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Shuttling Process in [2]Rotaxanes. Modeling by Molecular Dynamics and Free Energy Perturbation Simulations Xavi Grabuleda, Petko Ivanov,† and Carlos Jaime* Department of Chemistry, Faculty of Sciences, UniVersitat Auto` noma de Barcelona, 08193 Bellaterra, Spain ReceiVed: March 14, 2003; In Final Form: May 14, 2003
The first application of a methodology previously developed and tested on pseudorotaxanes is presented here in the study of the structure and the energetics of [2]rotaxane 1. The approach is based on the AMBER force field with RESP charges, and on an explicit solvent model for acetonitrile. With this model, the experimentally observed free energy difference (0.98 kcal mol-1) between the two translational isomers of 1 (computed ∆G ) 1.06 ( 0.04 kcal mol-1) was correctly reproduced. The linear component of the suprastructure adopts an extended conformation, as suggested by the free energy perturbation simulations.
Introduction Rotaxanes are among the most frequently used systems for building artificial molecular machines.1,2 These fascinating molecules contain a linear-shaped fragment threaded through one or more macrocyclic rings.3 The linear chain is usually flanked by large groups that prevent it from slipping out of the macrocycle: these are true rotaxanes. When large groups (blockers) are not present, the linear component is unhindered by a high enough barrier and can then slip out of the macroring: these are pseudorotaxanes. Intermediate situations can be found depending on the experimental conditions (solvent, temperature, etc.).4 While pseudorotaxanes are in fact inclusion complexes, they can be studied using the methodologies of host/ guest chemistry. Rotaxanes are thus a new class of molecules having their components interlocked mechanically. In contrast to the extensive developments in the synthesis of rotaxanes2 and their derivatives,5 as well as developments in their nanotechnology,6 computational studies aimed at rationalizing and predicting the underlying processes are rather scarce. In fact, there are few articles on computational studies on rotaxanes,7,8 on pseudorotaxanes,9,10 or on catenanes.11,12 The largest number of such theoretical studies involve rotaxanes with cyclodextrins as the macrocycles.13 A recent study indicates that the macrocycle rotation around the thread depends on the experimental conditions, and these results have been confirmed by independent NMR measurements and by theoretical modeling.14 The utilization of catenanes and rotaxanes as molecular machines is due mostly to their dynamic mechanical bond, which can be controlled at the molecular level by applying external stimuli.15 We reported results16 from molecular dynamics (MD) and free energy perturbation (FEP) studies17 of two pseudorotaxanes formed by the inclusion of electron-rich aromatic subunits, benzidine and 4,4′-biphenol, in an electron-deficient receptor, cyclobis(paraquat-p-phenylene), hereinafter called complexes 2 and 3, respectively. The AMBER force field18 and a six-site solvent model of acetonitrile19 were used in the computations. The supramolecular geometry of the inclusion complexes was studied, as well as the difference in the free energy of complexation of 2 and 3. According to the experimental data,20
the aromatic “station” of benzidine (pseudorotaxane 2) manifests a clearly pronounced stronger preference for complexation in comparison with 4,4′-biphenol (3). The estimated association constants are 1044 and 140 M-1 for 2 and 3, respectively. These aromatic residues are now incorporated into a polyether chain, thus yielding a [2]rotaxane (1). After testing the computational scheme in the study of pseudorotaxanes,16 and having succeeded in reproducing the available experimental data, we now go further and consider the challenging task of modeling the shuttling process in [2]rotaxane systems. As a first step along this line, we applied the methodology to [2]rotaxane 1, formed by cyclobis(paraquat-pphenylene) plus a polyether chain that contains one benzidine station and one 4,4′-biphenol station, as well as two triisopropylsilyl blockers at the extreme ends. We intend to elucidate here some aspects pertaining to [2]rotaxane 1, namely the following: (i) The first is the most probable conformations of the translational isomers of [2]rotaxane 1; the forces governing the folding of the linear chain, the role of the π-π stacking interactions, and the [CH‚‚‚O] hydrogen bonds; and the effects of the solvent on the geometry and the conformation of the superstructure. (ii) The second is whether our computational approach, based on the free energy perturbation method, is able to reproduce the free energy difference between the two translational isomers of [2]rotaxane 1. J. F. Stoddart and co-workers determined the relative populations of the two translational isomers of 1 at 229 K and in acetonitrile as solvent.21 The isomer with the benzidine station included in the macroring participated with 84%, while 16% presence was estimated for the isomer with the 4,4′-biphenol portion in the interior of the cavity. These relative populations correspond to a free energy difference ∆G ) 0.98 kcal mol-1 between the two translational isomers of 1. We assumed, as a first approximation, the modeling of the process by considering the structural and energy differences between the two translational isomers (Figure 122). Computational Methodology
* Corresponding author. E-mail:
[email protected]. † On a sabbatical leave from the Institute of Organic Chemistry with Centre of Phytochemistry, Bulgarian Academy of Sciences, Sofia.
