Clathrate Structure Determination by Combining Crystal Structure Prediction with Computational and Experimental 129Xe NMR Spectroscopy

Abstract An approach is presented for the structure determination of clathrates using NMR spectroscopy of enclathrated xenon to select from a set of predicted crystal structures. Crystal structure prediction methods have been used to generate an ensemble of putative structures of o‐ and m‐fluorophenol, whose previously unknown clathrate structures have been studied by 129Xe NMR spectroscopy. The high sensitivity of the 129Xe chemical shift tensor to the chemical environment and shape of the crystalline cavity makes it ideal as a probe for porous materials. The experimental powder NMR spectra can be used to directly confirm or reject hypothetical crystal structures generated by computational prediction, whose chemical shift tensors have been simulated using density functional theory. For each fluorophenol isomer one predicted crystal structure was found, whose measured and computed chemical shift tensors agree within experimental and computational error margins and these are thus proposed as the true fluorophenol xenon clathrate structures.


Introduction
Over the past few years,t he combined use of solid-state nuclear magnetic resonance (NMR)a nd computational methods has developed into ap ractical methodf or determining crystal structures. [1] This is due to the sensitivity of NMR chemical shifts to the molecular environment in ac rystal, and the reliability of methods for predicting the relative NMR shielding of atoms in different environments. The approach involves first predictingt he full set of low energy crystal structures available to am olecule, followed by chemical shielding calculations, which are matched against the measured chemical shifts of am aterial. Applications to organic crystalsh ave found that, given as et of predicted crystal structures, the isotropic 1 H chemicals hifts are usually sufficient to identify which of the predicted structures corresponds to the material under investigation. [2] Kazankin et al. [3,4] reported that xenon clathrates can be formed froms everalm onosubstituted phenol compounds. With the exception of phenol, [5] hydroquinone, [5][6][7][8] p-cresol, [9] and p-fluorophenol, [10] Xe clathrates have not been described in the Englishl iterature and have remained relatively unknown in the West. The crystal structures of o-a nd m-fluorophenol xenon clathrates have, to our knowledge,n ever previously been determined. The NMRp roperties of Xe included in porouss tructures gives ap otentially sensitive probe of the clathrates tructure, which is explored here as am eans of determiningt he structures of the o-a nd m-fluorophenol xenon clathrates.
The first 129 Xe NMR experiments werep erformed in 1951, [11] but only am odest number of furthers tudies appeared until the early 1980s when Ripmeester and Davidsoni nvestigated enclathrated xenon [12] and Ito and Fraissard proposed the use of 129 Xe NMR spectroscopyf or probing the properties of zeolites. [13] Today,t he applicationr ange of 129 Xe NMR spectroscopy extends from materials property studies of micro-and mesoporouss olids through polymers, liquid crystals, proteins,a nd biosensors, to magnetic resonance imaging (MRI) for medical purposes. [14][15][16][17] The reason for using xenont op robe the properties of various materials arises from the high sensitivity of the shielding of 129 Xe to its local environment, and that the variability in the shieldings tems exclusively from environmental effects. [18][19][20] Another reason is the good NMR receptivity of 129 Xe, which is about 33 times that of 13 C. Ad isadvantage in some cases may be the long 129 Xe spin-lattice relaxation time T 1 ,w hich is, for example, several minutes in xenon clathrate hydrate. [12] The applicationr ange of 129 Xe NMR spectroscopy and MRI further widened when the so-called opticalp umping or hyperpolarization techniquew as invented, [21] enabling the increase of the 129 Xe polarization by up to four or five orders of magnitude and making experimentsp ossible with very small amounts of xenon gas.
