Conformational Flexibility of Hybrid [3]- and [4]-Rotaxanes

The synthesis, structures, and properties of [4]- and [3]-rotaxane complexes are reported where [2]-rotaxanes, formed from heterometallic {Cr7Ni} rings, are bound to a fluoride-centered {CrNi2} triangle. The compounds have been characterized by single-crystal X-ray diffraction and have the formulas [CrNi2(F)(O2CtBu)6]{(BH)[Cr7NiF8(O2CtBu)16]}3 (3) and [CrNi2(F)(O2CtBu)6(THF)]{(BH)[Cr7NiF8(O2CtBu)16]}2 (4), where B = py-CH2CH2NHCH2C6H4SCH3. The [4]-rotaxane 3 is an isosceles triangle of three [2]-rotaxanes bound to the central triangle while the [3]-rotaxane 4 contains only two [2]-rotaxanes bound to the central triangle. Studies of the behavior of 3 and 4 in solution by small-angle X-ray scattering and atomistic molecular dynamic simulations show that the structure of 3 is similar to that found in the crystal but that 4 has a different conformation to the crystal. Continuous wave and pulsed electron paramagnetic resonance spectroscopy was used to study the structures present and demonstrate that in frozen solutions (at 5 K) 4 forms more extended molecules than 3 and with a wider range of conformations.


EPR measurements S9
Distance Distribution Graphs S13 Figure S10: Distance distribution for 3 derived from crystallographic data S13 Figure S11: Distance distribution for 4 derived from crystallographic data S13 Experimental and Calculated SAXS and AMDS data S14 Figure S12: Observed and calculated SAXS data for 3 and 4 S14 Table S2: Experimental and calculated radius of gyration data for 3 and 4 S15 DEER Simulations S16 Table S3: DEER simulation parameters S17 Figure S13: Field dependent orientation dependent simulation results S18 Figure S14: Parameters for generating models for DEER library S19 Figure S15: RMSD of simulation fits to experimental data for each iteration S20 Figure S16: Distributions of DEER library fits relative to structures of 3 and 4 S20

Analysis of Multi-spin effects in DEER S20
Figure S17: Results of multi-spin analysis using power-scaling S21 S3 for 3 hr. Excess NaBH4 (0.95 g, 25 mmol) was added and the reaction mixture was stirred for 5 hr. The reaction was quenched with water (20 mL) and the residue was extracted with chloroform (3 x 25 mL). To a solution (room temperature) of 2 (0.5 g, 0.20 mmol) in THF (25 mL), 1 (0.15 g, 0.13 mmol) was added and the solution stirred for 10 minutes, filtered, then acetonitrile (5 mL) was added to the solution. Green crystals suitable for single crystal X-ray diffraction were grown via slow evaporation of the solvents over 48 hours. The crystals were separated by filtration and washed with THF, then acetonitrile. Yield: 0.22 g (38%).

Crystallography
Data Collection. X-Ray data for compounds 3 and 4 were collected at a temperature of 150 K using a Rigaku Supernova with Mo-Kα radiation (λ = 0.71073 Å) equipped with a Eos CCd detector and a Rigaku FR-X with Cu-Kα radiation (λ = 1.5418 Å) equipped with a HypixHE6000 detector, respectively. Both instruments were equipped with an Oxford Cryosystems nitrogen flow gas system. Data was measured using CrysAlisPro suite of programs.
Crystal structure determinations and refinements. X-Ray data were processed and reduced using CrysAlisPro suite of programmes. Absorption correction was performed using empirical methods (SCALE3 ABSPACK) based upon symmetry-equivalent reflections combined with measurements at different azimuthal angles. S2 The crystal structures were solved and refined against all F 2 values using the SHELXL and Olex 2 suite of programmes. S3 Despite the highly intense X-ray source, crystals of 3 and 4 present a diffraction limit of 1 Å, and 1.5 Å respectively.
All atoms in the crystal structure of 3 were refined anisotropically with the exception of the hydrogens atoms.
In the crystal structure of 4, only the metals atoms were refined anisotropically in order to keep the highest data/parameters ratio. Hydrogen atoms were placed in the calculated idealized positions for both 3 and 4. The pivalate ligands were constrained to have idealized geometries using RESI Shelxl commands. Some pivalates were heavily disordered and modelled over two positions where possible. The C-C distances in the aliphatic chains were restrained using fixed distance and same distance restraints. The atomic displacement parameters (adp) of the ligands have been restrained using similar Ueq and rigid bond restraints.
The crystal structure of both 3 and 4 present large voids filled with a lot of featureless electron density; a large number of A and B alerts were found, especially for the structures of 3 and 4, due to the crystal poor resolution obtained for the two crystal structures. Unfortunately this resolution is common in large molecules with large intermolecular spaces filled with disordered solvent molecules. This effect is also common in proteins, so a similar approach (Rigid Body) was used to refine the structure of the [4]-and [3]-rotaxanes. Most of the pivalate ligands were restrained/constrained to have idealized geometries and allowed to refine the position and the orientation.