We followed the same computational protocol as described in our previous paper.16 Simulations were performed in the gas
10.1021/jp034658l CCC: $25.00 © 2003 American Chemical Society Published on Web 07/08/2003
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TABLE 1: Average Values of Energy Terms (in kcal mol-1) Obtained from the Molecular Dynamics Simulations of [2]Rotaxane 1, Carried out at 298 K in Gas Phase or in Acetonitrile as Solvent and in the Presence of Counterions conditions
station included
conformation of linear component
total potential energy
stretching
bending
torsion
gas phase in acetonitrile
benzidine benzidine benzidine 4,4′-biphenol 4,4′-biphenol
unfolded unfolded folded unfolded folded
236.8 -30 147.3 -27 394.9 -29 226.7 -25 677.9
116.4 747.4 666.0 724.0 648.5
107.6 2391.4 2146.6 2320.4 2050.5
56.9 67.3 64.8 66.9 65.4
van der Waals 1,4 other 68.1 13.0 17.0 15.8 23.2
-59.5 -3632.0 -3410.2 -3531.0 -3124.1
electrostatic 1,4 other 285.7 -25 260.9 -22 715.8 -24 477.1 -21 453.1
-338.2 -4473.5 -4163.3 -4345.7 -3896.3
Figure 1. Shuttling process of [2]rotaxane 1, with experimental ∆G° (determined in acetonitrile). The figure also schematically presents the FEP carried out in this work.
Figure 2. Snapshot of [2]rotaxane 1 showing hydrogen bond interactions and their average values. The blockers are not included in the figure for the sake of clarity.
phase, as well as with acetonitrile as an explicit solvent,19 and chloride ions added as counterions.16 The parm94 force field was used throughout this work.23 The windows method was used for the FEP computations.18,24 RESP charges25 were obtained by fitting to ab initio HF/6-31G* molecular electrostatic potential26 and introducing some restrictions based on equivalences of conformations due to symmetry (see Supporting Information for details). The atomic charges used for cyclobis(paraquat-p-phenylene) are the same as we have described them elsewhere.16 The AMBER force field was parametrized using the 6-31G* basis set.27 The same basis set was used here in order to be in line with the requirements for an internal consistency of the model. Moreover, the size of the problem (too-big fragments) also prevented us from being more exact in the development of the atomic charges and to obtain them from higher level of ab initio theory and with a larger basis set. Obviously, not too much significance should be ascribed to computed energy differences of less than 0.5 kcal/mol.28
Preliminary Results in the Presence of Counterions. The simulations of [2]rotaxane 1 carried out in the gas phase at 298 K and in the presence of counterions were aimed at checking the behavior of 1 in molecular dynamics simulations that are 40 times longer than the simulations carried out with MacroModel.29,30 These simulations positioned the chloride ions in the neighborhood of the benzidine aromatic station. The van der Waals and the electrostatic interactions contributed mostly to the stability of the suprastructure (Table 1). The optimized geometry of the complex closely resembles the crystallographic structural data for the cyclophane: a rectangular shape, slightly curved.34 Although the simulation was started with an extended conformation of the polyether chain, the linear portion was folded when the simulation was completed. The 4,4′-biphenol unit is brought into position to participate in π-π stacking interaction with one of the residues of the paraquat, which is at an average distance of 3.4 ( 0.1 Å from the benzidine station included in the cavity, and 3.3 ( 0.1 Å from the nonincluded 4,4′-biphenol station. The 4,4′-biphenol unit is oriented parallel to the paraquat residue with the oxygen atoms opposite the nitrogen atoms of the paraquat (favorable electrostatic interactions). The stabilizing effect of these interactions is high enough for these interactions to remain present during the whole simulation. Attractive interactions are also observed between the oxygen atoms of the polyether chain and some of the protons of the cyclophane ([CH‚‚‚O] hydrogen bonds).35 Except for the oxygen atoms linked to the blockers, all other oxygens participate in at least one hydrogen bond interaction. These hydrogen bond interactions are shared among the hydrogens of the paraquat residues, the p-phenylenes, and, in some cases, the hydrogens of the Csp3 atoms of the cyclophane. As a total, nine hydrogen bond interactions are displayed during the simulation (see Figure 2 where, for clarity, the blockers are not included in the presentation), and these interactions cause the folding of the chain in the neighborhood of the cyclophane, in accord with the experimental observation in related [2]rotaxanes.31,32
