Cascade Dynamics of Multiple Molecular Rotors in a MOF: Benchmark Mobility at a Few Kelvins and Dynamics Control by CO2

Achieving sophisticated juxtaposition of geared molecular rotors with negligible energy-requirements in solids enables fast yet controllable and correlated rotary motion to construct switches and motors. Our endeavor was to realize multiple rotors operating in a MOF architecture capable of supporting fast motional regimes, even at extremely cold temperatures. Two distinct ligands, 4,4′-bipyridine (bipy) and bicyclo[1.1.1]pentanedicarboxylate (BCP), coordinated to Zn clusters fabricated a pillar-and-layer 3D array of orthogonal rotors. Variable temperature XRD, 2H solid-echo, and 1H T1 relaxation NMR, collected down to a temperature of 2 K revealed the hyperfast mobility of BCP and an unprecedented cascade mechanism modulated by distinct energy barriers starting from values as low as 100 J mol–1 (24 cal mol–1), a real benchmark for complex arrays of rotors. These rotors explored multiple configurations of conrotary and disrotary relationships, switched on and off by thermal energy, a scenario supported by DFT modeling. Furthermore, the collective bipy-ring rotation was concerted with the framework, which underwent controllable swinging between two arrangements in a dynamical structure. A second way to manipulate rotors by external stimuli was the use of CO2, which diffused through the open pores, dramatically changing the global rotation mechanism. Collectively, the intriguing gymnastics of multiple rotors, devised cooperatively and integrated into the same framework, gave the opportunity to engineer hypermobile rotors (107 Hz at 4 K) in machine-like double ligand MOF crystals.

several series of exposure frames collected at different temperatures between 275 and 110 K. 1 An absorption correction was applied with the program SADABS. 2 The structure were solved with ShelxT 3 and refined on F 2 with full-matrix least squares (ShelxL 4 ), using the Olex2 software package. 5 According to variable temperature X-ray diffraction analysis, and DSC analysis, the system experiences a phase transition around 220 K. The inspection of the dataset collected at 275 K shows the presence of systematic extinctions consistent with a C lattice (hklextinct: h+k=2n+1). On the other hand, the data collection at 110 K (using the same unit cell metric) shows only a systematic weakness for the same class of reflections, pointing to the presence of a primitive lattice. The overall analysis of the systematic extinctions points to the Cmma space group (β phase) for the dataset collected at 275 K, and to the Pcca space group (α phase) for the 110 K dataset, respectively. For both α and β phases the unit cells were reoriented in order to adhere to the conventional space group notation (Cmma or Pcca). In the α phase, the central carbon atoms of the bicyclo(1.1.1)pentane (BCP) were found disordered in two positions, which were refined with 0.83(anisotropic)/0.17(isotropic) site occupancy factors. Moreover, one of the aromatic ring of the bipyridine was found disordered over two sites, which were refined with 0.74/0.26 site occupancy factors. The β phase exhibits the BCP fragment severely disordered by rotation along the vector linking the carboxylic functions. Six distinct images, belonging to two groups related by symmetry, could be refined. Within each group, the C and H atoms were refined with 0.12/0.16/0.22 site occupacy factors (0.5 overall for each group).
The C atoms of BCP were refined with isotropic displacement parameters. In the β phase, the two aromatic rings of the bipyridine are disordered over two equivalent sites according to the presence of a crystallographic plane of symmetry. The hydrogen or deuterium atoms were placed at their calculated positions. CCDC deposition numbers 2069996, 2069997 and 2069998 for FTR-P1d at 110, 160 and 275 K, respectively, contain the supplementary crystallographic data for this paper.

