Inside information on xenon adsorption in porous organic cages by NMR

In-depth experimental and computational 129Xe NMR analysis of extraordinarily efficient adsorption of xenon in a porous organic cage.


y to this solution
s a catalyst for imine bond formation.Finally, a solution of (R,R)-1,2-diaminocyclohexane (5.0 g, 44.64 mmol) in DCM (100 mL) was added.The unmixed reaction was covered and left to stand.Over 5 days, all of the solid triformylbenzene was consumed, and octahedral crystals grew on the sides of the vessel.The crystalline product was removed by filtration and washed with 95% ethanol/5% DCM.Yield: 6.5 g, 83%. 1 H NMR (CDCl3): δ 8.15 (s, CHdN, 12H), 7.89 (s, ArH, 12H), 3.33 (m, CHN, 12H), 1.9_1.4(m, CH2, 48H) ppm. 13C NMR (CDCl3): δ 159.1, 136.7, 129.5, 74.7, 33.0, 24.4 ppm.MS (ES+): 1118 ([M+H]+).Accurate mass calculated for C72H85N12: 1117.7020.Found: 1117.7065.

The Xe@CC3-R samples were prepared in the following way: The CC3-R cage material was transferred into a 5-mm medium wall NMR tube.The NMR tube was then connected to a vacuum line and dried overnight at 106 °C under vacuum.A proper volume of Xe gas ( 129 Xe isotope enriched 91%) was then transferred into the NMR tube (to get required amount of 129 Xe for the HL sample, at the end the rest of Xe was condensed in the sample by liquid N2).Finally, the NMR tube was immersed in liquid N2, and the tube was sealed with a flame.The molar ratio between Xe and CC3-R material (Xe:CC3-R) in the NMR tube was calculated to be 0.1:1 for the LL, 0.52:1 for the ML and 3.3:1 for the HL samples.In the ML sample 99 % of Xe and in the HL sample 80 % of Xe are bound by the CC3-R material at RT giving 0.025 bar and 3.9 bar xenon gas pressures inside the tube, respectively.Based on this, the actual molar ratio of bound 129 Xe in the HL sample is 2.4:1. 129Xe NMR experiments were carried out using Bruker Avance III 600 spectrometer with the magnetic field of 14.1 T and 129 Xe frequency of 166 MHz.A 5-mm BBFO probe with z-gradients was used in the experiments.Temperature series were measured with a temperature stabilization time of 60 min.The reading temperatures were calibrated with standard Bruker samples. 129Xe chemical shifts were referenced with respect to low pressure Xe gas.Some broad temperature range experiments, which required N2 cooling, were performed using Bruker Avance III 300 spectrometer with the magnetic field of 7.1 T and 129 Xe frequency of 83.0 MHz.NMR spectra.Basic 129 Xe spectra were measured using pulse angle 90º with 1 scan.For the HL sample, a high SNR spectrum with 24576 scan using 15º pulse angle was recorded as well at room temperature.The equilibrium of bound and free xenon gas was studied by measuring 129 Xe spectra both from the CC3-R and gas regions of the sample.The gas region was measured by turning the sample upside down (a piece of glass wool prevented the moving of the cage material).The ML spectra were accumulated with 64 scan with 400 recycling delay and the HL spectra only with

scan.


NMR expe
iments

T1 relaxation experiments.T1 relaxation times of 129 Xe were measured using inversion recovery pulse sequence.The recycling delays were 80, 80 and 150 s, and the number of accumulated scans was 1, 2 and 1 for the LL, ML and HL samples, respecti ely.T2 relaxation experiments.T2 relaxation times of 129 Xe were measured using CPMG pulse sequence.The recycling delays were 60, 60 and 200 s, and the number of accumulated scans was 8, 4 and 2 for the LL, ML and HL samples, respectively CEST experiments.In the 129 Xe CEST NMR experiments, the B1 field strength of the CW varied between 5.7 and 30 T (power from 1 to 30 mW).The CW pulse length varied from 5 to 15 s.The recycling delays and number of accumulated scans were 42, 70 and 150 s, and 16, 1 and 1 for the LL, ML and HL samples, respectively.Di fusion experiments. 129Xe diffusion measurements were carried out using a PGSTE experiment with bipolar gradients.The recycling delays and number of accumulated scans were 60, 55 and 150 s, and 16, 1 and 8 for the LL, ML and HL samples, respectively.Diffusion delay Δ was varied from 0.05 to 25 s and length of the gradient pulse  from 0.3 to 2 ms.      and Table S1).There is a minimum in the curve around 200 K.The discontinuity in the T1 trend around 280 K is a consequence of a hysteresis effect because of the restart of the experiment.