Results and Discussion Preliminary MD studies of 1, as well as the [2]rotaxanes with two benzidine and two 4,4′-biphenol aromatic stations,29 employing the same methodology (MM3* force field30) from our earlier studies on [2]rotaxanes,8 revealed deficiencies when modeling some interactions present in the supramolecular systems: the π-stacking interactions were lost in the course of the simulation, while these interactions are present in the X-ray structures resolved for [2]rotaxanes.31 Besides, a wrapping effect due to hydrogen bonding is produced in the vicinity of the cyclophane32 (see Supporting Information) for similar [2]rotaxanes. There are computational studies on isolated pseudorotaxane species using semiempirical methods33 that are also indicative of the importance of the π-π stacking interactions. It is of methodological significance to test the AMBER force field performance on 1 to determine its role in the modeling of such suprastructures.
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Figure 3. Variations of the distances between the geometric centers of the two aromatic stations (in red) and between the Si atoms of the blockers (in blue).
The differences in the results obtained with the MM3* force field29,30 were also demonstrated, as regards the stabilization effect of the π-π stacking interactions. Moreover, these interactions remained present during the whole simulation at 298 K. Results for [2]Rotaxane 1 in Acetonitrile as an Explicit Solvent. The simulations were executed for the two translational isomers, and for two cases which differ from each other by the conformation of the linear component in the starting structure, namely, whether this unit is folded or not in the close vicinity of the cyclophane (Table 1; see Supporting Information for the details of the simulation protocol). The complexes were merged in acetonitrile as an explicit solvent. Translational Isomer of the Benzidine Station. (a) Unfolded Linear Component. In this case, the tetracationic cyclophane macroring encircles the benzidine residue. The van der Waals and the electrostatic interactions are the decisive contributions for the stability of the superstructure (Table 1). The very large negative value for the energy term corresponding to the 1,4-electrostatic interactions is due to the great number of these interactions present in the solvent molecules, and does not contribute to the binding energy of the complex. The geometry of the cyclophane remained the same as that obtained in the preceding simulations, and in accord with the experimental determinations. The position of the benzidine station in the cavity of the cyclophane is characterized by the distances 0.7 ( 0.5 and 3.7 ( 0.5 Å between the center of the cavity and the geometric centers of the aromatic rings of the benzidine residue. The cyclophane is closer to the aromatic ring from the side of the 4,4′-biphenol station. We can consider the variations of the distance of the 4,4′-biphenol residue with respect to the center of the cavity, or the distance between the Si atoms of the two blockers (Figure 3) as a measure of the folding of the linear component. The computed average values of these two distances are 15.1 ( 0.8 and 41.7 ( 1.4 Å, respectively. The structure depicted in Figure 3 corresponds to the last structure sampled in the simulation. Although there are gauche conformations about some of the -OCH2CH2O- bonds, neither hydrogen bonds between the oxygen atoms of the linear component and hydrogen atoms of
the cyclophane are formed nor a π-π stacking interaction with the participation of the aromatic station not included in the cavity is present. Another aspect of the simulation is the structural organization of the solvent molecules around the [2]rotaxane 1 (see Supporting Information for details). The atom-atom radial distribution functions were estimated for the solvent molecules surrounding the pyridine residues of the cyclophane and for the functional groups of the aromatic stations. Twelve acetonitrile molecules were found positioned at distances not exceeding 4.6 Å from the pyridine nitrogens of the cyclophane. One acetonitrile nitrogen atom is at a distance for hydrogen bonding with a hydrogen atom of each amino group. The analyses display an alternation in the orientations of the acetonitrile molecules along the polyether chain as a function of the interactions with the -CH2- groups or with the oxygen atoms. A slight tendency was noticed for the solvent molecules to orient with the nitrogen atoms in the direction of the carbon atoms of the isopropyl groups. Between 13 and 16 