Powder x-ray diffraction diffraction (PXRD). Powder X-ray diffraction experiments were
performed on a Rigaku Smartlab SE equipped with a Cu Kα radiation (Kα1 = 1.540598 Å, Kα2 = 1.544426 Å, Kα ratio 0.5, Kαav = 1.541874 Å) operating at 40 KV and 30 mA with a Cu kβ radiation filter and a Hy-Pix 400 2D detector working in 1D detection mode. Data were collected under Bragg-Brentano geometry using a 2.5° incident soller slit and a 2.5° receiving slit over a range for 2θ of 3.0 -60.0° with a step size of 0.02° and a scan speed of 1.0°·min -1 .
Variable temperature experiments were performed using an Anton Parr TTK 600 low temperature chamber operating with liquid nitrogen cooling system. The chamber is connected to a two-stage rotary pump and a gas pressure system and vacuum/pressure gauges to measure the pressure inside the chamber ( Figure S1). Variable temperature powder X-ray diffraction (VT-PXRD). The sample was activated under high vacuum at 140°C and quickly loaded in the sample holder and inserted into the TTK 600 chamber. The chamber was evacuated (p = 1.5*10 -2 Torr) and the sample was heated to 140°C.
Vacuum measurements were performed under dynamic vacuum (p = 1.0*10 -2 Torr); VT-PXRD experiments under constant pressure were performed introducing in the chamber a specific pressure of CO2. A heating ramp with a loop cycle was programmed: the sample was cooled/heated at each target temperature at constant rate (10 K/min), equilibrated for 30 minutes and the PXRD pattern was collected (Scheme S1). The measurement were performed between 390 K and 210 K for vacuum collection and between 390 K and 250 K under CO2 atmosphere. Scheme S1. In-situ variable temperature X-ray diffraction (VT-PXRD). The sample was heated under a constant heating rate up to target temperature (heating ramp, 10 K/min) and equilibrated for 30 minutes (holding time) before PXRD pattern collection at constant temperature.
Variable pressure powder X-ray diffraction (VP-PXRD). The sample was activated under high vacuum at 140°C and quickly loaded in the sample holder and inserted into the TTK 600 chamber.
The chamber was evacuated (p = 1.5*10 -2 Torr) and the sample was heated to 140°C. The sample was cooled to 293 K with a heating rate of -10 K/min under dynamic vacuum. At 293 K the vacuum was switched off and the first CO2 amount was dosed inside the system (100 mbar). The sample was equilibrated for 30 minutes before PXRD pattern collection. The pressure was manually increased and the process was repeated for each pressure point (Scheme S2).
Scheme S2. In-situ variable pressure x-ray diffraction (VP-PXRD). A known pressure of CO2 was loaded inside the TTK 600 chamber. The sample was equilibrated for 30 minutes after each dosing to reach the equilibrium and the PXRD data were collected. The process was repeated for each pressure point.
PXRD Structural Rietveld Refinement conditions. Indexing and Rietveld refinement were performed using the TOPAS-Academic-64 V6 software package. 6 The initial input structure used for the PXRD refinement was generated using the CASTEP code (DFT) within the Biovia Materials Studio software package. 7 The DFT optimizations had the unit-cell restrained to the PXRD indexed cell parameters while all the molecules could be optimized. Optimizations were performed using the GGA PBE functional with Grimme's DFT-D dispersion correction, thresholds for geometry optimization and SCF convergence were chosen as 2 × 10 -6 eV. First, the unit-cell parameters where kept fix while all the atoms could optimize. This is followed by Rietveld refinement of the unit-cell parameters with all the atoms' fractional coordinates kept fix throughout the refinement process. The structure is cycled through the DFT optimization and Rietveld refinement until the structure showed no significant changes. The background was fitted and refined using a Chebyshev polynomial with 20 coefficients in the PXRD trace range from 3° to 60° 2theta with baseline shift refinement. Other corrections include Specimen Displacement, Divergence Sample Length, Absorption with Sample Thickness Shape Intensity and Specimen Tilt. The peaks were fitted using a modified Thompson-Cox-Hastings pseudo-Voigt "TCHZ" profile. Preferred orientation was considered using a sixth-order Spherical Harmonics refinement. The accuracy of temperature controller were ±2° K in all explored range.
