Gas Uptake and Thermodynamics in Porous Liquids Elucidated by 129Xe NMR

We exploited 129Xe NMR to investigate xenon gas uptake and dynamics in a porous liquid formed by dissolving porous organic cages in a cavity-excluded solvent. Quantitative 129Xe NMR shows that when the amount of xenon added to the sample is lower than the amount of cages present (subsaturation), the porous liquid absorbs almost all xenon atoms from the gas phase, with 30% of the cages occupied with a Xe atom. A simple two-site exchange model enables an estimate of the chemical shift of 129Xe in the cages, which is in good agreement with the value provided by first-principles modeling. T2 relaxation times allow the determination of the exchange rate of Xe between the solvent and cage sites as well as the activation energies of the exchange. The 129Xe NMR analysis also enables determination of the free energy of confinement, and it shows that Xe binding is predominantly enthalpy-driven.


Purification of 4-(trifluoromethoxy)benzyl alcohol (TBA)
Purification of the solvent was performed by vacuum distillation -first and last 10% of distillate was disposed of, and TBA was collected at steady state (72 °C @ 1.9 x 10 −1 mbar, brown-red solution to near colourless liquid).

Molecular dynamics simulations
Molecular dynamics (MD) simulations for the studied systems were run with the xTB program package 3 .Separate simulations for both the CC3-R and the CC13 cage structures were carried out and in both cases a xenon atom was placed inside the PL cage that, in turn, was surrounded by 164 TBA solvent molecules.In addition, simulations were performed for a xenon atom surrounded by only the 164 TBA molecules.The semi-empirical, extended tight-binding method GFN2-xTB 4 was used to generate the energy and forces for the leapfrog MD algorithm run with a 1 fs timestep in all the three cases.The simulations were carried out in the constant particle number, volume and temperature (NVT) ensemble with the thermostat set to a constant temperature of 300 K.
The initial geometries for the MD simulations, depicted in Figure S1, were determined using the Packmol program 6 .For CC3-R and the CC13 simulations, a cage molecule with a xenon atom inside was placed at the centre and the TBA molecules were placed evenly around it within a radius of 25.0 Å.For the simulation without the cage, the TBA molecules were placed around a xenon atom at the centre, again within a 25.0 Å radius.These geometries were then optimized by using the xTB program package with the same GFN2-xTB method that was also used in the following MD simulations.
In the MD simulations, a logfermi type spherical cavity potential of R sphere = 40 a 0 (21.2Å) radius was used to keep the solvent molecules confined around the origin.The cages with encapsulated Xe atom were further confined at the center of solvent with the cavity potential of the same type, with R sphere = 25 a 0 (13.2Å).In the TBA simulations without the cage molecule, the Xe atom was confined at the center of the solvent using smaller cavity potential with R sphere = 15 a 0 (7.9 Å).
In addition to the original simulation starting from the optimized structure, three and two independent MD simulations for CC3-R and the CC13 systems, respectively, were started from the same structure taken from the original simulation but with different starting velocities for the nuclei.The approach enabled trivial parallelism that provided more data and more efficient probing of the phase space.
A similar approach for the neat TBA system was not successful as the Xe gained additional velocity probably due to the interaction with the confinement potential in the begin-freely inside the larger droplet confinement) resulting simulations drifting far from equilibrium.Therefore, only the original, well equilibrated TBA simulation was included in the averaging.
After the equilibration period of 5 ps, the snapshots were taken at 0.25 ps intervals from the simulation trajectories and Xe NMR shieldings were computed for the extracted cluster models.The data was collected from each simulation and combined together.Hence, 60 ps (one simulation), 186 ps (four), and 135 ps (three) of data for TBA, CC3-R, and CC13, respectively, were obtained for statistical analysis.The correlation length was estimated to be ≤ 1 ps with both data-halving 7 and block-averaging methods 8 .We chose a 1 ps sampling frequency for thermal averages and errors reported in Table S1.Convergence of the Xe chemical shifts is shown in Fig. S2 and thermal averages are displayed in Fig. S3. 129Xe NMR shielding calculations with the Turbomole 9,10 code were carried out at scalarrelativistic X2C level 11 with x2c-TZVPall-s basis set for the Xe atom optimized for shielding A single value for the scrambled CC3 3 :13 3 −R was obtained.
calculations 12 , as well as both x2c-SVPall and x2c-TZVPall basis sets 13 for other atoms.
In order to efficiently carry out hundreds of preliminary NMR calculations, the pure PBE density functional 14 was used.It is expected to provide good estimates for the correction due to better basis set for other than Xe atom (x2c-TZVPall -x2c-SVPall), so-called basis set effect (BSE) listed in Table S1.It should also give reasonable first estimates for Xe shift differences in different environments.
Figure S3.Thermal averages (T = 300 K) of 129 Xe chemical shits in porous liquid (PL) and in neat TBA solvent, as well as the shift differences with various DFT functional/basis set combinations for scalar-relativistic X2C NMR shielding calculations (see Table S1).Experimental results are also shown.
The best Xe chemical shift estimates at the scalar-relativistic X2C level (B-TZVP in Table S1, BHandHLYP/TZVP in Figure S3) are in very good agreement with the experimental shifts both in the neat TBA solvent and in PL environments, which naturally leads to very similar TBA -PL shift difference obtained from the two-site model analysis of the experimental data.
It is clear that the DFT functional choice is more important than the choice of the basis set for atoms surrounding the Xe, as even the BHandHLYP/SVP level gives reasonable chemical shifts for the PL.It also provides correctly signed, albeit underestimated TBA -PL shift difference due to over-/underestimated cage/TBA chemical shifts, on account of the basis set.The reason is that the DFT functional effect (DFE in Table S1) is much larger inside the cages than in the TBA solvent.
Actually, the basis set effect (BSE) is also very important as it is larger and to the opposite, i.e. increasing shift direction, as compared to DFE in the neat TBA solvent.This leads to an almost perfect error cancellation at the PBE/SVP level (P-SVP in Table S1) and almost correct Xe chemical shift in the neat TBA.However, the result is a clear example of the danger of reaching the right answer for the wrong reasons.This is evident as the PBE/SVP method leads to totally erroneous TBA -PL shift difference, with the wrong sign, due to the huge overestimation of the 129 Xe chemical shift in the CC3-R and CC13 cages, where DFT functional and basis-set errors are to the same direction.
Therefore, the lowest but still economical computational level for NMR shielding calculations of Xe inside molecular cavities, is to carry out BHandHLYP calculations with a locally dense x2c-TZVPall-s(Xe)/x2c-SVPall(other) basis sets.Basis-set correction can be estimated either with pure a DFT GGA functional (PBE), as done currently, or with a few demanding hybrid BHandHLYP calculations for a small subgroup of samples.

