Encapsulation of xenon by bridged resorcinarene cages with high Encapsulation of xenon by bridged resorcinarene cages with high 129Xe NMR chemical shift and efficient exchange dynamics 129Xe NMR chemical shift and efficient exchange dynamics

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INTRODUCTION
2][3][4] The biosensors include functionalized cages encapsulating Xe atoms.The spatial distribution of the biosensors in living systems is monitored by 129 Xe MRI. 129Xe chemical shift is very sensitive to changes in the local physical and chemical environment of Xe, providing information about Xe encapsulation and biosensor binding.MRI sensitivity of 129 Xe can be improved up to seven orders of magnitude by combining spin-exchange optical pumping (SEOP) nuclear hyperpolarization method 5 with chemical exchange saturation transfer (CEST) technique. 6Therefore, Xe biosensors allow molecular imaging even at nano-or picomolar concentrations.For example, the method has been exploited in cell tracing, 7 biothiol detection, 8 and in vivo bioimaging of living rats. 9e sensitivity and specificity of the Xe biosensor is strongly affected by the properties of the cages encapsulating Xe atoms. 4For example, the cages should have a high enough affinity toward Xe so that the encapsulation takes place; the encapsulated 129 Xe should provide a signal at chemical shift distinct from solvent and other signals; the exchange rate of Xe between encapsulated and solvent pools should be high enough for efficient CEST but slow enough for resolving the sites in the nuclear magnetic resonance (NMR) timescale; and the cage should be functionalizable for targeting a desired biological target.
Cryptophane cages are considered as the gold standard for Xe biosensor applications as they exhibit the highest Xe binding constant. 2However, they are not commercially available, their synthesis requires multiple steps, and yields are very low. 2 Therefore, alternative biosensor cage structures are actively screened to overcome these drawbacks.One commonly used cage structure is cucurbit [6]uril (CB6), which is a commercially available macrocyclic host. 10It suffers from limited solubility and promiscuous molecular recognition behavior where Xe is easily replaced by other guests, and post-functionalization of CB6 is very challenging. 11Variable other macrocycle and cage compounds have also been introduced as potential candidates, such as cucurbituril-based rotaxanes, 12 pillararenes, 13,14 hemicarcerands, 15 Fe 4 L 6 cages, 16,17 cyclodextrins, 18,19 calixarenes, 20 and chiral bisurea-bisthiourea macrocycles. 213][24] The payload of Xe has also been increased by so-called super hosts, including gas vesicles, 25 nanoemulsions, 26 bacteriophages, 27 nanodroplets, 28 genetically encoded proteins, 29 and functionalized liposomes and micelles. 30,31he cage molecule can also be associated with a lipid layer, which aids in transportation into the body. 32,33The strengths and weaknesses of each Xe biosensor host type are evaluated thoroughly in the recent review by Jayapaul and Schro ¨der. 2 Here, we introduce a class of potential biosensor cage structures based on two resorcinarene supramolecules bridged either by aliphatic carbon chains or piperazines.Resorcinarene is a calixarene-type macrocycle formed by a simple synthesis. 34annich condensation is a common procedure to modify the aromatic ring structure and form cage structures by connecting two resorcinarene structures with amine linkers. 35By adjusting the linker structure, the properties of the cage can be easily modified, and different variations of cage structures can be synthesized.We report first principles computational predictions of chemical shifts of 129 Xe atoms in both aliphatically bridged and piperazine-bridged resorcinarenes.The modeling provides the direct 129 Xe chemical shift information with microscopic interpretation, which has earlier revealed beneficial details about the encapsulation of Xe in cryptophanes, 36,37 Fe 4 L 6 cages, 16,17 Buckminster fullerene, [38][39][40] clathrates, 41 zeolites, 42,43 metal organic frameworks, 44,45 porous organic cages, 46,47 liquid crystals, 48 and water. 49Encapsulation of Xe in the cages in methanol solvent is confirmed by experimental 129 Xe CEST and T 2 relaxation analysis.Furthermore, simulations of CEST spectra reveal essential exchange rates and binding constants.