Structural two-phase Rietveld refinement was performed on all powder X-ray diffraction patterns of FTR-P1d under vacuum at variable temperatures and FTR-P1d·xCO2 at variable pressure/temperature. The Rietveld refinement was carried out considering both phases (α-and βphase) resulting in the percentage of αand β-phase for FTR-P1d as function of temperature and for  8 experiments were performed at 293 K at a spinning speed of 12.5 kHz using a recycle delay of 5 s and contact times of 2 and 0.05 ms. The experiments collected at 210 K were performed at a spinning speed of 8 kHz. The 90° pulse for proton was 2.9 µs. Quantitative 13 C{ 1 H} Single-Pulse Excitation (SPE) experiments were run using a 90° pulse of 4.6 µs and a recycle delay of 60 s. Crystalline polyethylene was taken as an external reference at 32.8 ppm from TMS. Phasemodulated Lee−Goldburg (PMLG) heteronuclear 1 H-13 C correlation (HETCOR) experiments coupled with fast magic angle spinning allowed the recording of the 2D spectra with a high resolution in both hydrogen and carbon dimensions. 9 Narrow hydrogen resonances, with line widths on the order of 1−2 ppm, were obtained with homonuclear decoupling during t1; this resolution permits a sufficiently accurate determination of the proton species in the system. The 2D 1 H -13 C PMLG HETCOR spectra were run with an LG period of 18.9 μs. The efficient transfer of magnetization to the carbon nuclei was performed by applying the RAMP-CP sequence. Quadrature detection in t1 was achieved by the time proportional phase increments method (TPPI). The carbon signals were acquired during t2 under proton decoupling by applying the two-pulse phase modulation scheme (TPPM). 10 The 2D 1 H-13 C PMLG HETCOR NMR spectra of PDR-3 were conducted at 298 K under magicangle spinning (MAS) conditions at 12.5 kHz with contact times of 2, 1, 0.5, 0.1 and 0.05 ms.
Quantitative solid-state 1 H SPE MAS NMR spectra were performed with a Bruker Avance III 600 MHz instrument operating at 14.1 T, using a recycle delay of 20 s. A MAS Bruker probe head was used with 2.5 mm ZrO2 rotors spinning at 30 kHz. The 90° pulse for proton was 2.9 μs. The 1 H chemical shift was referenced to adamantane. 2 H NMR line shape. The deuterium NMR line shape is sensitive to the molecular motion and the time scale over which the motion occurs. In the absence of molecular motion, the frequency of a given deuteron is ruled by: where 0 is the Zeeman frequency; η is the asymmetry parameter and the polar angle θ and φ specify the orientation of the magnetic field with respect to the principal axis of the electric field gradient tensor. The parameter η is usually zero for C-D bonds, meaning that the electric field gradient tensor is axially symmetric. If η is taken as zero, the NMR frequencies of the two transitions are given by: This means that the frequencies of the NMR lines depend upon the angle θ formed between the C-D bond and the external magnetic field. In isotropic samples, the summation of the signals for all possible orientations gives rise the static Pake spectrum ( Figure SXa), where the splitting d between the singularities is about 135 kHz for aromatic C-D bonds.
Molecular motion of p-phenylene moieties about their para-axis causes the lineshape to change in a way that depends on the geometry and time scale of the motion. If motion is considerably fast on the deuterium NMR time scale, the averaged NMR frequency is described by: Where ̅ and ̅ are respectively the coupling constant and the asymmetry parameter for the averaged electric field gradient tensor. In this case ̅ may be different from zero. Fast discrete reorientation by 180° flips around the para-axis results in the lineshape shown in Figure  The single simulations of jump mechanisms were than linearly combined to fit the experimental results.