The work of Ripmeester and Davidson [12] revealed the potential of 129 Xe NMR spectroscopy in studies of clathrates. The 129 Xe NMR spectrumo fx enon clathrateh ydrate consists of two broad resonance lines:o ne at 152 AE 2ppm and the other at 242 AE 2ppm downfield (smaller shielding) from the low pressure gas peak. The former resonance arises from xenon in large cages, and the latter from xenon in small cages. Thus, the 129 Xe chemical shift relates to the size of cages. [22] Furthermore, the resonance at 152 ppm displays ac ylindrically symmetric powder lineshape with ac hemical shift anisotropy of 32 AE 3ppm;t he resonance lineshape relates to the shape of the cage accommodating the xenon atoms. The line intensities in turn relate to the occupation number.A ni llustrative example is the distribution of xenon atoms in the alpha cages of the NaA zeolite. [23] The 129 Xe NMR spectrum of xenon in NaA consists of several distinct signals, the chemical shift being determined by the occupation number of acage.
Modeling of 129 Xe NMR spectra of clathrate cages dates back to the studies of chemical shifts [24] and NMR line shapes [25] inside clathrate hydrates tructures Ia nd II, whichw ere modeled as molecular clusters extracted from the clathrate structures. Similarq uantum chemical clusterm odelsw ere also appliedi ns tudies of Xe inside fullerenec ages, [26,27] for which both relativistic [28,29] as well as dynamical and environmental [29,30] effects were studied. Current clusterm odeling makes use of recent advances in the development of relativistic quantumc hemistry methods, which have enabled very demanding studies of large heavy-element systems such as cryptophanes [31] and self-organizing metallo-supramolecular cages. [32] Diffraction is the usual method for crystal structure solution. Structure determination of clathratesb yd iffraction methods can, however,b eh indered by their instability.F or the materials studied here, it was not possible to obtain ap owder X-ray diffraction (PXRD) pattern from the m-fluorophenol clathrate and only al ow resolution diffractionp attern could be obtained from the o-fluorophenol clathrate, from which structure determinationw ould not be possible. Therefore, 129 Xe NMRs pectra cannotb ec ombined with PXRD experiments as usually done for identifying new clathrate phases. [33,34] The exceptional sensitivity of xenon's chemical shifta nisotropy to its environment should enable the distinctionb etween different candidate clathrate structures. This hypothesis was investigated by com-paring experimentally observed and quantum chemically modeled 129 Xe NMR isotropic and anisotropic shift parameters in clathrates tructures obtained by computational crystal structure prediction (CSP).
CSP has until recently been focusedp rimarily on predicting the single thermodynamically stable structure, or possibly af ew low-energy polymorphs. The lowest energyc rystal structures available to ag iven molecule are, in all but very rare exceptions, [35] close-packed,l eaving no room for the inclusion of guest molecules. There have been few reports of the prediction of porous molecular crystals [36][37][38] or solvates. [39][40][41] The empty host molecule frameworks of observedi nclusion structures have been shown to often exist as local minima on the lattice energy surface, albeit sometimes at relatively high energies compared to close-packed alternative structures. [41][42][43] This suggestsa ne fficient approacht ot he discovery of inclusion structures:s earching for stable, empty frameworks using CSP methods and subsequently inserting the guest.T his method should be particularly suited to weakly interacting guestss uch as Xe, where inclusion is expected to leave the host framework relativelyu nperturbed. Thea pproach should be more efficient than searching the dramatically larger multi-component phase space defined by the host and guest together.
In this study,C SP calculations were performed for o-a nd mfluorophenol with the specifica im of predicting realisticx enon clathratec omplexes for whichc alculated 129 Xe NMR parameters can be compared to measured spectra.A dvanced first principles density functional theory (DFT) electronic structure calculations of the 129 Xe NMR shielding tensors, with ap roper inclusion of electron correlation as well as relativistic, periodic, and dynamicale ffects, have been carried out for as et of predicted structures. Ac omparison of the simulated isotropic and anisotropic Xe chemical shift parameters with experimentally observed solid state 129 Xe NMR data allows the identification of the crystal structureso ft hesee lusive clathrates.