Computational modeling predicts xenon encapsulation and 129 Xe chemical shifts
The computationally modeled structures of the aliphatically bridged and piperazinebridged resorcinarene cages ABR-6 and PBR-3 are illustrated in Figures 1A and 1B, respectively.In the computational modeling, the structures of the cages were optimized with a xenon atom inside the cages, also considering the effect of methanol solvent (see computational section in experimental procedures).The PBR-2 cage is otherwise like the PBR-3 cage, but the lengths of the carbon chains pointing outward from the resorcinarenes are two instead of three.
The volume of the optimized ABR-6 cage cavity was relatively small, only 52 A ˚3, compared with the van der Waals volume of Xe, 42 A ˚3.The ratio of the guest/host volumes is 0.81, which is larger than the optimal ratio of 0.55 G 0.09 for encapsulation. 50The ABR-6 cavity volume is also smaller than that of cryptophane-A (87-119 A ˚3) 51,52 and cryptophane-1.1.1 (81 A ˚3). 53 The PBR-2 and PBR-3 cages include a long, hourglass-shaped cavity (Figure 1B), in which xenon atoms have two potential binding sites at each end of the cavity.The overall volume of the cavity is 163 A ˚3. Therefore, the volume of one binding site is about 81 A ˚3, and the guest/host volume ratio is 0.52, which is close to the optimal ratio.The simulations imply that the PBR cages could potentially encapsulate two xenon atoms simultaneously.
The nudged elastic band (NEB) simulations 54,55 show that the potential energy of xenon atom entering or exiting the ABR or PBR cages is smaller when the path goes through the sides of the cages (horizontal direction in Figure 1) instead of the ends (vertical direction).The exit potential energy barrier is about three times higher through the end than through the side (ABR-6: 246 vs. 59 kJ/mol, PBR-3: 250 vs. 88 kJ/mol).The potential energies for PBR-2 are almost identical to PBR-3.This implies that the sides are the predominant entrances for xenon encapsulation, which is reasonable considering the flexible nature of the aliphatic and piperazine chains bridging the resorcinarenes.On the other hand, the NEB simulations do not consider the entropic contributions.
We calculated the 129 Xe chemical shifts of xenon inside the cages at equilibrium geometry using the density functional theory (DFT) method, including both scalar relativistic (SR) and spin-orbit (SO) relativistic effects (see ''X2C + SO'' results in Table S5).Furthermore, we took the temperature-dependent motion of a xenon atom inside the cavity into account by MC averaging over potential energy and 129 Xe chemical shift surfaces (Figure 1, Tables S6 and S7) computed at SR level (the cage mobility was not considered).
The averaged computational 129 Xe chemical shift of xenon in ABR-6 is 345 ppm at 300 K.The shift is much higher than typical shifts in cryptophanes (30-70 ppm), 2 and it is even higher than the extraordinarily high chemical shift of a permetallated cryptophane cage (308 ppm). 56The high chemical shift is a consequence of the small size of the ABR-6 cavity; chemical shift of Xe is known to increase with decreasing pore/cavity size. 57We note that, contrary to the permetallated cryptophane cage, 56 ABR-6 does not include metal ions.Therefore, instead of metal effect, 37 the large Xe shift in ABR-6 is due to high density of virtual electronic states provided by neighboring cage atoms, which are available for the paramagnetic deshielding contribution. 58The shift is outside the typical experimental observation window, and the computational predictions guided us to the appropriate chemical shift range in the CEST experiments.
The calculated chemical shift of a single xenon atom inside the PBR-3 is 109 ppm at 300 K, which is also slightly higher than the typical shift in cryptophanes, once again due to the slightly smaller volume of the binding site within the PBR-3 cage.When the cage includes two xenon atoms, the calculated shift increases ca.45 ppm due to Xe-Xe interactions (Table S8), being 154 ppm.Consequently, the simulations predict that one might observe two bound xenon signals from the PBR-3 cages.The calculated chemical shift of a single xenon in the PBR-2 cage is 7 ppm smaller than in the PBR-3 cage.