Experimental results


129 Xe spectra


Relaxation measurements


Exchange rates
Figure S7
. Simple two-site exchange model used in the analysis.C refers to the cage cavity and W to the window cavity.Kinetic constants representing the exchange of xenon from cage to window cavity is kc, and kw is the constant for opposite exchange.

Table S2.Exchange rates kc, kw and kex (kex = kc + kw) of xenon between the cage and window cavities determined by substituting experimentally determined T2 relaxation times (see Table S1), calculated chemical shifts of Xe in the cage and window cavities (see Figure 2 C) and populations Xc and Xw (shown in the two columns on the right and Figure 2 D) into Eq.2. The populations were calculated from the chemical shifts using Eq. 1.

T(K) kc (10 8 s -1 ) kw (10 8 s -1 ) kex (10  Simulations of CEST spectra for the four-site exchange were performed by using four sets of Bloch's equations [1] coupled by kinetic terms according to Figure S11 (ksc,kcs,kfc,kcf,kcw,kwc). The resulting set of the equations was solved numeri

ed 129 Xe NMR signal amplitude as a function of the resonance off
et).

Required parameters in the simulation were either known from experiment, or optimized, or estimated from quantum chemistry methods.Nutation frequencies were determined from experimental /2-pulses at a given power level.T1 and T2 times were measured experimentally, and it was assumed that there is no difference in these quantities between cage and window sites,    The temperature dependence of the diffusion coefficient is represented by the Arrhenius function
        RT E D D D exp 0 , (S1)
where D0 is the pre-exponential factor, ED is the activation energy for diffusion, and R is the gas constant.Taking a natural logarithm from each side, Eq.S1 becomes the following form:
         T R E D D D 1 ln ln 0 . (S2)
Plot of lnD with respect to 1/T is shown in Figure S14.The slope (-ED/R) yields ED = (10.1  0.3) kJ/mol for the ML sample.
Xef + Bf = Xeb, (S3)
where Xef is the amount of free Xe atoms, Bf is the amount of free binding sites in CC3-R and Xeb is the amount of bound Xe atoms.Because there are three binding sites per each cage molecule in the material (one cage cavity site and two window cavity sites), Bf  3Cn, where Cn is the amount of cage molecules in the sample.On the other hand, Bf = 3Cn -Xeb.Therefore, the equilibrium constant is
KN fb = Xeb/(XefBf) = Xeb/[Xef(3Cn -Xeb)]. (S4)
The relative amounts of Xe in the free and bound gas sites were determined by integrating the NMR signals measured from the CC3-R and free gas regions (see Figure were obtained from the total volumes of free gas and the mass of CC3-R in the sample tubes.The values were substituted into Eq.S4 in order to determine the equilibrium constants.Thermodyn ta by a standard van't Hoff plot analysis, resulting in the following values for the changes of Gibbs free energy, enthalpy and entr

y, for


Equilibrium between xenon in the
cage and window cavities


Chemical equation describing equilibrium cage and window cavities is

Cf + Xew = Wf + Xec, (S5)

where Cf the amount of free cage binding sites, Xew is the amount of xenon atoms in window cavities, Wf is the amount of free window binding sites, and Xec is the amount of Xe atoms in the cage cavities.Because there are one cage cavity and two window cavities per each cage, Cf  Cn and Wf  2Cn, where Cn is the amount of cages in the sampl -Xew.Therefore, the equilibrium constant is
Kp cw = WfXec/(CfXew) = (2Cn-Xew)Xec/[(Cn-Xec)Xew]. (S6)
Using the populations of the cage and window cavities shown in Figure 2 D and Table S2, the equilibrium constants were calculated by Eq.S6, and thermodynamic parameters were determined by a standard van't Hoff analysis.In the cases of the LL and ML samples, the cage cavity binding is favored, with the changes of Gibbs free energy, enthalpy and entropy of ΔG = -


Computational modeling

As xenon is an ideal guest for supramolecular systems (chemically inert nature with easily polarized electron cloud), it also opens up interesting possibilities through the modeling of the atomic-scale dynamics of the guest, as was recently demonstrated in Ref. 2 for Xe in an iron-based cage.Xe NMR has also been utilized in studying the structure of ionic liquids [3] by combining classical molecular dynamics with relativistic density functional theory (DFT) calculations.The dynamic, solvent, and relativistic effects to the average Xe chemical shift have been studied in Xe@C60 dissolved in benzene [4], demonstrating that, while relatively small in comparison to the nonrelativistic static model, these effects are essential for obtaining good agreement with experiments.Whereas NMR experiments yield the true time-averaged point of reference, the theoretical model is able to

rovide minute details of, e.g., the three-dimensional atom
c positions as well as potential energy and chemical shift surfaces, which allow distingui the guest Xe as well as deducing how and why the NMR parameters are accumulating to the observed values in a given temperature.