S6
As we can observe in Figure S1, the structural model of the three different knots were built on a broad shaped electron density maps due to the poor resolution 1.5 Å of the data collected. Tert-butyl groups were especially poorly resolved due to the most probable disorder of the group. As consequence the values of R1, wR and wR2 factors are larger than for standard crystal structures.
CCDC 2008796-2008796 and CCDC 2008796-2008797 contain the supplementary crystallographic data for 3 and 4 respectively for this paper. The data for these can be obtained free of charge via www.ccdc.cam.ac.uk/conts/retrieving.html (or from the Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB21EZ, UK; fax: (+44)1223-336-033; or deposit@ccdc.cam.ac.uk).    Figure S1 with blue (N) and dull yellow (S). t Bu(pivalate) groups and hydrogens omitted for clarity.

EPR Measurements
Continuous wave Q-band (~34 GHz) EPR spectra were recorded with a Bruker EMX580 spectrometer, while pulsed Q-band (~34 GHz) EPR data was collected on a Bruker ELEXSYS 580 FT spectrometer. The continuous wave data were collected on polycrystalline powders and on solutions in toluene at 5 K (unless otherwise stated) using liquid helium cooling. Pulse EPR data were collected from dry and degassed toluene solutions at 3 K (unless otherwise stated) using a Cryogenic cryogen free variable temperature cryostat incorporating a closed helium circuit. Spectral simulations were performed using the EasySpin 5.1.4 simulation software S6 unless stated otherwise.
All DEER measurements were worked up via DeerAnalysis S7 ; a background correction was applied to the dipolar evolution trace, before Fourier transformation to obtain a Pake pattern. Distance distributions were obtain using Tikhonov regularizations (in DeerAnalysis). S8 The optimum regularization parameter α for 3 and 4 was lower (less smoothing and a more resolved distance distribution) for 3. Despite this we find broader distance distributions for 3, and a larger number of independent distances in 4. Reducing α for 3 did not result in resolution of any extra independent distances. Therefore, the differences in distance distribution for 3 and 4 appear to be intrinsic to the molecules. Attempts to increase α for 4, to replicate the distance distribution of 3, resulted in a grossly over-smoothed dipolar evolution trace.
A correction factor of 0.945 and 0.922 was applied to the distance distributions of 3 and 4, respectively. This accounts for the difference in g-values at the pump and observation pulse, as DeerAnalysis assumes g = 2.0023. S9 Ghost suppression was applied for 3, but this did not alter any of the results. S10 Figure S5. Experimental CW EPR X-Band (ca. 9.5 GHz) and S-Band (ca. 3.8 GHz) (top and bottom respectively) solution spectra of 3 using a 3 mM sample in dry toluene at 5 K (black), and simulation (red).      Figure S10. Distribution of distances between metals atoms in 0.5 Å increments for {Cr 7 Ni}…{Cr 7 Ni}; taken from the crystal structure of 3. Figure S11. Distribution of distances between metals atoms in 0.5 Å increments for {Cr 7 Ni}…{Cr 7 Ni}; taken from the crystal structure of 4.

