Chemically Induced Mismatch of Rings and Stations in [3]Rotaxanes

The mechanical interlocking of molecular components can lead to the appearance of novel and unconventional properties and processes, with potential relevance for applications in nanoscience, sensing, catalysis, and materials science. We describe a [3]rotaxane in which the number of recognition sites available on the axle component can be changed by acid–base inputs, encompassing cases in which this number is larger, equal to, or smaller than the number of interlocked macrocycles. These species exhibit very different properties and give rise to a unique network of acid–base reactions that leads to a fine pKa tuning of chemically equivalent acidic sites. The rotaxane where only one station is available for two rings exhibits a rich coconformational dynamics, unveiled by an integrated experimental and computational approach. In this compound, the two crown ethers compete for the sole recognition site, but can also come together to share it, driven by the need to minimize free energy without evident inter-ring interactions.

Flash column chromatography was performed using Sigma Aldrich Silica 40 (230-400 mesh size or 40-63 μm) as the stationary phase. Size exclusion chromatography was performed using Biorad Biobeads SX-3 as the stationary phase. Thin layer chromatography was performed on TLC Silica gel 60 F254 coated aluminium plates from Merck. Hydrogenation reactions were carried out in a H-Cube flow reactor equipped with a 10 % Pd/C catalyst at a H2 pressure of 10 bar and a flow rate of 1 mL min -1 using methanol as the solvent.
Deprotonation experiments were carried out in acetonitrile using triethylamine (pKa = 18.8) or phosphazene compounds as heterogeneous [B1, polystyrene-supported BEMP] and homogeneous [B2, P1-t-Bu), pKa = 26.9] bases. The pKa values for the ammonium stations were calculated based on the titration curve fitting, carried out on the HyperSpec suite. The error on the pKa values is estimated to be ±0.1 units, calculated as the average mean square root in the pKa values of the ammonium stations investigated.

Quantum chemical calculations
A model structure of the complex RotH2 3+ , consisting of two identical dibenzo-24-crown-8 (DB24C8) rings interlocked with an axle containing two lateral dibenzylammonium (Am) and one central triazolium (Tz) stations, was optimized by adopting the D95(d,p) 1 basis set and the range-separated hybrid functional ωB97XD 2 as density functional approximation to DFT.
From this optimized structure, two different starting geometries for the RotH 2+ model were created by removing one proton from one of the two lateral dibenzylammonium stations. These computational models correspond to the two isomers RotH 2+ -I and RotH 2+ -II, formed upon mono-deprotonation of the parent compound RotH2 3+ . In particular, the starting structures for RotH 2+ -I and RotH 2+ -II were obtained by deprotonating the Am on the methyl group side, and the Am on the ethyl group side, respectively. These two geometries were optimized at the same level of theory as RotH2 3+ -namely, ωB97XD/D95(d,p).
The calculations of the NMR spectra of the above-mentioned optimized structures of RotH2 3+ RotH 2+ -I and RotH 2+ -II, were performed by using as basis set a QZP (quadruple-ζ with polarization) for all the protons 3 and cc-pCVDZ (double-ζ with polarization and tight-core) for the heavy atoms 4 (O, C, N) and adopting a DFT approximation optimized for proton NMR chemical shifts 5 . The chemical shifts of all the protons were calculated by taking as a reference the chemical shift of the protons of tetrametilsilane (TMS). The chemical shifts of the protons reported in this work were calculated from the average over equivalent protons.
The above calculations were performed with the Gaussian 09 code 6 using an implicit solvent model for CH2Cl2 or CH3CN. 7