The experiments were performed on the MOF containing perdeutero-bipy (FTR-P1d) under 150 mm torr of He in a sealed glass vial. The sample with CO2 was loaded at 3.5 bar at 298 K. At low temperature (210 K) the estimated loading of the sample is equal to 1.70 mmol g -1 , corresponding to 95% of full loading. The value is almost constant until 291 K, then there is a progressive decrease in loading reaching the value of 1.13 mmol g -1 at 350 K that corresponds to 63% of full loading.
For the interpretation of the 2 H NMR spectra, we considered several rotational mechanisms. Other angles generated simulated profiles which do not match the experimental values. In Figure S3 and S4 the 2 H NMR lineshapes of different rotational angles at a fixed frequency and viceversa of variable frequencies at fixed rotational angles are reported, showing the high sensitivity of singularity separation values.
For the ±28° jumps we applied a similar procedure: we generated the lineshapes considering several rotational angles and frequencies and then selected the angle which generated the best match with the 2 H NMR profile. Figure S3. 2 H NMR spectra of C-D bond in an aromatic ring considering a 4-site reoreintational mechanism and k = 10 8 Hz. Each profile corresponds to a full turn of rotation with specific angles.
As an example the angle value of 80° (orange line) indicates full rotation of C-D bond at ±40° and ±140°. Figure S4. 2 H NMR spectra of C-D bond of an aromatic ring, considering a 4-site mechanism at fixed rotational angles and variable frequencies. Each profile corresponds to a full turn of rotation ±40° and ±140° (0-80°-180°-260°).

H Trelaxation times
We performed 1 H-NMR measurements using a home-made set-up based on an Apollo spectrometer (TecMag). We generated static magnetic fields µ0H ≤ 1.1 T with an electromagnet (Bruker) and higher field values with a superconducting magnet (Cryomagnetics). We investigated the temperature window 5 K ≤ T ≤ 300 K using a flux cryostat (Oxford Instruments) with liquid nitrogen and liquid helium as cryogenic liquids. Based on several previous calibrations on this cryostat using a control thermocouple on the probe close to the position of the sample, we associate an uncertainty ± 0.4 K to each temperature value. Additionally, we accessed temperatures 1.6 K ≤ T ≤ 4.2 K using a static cryostat (International Cryogenics) by vapour pumping over a liquid helium bath. In these conditions, we kept control on the temperature value by measuring the vapour pressure over the helium bath referring to the pressure-temperature phase diagram of helium. Based on several previous calibrations on this cryostat using a control thermocouple on the probe close to the position of the sample, we associate an uncertainty ± 0.1 K to each temperature value. We prepared an ad-hoc resonant RLC circuit with a coil, used to generate the alternating magnetic field and to detect the 1 H-NMR signal inductively, and a combination of fixed and variable capacitors aimed at the optimization of the tuning/matching of the overall impedance at the working frequency. We tailored the coil specifically for the samples -which were sealed in quartz tubes -aiming at the maximization of its filling factor. We quantified the spin-lattice relaxation time T1 of the sample by means of the following conventional inversion recovery radiofrequency (RF) pulsed sequence.

Scheme 3.
Here, π/2 and π represent RF pulses, whose effect is to tilt the nuclear magnetization away from the quantization axis by the indicated angle. Typically, the duration of π/2 pulses was around 2 -3 µs. τ is a variable time with characteristic values ≈ 20 µs < τ < 100 s, whereas τe ≈ 20 -60 µs. We calibrated the idle time τr at all the temperature values in such a way that τr > 4 T1. For each τ value, we numerically integrated the solid spin-echo developing after a time ≈ τe from the last π/2 RF pulse and plotted the resulting integral I as a function of τ in order to visualize the recovery of the nuclear magnetization towards the thermodynamical equilibrium condition (see the left-hand panel of Figure   S5 for a representative example at fixed temperature for the sample under vacuum). We fitted the experimental data by means of the expression parameter β accounts for deviations of the recovery-law from the purely-exponential behaviour expected for spin-1/2 nuclei in homogeneous environments. Within the accessed experimental window, we measure values β > 0.85 for the sample under vacuum, suggesting local homogeneous conditions and a negligible distribution of T1 values. The situation is markedly different for the sample under CO2 athmosphere. Here, for T < 160 K, we measure sizeably lower values of β with a non-trivial dependence of this quantity on temperature. Moreover, for temperatures T < 90 K, the fitting quality based on Eq. 1 decreases considerably, as shown in the right-hand panel of Figure S5.