acetonitrile molecules are near the carbon atoms of the isopropyl groups. The structure of the solvent around the voluminous blockers can be characterized as not having preferred orientations of the solvent molecules. (b) Folded Linear Component. In this case the linear portion is folded in close proximity to the cyclophane. The number of atoms of solvent molecules is different in this and in the previous simulations, so we cannot directly compare the absolute magnitudes of the energy contributions in Table 1. The superstructure with the linear component in an extended conformation has a larger number of solvent molecules: 6336 vs 5736 total number of atoms. The position of the benzidine station in the cavity of the cyclophane is characterized in this case by the distances 0.9 ( 0.7 and 4.3 ( 1.1 Å between the center of the cavity and the geometric centers of the aromatic rings of the benzidine residue. The most relevant structural phenomenon that characterizes the simulation is the loss of the π-π interaction between the 4,4′-biphenol residue and one of the units of the paraquat. The disappearance of this interaction occurs gradually during the course of the simulation. Figure 4 illustrates this behavior together with representative structures picked up from those sampled at three different stages (numbered from 1 to 3 in Figure
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Figure 4. Variations in the distances between the geometric centers of the biphenol station and each of the paraquat residues, and snapshots of representative structures.
Figure 5. Illustration of the formation and breaking of hydrogen bonds during the MD simulation. With d1, d2, d3, and d4 are designated possible distances of hydrogen bonds. Only a portion of [2]rotaxane is depicted for the sake of clarity.
4). The alignment of the 4,4′-biphenol residue is accompanied by an increase in the number of hydrogen bond interactions between the oxygen atoms of the polyether chain from the side of the benzidine station and aromatic hydrogen atoms of the paraquat residues of the cyclophane. The appearance of attractive interactions as a result of the formation of hydrogen bonds is illustrated by Figure 5. Only one hydrogen bond is observed between the linear component and the cyclophane at the end of the initial 200 ps of the simulation (d1 in Figure 5). One more hydrogen bond in the same region is formed in the time span between 200 and 400
ps (d2 in Figure 5). Thus, two aromatic hydrogens of the cyclophane are in brief contact with one of the oxygen atoms of the linear component. Two more hydrogen bonds of the same type are formed during the last 100 ps of the simulation (d3 and d4 in Figure 5). The average distances of the four hydrogen bonds are 2.4 ( 0.1, 3.1 ( 0.1, 2.7 ( 0.1, and 3.0 ( 0.1 Å for d1, d2, d3, and d4, respectively. Conclusions similar to those drawn for the case of the unfolded linear component can be deduced regarding the structure of the solvent around 1. Despite the similarity of the results, the curves of the radial distribution functions in this
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TABLE 2: Free Energy Differences (∆G, kcal mol-1) for the Different Shuttling Processes of [2]Rotaxane 1 Estimated with the FEP Method unfolded ∆G
folded
benzidine f 4,4-biphenol
4,4-biphenol f benzidine
benzidine f 4,4-biphenol
4,4-biphenol f benzidine
1.10
-1.02
2.28
-2.22
case (see Supporting Information for details) are slightly broader and of lower height in most of the cases. These facts corroborate both the lower degree of folding of the linear component (compared with the previous simulation) and the subsequent loss of the solute-solvent interactions. According to those data, one of the aromatic rings of the benzidine station remains preferentially inside the cavity of the cyclophane, thus preventing the interaction of the adjoining amino group with the solvent molecules. Translational Isomer of the 4,4′-Biphenol Station. (a) Unfolded Linear Component. In this case, the tetracationic cyclophane macroring encircles the 4,4′-biphenol residue. The analysis of the structural data contained in the sampled structures revealed a clear tendency of the benzidine station to remain away from the residues of the paraquat. The average distance between the geometric center of this aromatic unit and the center of the cavity is 19.6 ( 1.6 Å. This value is significantly larger than the analogous quantity for the case when the 4,4′-biphenol station is the one not included in the cavity (15.1 ( 0.8 Å). Here again we observe conformational changes, basically manifested in the presence of gauche conformations about