Ab initio molecular dynamics and Metadynamics calculations
The finite-temperature behavior of Rot + was modelled via ab initio molecular dynamics, 8 combined with statistical sampling according to the ab initio metadynamics 9,10 scheme.
A Generalized Gradient Approximation to density functional theory (DFT) was used to describe electronelectron interactions -in particular, the PBE functional in combination with empirical dispersion corrections (i.e. PBE-D2). 11,12 Ion cores-electron interactions were treated with ultra-soft pseudopotentials. 13 Plane-waves (PW) were used as basis set. The cutoffs for the PW expansion of the wavefunctions and density were 25 Ry and 200 Ry, respectively. Calculations were performed using periodic boundary conditions, which were applied to a simulation cell of size 70×30×30 Å. Such a size is sufficiently large to allow for a Γ-point-only sampling, and to minimize interactions of the rotaxane with periodic images.
Each simulation system was constituted by the neutral ring DB24C8 and by the positively charged axle. In all cases, the simulation cell contained a total of 255 atoms.
A guess configuration was obtained by removing one proton from both the two lateral dibenzylammonium stations of the parent compound. Ab initio molecular dynamics (AIMD) equilibration (elapsed time: 10 ps) was performed at 300K (27 °C). This temperature was chosen in order to favour a faster equilibration of the system. Additionally, it corresponds roughly to the central part of the temperature conditions at which the variable temperature NMR experiments were conducted (T = from -40 to 70 °C).
The simulations were carried out in the canonical NVT ensemble and with Nose-Hoover chain thermostats for the ionic degrees of freedom. 14,15 The AIMD equations 8,16 were integrated with a time step of 5 atomic units (a.u.), i.e. 0.121 fs. The (fictitious) mass of the wavefunction's coefficients was 500 a.u.
The shuttling process was explored by performing two ab initio metadynamics (MTD). In the first run, we selected as collective variable (CV), the displacement of the 8 oxygen atoms of the DB24C8 macrocycle on the side of the ethylene bridge, with respect to the nitrogen atoms of the Tz station (see path B→ C in Figure 10, main text). In the second run, we adopted as CV the displacement of the 8 oxygen atoms of the ring on the methylene bridge side with respect to the Tz nitrogen atoms (see path B→A in Figure 10, main text). For the evolution of the CV, we employed the Lagrange-Langevin dynamics with friction of 0.001 a.u. The selected target temperature was 300 K as in the equilibration runs. The metadynamics parameters adopted for the gaussian hills in the production simulations were the following in all the runs: perpendicular width = 0.02 a.u., height = 0.002 a.u. The sampling was accomplished in ~3000 metadynamics steps.
Due to the size of the simulation cell, all the PW simulations were performed in the gas phase.
All PW calculations were carried out with the CPMD (Car-Parrinello-Molecular-Dynamics) computer program 17 running on the Shaheen II supercomputer at Kaust. Figure S1. Synthetic route to the Boc-protected intermediate 1.

Tricationic [3]rotaxane, RotH2 3+
Under a dinitrogen atmosphere, compound 7 (254 mg, 0.13 mmol) was dissolved in iodomethane (13 mL) and the resulting solution was stirred for 48 h at room temperature under exclusion of light. Upon reaction completion, the solvent was removed under reduced pressure providing a yellow solid, which was dissolved in the minimum amount of acetonitrile. Addition of a saturated aqueous solution of ammonium hexafluorophosphate led to the precipitation of a yellow solid, which was isolated, dissolved in dichloromethane and washed with a saturated aqueous solution of ammonium hexafluorophosphate (3×5 mL) and water (3×5 mL) and dried over MgSO4. Filtration and removal of the solvent under reduced pressure provided the product RotH2 3+ as a yellow solid (246 mg, 91%). 1

Tricationic axle, 9
Under a dinitrogen atmosphere, compound 8 (241 mg, 0.25 mmol) was dissolved in iodomethane (15 mL) and the resulting solution was stirred for 48 h at room temperature under exclusion of light. Upon reaction completion, the solvent was removed under reduced pressure providing a yellow solid, which was dissolved in dichloromethane (30 mL) and washed with KPF6(aq) (3×15 mL). The organic fraction was isolated, the solvent removed under reduced pressure and the residue dissolved in trifluoroacetic acid (10 mL) and stirred at room temperature for 16 h. The acid was removed under reduced pressure and the crude product suspended in ethyl acetate (30 mL) and washed with Na2CO3(aq) (3×30 mL). Removal of the solvent from the organic fraction provided a solid that was dissolved in the minimum volume of methanol (1 mL) and reacted with 37% HCl (few drops). Addition of a saturated methanol solution of (H4N)PF6 (3 mL), followed by precipitation through dropwise addition of water provided a colourless solid which was filtered and purified by sonication in diethyl ether to obtain the product 9 as a colourless solid (124 mg, 41%). 1 32 (s, 36H, 1+29). 13

Thermodynamic analysis
The pKa values of the individual rotaxane species were determined from NMR spectroscopic and UV-visible titration data according to the procedure shown in Figure S47. The only assumption made in the calculation is that RotH 2+ -I and RotH 2+ -II exhibit the same molar absorption coefficient at the observation wavelength. This is very reasonable because the two forms differ only for the position of the encircled ammonium unit with respect to the triazolium, and the DB24C8-dibenzylammonium interaction does not cause appreciable changes in the UV-visible absorption spectrum. 18 Figure S47. Determination of the acid dissociation constants of RotH2 3+ , RotH 2+ -I and RotH 2+ -II. Figure S48. Graphical representation of the starting co-conformation of the Rot + monocation for the ab initio MTD runs. Color codes: C=cyan spheres; N=blue spheres; O=red spheres; H=white spheres. The part of the axle containing the ethyl bridge is on the left side of the [3]rotaxane in this representation, while the part of the axle containing the methyl bridge is on the right side. The positively charged Tz station is in the middle of the axle, between the two DB24C8 macrocycles.