Xe NMR measurements show xenon encapsulation and exchange dynamics
Direct thermally polarized 129 Xe spectra of all the three cages include only a single, relatively narrow peak at around 142 ppm at 300 K, originating from 129 Xe in the methanol solvent (Figure 2).The concentration of Xe in methanol, which was calculated to be about 350 mM at 4 atm pressure using the Ostwald coefficient L = 2.09, 59 is 350 and 175 times higher than the concentrations of the ABR-6 and PBR cages (1 and 2 mM), respectively.Therefore, the signal of 129 Xe in the cages is hundreds of times smaller than the solvated 129 Xe signal, vanishing to the noise.However, thermally polarized 129 Xe CEST spectra include additional peaks, which reveal that some of the cages encapsulate xenon.The bound xenon signals become visible due to the significant sensitivity enhancement (three to four orders of magnitude) provided by CEST. 2 The CEST spectra of ABR-6 include a broad and low dip of encapsulated 129 Xe above 300 ppm.The spectra were simulated using a two-site (solvent and cage sites) exchange model and Bloch-McConnell equations (dotted lines in Figure 2).The CEST simulations were not performed to ABR-6 data at 300 K because of the very broad signal due to fast exchange.According to the simulations, the chemical shift of 129 Xe in the ABR-6 cage is 340 G 4 ppm at 280 K (Figure 3A), which is in excellent agreement with the shift predicted by the DFT calculations (345 ppm at 300 K).The exchange rate k CS is very high, 52,000 G 3,000 s À1 at 280 K (Figure 3B).It is much higher than k CS for commonly used cryptophane-A-monoacid (CrA) cage in DMSO, 317 s À1 , 60 and even higher than for CB6 (1,470 s À1 in PBS buffer), which has an open ring structure. 10The relative population of the cage site (i.e., the relative amount of bound Xe) is low, 0.00150 G 0.00014 at 280 K (Figure 3C), predominately due to the much lower cage concentration than Xe concentration.About 52% of cages are occupied by Xe at 280 K. Xe binding constant is rather low, 3.1 G 0.7 M À1 at 280 K (Figure 3D), compared with the typical range of different cryptophane cages, 5-3,000 M À161,62 ; increasing water solubility with polar groups makes binding constants even larger, 2 and the water-soluble versions of CrA have binding constants up to 30,000 M À1 . 56,63,64On the other hand, the ABR-6 Xe binding constant is similar to many other novel alternative biosensor candidates, such as gas binding proteins (40 M À1 ), 2 Fe-MOP (16 M À1 ), 16 a-cyclodextrin (20 M À1 ), 65 and calix [4]arene derivative (14 M À1 ). 20e CEST response of the PBR-3 sample includes strong asymmetric broadening toward lower chemical shifts, which indicates the Xe encapsulation.Furthermore, there is weak broadening toward high chemical shifts as well, especially at the lowest temperatures.This may be an indication of simultaneous encapsulation of two Xe atoms in the hourglass-shaped cage.Therefore, in the CEST spectra simulations, we used a three-site exchange model instead of two.As visualized in Figure 2B, the sites include the solvent pool (S) and two cage pools corresponding to single (C1) and double (C2) Xe loading.An interesting detail in the model is that when one Xe is released from the C2 pool to solvent, simultaneously the remaining Xe changes from C2 to C1 pool without any physical exchange.According to the CEST simulations, chemical shift of a single 129 Xe in the PBR-3 cage is 114 G 1 ppm (Figure 3A), being close to the shift predicted by the DFT calculations (109 ppm).The shift of the double-loaded cage is higher with a value of 210 G 20 ppm at 300 K, which is in qualitative agreement (right direction) with the DFT prediction (154 ppm).Probably both simple droplet model as well as entailing approximations by semi-empirical theory in molecular dynamics (MD) simulations cause the underestimation of the chemical shift due to double occupation.The single-loading exchange rate k C1S is high, 12,000 G 3,000 s À1 at 300 K (Figure 3B), but about four times smaller than for ABR-6 cage.The double-loading exchange rate (28,000 G 9,000 s À1 at 300 K) is even higher because there are two Xe atoms that can exit instead of one.The relative populations of the cage sites C1 and C2, 0.00015 G 0.00003 and 0.000031 G 0.000009 at 300 K (Figure 3C), are about ten times smaller than in the ABR-6 cage, although the concentration of PBR-3 cages is two times higher.Only about 3% of the cages are occupied by Xe.Xe binding constant in PBR-3 is low, 0.09 G 0.02 M À1 , about 30 times smaller than in ABR-6.
