Vibrational circular dichroism spectroscopy for probing the expression of chirality in mechanically planar chiral rotaxanes

Mechanically interlocked molecules can exhibit molecular chirality that arises due to the mechanical bond rather than covalent stereogenic units. Developing applications of such systems is made challenging by the absence of techniques for assigning the absolute configuration of products and methods to probe how the mechanical stereogenic unit influences the spatial arrangements of the functional groups in solution. Here we demonstrate for the first time that Vibrational Circular Dichroism (VCD) can be used to not only discriminate between mechanical stereoisomers but also provide detailed information on their (co)conformations. The latter is particularly important as these molecules are now under investigation in catalysis and sensing, both of which rely on the solution phase shape of the interlocked structure. Detailed analysis of the VCD spectra shows that, although many of the signals arise from coupled oscillators isolated in the covalent sub-components, intercomponent coupling between the macrocycle and axle gives rise to several VCD bands.


Experimental Spectra
Vibrational absorption (VA) and VCD spectra were recorded using a Biotools Chiral-2X spectrometer. All samples were measured for 48 h using a 75 µm BaF2 sample cell. The rotaxanes were dissolved in CDCl3 (0.15 M and 0.09 M for rotaxanes 1 and 2, respectively). The spectrum of pure CDCl3 was used as a baseline. The enantiomeric VCD spectra have been subtracted from each other to remove baseline artifacts.

Computational Modelling of Vibrational Circular Dichroism Spectra
Conformational search and DFTB optimisation: A conformational search was performed on rotaxanes (R,Rmp)-1 and (Rmp)-2 using the Macromodel program in the Schödinger software suite (v11.9). 2,3 This search was performed by generating 10,000 starting structures using 100 steps per rotational bond and a combination between bond rotations and low-frequency mode translations. The generated structures were optimized with the OPLS3E forcefield using the Conjugate Gradient method. The maximum atom deviation cut-off was set to 0.5 Å, the probability of a rotation/molecule translation to 0.5 Å and the minimum and maximum distance for low-mode moves to 3 and 6 Å. During the searches, each low energy conformation was identified multiple times (12 or more for (R,Rmp)-1, 7 or more for (Rmp)-2)). The generated conformers were filtered by hand to remove structures in which the macrocycle was disconnected from the axle by rotating one component through the other. Conformations within 10 kcal/mol of the lowest energy structure were subsequently optimized with the Amsterdam Density Functional (ADF2019) software package using the density functional based tight-binding (DFTB3) method together with the 3ob-3-1 parameter set. 4,5,6,7 This yielded 687 and 709 unique conformations for (R,Rmp)-1 and (Rmp)-2 respectively, making it computationally very costly to perform full density functional theory (DFT) calculations on all conformations.
Conformational clustering and DFT (BP86/TZP; ExactDensity option in ADF2019) optimisation of conformers: All conformations within 2 kcal/mol of the lowest-energy conformation based on the DFTB3 energies were optimised by DFT. To ensure low energy conformations were not missed, a distance matrix was computed for the remaining structures using the sum of the differences in pair-wise interatomic distances (excluding H atoms attached to carbon) between two structures. This distance matrix was then used to cluster the remaining conformations into 30 groups using the agglomerative hierarchical clustering function with average linkage in MATLAB. 8 The two conformers with lowest energy (DFTB3) of each group were optimized by DFT and, if the energy was found to be within 2 kcal/mol of the lowest-energy conformer found by DFT, all other structures in that cluster were also optimized using DFT. In total, 220 and 261 conformations were optimized using DFT for rotaxanes (R,Rmp)-1 and (Rmp)-2, respectively.
VCD modelling: Finally, the VA and VCD spectra of all conformations within 2 kcal/mol of the lowest-energy conformation found by DFT were computed (DFT, TZP/BP86 level of theory using the ExactDensity option in ADF). 9,10,11,12 The generated spectra were then averaged using Boltzmann weighting. The computed VA and VCD intensities were convoluted with a Lorentzian function using a full-width at half-maximum of 8 cm −1 while the computed frequencies were scaled using the method developed by Shen et al. 13 .   Figure S3: Comparison between VA and VCD spectra of low-energy conformations of rotaxanes (black) and their Boltzmann averaged spectra (red). Panel (a) displays computed spectra of (R,Rmp)-1 and panel (b) computed spectra of (Rmp)-2. Panel (c) shows a comparison between the VA and VCD spectra of the lowest-energy conformers of (R,Rmp)-1 (black) and (Rmp)-2 (red). Figure S4: Comparison between the VA and VCD spectra of the lowest-energy conformer of (R,Rmp)-1 (black) and the spectra of the same conformer but with its chiral center inverted to form the (S,Rmp)-1 diastereomer (blue) (the H and Bn substituents were exchanged on the stereogenic C and the structure subsequently optimized to a minimum by DFT). Figure S5: (a) Comparison between VA and VCD spectra of the lowest-energy conformer of (Rmp)-2 (black), as well as of its macrocycle (red) and thread (blue) separately. (b) Comparison between VA and VCD spectra of the lowest-energy conformer of (Rmp)-2 (black), the sum of the spectra of the macrocycle and the thread (green), and the difference between the sum spectra of the macrocycle and thread and the spectrum of the complete rotaxane (orange).

Figure S6
: Nuclear displacement vectors (orange) of nine normal modes of the lowest energy conformer of (R,Rmp)-1 with the highest computed rotational strength (R01) in the region between 900 and 1800 cm -1 . To illustrate the source of the VCD intensity of each mode, the radius of the atoms was scaled with the magnitude of the associated atomic EDTMs using the novel VCDtools implementation in ADF. 15 Frequencies υ are given in cm -1 , R01 in 10 -44 esu 2 cm 2 .