For the sample under CO2 atmosphere we obtained a much better description of the experimental recovery curves using the fitting function i.e., a multi-exponential recovery with two components (here labelled as f and s) for all the temperature values T < 160 K. We have no evidence of the multi-exponential character of the recovery for T > 160 K, so we used Eq. 1 for the fitting procedure also for the sample under CO2 atmosphere in this temperature limit. Figure S5. The left-hand panel shows the recovery of the nuclear magnetization in a representative T1 experiment at T = 1.6 K and µ0H ≈ 0:38 T for the sample under vacuum. The continuous line is a best-fitting curve according to Eq. 1. The right-hand panel shows the recovery of the nuclear magnetization in a representative T1 experiment at T = 75 K and µ0H ≈ 1.08 T for the sample under CO2 athmosphere. The continuous lines are best-fitting curves according to Eqs. 1 and 2 (dashed and continuous lines, respectively).
The 1 H T1 relaxation times as function of temperature were fitted with the linear combination of six Kubo-Tomita equations: Where 0 is the maximum rotation period, is the activation energy and is the relaxation constant of the ℎ component and the angular Larmor frequency of the nucleus. 13 Computational Details. Atomic coordinates were imported from the refined crystal structures. All atoms in the frameworks were optimized as part of

Molecular Mechanics (MM).
All MM calculations were performed using the Forcite-Plus module using a modified Dreiding ForceField with an Ewald summation method for both Electrostatics and van der Waals. Only the torsional potential described by *-C_31-C_R-* were modified to fit the rotational potential of the BCP rotor more accurately ( Figure S3). The total rotational barrier for an isolated rotor is 48 cal/mol as a six-fold potential. Since there are six of these tortional forcefield parameters applied to one rotor, the value was set 8 cal/mol.

THERMOGRAVIMETRIC ANALYSIS (TGA)
FTR-P1 and FTR-P1d were treated under high vacuum at 140°C to remove moisture and guest species. Thermogravimetric analyses were performed under oxidative conditions (dry air, 50 mL/min) from 30 to 1000°C.     to column aligned with the bipyridine linker, and correspond to approximately 7% and 9% of the unit cell volume, respectively (probe radius 1.2 Å, contact surface), Figure S12.

POTENTIAL ENERGY SCANS FOR THE BCP CONFORMATIONS AND ROTORS IN FTR-P1
DFT scans using reduced model containing only BCP rotors. Potential energy scans were performed using the GAUSSIAN16 software available through the CINECA high performance computing centre. 15

Determination of CO2 enthalpy of sorption by direct sorption-coupled microcalorimetry.