The 129 Xe CEST spectrum of PBR-2 cage includes only a symmetric solvent resonance, without any sign of encapsulated Xe signal.According to the DFT predictions, the signal of a single encapsulated Xe has about 7 ppm smaller chemical shift than in PBR-3 cage, which should be well resolved in the spectrum without disruptive overlapping with the solvent signal.Therefore, the CEST experiments imply that, contrary to PBR-3, the PBR-2 cage does not encapsulate Xe, regardless of the very similar structure of the cages.We expect that this is a consequence of the fact that all the residual solvent from synthesis and purification was removed in PBR-3, but PBR-2 still had some tightly encapsulated alcoholic (ethanol and methanol) solvents.It is likely that the entrapped solvent prevents the encapsulation of Xe in PBR-2. 35laxation measurements provide alternative contrast for xenon encapsulation and exchange dynamics Relaxation measurements offer an alternative perspective on Xe dynamics in the samples.T 1 relaxation times of 129 Xe in the PBR-2 and PBR-3 samples are long and almost equal, 260 and 263 s at 300 K, respectively (Figure 4).Providing that PBR-3 cages encapsulate Xe but PBR-2 cages do not, it seems that T 1 is not sensitive to exchange, which is reasonable, as the exchange rate ($10 kHz) is much lower than the Larmor frequency (166 MHz).66 T 1 in the ABR-6 sample is slightly lower, 214 s at 300 K, because it was measured at a lower field (138 MHz).66 T 2 of 129 Xe in the PBR-2 sample (60 s at 300 K) is much longer than that in the ABR-6 and PBR-3 samples (23 and 650 ms, respectively).T 2 of 129 Xe is known to be very sensitive to chemical exchange, 46,47 and the long T 2 provides an additional confirmation that PBR-2 does not encapsulate Xe, while the short T 2 affirms Xe binding in PBR-3 and ABR-6 cages.
According to a simple two-site exchange model, in which T 2 relaxation is assumed to arise from varying chemical shift due to exchange between two sites, T 2 relaxation rate R 2 = 1/T 2 is 67,68 where c S and c C are the relative populations of Xe in the solvent and cage sites,  Using the parameters given by the CEST simulations (Figure 3), Equation 1 predicts that T 2 values of the ABR-6 and PBR-3 samples are 14 G 4 ms at 280 K and 600 G 300 ms at 300 K, respectively, which are in good agreement with the corresponding experimental T 2 values, 19 and 652 ms.Therefore, the model provides a reasonable explanation for the shorter T 2 of the ABR-6 sample, which predominantly originates from a larger chemical shift difference between the cage and solvent sites than in the PBR-3 sample.Furthermore, it confirms that the parameter values resulting from the CEST simulations are reliable.Overall, the relaxation experiments show that T 2 offers extremely sensitive contrast for Xe binding; T 2 of PBR-3 sample was about 90 times shorter than that of PBR-2 due to the encapsulation.This contrast could be exploited in the biosensor studies instead of CEST contrast because T 2 can be measured very efficiently even in a single scan by the CPMG (Carr-Purcell-Meiboom-Gill) method.This was demonstrated earlier by Kunth et al. for Xe encapsulated by cryptophane-A monoacid (CrA-ma) and CB6 cages. 68As pointed out by Kunth et al., relaxation rate is approximately linearly dependent on the concentration of cages, and exchange-induced relaxivity r 2 = DR 2 /DC (where DR 2 and DC are the changes in relaxation rate and cage concentration, respectively) is a useful parameter to compare T 2 relaxation contrasts of the cages for Xe encapsulation.ABR-6 has much higher relaxivity (r 2 = 53 s À1 mM À1 ) than PBR-3 (r 2 = 0.83 s À1 mM À1 ); it is higher than relaxivity of CrA-ma (r 2 = 13 s À1 mM À1 ) but lower than that of CB6 (r 2 = 870 s À1 mM À1 ). 68Naturally, in the biosensor applications the contrast is diminished due to Xe interactions with proteins and other constituents of the sample, but even in those conditions, detectable contrast remains. 69visioning ways to make cages water soluble The ABR-6 and PBR cages studied in this work were dissolved in methanol.In biosensor applications, the water solubility of xenon binding cages is essential for in vivo studies.