Preparation of samples
Clathrate samples were prepared from commercially available oand m-fluorophenol (Aldrich, 98 %a ssay) and used directly without purification. The substances were transferred into pyrex glass tubes (4 mm outer diameter,0 .8 mm walls) and connected to av olume-calibrated vacuum line. Twoc ycles of freeze-thaw were applied to reduce oxygen content. Isotopically enriched 129 Xe gas (Chemgas, 89 %e nrichment) was then frozen into the evacuated tubes. The amount of transferred gas was controlled by the pressure drop in the vacuum line, measured with ad igital pressure gauge (1 hPa precision). The amount of gas inserted into the tubes was chosen to be sufficientf or saturation of a3 :1 host-guest clathrate stoichiometry and with excess to pressurize the sample tube so as to maintain clathrate structural stability at the desired experimental temperature of 250 K. [3,4] The glass sample tubes were flame sealed, cooled in liquid nitrogen, and equilibrated for aperiod of two weeks at ca. 243 Kp rior to NMR measurements.

NMR experiments
The 129 Xe NMR spectrum of xenon in m-fluorophenol was measured at 251 Ko naBruker DSX300WB spectrometer ( 129 Xe Larmor frequency 83.03 MHz) using a7mm variable angle spinning (VAS) probe head (DOTY Scientific, Inc.,U SA), without spinning. The static powder spectrum (the axis of the solenoid coil was set perpendicular to the external magnetic field) was observed while applying cross-polarization (CP) and proton decoupling. The following acquisition parameters were used: 129 Xe pulse width 5 ms, 1 H decoupling pulse width 16 ms, mixing time 5.4 ms, repetition time 35 s, strength of the 1 Hd ecoupling field 34 kHz, and number of collected free induction decay (FID) signals 220. The aim of applying proton decoupling was to diminish the effect of the 129 Xe-1 H dipolar coupling on the line width. The 129 Xe chemical shift was measured relative to the isotropic 129 Xe chemical shift in hydroquinone, in which the shift relative to zero-pressure xenon is known to be 222.1 ppm. Te mperature calibration was based on the measurement of the 1 Hc hemical shift difference in as eparate methanol sample. [44] Prior to Fourier transformation the FID signal was multiplied by an exponentially decaying apodization function leading to % 100 Hz line broadening.
The 129 Xe NMR spectrum of xenon in o-fluorophenol was in turn measured at 253 Ko naB ruker DPX400 spectrometer ( 129 Xe Larmor frequency 110.70 MHz) using a5mm broad band observe (BBO) probe head. 129 Xe chemical shift is given with respect to the signal of zero-pressure xenon gas, which was determined using two samples with known xenon pressure and extrapolation using the second virial coefficient. Te mperature calibration was in this case performed using 1 Hc hemical shifts in methanol, but with methanol placed in the annulus of ad ouble tube system (outer tube 5mm, inner tube 4mm). A 129 Xe pulse width of 29.5 msw as applied. Prior to Fourier transformation, the FID signal was multiplied by an exponentially decaying apodization function leading to 50 Hz line broadening.
The elements of the chemical shift tensors were determined in both cases using Dmfit. [45] The uncertainties were estimated to be AE 0.2 ppm, AE 0.4 ppm, and < 0.04, respectively,i nt he three adjusted NMR parameters:i sotropic chemical shift (CS) d d iso = s ref iso Às iso referenced to the zero-pressure limit Xe gas, chemical shift anisotropy (CSA) Dd = d zz À(d xx + d yy )/2 with positive/negative values for prolate/oblate spheroids along the z-direction and asymmetry parameter h = (d yy Àd xx )/(d zz Àd iso )w ith the value 0f or an axially symmetric tensor (with respect to z)a nd 1f or the fully asymmetric case, when d yy = d iso .T he isotropic Xe nuclear shielding constant is the trace of the shielding tensor, s iso = (s xx + s yy + s zz )/3. The components of the principal axis system (PAS) of the Xe shift tensor follow Haeberlen'sc onvention: [46] j d zz Àd iso j ! j d xx Àd iso j ! j d yy Àd iso j .Ar elatively large contribution to the uncertainties arises from the wavy background in the experimental spectra, which was therefore eliminated.

Powder X-ray diffraction
Samples of both o-a nd m-fluorophenol were prepared in glass capillaries. Xenon gas was frozen into the evacuated capillaries, which were flame-sealed after submerging in liquid N 2 .C apillaries containing the samples were kept immersed in liquid N 2 prior to mounting in ap re-cooled single-crystal diffractometer.D iffraction data were collected at 100 Ku sing graphite monochromated Mo Ka radiation.

Crystal structurep rediction
Molecular geometries, energies, and charge densities, calculated by DFT using Gaussian 09 [47] with the B3LYP [48,49] functional and 6-311G(d,p) basis set, were used throughout the CSP calculations. Twos table, planar conformers of each molecule were identified ( Figure 1) and DFT predicts that their energies are sufficiently close that either could form low energy crystal structures. [50] Therefore, both conformers of both molecules were included in the CSP study.
Hypothetical crystal structures were generated with the rigid DFToptimized molecular geometries using Monte Carlo simulated annealing [51] with Materials Studio. Searches were performed in the most commonly observed space groups of known molecular organic crystal structures;2 5s pace groups were searched with one molecule in the asymmetric unit (Z' = 1) and 5s pace groups with Z' = 2, including all combinations of the two conformers in the asymmetric unit.
Structures with al attice energy within a1 5kJmol À1 window from the lowest energy structure were further refined with an anisotropic, atomic multipole-based intermolecular atom-atom potential model, [52] combined with aD FT treatment of intramolecular energies and geometries. Duplicate crystal structures were removed using the Compack [53] program and the resulting unique structures were re-optimized using the CrystalOptimizer [54] program to treat flexibility of the hydroxyl group within each crystal structure. Full details of the conformational analysis and CSP methods are provided in the Supporting Information.