Sorption-coupled microcalorimetry allowed direct measurement of the enthalpy variation related to CO2 adsorption. The calorimetry data were recorded on a Setaram μDSC7 Evo instrument equipped with a high pressure sample holder. CO2 dosing and adsorption isotherms collections were performed with a Micromeritics ASAP 2050 adsorber coupled to the μDSC module. The set-up allowed simultaneous determination of CO2 adsorption isotherms and of heat exchanged during the adsorption process at each adsorption step. 16 Sorption-coupled microcalorimetry measurements were performed twice at 293 K and the two different runs were averaged to reduce experimental errors. Figure S45. Heat flow measured of the adsorption of CO2 for FTR-P1 using the ASAP 2050 and μDSC7 coupled system. The top and bottom are the duplicate experiments and the insets shows an expanded timeline. Each peak represents a gas dose and therefor an adsorption point.           Simulations for determination of the gas arrangements and interaction energies. CO2 arrangements were determined using GCMC fixed loading simulations using one molecule per unit-cell. DFT optimizations (CASTEP) were performed to obtain the energies used to determine the most probable CO2 arrangements. The optimizations were performed using the GGA PBE functional with Grimme's DFT-D dispersion correction, and thresholds for geometry optimization and SCF convergence were chosen as 2 × 10-6 eV. Single point energies, calculated using CASTEP, were used to determine the interaction energies which were calculated as follows: The full crystal structure with the guest molecules included.
(ℎ -2): ℎ ℎ - Figure S56. Rietveld fits of X-ray data for FTR-P1d·4CO2, collected at 253 K under 2 bar CO2, using the TOPAS-Academic-64 V6 software package. 6 The HKL indices are indicated as green markers and the difference plot are shown below. The black and red represent the observed and calculated traces respectively while the dotted yellow line represent the background plot.

RIETVELD REFINEMENT of FTR-P1d·4CO2
Table S13. Unit cell parameters of FTR-P1d·4CO2 from the Rietveld refinement of powder X-ray diffraction pattern collected at 253 K.

MOLECULAR MECHANICS (MM) 2D SCANS
The 2D scans for rotor pairs R1-R2 and R1-R3 were considered, like the DFT calculation. The calculation was performs considering periodic boundary conditions using a 2 x 2 supercell of both FTR-P1d (Empty, α-phase) or FTR-P1d·4CO2 (α'-phase). The computational models are shown in Figure S69. The metal-carboxylate paddle-wheel node was treated as a rigid body, i.e., the internal coordinates of the paddle-wheel atoms are preserved during the optimization.
The unit-cell parameters were free to optimize at each step of the scan. The scan was performed from 0° -360° with a step size of 5° for the 1 st scan parameter (rotational torsion angle of R1, Figure S69) and 0° -240° with a step size of 5° for the 2 nd scan parameter (rotational torsion angle of R2 and R3). Since rotor has a 3-fold symmetry, the energies repeat every 120° and thus the 2 nd scan parameter could be extended to 360° by using the data calculated between 0° -240°. Figure S69. The computational models used for the molecular mechanics 2D scan for FTR-P1d (Empty, α-phase) or FTR-P1d·4CO2 (α'-phase). The scanning rotors R1, R2 and R3 are indicated. The scan was performed in pair of only R1-R2 and R1-R3, similar to the DFT calculations.

COMPARISON BETWEEN DFT AND MOLECULAR MECHANICS 2D SCANS