several -OCH2CH2- bonds of the linear portion. The position of the 4,4′-biphenol residue is characterized by the aromatic ring from the side of the blocker being included in the cavity. The other aromatic ring (from the side of the benzidine station) remains accessible for the solvent molecules. The corresponding distances between the center of the cavity and the geometric centers of the aromatic rings of the 4,4′biphenol residue are 0.6 ( 0.4 and 4.7 ( 0.5 Å, respectively. A distinct feature of the results from this simulation is the presence of hydrogen bonds between the oxygen atoms of the polyether chain connecting the 4,4′-biphenol unit with the blocker, and several aromatic hydrogen atoms of the cyclophane. These hydrogen bond interactions are rather weak; therefore, variations are observed in the number and the positions in space of these interactions during the simulation. An increase is observed in the number of hydrogen bond interactions between the hydrogen atoms of the amino group of the benzidine unit and the nitrogen atoms of the acetonitrile molecules. This increase originates because the benzidine residue is not included in the cavity. The folding of the polyether chain, bridging the oxygen of the 4,4′-biphenol unit with the blocker, hinders the interactions of the oxygen atoms of the aromatic residue with the solvent molecules. As a result, the interactions between these oxygen atoms and the hydrogen atoms of the methyl groups of the solvent molecules are seen practically to disappear. (b) Folded Linear Component. The simulation revealed the existence of a π-π stacking interaction between the benzidine residue which is not included in the cavity and one of the units of the paraquat. The two aromatic species maintain a parallel mutual alignment during the whole simulation. The average distance between the center of the cavity of the cyclophane macroring and the geometric center of the benzidine residue is 3.9 ( 0.2 Å and does not vary significantly. The localization of the 4,4′-biphenol aromatic station in the interior of the macroring resembles the situation in the previous case: namely, the aromatic ring from the side of the blocker is preferentially positioned in the center of the cavity, while the
other aromatic ring is displaced out of the cyclophane. One of the faces of the latter aromatic unit remains accessible to solvent molecules, and the other face is partially protected by the folding of the linear component. The corresponding distances between the center of the cavity and the centers of the two aromatic rings are 1.5 ( 1.4 and 3.5 ( 1.8 Å, respectively. Obviously, the formation of hydrogen bonds between aromatic hydrogen atoms of the cyclophane and the oxygen atoms facilitates the folding of the linear polyether chain of [2]rotaxane 1. The hydrogen bonds are stronger in this case and are preserved in the course of the simulation. As is to be expected, differences in the solute-solvent interactions have to be present in this case. These differences produce the folding of the linear component. This is confirmed by the estimates of the atom-atom radial distribution functions (see Supporting Information). Free Energy Perturbation (FEP) Simulations in Acetonitrile. The preceding molecular dynamics simulations allowed us to study the evolution with time of the translational isomers of [2]rotaxane 1, such as the most pronounced geometric characteristics of the suprastructures. Next, we used FEP calculations to estimate the free energy difference between the two translational isomers. We followed the scheme proposed in Figure 1 in order to accomplish this task. We carried out additional molecular dynamics simulations on a modified [2]rotaxane 1, with two dummy atoms added for the purpose of performing the mutation displayed in Figure 1: the functional groups of the aromatic residues were perturbed until one of them converted into the other. The translational isomer with the benzidine unit included in the cavity was considered, both with a folding and without a folding of the linear component. Notably, starting from the structure with the linear component in an extended conformation, we arrived at a final situation with the same conformation preserved. Analogously, when we started from a molecular structure with π-π interactions present, these interactions were preserved also in the structures sampled during the simulation. These data contrast with the results of the preceding MD simulations. We think, however, that rather than indicating any anomaly, this observation confirms the necessity for sufficiently large simulations in order to achieve more efficient