomers in the HMOF or the nonperiodic structure was calculated using the formula: ΔÆΔEæ = ÆΔERæ - ÆΔESæ. The GCMC and MC simulations in this study were well equilibrated, and the results are not sensitive to the initial positions of the sorbate molecules. In addition to the ensemble-averaged quantities, simulated annealing using MC in the NVT ensemble was employed to identify the energy minima ΔE0 of the two DMA enantiomers in the HMOFs. The energy difference of the two enantiomers at the global energy minima was calculated using the formula: R Δ(ΔE0)=ΔER 0 - ΔE0 . The temperature of the system was cooled from 1500 to 0.01 K in 13 steps. During each step, 1  105 MC steps were performed on each sorbate molecule. The simulated annealing was repeated 500-1000 times to ensure that global energy minima of the sorbates within the HMOFs were found.

(29) Sholl, D. S. Langmuir 1998, 14, 862–867. (30) Szabelski, P.; Panczyk, T.; Drach, M. Langmuir 2008, 24, 12972–12980.

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Figure 2. Calculated adsorption isotherms for a racemic mixture of (R,S)-1,2-dimethylallene (DMA) in (a) HMOF 1, (b) HMOF 2, and (c) HMOF 3 at 300 K and the enantiomeric excess (ee) of the DMA enantiomers in (d) HMOF 1, (e) HMOF 2, and (f) HMOF 3.

Results and Discussion Adsorption Isotherms and Energy Differences. Figure 2 shows the enantioselective adsorption isotherms and the enantiomeric excess (ee) of the DMA enantiomers in HMOFs 1-3. Although the three HMOFs are made from the same chiral linker, their enantioselectivities for DMA are quite different. While HMOF 2 and HMOF 3 show good enantioselectivity between the DMA enantiomers, HMOF 1 showed only weak enantioselectivity. The enantiomeric excess (ee) is defined as the absolute difference between the mole fractions of the two enantiomers. The maximum ee values of the DMA enantiomers in HMOFs 1-3 are 6%, 28% and 45%, respectively. The average potential energies ÆΔEæ and the average potential energy differences |ΔÆΔEæ| are displayed in Table S2 in the Supporting Information. They are consistent with the isotherms and the ee; that is, the more favored enantiomer has the lower average potential energy of adsorption. It is interesting to note that the ee values shown in Figure 2 decrease with increasing fugacity in all three HMOFs, which suggests that the low energy states in HMOFs 1-3 are more enantioselective than the higher energy states. To elucidate this, the global energy minima ΔE0 of the DMA enantiomers in HMOFs 1-3 were calculated by simulated annealing and are also shown in Table S2 in the Supporting Information. Similar to the average potential energy differences |ΔÆΔEæ|, the differences between the minimum energies |Δ(ΔE0)| also agree qualitatively with the ee values seen in Figure 2; that is, HMOF 2 and HMOF 3 have larger |Δ(ΔE0)| values and larger ee values, while HMOF 1 has a low |Δ(ΔE0)| value and enantioselectivity. To further investigate how important the global potential energy minima are for enantioselective adsorption, the potential energy histograms of a DMA enantiomer in the three HMOFs were tabulated and are shown in Figure 3. It is seen that, for HMOFs 1-3, the differences in overall potential energies |ΔÆΔEæ| of the DMA enantiomers are mainly due to the energy differences around the global potential energy minimum states |Δ(ΔE0)| of 10732 DOI: 10.1021/la901240n