Computational results
The starting co-conformation was identical for the MTD runs, it features the two rings at opposite sides of the Tz station ( Figure S48). Such co-conformation (including both positions and velocities) represents the zero of our MTD sampling. The considered CV implied the displacement of the oxygen atoms of one ring with respect to the nitrogen atoms of the Tz station ( Figure S48). As there are two rings, we performed two different MTD runs picking alternatively one of the two rings to transit along the axle. As the initial co-conformation for the MTD samplings was identical (and taken as the zero of the processes) we collapsed the free energy profiles of the different runs in one single profile ( Figure 6 in the main text).
Overall, we detected three deep minima in the free energy profile. In order to calculate thermally averaged proton chemical shifts, we sampled some tens of co-conformations extracted from the regions corresponding to the three free energy minima and used such co-conformations for the calculations of the proton NMR data. The chemical shifts computed from the three sampled regions were then averaged.
In the optimized geometry of parent compound RotH2 3+ ( Figure S49), each of the two DB24C8 macrocycles are located on a positively charged Am station. Besides the favorable electrostatic interactions of the oxygen atoms of the rings with the positively charged dibenzylammonium moieties, the structure is stabilized by π-π interactions between the phenyl groups of both rings and the aryl stoppers of the axle. This feature is clearly evidenced by the face-to-face arrangement of the aromatic moieties of the rings with the close aryl groups of the axle. Also, strong hydrogen bonds are formed between the -NH2 + moieties of Am stations and the oxygen atoms of the rings. The hydrogen bond distances are 1.857 and 1.882 Å for the ring on the ethyl side and methyl side, respectively. Figure S50. Optimized geometry of RotH 2+ -I (B2). Color codes as in Figure S48.  Figure S48.
The optimized geometries of the dications RotH 2+ -I and RotH 2+ -II are reported in Figure S50 and Figure S51, respectively. The structures of these dications are markedly different with respect to the trication, because of the absence of face-to-face π-π interactions of the rings with the aryl moieties of the axle. Also, the two dicationic structures are also significantly different between each other.
Specifically, in RotH 2+ -I (deprotonation of the Am on the methylene side), the ring which was previously on the methylene side, upon deprotonation has translated along the axle up to the Tz station, and has formed a new hydrogen bond with the Tz proton (distance H(Tz)-Oring = 2.118 Å). The ring on the ethylene side remains bound to its Am station -which is still protonated -via a hydrogen bond interaction (distance H(NH2 + )-Oring = 1.910 Å). No substantial rearrangement of the methyl side of the axle are noticed, which remains approximately in a linear conformation.
Conversely, in RotH 2+ -II (deprotonation of the Am on the ethylene side), the ring which was previously on the ethylene side, upon deprotonation of its Am station has migrated to the Tz station and has formed a new hydrogen bond with the Tz proton (distance H(Tz)-Oring = 2.050 Å). The ring on the methylene side remains bound to its Am station -which is still protonated -via a hydrogen bond interaction (distance H(NH2 + )-Oring = 1.894 Å). Interestingly, this translational movement has been accompanied by a noticeable rearrangement of the ethylene side of the axle, suggesting a greater conformational flexibility with respect to the methylene side of the axle.
The energy difference between the optimized geometries RotH 2+ -I and RotH 2+ -II amounted to 1.4 kcal mol -1 in favour of the RotH 2+ -II structure. The slightly greater stability of RotH 2+ -II may be ascribed to the edge-to-face π-π interaction of the ring on the methylene side of the axle, evidenced in Figure S51, as well as to the stronger hydrogen-bond interactions between the rings and the axle components. Figure S52 reports the computed 1 H-NMR spectra of the parent compound RotH2 3+ and of dications RotH 2+ -I and RotH 2+ -II, while Figure S53 reports the the computed 1 H-NMR spectra for the three free energy minima obtained from the free energy profile, labelled as A, B, C (see also main text). Graphical representations of three co-conformations sampled from the above-mentioned energy minima A, B, C are reported in Figures S54, S55 and S56, respectively.  Figure S54. Co-conformation of Rot + sampled from free energy minimum A. Colors as in Figure S48. Figure S55. Co-conformation of Rot + sampled from free energy minimum B. Colors as in Figure S48. Figure S56. Co-conformation of Rot + sampled from free energy minimum C. Colors as in Figure S48.