Selection of likely clathrate host structures
Lattice energy differences between polymorphs are usually very small and rarely exceed 8kJmol À1 . [55] Since voids in crystal structures are thermodynamically unfavorable, [42,56] structures within al arger energy range than in the usual application of CSP to polymorph prediction were considered as putative inclusion frameworks. Crystal structures within an energy cutoff of 13 kJ mol À1 above the global minimum for each molecule were considered. To guide the selection of potential clathrate host frameworks, the guest-to-host volume ratio R g in 31 representative clathrate structures, taken from the Cambridge Structural Database (CSD), were examined (see Supporting Information for details). The volume ratio R g is calculated with Equation (1): where V g is the van der Waals volume of the guest molecule and V H is an individual void's contact volume. [57] One xenon atom was inserted at each cavity'sc entroid coordinates and the resulting xenon clathrate structures were geometry-optimized as described above, assuming rigid molecules, imposing no space group symmetry and using an ad hoc exp-6 potential for xenon.

129
Xe NMR shielding calculations The three 129 Xe NMR parameters of the predicted structures were modeled and compared with the experimental data in several stages. In NMR modeling the chemical shift reference is af ree Xe atom. In the first step, all predicted clathrate structures were subjected to nonrelativistic (NR) NMR modeling of cluster models. The results from the NR cluster models were used to identify likely candidates for the experimentally observed clathrate structures. These candidates were then further studied using DFT calculations on their fully periodic models. Finally,afew crystal structures that agreed best with experimental NMR results were chosen for more detailed modeling. Full details are given in the Supporting Information.

Screeningofstructures by cluster modeling
The NMR parameters of probable clathrate structures were first modeled using clusters consisting of as ingle xenon-occupied cavity,i ncluding the Xe atom and all nearby fluorophenol molecules. Nonrelativistic Xe shielding tensor calculations were performed on the cluster models using Turbomole. [58] The BHandH-LYP [59,60] hybrid functional, including 50 %o fe xact Hartree-Fock (HF) exchange (EEX), was chosen based on benchmark calculations on the xenon-benzene system, where high quality nonrelativistic ab initio Xe chemical shifts are reproduced reasonably well. [29] BHandHLYP has been shown to slightly underestimate Xe chemical shift and anisotropy,l eaving room for improvements in the modeling by approaching the experimental values from below for Xecontaining molecules, [61][62][63] Xe atoms moving freely inside buckminster fullerenes, [29,30] and in self-organizing metallo-supramolecular cages. [32] Those studies show that the typical overestimation of Xe CS and CSA by pure generalized gradient approximation (GGA) DFT functionals, such as PBE [64] and BLYP, [59,65] is partly compensated when the amount of exact HF exchange is increased in B3LYP (EEX = 20 %) and BHandHLYP (EEX = 50 %) hybrid functionals. Calculations have been performed with am ixed basis set denoted as MHA/SVP (see Supporting Information for details). Tkatchenko-Scheffler (TS) dispersion correction, [66] denoted as PBE-TS structures from now on.

Periodic modeling of likely candidates
Following optimization, NMR shielding tensors were computed with the PBE functional using the gauge-including projector augmented wave (GIPAW)m ethod [67,68] (see Figures 6a nd 7b elow). These periodic DFT results include the scalar relativistic (SR) effects on Xe shielding at the 1-component zeroth-order regular approximation (ZORA) [69,70] level of theory.D etails of the periodic calculations with CASTEP [71,72] are in the Supporting Information.

