Influence of axle length on the rate and mechanism of shuttling in rigid H-shaped [2]rotaxanes

Shuttling rates for neutral and charged [2]rotaxanes with rigid axles varying in lengths from 7.4 to 20.3 Å were found to be independent of the length of the axle, except when the distance was short enough to allow the ring to interact with both recognition sites which provided a short-cut mechanism that significantly lowered the energy barrier.

The neutral species R1 could not be cooled down far enough to attain the limiting chemical shifts. We observed the coalescence temperature at 183 K, but nothing further. This data has been published S8 and the VT spectra are available in the ESI of that article. By assuming the separation of the limiting peaks to be approximately 1000 Hz -this is about the average of the other (n = 2,3,4) samples -we roughly estimated an upper value for Gc ≠ to be 7.73 kcal/mol.

X-ray Crystallography
General: Crystals were frozen in paratone oil inside a cryoloop under a cold stream of N2. X-ray intensity data were collected at 173(2) K using a Bruker APEX diffractometer equipped with an APEX area detector. The raw area detector data frames were reduced and corrected for absorption effects using the SAINT+ and SADABS programs. S9 Final unit cell parameters were determined by least-squares refinement taken from the data set. Diffraction data and unit-cell parameters were consistent with the assigned space groups. The structures were solved by direct methods with SHELXT. S10 Subsequent difference Fourier calculations and full-matrix leastsquares refinement against |F 2 | were performed with SHELXL-2014 S10 using OLEX2. S11 All nonhydrogen atoms were refined anisotropically and hydrogen atoms placed in idealized positions and refined using a riding model. See Tables S1 and S2 for a summary of data collection, solution and refinement details. Complete details of the structures can be obtained from the Cambridge Crystallographic Data Centre at www.ccdc.cam.ac.uk for CCDC accession numbers 1563641, 1563642, 1563643 and 1563644.

X-ray structure of [2]Rotaxane R5
Single crystals were obtained from slow evaporation of a DMF solution of R5. Crystals of formula R5(DMF)2 were of good quality. Data was collected using MoK radiation ( = 0.71073 Å). The asymmetric unit contained one molecule of the [2]rotaxane (C88H96N4O8) and two molecules of DMF. The structure was solved in the triclinic space group P-1 (#2). One of the tBu groups was disordered and modelled with occupancies of 81:19 using PART and FVAR. See Table S1 for details.

X-ray structure of [2]Rotaxane [R5-H2][BF4]2
Single crystals were obtained from slow evaporation of a toluene solution of R5-H2][BF4]2. Crystals of formula [R5-H2][BF4]2(toluene)4 were of good quality. Data was collected using MoK radiation ( = 0.71073 Å). The asymmetric unit contained one molecule of the dicationic [2]rotaxane (C88H98N4O8), two BF4 anions, three molecules of toluene and one water molecule. The structure was solved in the triclinic space group P-1 (#2). Two of the tBu groups were disordered and both modelled with occupancies of 53:47 using PART and FVAR. Both anions were disordered and restrained with SAME & SIMU commands and modelled with occupancies of 84:16 and 79:21 respectively using PART and FVAR. The toluene molecules were included as rigid groups using a combination of SADI restraints. See Table S1 for details.

Methods and Computational Details
Quantum mechanics calculations were carried out in the framework of the Density Functional Theory (DFT) methods incorporated in the GAUSSIAN09 package. S12 The ground state equilibrium structures and the transition state (TS) structures of the dibenzo[24]crown-8 (DB24C8) macrocycle and an H-shaped axle, forming a rotaxane, were fully optimized without symmetry restraints. The track length of the axle was varied in terms of the amount (n) of phenylene spacers, increasing from n=1 to n=4. The Becke-3-parameter-Lee-Yang-Parr hybrid functional (B3LYP), S13 which incorporates 20% of Hartree-Fock exact exchange, was employed as it has been reported to achieve good agreement with X-ray geometrical structures of even large molecular systems. S14 The Gaussian-type basis set 6-31G(d,p) S15 was employed for all atoms and the dispersion correction (DFT-D3) to the energy was included in all the calculations using the Grimme scheme. S16 Molecular structures of the starting and finishing points for the shuttling of the rotaxane, which were constructed with the DB24C8 macrocycle in each extreme of the axle, were optimized to find stationary point geometries. The structures of the TS between these geometries were optimized by applying Schlegel's synchronous-transit-guided quasi-Newton (QST3) method. S17 The nature of the found stationary points on the potential energy surface (PES) was characterized by the computation of the harmonic vibrational frequencies obtained by the examination of the Hessian matrix, which is constituted by the second derivative of energy with respect to the spatial coordinates of the systems. The transition states were verified to be first order saddle points with only one negative eigenvalue. Implicit solvation effects were taken into account by means of the Polarized Continuum Model (PCM) using dichloromethane (DCM,  = 8.93). S18