Cavity model structures

The crystal structure of the solid material studied in this work consists of hollow cavities formed by hexagonal carbon rings, connected to each other by carbon and nitrogen atoms to form substructures of tetrahedral symmetry.Molecular density functional theory (DFT) modeling was based on three fixed-geometry cavity structures that represent the essential features of the two sites that xenon occupies.The smallest model (dubbed cage, see Figure S17) comprises of a single hollow N12C72H84 structure with tetrahedral symmetry and four openings that, in the real crystal

tructure, act as gatewa
s to other such hollow cavities.The slightly larger model (dubbed window, N24C144H168) consists of two such adjacent tetrahedral units, with the interesting cavity being the tunnel between the two units.In both models, only a single 129 Xe was present, positioned at the center of the corresponding cavity for static calculations.The largest model is made of five tetrahedral cage units (N60C360H420) and used to study the loading effects with different occupations of cage and window cavities.


DFT calculations

Density functional theory calculations were performed with the hybrid BHandHLYP functional [5−7], using the Turbomole [8] code to obtain energy and chemical shift (CS) data for the dynamics simulations at the nonrelativistic (NR) level.Amsterdam Density Functional (ADF) [9−11] program package was used for relativistic calculations at the zeroth-order regular approximation (ZORA) [12−16] level of theory including either scalar relativistic only (SR-ZORA) or both scalar and spinorbit relativistic (SO-ZORA) effects and using a Gaussian nuclear model [17].ADF version 2014 was used for all calculations except for testing the newer exchange-correlation kernel available in

ersion 2016 (vide infra)
The DFT-D3 dispersion correction [18] was used in potential energy calculations.All-electron co-r[2,19,20]/def2-SVP[21] (Turbomole) and jcpl/TZP (ADF) basis sets were used for Xe/other atoms.The dynamical contributions to the 129 Xe CS were obtained using canonical NVT Metropolis Monte Carlo simulations at a series of temperatures in the range 1-400 K. Further DFT functional tests were performed with PBE [22], BLYP [5,6] and B3LYP [5,6,23] (vide infra).

Chemical shifts are calculated with the approximation  = (Xe atom) − (system) 1 − (Xe atom) ≈ (Xe atom) − (system) that holds well when the reference shielding constant is small.In this case the error is ca.0.14 ppm in the cage cavity.


Computed chemical shifts at the centers of the cavities

The calculated xenon NMR shielding constants and chemical shifts with respect to atomic Xe computed with ADF code using jcpl/TZP basis sets are listed in Table S5.Not accounting for dynamical contributions, the best computational static (Stat) estimates for the chemical shifts of Xe wrt. a free Xe atom (at SO-ZORA/BHandHLYP level for Xe atom at the center of the corresponding cavity) is ca.-21.1 ppm in the cage and +181.4 ppm in the window cavity.Hence, Xe is shielded at the centre of the cage cavity (negative chemical sh

t wrt. a free Xe
tom, corresponding to a lowpressure Xe gas reference), unlike the typical deshielding that it experiences in the window cavity.Xe atom in the cage is therefore 202.5 ppm more shielded than inside the window cavity.This shielding difference is 242.0, 247.6, and 222.1 ppm with PBE, BLYP, and B3LYP functionals, respectively, at the same theoretical SO-ZORA level.


DFT functional tests

Increasing the portion of exact exchange in the DFT functional series BLYP, B3LYP and BHandHLYP result in larger shielding (more negative chemical shifts) but smaller shielding difference between the cage and window cavity.These results are in accordance with earlier findings that the pure DFT functionals tend to overestimate the Xe CS, and while there is some overestimation with BHandHLYP as well, it is typically closer to the correlated ab initio methods as compared to BLYP and B3LYP [24−28].PBE and BLYP yield highly similar, i.e., overestimated results at all levels of theory.Hence, the hybrid BHandHLYP is expected to produce the best results for both

emical shifts, resulting also in the best estimation for
the shielding difference between the cage and window cavities.The hybrid DFT effects can be taken into account via scaling of the periodic GGA results.