Hence, we propose several potential synthetic directions toward enhancing the water solubility of ABR-6 cage structure without affecting the hydrophobic cavity of the cage.1][72] Utilizing similar principles, ABR-6 can be functionalized with these charged moieties to increase the water solubility, as illustrated in Figures S1A and S1B.Two alternative routes are represented in Figures S1C and S1D. 70,71Although these modifications as well as the change of solvent affect the structure of the cages, we anticipate that the structural changes are not significant, and therefore the bound Xe chemical shifts are expected to be close to those in unmodified cages in methanol solvent.On the other hand, chemical shift of free Xe in solvent increases about 48 ppm when solvent is changed from methanol to water. 73Therefore, the chemical shift difference between the solvent and dominant single-loading cage sites is expected to increase in PBR-3 cage in water, improving resolution.In ABR-6, the difference is expected to decrease, but, due to the exceptionally high chemical shift of bound Xe in ABR-6 (about 340 ppm), the effect of the decreased difference on resolution is assumed to be insignificant.
In conclusion, we introduced a class of cages based on two resorcinarene macrocycles bridged by aliphatic carbon chains or piperazine, which can encapsulate Xe in methanol solvent and are therefore promising potential alternative cages for Xe biosensor applications, if they are modified water soluble as envisioned in the article.Thermally averaged first principles DFT calculations predicted an extraordinarily high chemical shift (345 ppm) of 129 Xe in the aliphatically bridged resorcinarene cage ABR-6.The shift is outside the typical range of 129 Xe resonances, thus providing unambiguous contrast for potential biosensor applications.Furthermore, the DFT calculations forecasted a signal of single encapsulated 129 Xe in the PBR cages at around 110 ppm and another higher chemical shift signal from the cages loaded with two Xe atoms.Experimental thermally polarized 129 CEST spectra confirmed the encapsulation of Xe in ABR-6 and PBR-3 cages, and the observed 129 Xe chemical shifts of bound xenon were in excellent agreement with the DFT predictions.The binding constants of the ABR-6 and PBR-3 cages are modest, about 3 and 0.09 M À1 .However, the exchange rates are extraordinarily high, 52,000 and 12,000 s À1 , making the CEST response of the cages very strong because of high turnover, regardless of the low binding constant.This is promising for potential biosensor applications.We envision that the binding constant could be significantly increased by making the cages water soluble through the procedures described in the article. 56,63,64Improved binding constant may be needed to avoid potential competing guests preventing Xe encapsulation. 74Furthermore, changing methanol solvent to water may decrease saturation powers required in the CEST experiments if the relative size of bound Xe pool increases and exchange rate slightly reduces.The concentration of cages was rather high (1-2 mM) in the thermally polarized experiments reported in this article.However, the sensitivity of the CEST and relaxation experiments can be enhanced up to five orders of magnitude by SEOP hyperpolarization method, 5,6 potentially making cage concentrations observable.Overall, the article clearly shows how combining state-of-the-art dynamical modeling of 129 Xe NMR chemical shift with modern experimental methods provides interesting and valuable information on Xe encapsulation in bridged resorcinarene cages, and it paves the way for finding affordable, readily synthesizable, efficient biosensor cages.