the DMA enantiomers. This illustrates the key role of the potential energy minima in the enantioselective adsorption. To isolate the effect of linker packing, the energy histograms of the two DMA enantiomers in HMOFs 1-3 were also tallied with the atoms in the metal centers, auxiliary ligands, and counterions treated as hard spheres (ε/k ∼ 0). The results are shown in Figure 4. It is seen that these modifications barely change the shapes and trends of the histograms. HMOF 3 remains the most enantioselective for the DMA enantiomers, followed by HMOF 2 and HMOF 1. Furthermore, the overall differences between the energies of the DMA enantiomers are still due to the energy differences around the energy minima. Figure 4 convincingly shows that the packing of linker L in HMOFs 1-3 is the dominant factor affecting the global energy minima, the average potential energy differences, and the enantioselectivity between the DMA enantiomers. Effect of Linker Packing on Enantioselectivity. To further examine how the packing of linker L affects the global potential energy minimum states, the linkers that interact with the DMA enantiomers at the global energy minimum states in HMOFs 1-3 were isolated and are shown in Figure 5. Dispersive interactions vanish rapidly with distance; therefore, only the linkers that fall within (or partially within) the Lennard-Jones cutoff of the DMA enantiomers at their energy minimum states are included in Figure 5. These linkers will be referred to as chiral clusters. To better visualize the chiral clusters, the metal ions, auxiliary ligands, and counterions are not shown. In Figure 5, it is seen that, in the chiral cluster of HMOF 1, there are only two linkers interacting with the DMA enantiomers, while in HMOF 2 and HMOF 3 there are three and six linkers interacting with the DMA enantiomers, respectively. The linkers in the chiral clusters are packed according to the symmetry operations defined by the space group of the HMOF. To make a direct comparison between the chiral clusters and a single linker L, the average potential energy ÆΔEæ, the potential energy minima ΔE0, the average potential energy difference |ΔÆΔEæ|, and the Langmuir 2009, 25(18), 10730–10736

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Figure 3. Energy histograms of the DMA enantiomers in (a) HMOF 1, (b) HMOF 2, and (c) HMOF 3.

Figure 4. Energy histograms of the DMA enantiomers in (a) HMOF 1, (b) HMOF 2, and (c) HMOF 3 when the metal centers, auxiliary ligands, and counterions are treated as hard spheres.

Figure 5. Global potential energy minima of DMA enantiomers in HMOFs 1-3, with the surrounding linkers that form chiral clusters. DMA molecules are shown with a space-filling model, while chiral clusters are shown in a stick model. In the DMA molecules: C (gray), H (white), CH3 (violet red). In the chiral clusters: C (gray), H (white), Cl (green), N (blue), O (red), Cd (yellow).

potential energy minima difference |Δ(ΔE0)| of the DMA enantiomers around these chiral clusters and a single linker L were Langmuir 2009, 25(18), 10730–10736

calculated and are listed in Table S3 in the Supporting Information. It is seen that a single linker L shows very small |ΔÆΔEæ| and |Δ(ΔE0)| values for the two DMA enantiomers, while multiple linkers in the chiral clusters dramatically increase the |ΔÆΔEæ| and |Δ(ΔE0)| values for the two DMA enantiomers. In addition, the increase in |ΔÆΔEæ| and |Δ(ΔE0)| increases with the number of linkers that are present in the chiral clusters. To further explore the effect of linker packing on the enantioselectivity, three simple hypothetical chiral clusters (HCCs) were constructed as shown in Figure 6. HCC 1 consists of two linkers L spaced by a distance of D, with the binaphthyl groups on the two linkers arranged parallel to one another. HCC 2 consists of three linkers with the same orientation arranged in an isosceles right triangle with a side length of D. HCC 3 consists of four linkers L with the same orientation arranged in a square with a uniform side length of D. The average potential energies ÆΔEæ and the average potential energy differences ΔÆΔEæ of the DMA enantiomers interacting with the chiral clusters were studied to assess the effect of the number of chiral linkers in the HCCs and the HCC size as measured by D. During the simulation, HCC atoms were taken to be fixed in space. The value of D was varied from 5 to 12 A˚ for the hypothetical chiral clusters. When D is sufficiently small, the linkers in the HCCs form enclosures (or sandwiches in the case of HCC 1) that can host the DMA molecules. The average potential energies ÆΔEæ and the average potential energy differences ΔÆΔEæ of the DMA enantiomers around the three hypothetical chiral clusters (HCCs) are shown in Figure 7. It is seen that, in all three hypothetical chiral clusters, the ÆΔEæ values follow the same trend. Namely, the ÆΔEæ values for both enantiomers decrease with decreasing D until a critical value of D is reached where the ÆΔEæ values begin to increase. The initial decrease in ÆΔEæ is due to the formation of enclosures of suitable size for the DMA enantiomers, and the increase in ÆΔEæ after the minimum is reached is due to the formation of overly tight enclosures that becomes less accessible to the DMA enantiomers gradually. This is also illustrated in Figure 8 for HCC 3 for three different values of D. As D is decreased even further, ÆΔEæ actually decreases gradually. This occurs because, at this stage, most of the DOI: 10.1021/la901240n