Relativistic contributions to Xe chemical shift

With the BHandHLYP functional, relativistic effects at the SO-ZORA level increase the chemical shifts by ca.+3.4 ppm (14%) and +35.6 ppm (24%) in the cage and window cavities, respectively, as shown in Table S5 and Figures S18 and S19.The other hybrid functional, B3LYP, produces qualitatively similar relativistic effects (+4.9 ppm for cage and +38.2 ppm for window).The pure DFT functionals, PBE and BLYP, give slightly larger relativistic contributions in the window cavity (ca.+42 ppm), following the general trend of overestimation by them.In the window cavity, the main relativistic contribution is SR, which accounts for slightly more than 70% of the effect with all the tested functionals.In the cage cavi

the SO outgrows the
R contribution when the amount of exact exchange increases, and with the BHandHLYP functional the SO contribution is larger than SR by 1.0 ppm, covering 65% of the relativistic effects.With pure DFT functionals, the roles are changed.The SO contribution is relatively large but not of equal size in both cage and window cavities and, hence, it should be included as a correction to the SR-ZORA level in periodic modeling.


Exchange-correlation kernel in ADF 2016

The use of the improved exchange-correlation kernel available in ADF version 2016 was tested using the B3LYP functional (see Table S5), and found to account for ca.+7 ppm to the isotropic Xe shielding constants of free Xe atom and Xe inside the cage cavity, but resulting in only a negligible, ca.+0.2 ppm, modification to the corresponding Xe chemical shift.


Dynamical modeling and total estimate of the 129 Xe

hemical shift

Dynamical modeling yielded positi
e contributions to the 129 Xe chemical shift in both cage and window cavities, as shown in Table S6 and Figure S20.In short temperature ranges above 50 K, such as the low and high temperature ranges shown in Figure S20, the dynamical contribution is roughly linear, in the cage (window) cavity approximately +74 ppb/K (+90 ppb/K) and +64 ppb/K (+51 ppb/K), correspondingly.The room-temperature dynamical contributions, +43.


Loading effect on Xe shifts in cage and window cavities

The effect due to different Xe loadings in neighboring cavities is tested with models including one, two, and five cages shown in Figure S17 and the results are listed in Table S7.The full loading of the neighboring cavities decreases the Xe chemical shift, i.e.Xe becomes more shielded, as compared to the case where cavities are empty.The effect is much smaller than relativistic and motional effects of Xe.As the effect is about similar size in both cavities, ca.-14 ppm, it has an insignificant effect on the chemical shift difference between cavities.

Figure S1 .
S1
Figure S1.High SNR spectrum of the HL sample measured with 24576 scans using a pulse angle of 15° at 14.1 T. A small free gas signal is visible around 0.6 ppm.No window or cage cavity signal is visible around 211 or 22 ppm, although SNR is about 4000.


Figure S2 .
S2
Figure S2.Spectra of ML sample at temperature range of 153-193 K measured at 7.1 T. At the lowest temperatures, the signal becomes broader

ecause of gradual transition from fast t
intermediate exchange rate region.Because separated signals from the cage and window cavities around 20 and 200 ppm are not resolved, the system is not in the slow exchange region even at the lowest temperature.


Figure S3 .
S3
Figure S3.Chemical shift of the ML sample in a broad temperature range, measured at 7.1 T. The shift increases quite linearly with t

perature.


Figure S4 .
S4
Figure S4.T1 relaxation times of 129 Xe
n CC3-R samples at variable temperature, measured at 14.1 T.


Figure S5 .Figure S6 .
S5S6
Figure S5.T2 relaxation times of 129 Xe in CC3-R samples at variable temperature, measured at 14.1 T.


2. 4 Figure S10 .
4S10
Figure S8.129Xe CEST spectra of the LL sample with variable temperature, CW pulse power and length shown in the figure, measured at 14.1 T.


2. 6
6
Figure S12.Integral of the signal in the diffusion experiments as a function of gradient strengt

spectra for the LL sample at 298 K (left) and 255 K (rig
t).Two components are clearly visible.The faster decaying component arises from interparticle diffusion, the slower component from diffusion inside the CC3-R particles.


Figure S13 .
S13
Figure S13.Integral of the signal in the diffusion experiments as a function of gradient strength spectra for the ML sample at 298 K (left), 255 K (middle) and 298 K (right).The diffusion delay is longer (5 s) in the right experiment than in others (0.2 s).Two components are clearly visible.The faster decaying component arises from interparticle diffusion, the slower compo