DFT -Reduce model comprising only FTR moieties as positioned within the crystal structure. MM -Periodic model comprising a 2 x 2 supercell (4 x unit-cell) Figure S70. Comparison of the DFT and molecular mechanics (MM) 2D scans for the rotor pairs R1-R2 and R1-R3. The 2D contour maps are plotted on the same ΔE scale (0 -7 kcal/mol) and contour levels for direct visual qualitative comparison. The MM calculations are observed to be ca. 1 kcal/mol higher than the DFT 2D scans. Figure S71. The 2D DFT scans results for R1-R2 as calculated by molecular mechanics (2 x 2 supercell) and compared to the DFT calculations (reduced model comprising FTR rotors). Top: graphical illustration of the model. Middle: The 2D contour maps with the rotation of rotors pairs R1 and R2 on the Y-and X-axes with the colours indicating the ΔE. The colour scale ranges from 0 kcal/mol (blue) to 7 kcal/mol (red). This energy range was chosen for comparison to the R1-R3 2D scans. The lines indicate the most optimal Gearing (G, clockwise and counterclockwise rotations, i.e., the rotors rotate in opposite directions) and Anti-gearing (AG, clockwise -clockwise and counterclockwise -counterclockwise rotations, i.e., the rotors rotate in the same directions) pathways on the energy surfaces, with the relative rotor rotational offset indicated for each. Bottom: The ΔE plot for the most optimal gearing and anti-gearing rotations. The DFT and MM ΔE (energy barrier) for G and Ag are shown per rotor. Figure S72. The 2D DFT scans results for R1-R2 as calculated by molecular mechanics (2 x 2 supercell) and compared to the DFT calculations (reduced model comprising FTR rotors). Top: graphical illustration of the model. Middle: The 2D contour maps with the rotation of rotors pairs R1 and R2 on the Y-and X-axes with the colours indicating the ΔE. The colour scale ranges from 0 kcal/mol (blue) to 7 kcal/mol (red). This energy range was chosen for comparison to the R1-R3 2D scans. The lines indicate the most optimal single rotor rotation pathways on the energy surfaces. Bottom: The ΔE plot for the most optimal single rotor rotations. The DFT and MM ΔE (energy barrier) are shown per rotor. Pathway 1 (P1): The rotation rotor R1 with R2 in the Global minimum position (0 -15°) and the rotation rotor R2 with R1 in the Global minimum position (0 -15°). Pathway 2 (P2): The rotation rotor R1 with R2 in the Local minimum position (60 -75°) and the rotation rotor R2 with R1 in the Local minimum position (60 -75°). Figure S73. The 2D DFT scans results for R1-R3 as calculated by molecular mechanics (2 x 2 supercell) and compared to the DFT calculations (reduced model comprising FTR rotors). Top: graphical illustration of the model. Middle: The 2D contour maps with the rotation of rotors pairs R1 and R2 on the Y-and X-axes with the colours indicating the ΔE. The colour scale ranges from 0 kcal/mol (blue) to 7 kcal/mol (red). The lines indicate the most optimal Gearing (G, clockwise and counterclockwise rotations, i.e., the rotors rotate in opposite directions) and Anti-gearing (AG, clockwise -clockwise and counterclockwisecounterclockwise rotations, i.e., the rotors rotate in the same directions) pathways on the energy surfaces, with the relative rotor rotational offset indicated for each. Bottom: The ΔE plot for the most optimal gearing and anti-gearing rotations. The DFT and MM ΔE (energy barrier) for G and Ag are shown per rotor. Figure S74. The 2D DFT scans results for R1-R3 as calculated by molecular mechanics (2 x 2 supercell) and compared to the DFT calculations (reduced model comprising FTR rotors). Top: graphical illustration of the model. Middle: The 2D contour maps with the rotation of rotors pairs R1 and R2 on the Y-and X-axes with the colours indicating the ΔE. The colour scale ranges from 0 kcal/mol (blue) to 7 kcal/mol (red). The lines indicate the most optimal single rotor rotation pathways on the energy surfaces. Bottom: The ΔE plot for the most optimal single rotor rotations. The DFT and MM ΔE (energy barrier) are shown per rotor. Pathway 1 (P1): The rotation rotor R1 with R2 in the Global minimum position (0 -15°) and the rotation rotor R3 with R1 in the Global minimum position (0 -15°). Pathway 2 (P2): The rotation rotor R1 with R2 in the Local minimum position (60 -75°) and the rotation rotor R3 with R1 in the Local minimum position (60 -75°). Figure