Figure S1 .
Figure S1.Starting geometries of the MD simulations for: a) CC3-R, b) CC13, and c) cageless, neat TBA structure.VMD program 5 was used for the graphics.

Figure S2 .
Figure S2.Convergence of the simulated Xe chemical shift as a function of the simulation time, i.e., the number of snapshots with 1 ps sampling interval.

Table S1 .
Xenon chemical shift (ppm) simulation averages at T = 300 K (δ 300 K Xe w.r.t.σ Xe atom = 5847.8ppm) with standard errors of the mean (±SEM).X2C scalar-relativistic Xe NMR shielding calculations with different DFT functionals and basis sets are computed in the Turbomole code for the same 186, 135, and 60 snapshots of CC3-R, CC13, and neat TBA solvent, respectively.
a Xe chemical shift in neat TBA solvent.bEstimatedvalue for the scrambled CC3 3 :13 3 -R porous liquid (PL) is averaged over two independent averages for CC3-R and CC13: Z = 0.5(X + Y ).Linear propagation is used for the error estimate: SEM(Z) = SEM 2 (X) + SEM 2 (Y ).c Xe chemical shift difference between Xe in PL cages and in neat TBA solvent.Linear propagation of error is used for the sum of estimates of independent variables, see footnote b. d PBE calculations with x2c-TZVPall-s/x2c-SVPall basis sets for Xe/other atoms.e PBE calculations with x2c-TZVPall-s/x2c-TZVPall basis sets for Xe/other atoms.f BHandHLYP calculations with x2c-TZVPall-s/x2c-SVPall basis sets for Xe/other atoms.g Best result obtained as an average over B-SVP + BSE result for each individual snapshots.h

Table S2 .
Spin-orbit correction (SOC) on129Xe NMR chemical shifts (δ Xe ) estimated at zeroth-order relativistic approximation (ZORA) level.Average (AVG) effects over 10 samples with standard deviations (STD) and standard errors of mean (SEM) are reported.See the main text for details.Scalar-relativistic SR-ZORA result with respect to σ Xe atom = 5754.5ppm.bSpin-orbit and scalar-relativistic SO-ZORA result with respect to σ Xe atom = 6647.5ppm.c Spin-orbit correction computed as the SO-ZORA -SR-ZORA difference. a