Detailedmodeling of the most probable structures
After periodic NMR calculations of the DFT optimized structures, the most probable clathrate structures were selected for more detailed DFT NMR modeling using the Amsterdam Density Functional (ADF) program. [73,74] In addition to the NR and SR-ZORA quantum chemistry,A DF provides a2 -component spin-orbit SO-ZORA method also including SR effects. [69,75] Am uch wider range of DFT functionals than is currently available in periodic CASTEP can be used in ADF.C alculations were performed with the jcpl/TZP mixed basis set [76] (see Supporting Information for details) on clusters comprising as ingle cavity to test the influence of correlation treatment and the amount of EEX on NMR parameters using the PBE, BLYP,B 3LYP and BHandHLYP functionals at the SR-ZORA level. By using the results in scaling of the periodic PBE results, estimates of SR periodic BLYP,B 3LYP,a nd BHandHLYP results were obtained. It is expected that, as the electron correlation description is improved by an increasing portion of EEX, the calculated NMR parameters for the true crystal structures should approach the experimental results. Hence, the BHandHLYP-scaled periodic PBE results provide the best estimation of 129 Xe NMR parameters and lack only contributions due to molecular dynamics and relativistic SO effects. The latter were treated as an additive correction obtained from the difference of the static SR-and SO-ZORA cluster calculations with the BHandHLYP functional.
The effect of Xe dynamics at T = 300 Kf or 129 Xe NMR shielding parameters was modeled for the few most probable clathrates by canonical NVT Metropolis Monte Carlo (MC-NVT) of Xe motion on ap otential energy surface inside ac luster cavity with fixed PBE-TS optimized geometry.T he temperature effects on Xe chemical shift and anisotropy were calculated as the difference between the thermally averaged shielding tensor and the reference tensor with Xe at the center of the cage.
For further details, see the Supporting Information, which includes ad etailed description of crystal structure prediction (CSP) and its performance for the known high density crystal forms of the two fluorophenols, as well as the method to compute guest to host volume ratios. Revised Williams99 parameters for H…A interactions, as well as potential parameters for Fa nd Xe are described. Also included are:d etails of DFT structure optimization, Xe NMR calculations, and modeling of Xe dynamics;X eN MR results at different levels and their sensitivity to structure;d etails of powder Xray diffraction (PXRD) measurements and results, and an umber of clathrate structures in CIF format.

Results and Discussion
Experimental NMR results Both isomers formedc lathrates with xenon under the experimental conditions and allowed recording of properly shaped powderpatterns without active mixing and crushing of crystals where 129 Xe NMR powder patterns are expected to reflect only interactions of xenon atoms with the immediatelya djacent host molecules, the influenceo fn eighboring cages with xenon is expected to be negligible. [77] The spectrum of m-fluorophenol ( Figure 2) resembles that of b-hydroquinone, [8] b-phenol, and p-fluorophenol, with one notable difference;i th as the largest observed value of 129 Xe NMR CSA among known inclusion compounds: Dd = 183.3 ppm versus1 61.9, 171, and 164 ppm for hydroquinone, [78] phenol, [5] and p-fluorophenol, [79] respectively.S mall additional features in the observed spectrum of m-fluorophenol are attributed to amorphous host substance and xenon atoms adsorbed in this amorphous phase.
The 129 Xe NMR spectrumo fo-fluorophenol shows negative CSA (Figure 2), Dd = À47.5 ppm, in contrast to all previously known solid-state 129 Xe NMRp owder patterns of phenol clathrates for which positive CSA is observed. [5][6][7][8][9][10] Changes in the sign of the CSA can be observed in ag roup of porousc hannel-like dipeptides, [80] where CSA changes from positive to negative with increasing xenon gas pressure,a nd therefore with pronounced Xe-Xe interactions playing ag reater role. No changes of the NMR spectrum of o-fluorophenol clathrate have been observed when repeating the experiment with samples at different pressures. The small negative CSA may result from an axially symmetric but oblate environment around the xenon atom in this clathrate.
Powder X-ray diffractionr esults AP XRD pattern could not be obtained from m-fluorophenol clathrate, which transformed too quickly to the known high density form when transferred to the diffractometer.T his is confirmed by comparison of the measured PXRD pattern to that simulated from the known crystal structure. For o-fluorophenol,abroad powder pattern was obtained that does not correspond to either known crystal structures (see Supporting Information). The pattern is too broad to index, so it could not be used to determine the structure.