EXPERIMENTAL PROCEDURES
Resource availability Lead contact Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Ville-Veikko Telkki (ville-veikko.telkki@oulu.fi).

Materials availability
All materials generated in this study are available from the lead contact without restriction.

Data and code availability
All data supporting the findings of this study are presented within the article and supplemental information.This study did not generate any datasets.

Bridged resorcinarene cages
We studied two piperazine and one aliphatically bridged resorcinarene cages.Their syntheses are described elsewhere. 35,75e chains bridging resorcinarenes in the ABR cage include six carbon atoms, and therefore the cage is called ABR-6.Contrary to the PBR cages, polar hydroxyl groups of resorcinarene cups point outward in the ABR cages (Figure 5A). 75The two PBR cages are otherwise similar, but the length of carbon chains pointing outward from the resorcinarenes are two and three for the cages labeled PBR-2 and PBR-3, respectively (Figure 5B).

Sample preparation
Cage molecules were dissolved to MeOD-d 4 , and the solution was transferred into 10-mm (ABR cages) or 5-mm (PBR cages) medium-wall NMR tubes.The concentrations of the ABR and PBR cages were 1 and 2 mM, respectively.Thereafter, the NMR tube was connected to a vacuum line, immersed in liquid nitrogen, and 129 Xe isotope-enriched (91%) xenon gas was condensed into the sample.The final xenon gas pressure in the samples was estimated to be about 3-4 atm.
129 Xe NMR measurements Thermally polarized 129 Xe NMR experiments of the ABR-6 sample were carried out on a Bruker Avance III 500 spectrometer with a magnetic field of 11.75 T and 129 Xe frequency of 138 MHz using a 10-mm BBO probe with z-gradients.Thermally polarized 129 Xe NMR experiments of the PBR samples were measured on a Bruker Avance III 600 spectrometer with the magnetic field of 14.1 T and 129 Xe frequency of 166 MHz using a 5-mm BBFO probe with z-gradients.The temperature stabilization time was 60 min for the 10-mm and 30 min for the 5-mm samples in the variable temperature experiments.
129 Xe spectra were measured using a standard single-pulse program with a pulse angle of 15 for the 10-mm ABR-6 sample and 30 for the 5-mm PBR samples.The number of scans was 20,480 and 1,024, respectively.Recycling delay was adjusted according to the Ernst angle to maximize the signal-to-noise ratio per unit time: 0.03473T 1 in the case of the 15 pulse angle and 0.1433T 1 in the case of the 30 pulse angle.Experiment times were 2 days and 11 h, respectively.The 129 Xe spectra and CEST spectra were referenced with respect to the signal of the 2 atm 129 Xe sample set at 0 ppm.In the 129 Xe CEST NMR experiments of the 10-mm ABR-6 sample, the length and power of the continuous wave saturation pulse were 1 s and 200 mW (B 1 = 39 mT), respectively.Corresponding values for the 5-mm PBR samples were 5 s and 100 mW (B 1 = 59 mT).The number of accumulated scans was 8 and 2 for the ABR-6 and PBR samples, respectively.Recycling delay was adjusted according to Ernst's angle to be at least 1.2573T 1 , as the read pulse angle was 90 .
129 Xe T 1 and T 2 relaxation times were measured using standard inversion recovery and CPMG pulse sequences, respectively.In the CPMG experiments, the echo time was 1 ms, and eight time points were collected at appropriate echo numbers to observe T 2 decay.

CEST spectra simulations
The CEST simulations were done using the fast matrix-exponential method 76 for solving the Bloch-McConnell equations, 77 modified here to include a chemical exchange between small pools.The implementation was based on a previously published MATLAB code, 78 modified and rewritten to a Python language in this work.
The fitting was facilitated by Markov chain Monte Carlo simulation 79 implemented in Ha ˚kansson et al., 80 modified and rewritten into Python language in this work.