DEER Simulations
Simulations based upon the algorithm published in reference (S10), which makes use of functions from EasySpin, S6 were used initially to test the assumption that -due to the axiality of the g-tensor of the {Cr7Ni} rings -DEER data collected with the pump on the spectrum maximum, and with a detection offset of 100 MHz, results in traces that can be analysed using the orientation independent kernel of DeerAnalysis. S7 This assumption arises from the fact that both pump and detection pulses excite gperp (or gx,y) orientations of the gtensor, and that because both spin centres have axial g-tensors and that both pump and probe pulses excite gperp orientations, there will always be a gperp component of both centres that contribute to the DEER trace.
Such a trace will then give frequencies that correspond to the characteristic horns of the complete Pake pattern in the frequency domain. Such an assumption is not true when the pump and/or probe pulses are resonant with the part of the spectrum corresponding to gparallel (or gz).
Geometric models making use of the symmetry of the {Cr7Ni} ring g-tensors, and sampling all orientations of the two rings with respect to one another in 30° increments with a centre-to-centre distance of 2.032 nm (the average inter-ring distance observed in the X-ray and MD structures), were constructed. The spin density was arranged equally at eight points around a ring of radius 0.440 nm (the average radius from the X-ray structures), representing the spin delocalization over the eight metal ions in {Cr7Ni}. Although the spin distribution is not even, the positional disorder of the Ni(II) ion site over the {Cr7Ni} ring means that on average each position carries one eighth of a spin.
For each of these models three sets of DEER traces corresponding to the field positions indicated on the field sweep below ( Figure S13, top: orange, green and purple lines) were calculated using a pump π pulse length of 40 ns and detection π pulse lengths of 40 ns with a 100 MHz offset between pump and detection frequencies. Tikhonov regularization using an orientation independent kernel, corrected for the g-values of the system, was used to analyse the simulated traces and the resulting distance domains plotted.
The results show that for the spectra collected pumping on the signal maximum (middle, green box in Figure S13) all spin-spin orientations contain a component that when analysed with a Tikhonov regularization (corrected for the g-values of the pump and probe frequencies and field value) give a distance in the range of the input value 2.032 nm. The same is true for the simulation sampling the gperp portion of the spectrum at S17 lower field (top, orange box in Figure S13). This breaks down for the DEER datasets recorded at higher field (bottom, purple box in Figure S13) where gparallel contributes more to the EPR spectrum, and the DEER datasets where the dipolar vector is parallel to the gparallel vectors contain higher frequency contributions that are interpreted as shorter distances in the Tikhonov regularization. Table S3. Calculation parameters used in simulation of the orientation slective DEER traces displayed in Figure S13. Field of 1369.4 mT used in simulation of library of DEER traces fitted to experimental data.  Figure S13. Top left -models used in the geometeric test -red arrow alone represents the gparallel direction of the detection ring -coloured arrows represent the relative positions and orientations of the pump center orientations investigated. Colors of the pump centre orientation arrows correspond to time traces, spectra and distance distributions in lower part of figure. Top right -simulated CW spectra of pump and detection centers plotted relative to detection and pump pulse profiles. The orange, green and purple lines represent the field positions used to simulate the datasets displayed in lower part of figure. The data sets in the orange, green and purple boxes are (left to right) the simulated time traces (in black with fitted coloured Tikhonov fits), the simulated frequency domains and the Tikhonov fitted distance domains with correction for the g-values corresponding to the field and frequencies used.

S19
Secondly, minor modifications of the X-ray structures of 3 and 4 were used to generate a library of simulated DEER traces simulations (using the experimental parameters used in the DEER acquisition). These traces were fitted to the experimental traces using an iterative fitting procedure similar to reference (S11). 50 iterations were used and the improvement to the RMSD between the experimental and simulated data monitored. The contributing orientations were analyzed relative to the X-ray structures. The jagged nature of the frequency domain data for the simulation library approach (Figures 4 and 5, main text) is a result both of the small number of structures contributing to the result and that the simulation of the dipolar trace for each structure uses a discreet number of orientations of the molecule with respect to the external magnetic field defined by a spherical triangular grid with inversion symmetry and 90 knots per quarter meridian. Figure S16. Distibutions of DEER library fits of center of one ring plotted as coloured spheres relative to a fixed orienttion of the other ring plotted against the X-ray structures of the [4]-rotaxane (left) and [3]-rotaxane (right) for reference. The colours of the spheres indicate the number of times an orientation contibutes to the fit. 1 = blue, 2 = green, 3 = yellow, 4 = orange, 5 = red, 6 = magenta.

Multi-spin analysis
The DEER trace for the [4]-rotaxane was analyzed using the power scaling methodology for suppression of multi-spin effects in a three-spin system in DeerAnalysis2019 S7 to test for the existence of ghost peaks in the distance distribution. S12 The results of the analysis with and without this ghost suppression is presented in Figure S17. Overlaying the distance distributions shows very little difference between the two analysis methodologies, showing that there is no significant contribution from multi-spin effects to the data leading to S21 the presence of ghost peaks. This is somewhat expected as the inversion efficiency found from the modulation depth after power scaling is only λ = 0.0135. \ Figure S17. Time (top left) and frequency domain (top right) DEER data for the [4]-rotaxane with fits found using Tikhonov regularization in DeerAnalysis, with and without ghost peak suppression for a three spin system. The resulting distance distributions are shown both with intensities corresponding to the observed modulation depth of the signal (bottom left) and as functions normalised of the signal maxima (bottom right).