sampling of the configurational space of the system. Hence, the FEP calculations were carried out taking as starting points the two final structures obtained in these last MD simulations with dummy atoms included. The number of windows for the FEP simulations was 101. Each window had a size of 0.01 and 1500 cycles for equilibration, followed by 3500 productive cycles, with two cutoff distances for the nonbonded interactions, 13.0 and 16.0 Å, respectively. Counterions were also included in the consideration. Table 2 presents the FEP results for the perturbation of the benzidine residue of [2]rotaxane 1, when included in the cavity, and mutating it to the state characterized by the 4,4′-biphenol residue merged in the interior of the cyclophane. The average value of the free energy of this process in the case of extended linear component of 1 is 1.06 ( 0.04 kcal mol-1. When folding is present, this quantity acquires the value 2.25 ( 0.03 kcal mol-1. We recall that the experimental estimate for the free energy increase (∆G°) between the two translational isomers is 0.98 kcal mol-1.21
Shuttling Process in [2]Rotaxanes Conclusions This report presents an application to [2]rotaxane 1 of the methodology developed and tested on pseudorotaxanes.16 We succeeded in qualitatively reproducing the free energy difference between the two translational isomers of [2]rotaxane 1.21 The hydrogen bonding and the π-π stacking interactions have a significant stabilizing effect when an isolated suprastructure is simulated. The tetracationic nature of the cyclophane (allowing for strong stabilizing electrostatic interactions) and the absence of interactions with other molecules (to neutralize them) resulted in a folding of the linear component. The simulations in gas phase reproduced the data provided from the X-ray structural determinations, where the crystal packing forces contribute to the folding of the structure.31,32 The simulations with an explicit solvent are of decisive importance for evaluating and understanding the effect of the presence of the solvent molecules on the structure of [2]rotaxane 1. The structural reorganization, manifested in a folding of the linear portion in a way that brings the station not included in the cavity closer to one of the paraquat residues, is a key step in the process. The simulations also illustrated the importance of the π-π stacking interaction. Depending on the particular moment, the π-π stacking interactions will disappear in one part of the molecule, while contributions from such interactions simultaneously manifest themselves in other portions of the structure. This interpretation explains the loss of the π-π stacking interaction in one of the simulations. Notably, the information provided by the FEP calculations does not so much show the good values for the desired quantities obtained, as it raises the question, “which simulations yielded these values?” In that respect, we recall that we have used the set of atomic coordinates and velocities for [2]rotaxane 1 with an extended conformation of the linear component in order to arrive at an estimate in accord with the experimental determination at 229 K.21 This may provide a glimpse of the need to unfold the [2]rotaxane. The duration of the simulations appears to be an important limiting factor. The molecular dynamics simulations of [2]rotaxane 1 in acetonitrile present a study in accord with the highest standards that are practically feasible under the computational resources currently available. Evidently, much longer simulation times are required in order to reproduce the processes of folding and unfolding of the linear component, processes that are accompanied by significant conformational changes. Acknowledgment. The authors gratefully acknowledge the allocation of computational time by CESCA-C4. Much appreciated financial support was been obtained from the Ministerio de Ciencia y Tecnologı´a, Spain, through Grant PPQ2000-0369. Thanks are also due to the CIRIT (Generalitat de Catalunya, Catalonia, Spain) for a Visiting Professor grant to one of us (P.I.), and to the Universitat Auto`noma de Barcelona for a fellowship (X.G.). Supporting Information Available: Seven figures, one table, and details on the computational methodology, on preliminary MD studies, on gas-phase simulations and on the analysis for the solvent distribution around [2]rotaxane (PDF). This material is available free of charge via the Internet at http: //pubs.acs.org. References and Notes (1) Ballardini, R.; Balzani, V.; Credi, C.; Gandolfi, M. T.; Venturi, M. Acc. Chem. Res. 2001, 34, 445-455.
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