Crystal structurep rediction results
CSP resulted in an exceptionally large number of low energy crystal structures for each molecule (Figures 3a nd 4).
For o-fluorophenol, Z' = 2c rystal structures with both molecules in the cis-conformation are energetically favored. The known [81] high-pressure polymorph II (CSD refcode QAMWEH01) is located in the search, 0.8 kJ mol À1 above the global minimum ( Figure 3) and with as lightly higher density, as expected for ah igh pressure polymorph. The known lowtemperature polymorph I [81] (CSD refcode QAMWEH) is ad isordered Z' = 1.5 structure and could not be predicted with the methods employed here.
One crystal structure of m-fluorophenol is known [81] (CSD refcode QAMTUU)a nd corresponds to the global lattice energy minimum from the search.T he structure is geometrically well reproduced (with ad eviation in atomic positions in a1 5-mole- cule clustert aken from predicted and X-ray crystal structures of RMSD 15 = 0.203 ).
Overlays of both matches are included in the Supporting Information.T he successful reproductiono ft he known crystal structures of both molecules amongst the lowest energy predicted structures provides confidencei nt he sampling of crystal structures and of their lattice energy rankings.

Selection rules for clathrate structures
Because the inclusiono fg uest molecules in clathrates can significantlys tabilize the structure, using the lattice energyo ft he emptyh ost alone is not useful for selection of promising structures. The analysis of known clathrates found that the guestto-host volume ratio R g is normally distributed with am ean of 59 %a nd as tandard deviation of 8percentage units, in good agreement with Rebek's "55 %s olution" [82] and providingf urther evidencef or the empirical rule that R g in observed inclusion structuress hould fall in this limited range. [82,83] Of the predicted crystal structures within 13 kJ mol À1 of the global minimum for o-fluorophenol and m-fluorophenol, 230 and 223 are porous( having cavities > 10 3 ). 33 (o-fluorophenol) and 32 (m-fluorophenol) of the predicted structures have cavities of as uitablev olumet oa ccommodate xenon as aguest,which were take to be those with R g within three standard deviations (AE 3s)f or observed clathrates. These structures are encircledi nr ed in Figures 3a nd 4. The lowest energyo f these structures are 4.5 and 6.7 kJ mol À1 above the global minimafor o-a nd m-fluorophenol, respectively.

Screeningofstructures by cluster models
Examples of clusterm odelsu sed for initial screening are showni nF igure 5. As can be seen in Figures 6a nd 7, even for as et of structures with similarv oid volumes and packing energies, the computed NMR tensor parameters for 129 Xe vary widelyi nt he initial screening using cluster modelso ft he predicted structures.T his demonstrates the exceptional sensitivity of the 129 Xe NMR parameters to small differences in cavity size and shape.
Calculated NMR parameters for the 33 o-a nd 32 m-fluorophenol clathrate structures obtained with nonrelativistic DFT cluster models are tabulated in Tables S4 and S5 (Supporting Information). Many of these structures, including all predicted Z' = 2s tructures, have chemical shift tensors with significant asymmetry;t hese voids are clearly not compatible with the experimental spectra, in which h < 0.04. At this stage, only the   Optimization of the clathrate structure after insertiono ft he xenon into the host allowed the structures to relax in response to guest insertion. Despite very small structuralc hanges,t his significantly affectedt he calculated NMR parameters ( Figure S7 in the SupportingI nformation).
Because the screening level of theory is expected to underestimateb oth CS and CSA by af ew tens of ppm, structures with both properties of the correct sign and underestimated were focusedo n, also including af ew structures with overestimated CS for m-fluorophenol and slightly positiveC SA for ofluorophenol, for higherl evel calculations. This excludeda ll but five o-fluorophenol ands even m-fluorophenol structures; hereafter,t hese structures are referred to as oF_A to oF_E (in order of increasing energy,F igure 3) and mF_A to mF_G (Figure 4). All of these candidate clathrates tructures have space group symmetry R3 .

NMR chemical shift parameters from periodic DFT calculations
NMR shielding tensors werec alculated by periodic DFT for the five plausible o-fluorophenol and seven m-fluorophenol clathrate structures.P eriodicm odeling was found to be necessary and the geometry relaxation with periodic PBE-TSs hifts the CS and CSA towards larger magnitudes, corresponding to more elliptic, prolate (Dd > 0) and oblate (Dd < 0) m-a nd o-fluorophenol cavities, respectively.
NMR parameters from SR GIPAW/PBE calculations at the PBE-TS optimized geometries are tabulated in Ta bles S6 and S7 in the Supporting Information, and are displayed in Figures6and 7a sr ed diamondsc onnected with arrows to the corresponding screeningc luster result (green squares). It should be noted that the periodic results set upper limits on 129 Xe CS and CSA, as the PBE functional (and all pure GGA DFT functionals) overestimates the magnitudeso fb oth parameters. [29,32,[61][62][63] Althought he disagreement in CS and CSA of someo ft he candidate structures now makes them unlikely (such as oF_C, oF_E, and mF_G), all were kept forf urthera nalysis with more detailed NMR calculations.