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Figure 6. Hypothetical chiral clusters (HCCs).

Figure 7. Average potential energies ÆΔEæ and average potential energy differences ΔÆΔEæ of the DMA enantiomers interacting with the hypothetical chiral clusters (HCCs) plotted against the distance between the linkers in the HCCs (D).

DMA enantiomers are outside the overly tight enclosure. Bringing the linkers together by decreasing D increases the density of linker atoms that are able to interact closely with the DMA enantiomers, hence decreasing the ÆΔEæ values. 10734 DOI: 10.1021/la901240n

There are two key observations regarding the ΔÆΔEæ values from Figure 7. First, for all three hypothetical chiral clusters, the largest |ΔÆΔEæ| values occur at D values where the minimum of ÆΔEæ is reached, or at slightly smaller D values. This implies that these hypothetical chiral clusters are most enantioselective when a proper confinement that fits the DMA enantiomers is formed. For example, in HCC 3, the minimum ÆΔEæ for the DMA enantiomers occurs at D=7.75 A˚, and the region with significant enantioselectivity (|ΔÆΔEæ| > 1.0 kJ/mol) occurs at D = 7.057.50 A˚. To further study the effect of confinement, a single linker confined in a purely repulsive pore was constructed as shown in Figure S2 in the Supporting Information. Figure 9 shows the average potential energies ÆΔEæ and the average potential energy differences ΔÆΔEæ of the DMA enantiomers plotted against the radius R of the pore. It is seen from Figure 9 that as the pore radius decreases, the absolute values of both ÆΔEæ and ΔÆΔEæ increase. Nonetheless, the highest |ΔÆΔEæ| value obtained is well below 1.0 kJ/mol, which suggests that confinement alone is not enough to create a high enantioselectivity with a single linker. This suggests that proper confinement is a necessary but not a sufficient condition for high enantioselectivity. The second key observation from Figure 7 is that the maximum |ΔÆΔEæ| values increase with the number of linkers in the cluster: the maximum |ΔÆΔEæ| values in HCCs 1-3 are 1.9, 2.5, and 12.2 kJ/mol, respectively. This echoes the fact that the highest |ΔÆΔEæ| value in the HMOFs was obtained in HMOF 3, where six linkers form a chiral cluster to interact with the DMA enantiomers at their minimum energy states. The effect of the number of chiral linkers may be understood by the fact that when more linkers are involved, there are more atoms that are able to interact differently with the guest enantiomers, creating the higher enantioselectivity. Effect of Linker Modification on Enantioselectivity. The above discussion shows how the enantioselectivity may be enhanced through multiple linker interactions between the chiral clusters and the enantiomers. Because it is an integral part of the chiral clusters, the identity of chiral linker L is another important factor to consider. To investigate this, the atoms on the 6,60 positions of the binaphthyl moieties were modified, since these atoms interact closely with the DMA enantiomers at their global potential energy minima (see Figure 5). Specifically, HMOFs 1-3 were reconstructed using three derivatives of linker L with different halogen atoms on the 6,60 - positions of the binaphthyl moieties. The structures of the derivatives are shown in Figure 10. The positions of the halogen atoms (F, Br, and I) were obtained by quantum chemical calculations using density functional theory with the B3LYP functional26 and the 6-31G basis set on a linker with all atoms in the linker fixed except for the halogen atoms. Langmuir 2009, 25(18), 10730–10736

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Figure 8. Positions where 10 000 centers-of-mass of the DMA enantiomers have visited in three HCC 3s with different D values. Red, R-DMA; green, S-DMA. When D = 10.00 A˚, the enclosure is loose. When D = 7.75 A˚, the enclosure fits the DMA enantiomers well so that no DMA enantiomers can be found outside of the enclosure. When D = 7.15 A˚, the enclosure becomes too tight and some DMA molecules occupy the spaces outside of the enclosure.