Computational section
The reference equilibrium structures of both piperazine-bridged (PBR-2 and PBR-3) as well as aliphatically bridged (ABR-6) resorcinarene cages were optimized with a Xe inside the cage using Turbomole code. 81,82Optimizations were carried out with hybrid PBE0 functional 83 using D4 dispersion correction, 84 SR spin-free exact two-component (X2C) theory, 85 and x2c-TZVPall-s basis set for Xe 86 and def2-TZVP basis sets for cage atoms. 87The effect of methanol solvent on the structure was accounted for by COSMO model. 88The corresponding equilibrium structures for PBR-3 and ABR-6 are displayed in Figures 1A and 1B, respectively, and the XYZ-files of all three structures can be found in supplemental information.At the optimized equilibrium geometries, 129 Xe NMR nuclear shielding tensors were computed at the above-mentioned level of theory.In addition, the effect of nonrelativistic theory as well as electron correlation treatment with pure Perdew-Burke-Ernzerhof (PBE) 89 and another hybrid Becke-half-and-half-Lee-Yang-Parr (BHandHLYP) 90,91 DFT functionals were tested.SO effect on 129 Xe NMR chemical shift was estimated by carrying out both scalar (SR-ZORA) and scalar plus spin-orbit (SO-ZORA) relativistic zeroth-order regular approximation calculations 92,93 with ADF code. 94,95TZ2P-J basis set for Xe and DZP basis sets for cage atoms 96 together with a finite nuclear model 97 were used in ADF calculations.
We also computed potential energy and 129 Xe NMR shielding hypersurfaces at SR X2C level 98 in Turbomole code 81,82 inside unrelaxed PBR-3 and ABR-6 cages as well as relaxed ABR-6 cages (partially optimized cage geometries as Xe is displaced from the equilibrium position; see details in the supplemental information).In PBR-3, the performance of pure PBE functional was tested against benchmark [38][39][40] quality BHandHLYP functional.Produced potential energy surfaces and 129 Xe NMR shielding hypersurfaces were used in finite temperature canonical Monte Carlo (MC-NVT) simulation carried out with in-house MC-NVT code. 16In the ABR-6 cage, the effect of the relaxation of the cage structure (relaxed structures) as Xe atom moves inside was tested at first principles DFT/PBE-D4 level as well as with extended tight-binding (xTB) 99 semi-empirical GFN1-xTB 100 and GFN2-xTB 101 methods.
MD simulations at T = 300 K of a finite droplet consisting of either one or two Xe atoms inside PBR-3 cage surrounded by explicit solvent of 300 methanol molecules were carried out with GFN1-xTB method in xTB code. 99Xe NMR shielding averages were obtained by sampling snapshots from the MD trajectories.NMR calculations were carried out with Turbomole code at the same X2C/PBE/TZVP level (see above) for a cluster containing only Xe atom(s) and PBR-3 cage.
Cavity volumes of equilibrium structures were computed with Caver analyst code 51 using a probe radius of 1.2 A ˚with 10 5 samples.
To estimate the energy barrier associated with the Xe atom entering or leaving the cages, we used a zoom climbing image version of an NEB method implemented in ORCA 5.0.1. 54,55Calculations at GFN1-xTB, 100 GFN2-xTB, 101 and B97-3c 102 levels were done both in vacuo and with analytical linearized Poisson-Boltzmann (ALPB) 103 and SMD 104 implicit solvation models for methanol.As for the conclusions of this study, neither the level of theory nor the implicit solvation model was significant.Therefore, the reported results were carried out at GFN2-xTB level of theory in vacuo.

Figure 1 .
Figure 1.Computational modeling of xenon in resorcinarene cages Structures of (A) the aliphatically bridged (ABR-6) and (B) piperazine-bridged (PBR-3) resorcinarene cages.Carbon, oxygen, nitrogen, and hydrogen atoms are illustrated by brown, red, blue, and white colors, respectively.The large blue ball represents an encapsulated xenon atom.Examples of 129 Xe chemical shift (d) and potential energy (E) surfaces with respect to the equilibrium values of the encapsulated xenon are shown on the right.

Figure 2 .
Figure 2. Detection of encapsulation of xenon in resorcinarene cages 129 Xe direct (peaks up) and CEST (peaks down) NMR spectra of xenon in (A) ABR-6 as well as (B) PBR-2 and PBR-3 cages in methanol.Simulated CEST spectra are illustrated by dotted lines.Calculated shifts of 129 Xe in cages are shown by gray vertical dotted lines.The figures also visualize the two-and three-site exchange models that were used in the simulations.S and C refer to the solvent and cage sites, respectively.C1 and C2 refer to the PBR-3 cages filled with one and two Xe atoms, respectively.The CEST saturation pulse length and B 1 field strength for the ABR-6 sample were 1 s and 39 mT.The corresponding values for the PBR samples were 5 s and 59 mT.

Figure 3 .
Figure 3.Chemical and thermodynamic parameters for xenon encapsulation Parameters resulting from the simulations of 129 Xe CEST spectra of the ABR-6 and PBR-3 samples.(A) Chemical shifts.(B) Exchange rates.(C) Relative populations of the cage sites.(D) Binding constants.The error margins show the 95% confidence interval given by the Bayesian posterior distribution obtained by the MCMC simulation.

Figure 4 .
Figure 4. Relaxation times reflecting the exchange dynamics of xenon T 1 and T 2 relaxation times of 129 Xe in the ABR-6, PBR-2, and PBR-3 samples.