Results of detailed NMR calculation of the mostlikely candidates
Typically,t he crystal lattice effect, that is, the difference of 129 Xe NMR parameters between the periodic and clusterm odelso f the same PBE-TS optimized clathrate, increases both CS and CSA as seen in Ta bles 1a nd 2. The extento ft he change is, however,v ery case-specifica nd unforeseeable, which makes periodic modelinge ssential, in one form or another,i nt he present search for ab estc andidate of an unknown clathrate stucture.
The ADF/SR-ZORA resultsf or PBE-TS optimized cluster models wereu sed to extract correction factors (see detailsi n Supporting Information) by which the periodic, SR GIPAW/PBE results were scaled in order to obtain periodic estimates of   [a] Scalarr elativistic SR-ZORA calculations of ac luster model of one clathrate cavity with ADF code [73,74] using Xe/other = jcpl/TZPb asis sets. [76]   [a] Scalar relativistic SR-ZORA calculations of ac luster model of one clathratec avityw ith ADF code [73,74] using Xe/other = jcpl/TZPb asis sets. [76]  respectively.T he bestB HandHLYP-scaled periodic estimates bring one clathrate structure for each of the fluorophenol isomers into excellent agreement with the experimental NMR: oF_D and mF_A. For o-fluorophenol, the other CSP candidates in the PBE-TS crystal geometry have quite different periodic BHandHLYP 129 Xe CS and/orC SA values as compared to the experimental ones, whereas for m-fluorophenol the closest alternative candidates overestimate either the CS (mF_F) or CSA (mF_B). The BHandHLYP functional is expected to provide reasonable approximation for both quantities due to benchmarking against ab initio calculations. [61][62][63] In addition, the relativistic SO correction, obtained as the differenceb etween SO-and SR-ZORAc luster calculations with ADF (see Ta bles 1a nd 2), is added to the static BHandHLYP results of all structures (Figure 8a nd Figure 9). Due to its different physical origin, the SO effect is case-specifica nd may either increaseo rd ecrease the CS and CSA, althought he latter is affected slightly more.T he magnitude of the SO correction is, however,s maller than the dynamical correction (see below) and, hence, does not alter the identification of the best clathrate candidates.
The temperature effect of Xe dynamics at T = 300 Kw as modeledf or the two (oF_B and oF_D) and four (mF_A, mF_B, mF_E, and mF_F) most relevant clathrate candidates. Thed ynamical( DYN) correction was added to theS Oc orrected BHandHLYP results( BHandHLYP + SO). In all cases, the thermal averaging increases the magnitudes of both CS and CSA of 129 Xe. As seen in Figures 8a nd 9, the inclusion of DYN correction confirms the mostp robablec lathrate structure of both isomers. The effect on the simulated spectrai sa lso shown in Figure2.
It is evidentf rom Figure 8a nd 9( see also Tables S6 and S7 in the Supporting Information) that in all probability the crystal structures for o-a nd m-fluorophenol clathrates are oF_D and mF_A. For them,t he 129 Xe NMR isotropic chemical shift and chemicals hift anisotropies at different levelso ft heory encompass the experimental data. For both structures, the experimental NMRp arametersa re approached as the computational level is improved. The approximated periodic BHandHLYP results at PBE-TS optimized structures only slightly underestimate the chemical shift, leaving room for improvements by dynamic andr elativistic SO corrections. Astonishingly, the most accurate level of theoretical modeling almostq uantitatively reproduces the two NMR parameters that are clearly specific for ag iven clathrate. The remaining differences between experimental and computational data may be attributed to deficiencies in the structure as well as treatmentso fe lectron correlation and thermal averaging of the whole system.
The PXRD results providef urthere videncef or the CSP-129 Xe NMR determineds tructure of the o-fluorophenol clathrate;t he simulated diffraction pattern from oF_D is similar to the PXRD obtained from the clathrate sample (see Figure S11i nS upporting Information). PXRD of the present quality cannot, however, be used to unambiquously distinquish between the candidates structures.