Figure 9. Average potential energies ÆΔEæ and average potential energy differences ΔÆΔEæ of the DMA enantiomers in the pore shown in Figure S2 in the Supporting Information plotted against the pore radius (R).

Figure 10. Linkers L with different atoms substituted in the 6,60 positions of the binaphthyl moieties.

The average potential energies ÆΔEæ and the average potential energy differences |ΔÆΔEæ| of the DMA enantiomers in the modified HMOFs 1-3 were calculated and are shown in Table S4 in the Supporting Information. It is seen that the |ΔÆΔEæ| value of a single linker L barely changes when the modifications are made, whereas the |ΔÆΔEæ| values of HMOF 1 and HMOF 2 increase with increasing halogen size. For example, by using LI instead of LCl, the |ΔÆΔEæ| values for HMOF 1 and HMOF 2 increase from 0.65 to 1.18 kJ/mol and 4.07 to 5.11 kJ/mol, respectively. In other words, HMOF 1 and HMOF 2 are more enantioselective after the modification. A comparison of the energy histograms of DMA enantiomers in HMOF 1 and HMOF 2 before and after modification (not shown) shows that the increase in |ΔÆΔEæ| after the modification is mainly due to even more enantioselective lower energy states. Langmuir 2009, 25(18), 10730–10736

The changes in the |ΔÆΔEæ| values of the DMA enantiomers in modified versions of HMOF 3 are more complicated. While HMOF 3 LF and HMOF 3 LI are less enantioselective (|ΔÆΔEæ| = 1.92 and 0.25 kJ/mol, respectively), HMOF 3 LCl and HMOF 3 LBr are highly enantioselective (|ΔÆΔEæ| = 19.84 and 19.89 kJ/ mol, respectively). To find out why a subtle change in composition resulted in large differences in enantioselectivity, the energy histograms of the DMA enantiomers in HMOF 3 LF to HMOF 3 LI were calculated and are displayed in Figure 11. We noticed that the low energy states for all four materials are located almost exclusively at x=-0.07 to 0.07; y=0.00 to 0.12; z=0.43 to 0.57 in the unit cells of the modified versions of HMOF 3 (plus all other equivalent locations defined by symmetry). The energy histograms of the DMA enantiomers in these low energy states are also shown in Figure 11 (lines with 0 symbols). It is seen that the low energy states in HMOF 3 LF are accessible to both of the DMA enantiomers, while the low energy states in HMOF 3 LI are barely accessible to either of the DMA enantiomers. This explains the low enantioselectivities of HMOF 3 LF and HMOF 3 LI. On the other hand, the low energy states in HMOF 3 LCl and HMOF 3 LBr are accessible to only one DMA enantiomer, which explains the high enantioselectivities of HMOF 3 LCl and HMOF 3 LBr. To see why the accessibility of the low energy states of the DMA enantiomers is different in different modified HMOF 3, the low energy states of the DMA enantiomers and the Connolly surface (shown in gray) of the linkers surrounding these low energy states are visualized in Figure 12. The low energy states are situated in an open pocket that is defined by the six linkers (see also Figure 5). Note that as the modification goes from F to I, the pocket gets tightened gradually (see Figure 12). To examine how the tightening of the pocket affects the accessibility of the DMA enantiomers, the occupation frequency, f, of the low energy states and the average energy ÆΔEælow of a DMA enantiomer in the low energy states are given in Figure 12. The occupation frequency f is defined as the percentage of configurations that a DMA enantiomer stays in the low energy states as opposed to the other higher energy states during the MC simulation. It is seen from Figure 12 that, in HMOF 3 LF, the pocket is loose and it is almost equally accessible to both DMA enantiomers, with f = 71.5% and 72.0% for S-DMA and R-DMA, respectively. The average energies of S-DMA and R-DMA at the low energy states in HMOF 3 LF are also close (-57.8 and -56.8 kJ/mol, respectively). In HMOF 3 LCl, the pocket is tightened and the occupation frequency of S-DMA drops drastically to 22.1%, while the occupation frequency of R-DMA increases slightly to 77.2%. Clearly, as the pocket is tightened, it starts to prefer R-DMA much more than S-DMA. DOI: 10.1021/la901240n