S75. Comparison of FTR-P1d (Empty, α-phase) and FTR-P1d·4CO2 (CO2 loaded, α'phase) 2D scans for the rotor pairs R1-R2 and R1-R3. The 2D surface maps are plotted on the same ΔE scale (0 -7 kcal/mol) and contour levels for direct visual qualitative comparison. Figure S76. The 2D DFT scans results for R1-R2 as calculated by molecular mechanics (2 x 2 supercell) for the empty (FTR-P1d, α-phase) and CO2 loaded (FTR-P1d·4CO2, α'-phase) structures. Top: graphical illustration of the model. Middle: The 2D contour maps with the rotation of rotors pairs R1 and R2 on the Y-and X-axes with the colours indicating the ΔE. The colour scale ranges from 0 kcal/mol (blue) to 7 kcal/mol (red). This energy range was chosen for comparison to the R1-R3 2D scans. The lines indicate the most optimal Gearing (G) and Anti-gearing (AG) pathways on the energy surfaces, with the relative rotor rotational offset indicated for each. Bottom: The ΔE plot for the most optimal gearing and anti-gearing rotations. The DFT and MM ΔE (energy barrier) for G and AG are shown per rotor. Figure S77. The 2D DFT scans results for R1-R2 as calculated by molecular mechanics (2 x 2 supercell) for the empty (FTR-P1d, α-phase) and CO2 loaded (FTR-P1d·4CO2, α'-phase) structures. Top: graphical illustration of the model. Middle: The 2D contour maps with the rotation of rotors pairs R1 and R2 on the Y-and X-axes with the colours indicating the ΔE. The colour scale ranges from 0 kcal/mol (blue) to 7 kcal/mol (red). The lines indicate the most optimal single rotor rotation pathways on the energy surfaces. Bottom: The ΔE plot for the most optimal single rotor rotations. The FTR-P1d·4CO2 and FTR-P1d ΔE (energy barrier) are shown per rotor. Pathway 1 (P1): The rotation rotor R1 with R2 in the Global minimum position (0 -15°) and the rotation rotor R2 with R1 in the Global minimum position (0 -15°). Pathway 2 (P2): The rotation rotor R1 with R2 in the Local minimum position (60 -75°) and the rotation rotor R2 with R1 in the Local minimum position (60 -75°). Figure S78. The 2D DFT scans results for R1-R3 as calculated by molecular mechanics (2 x 2 supercell) for the empty (FTR-P1d, α-phase) and CO2 loaded (FTR-P1d·4CO2, α'-phase) structures. Top: graphical illustration of the model. Middle: The 2D contour maps with the rotation of rotors pairs R1 and R3 on the Y-and X-axes with the colours indicating the ΔE. The colour scale ranges from 0 kcal/mol (blue) to 7 kcal/mol (red). The lines indicate the most optimal Gearing (G) and Anti-gearing (AG) pathways on the energy surfaces, with the relative rotor rotational offset indicated for each. Bottom: The ΔE plot for the most optimal gearing and anti-gearing rotations. The DFT and MM ΔE (energy barrier) for G and AG are shown per rotor. Figure S79. The 2D DFT scans results for R1-R3 as calculated by molecular mechanics (2 x 2 supercell) for the empty (FTR-P1d, α-phase) and CO2 loaded (FTR-P1d·4CO2, α'-phase) structures. Top: graphical illustration of the model. Middle: The 2D contour maps with the rotation of rotors pairs R1 and R3 on the Y-and X-axes with the colours indicating the ΔE. The colour scale ranges from 0 kcal/mol (blue) to 7 kcal/mol (red). The lines indicate the most optimal single rotor rotation pathways on the energy surfaces. Bottom: The ΔE plot for the most optimal single rotor rotations. The FTR-P1d·4CO2 and FTR-P1d ΔE (energy barrier) are shown per rotor. Pathway 1 (P1): The rotation rotor R1 with R3 in the Global minimum position (0 -15°) and the rotation rotor R3 with R1 in the Global minimum position (0 -15°). Pathway 2 (P2): The rotation rotor R1 with R3 in the Local minimum position (60 -75°) and the rotation rotor R3 with R1 in the Local minimum position (60 -75°). Figure S80. The 2-phase Rietveld refinement of FTR-P1d for the PXRD traces collected under vacuum and cooling from 390 K to 270 K. The miller indices indicated are for peaks only present in the α-phase.