Description of the proposed clathrate structures
The crystal structurest hat werep roposed as the fluorophenol xenon clathrates belongt os pace group R3 ,w ith lattice parameters shown in Ta ble3.B oths tructures have three-fold screw axes parallelt ot he c lattice vector,r esulting in six-membered rings of host molecules held together with strong hydrogen bonds formed by practicallyi deal OH···O interactions. The hydrogen bondingf orms aR 6 6 (12) graph set, [84] which seems to be ac haracteristic feature in clathrates of phenold erivatives. Packingd iagrams are displayed in Figures 10 and Figure 11. Crystallographic information files (CIFs) are included in the Supporting Information. Both structures have three cavities per unit cell, with volumes 61.4 and 88.5 3 each for o-and m-fluorophenol, respectively,r esulting in R g values of 68.7 and 47.7 % for xenon,b oth within 1.5 standard deviations from the ideal ratio of 59 %.
Despite the same hydrogen bondinga nd crystal symmetry, the voids in the two structures are of quite differentg eometry. The void in oF_D has an oblate shape with ratios of the principal momentso ft he free volume (calculated from ag rid sampling in Platon) [85] of 1.00:1.00:0.85, with the short dimension oriented along the crystallographic c-axis. In contrast, mF_A has ap rolates hape with calculated ratio of dimensions of 1.00:1.00:1.20, elongated along the crystallographic c-axis. Thus, the sign of the CSA relatest ot he shape of the void, as expected, with an oblate cavity leadingt oan egative CSA and prolatecavity yielding ap ositive CSA.
The proposed structure of the o-fluorophenol Xe clathrate (oF_D) is one of the highest energy and one of the densest structures that was considered as ap ossible clathrate ( Figure 3). The stabilization of this structure must derive from the interactions of Xe with the host structure, whichs hould be large, due to the tight fit of Xe to the host cavities.
In contrast, the most likely structure of the m-fluorophenol Xe clathrate (mF_A) corresponds to the mosts table structure on the crystal structurel andscape (Figure 4) that containsc avities suitable for Xe enclathration; this structure's stabilityr elates, in part, to the stability of the host framework.

Conclusion
Detailed first principles NMR calculations have been used on candidates from CSP to proposestructures for the xenon clathrates of o-a nd m-fluorophenol. The exceptional sensitivity of the 129 Xe chemical shift tensort oi ts local environmenta llows comparisons between observed andc alculated NMR chemical shift parameters that have been used to directly confirm or reject hypothetical clathrate structures.B ased on these comparisons, likely crystal structures were proposed for the two clathrates. The proposed structures strongly resemble ap reviously known b-hydroquinone xenon clathrate [6] and have similar R 6 6 (12) hydrogen bonding motifs. [84] The unusual o-fluorophenol 129 Xe NMR powder spectrum, with its negative CSA, wasi nitially thought to suggest as tructural motif different from the known and commonR 6 6 (12) hydrogen-bonded double sandwich. Our results, however,c onfirm that the R 6 6 (12) motif is an important feature for clathrates of phenold erivatives that is presenti nb oth materials studied here.
Static solid-state NMR spectroscopy has clear benefitso ver high-frequency magic-angle spinning NMR spectroscopy,t hat would only result in isotropic chemical shifts rather than the complete chemical shift tensors. In this study,u sing isotropic shifts only would not have allowed the identification of the experimental clathrate structures among the predicted candidates.
The method presented here is ap owerful approachf or structure determination of porous materials, whichi sp articu-   larly useful in cases where powder diffraction patternse ither cannotb eo btained,o ra re insufficientf or structure determination. The success of the method is related to the high sensitivity of the 129 Xe NMR chemicals hift andc hemical shift anisotropy to minute detailso ft he cavity geometry,s uch that even structurally very similarc lathrates can have vastly different chemicals hift tensors. This sensitivity,h owever,a lso requires highly detailed NMR calculations;i na ddition to the proper treatment of electron correlation and relativistic phenomena, the inclusion of explicit crystal lattice effects,a sw ell as Xe dynamics, was necessary in order to precisely reproduce experimental NMR values. Developments in this area, along with progress in CSP algorithms, openu pn ew possibilities for the prediction and characterization of new porous materials by combining structure prediction with computational and experimental 129 Xe NMR spectroscopy.