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Figure 11. Energy histograms of the DMA enantiomers in (a) HMOF 3 LF, (b) HMOF 3 LCl, (c) HMOF 3 LBr, and (d) HMOF 3 LI. The lines with 0 symbols are energy histograms of the low energy states. See text for the definition of the low energy states.

too tight for both DMA enantiomers but it still prefers R-DMA. Finally, the tightest pocket, present in HMOF 3 LI, is no longer accessible to S-DMA, and it is only very weakly accessible to R-DMA (f = 4.9%). Since the other energy states in HMOF 3 LI are not enantioselective (see Figure 11), the overall enantioselectivity of HMOF 3 LI is low.

Conclusion The collective effect of multiple chiral selectors on enantioselective adsorption has been demonstrated using molecular simulations in three homochiral metal-organic frameworks (HMOFs). We have shown that multiple chiral selectors that form a suitably tight chiral enclosure yield high enantioselectivity. Based on our study, it is believed that HMOFs are good candidates for enantioselective adsorption, and they are well suited for increasing our understanding of the collective effects of multiple chiral selectors. Furthermore, the enantioselectivity of chiral clusters packed by multiple chiral selectors can be finely tuned by adjusting the molecular composition of individual chiral selectors. Acknowledgment. We thank Dr. David Dubbeldam for valuable discussions and the National Science Foundation (CTS0507013) for financial support. We also acknowledge TeraGrid for computational resources on Leer at Purdue University under Project Number TG-MCA06N048. Figure 12. Low energy states of the DMA enantiomers in the modified versions of HMOF 3. Green, S-DMA; red, R-DMA. The Connolly surface of the linkers surrounding the low energy states is shown in gray. The black arrow shows the tightening of the pocket formed by the linkers. f is the percent occupation frequency of the low energy states, and ÆΔEælow is the average potential energy of the low energy states.

Such a preference is also confirmed by the average energy ÆΔEælow. For example, ÆΔEælow of S-DMA increases from -56.8 to -53.1 kJ/mol, while ÆΔEælow of R-DMA decreases from -57.8 to -64.7 kJ/mol. As the pocket is further tightened in HMOF 3 LBr, the occupation frequency of both S-DMA and R-DMA decreases to 2.3% and 55.5%, which suggests that the pocket is getting a little

10736 DOI: 10.1021/la901240n

Supporting Information Available: Pseudocode describing the algorithm for estimating the average potential energy of a sorbate molecule in nonperiodic structures; illustration of a single linker confined in a purely repulsive cylindrical pore; Lennard-Jones parameters for the sorbate DMA and HMOFs 1-3; the ÆΔEæ, ΔE0, |ΔÆΔEæ|, and |Δ(ΔE0)| of the DMA enantiomers in HMOFs 1-3; the ÆΔEæ, ΔE0, |ΔÆΔEæ|, and |ΔÆΔE0æ| of the DMA enantiomers around the chiral clusters; the ÆΔEæ and |ΔÆΔEæ| of the DMA enantiomers in modified HMOFs 1-3 with linkers LF, LCl, LBr, and LI. This material is available free of charge via the Internet at http:// pubs.acs.org.

Langmuir 2009, 25(18), 10730–10736