Solid-state nuclear magnetic resonance study of polymorphism in tris(8-hydroxyquinolinate)aluminium

Tris(8-hydroxyquinolinate)aluminium (Alq 3 ) is a metal – organic coordination complex, which is a widely used electroluminescent material in organic light-emitting diode technology. Crystalline Alq 3 is known to occur in five polymorphic forms (denoted α , β , γ , δ , and ε ), although the structures of some of these polymorphs have been the subject of considerable debate. In particular, the structure of α -Alq 3 , which is a model for the local structure in amorphous films used in devices, is highly complex and has never been conclusively solved. In this work, we use solid-state nuclear magnetic resonance (NMR) and density functional theory (DFT) calculations to investigate the local structure of four Alq 3 samples. We find that the first structure proposed for α -Alq 3 is inconsistent with all of the samples studied, and DFT calculations further suggest that this structure is energetically unfavourable. Instead, samples containing the meridional ( mer ) isomeric form are found to contain local structures consistent with ε -Alq 3 , and a sample containing the facial ( fac ) isomeric form is consistent with a mixture of γ -Alq 3 and δ -Alq 3 . We also investigate the influence of different strategies for


| INTRODUCTION
Tris(8-hydroxyquinolinate)aluminium (Alq 3 ; Figure 1a) is a metal-organic coordination complex that has been of considerable interest for organic electronics and display technologies due to its efficient green luminescence. Alq 3 is typically prepared for applications by sublimation into amorphous thin films, although, since it was first prepared almost 30 years ago, [2] five different crystalline polymorphs of Alq 3 have also been identified (denoted α, β, γ, δ, and ε). [1,[3][4][5][6] These polymorphs have been the subject of extensive research to understand the link between the local structural chemistry and the emission properties. In particular, α-Alq 3 has been widely studied due to its high thermal stability and the fact that spectroscopic measurements show evidence that the local structure in thin films is similar to this polymorph. [7][8][9][10] However, the crystal structures of Alq 3 polymorphs have been the subject of considerable debate due to close similarities between some of them and, in some cases, difficulties in obtaining suitably crystalline samples for diffraction analysis.
The Alq 3 complex can occur in two isomeric forms, namely, a meridional (mer) isomer ( Figure 1b) and a facial (fac) isomer (Figure 1c). The nature of the isomeric form present in amorphous films and crystalline polymorphs is of particular interest as the fac conformation tends to give a significantly blue-shifted photoluminescence. [11] All of the proposed structures for the crystalline polymorphs contain a single isomeric form, although there have been conflicting reports of which isomer is present in several polymorphs. One of the most debated structures is α-Alq 3 , which was first characterised by Brinkmann et al. using powder X-ray diffraction (PXRD). [3] The authors proposed a triclinic crystal structure comprising a single crystallographic Alq 3 complex in the mer conformation. In a subsequent single-crystal X-ray diffraction (SCXRD) study, Rajeswaran and Blanton proposed a structure with the same unit cell parameters but which contained a disordered arrangement of Alq 3 complexes in the fac conformation. [5] Utz et al. interpreted a 27 Al magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectrum of α-Alq 3 in terms of a single second-order quadrupolar-broadened lineshape with a high asymmetry parameter, η Q , of 0.95. [12] Using a simple point charge model, it was shown that the experimental lineshape was consistent with the mer isomer for which a high η Q value of 0.91 was predicted. In contrast, for the fac isomer, a low η Q value close to 0 was predicted. Kaji et al. also reported a high-η Q 27 Al MAS NMR lineshape for α-Alq 3 , [13] although the appearance differed from the lineshape reported by Utz et al., with more features suggesting the presence of multiple sites. A subsequent 13 C CPMAS NMR study by the same authors further suggested that α-Alq 3 contains the mer conformation, although it did not provide any further information regarding the crystal structure. [8] Rajeswaran et al. subsequently revised their interpretation of the α-Alq 3 using SCXRD and proposed that it comprises a disordered arrangement of complexes in the mer conformation. [14] In addition to α-Alq 3 , the structures of the other polymorphs have also been studied. The structure of β-Alq 3 was solved by SCXRD by Brinkmann et al. in their initial study. [3] In the same study, a third polymorph (γ-Alq 3 ) was also identified, but only partial crystallographic information was obtained. The authors suggested that γ-Alq 3 contained the mer isomeric form, but Muccini et al. subsequently proposed a full structure containing the fac conformation on the basis of PXRD data. [4] The structure of δ-Alq 3 was solved in independent synchrotron PXRD [1] and SCXRD studies [6,15] and was found to be triclinic with a single crystallographic complex in the fac conformation. The last polymorph to be identified was ε-Alq 3 . The crystal structure was determined by F I G U R E 1 (a) Structure of Alq 3 with (b) mer and (c) fac isomeric conformations Rajeswaran et al. from SCXRD measurements on a crystal grown through sublimation. [5] The structure is also triclinic but contains three crystallographically distinct complexes in the unit cell, each in the mer conformation. The most recent structure of α-Alq 3 proposed by the same authors was described as a disordered analogue of ε-Alq 3 . [14] However, this structure was based on weakly diffracting crystals with a high degree of disorder, and therefore large residuals upon refinement. It is notable that not only was diffraction weak but also the data to parameter ratio is low even with the use of restraints.
The high sensitivity of solid-state NMR to the local chemical environment should make it a powerful and complementary probe for studying the structures of Alq 3 polymorphs. In particular, the 27 Al chemical shift and quadrupolar interaction is highly sensitive to the local coordination environment. Indeed, as mentioned above, two previous studies have used 27 Al static and MAS NMR to distinguish between Alq 3 polymorphs. However, some of the data presented in these studies was contradictory, and moreover, no direct link was made between the experimental NMR parameters and the published crystal structures. Because these studies were published more than 15 years ago, the calculation of NMR parameters for periodic structures has become much more routine through the use of widely available planewave density functional theory (DFT) codes incorporating the gaugeincluding projector-augmented wave (GIPAW) algorithm. [16,17] For commonly studied nuclei such as 27 Al, this approach has been shown to accurately reproduce the experimental chemical shift and quadrupolar parameters in a wide range of systems. [18][19][20][21] However, for molecular crystalline solids such as Alq 3 , one of the limitations of DFT is that it does not describe long-range intermolecular interactions. This often leads to unrealistic unit cell expansions during the geometry optimisation step that typically precedes the calculation of NMR parameters. In view of this, a number of semiempirical dispersion correction (SEDC) methods have been developed which modify the DFT total energy to account for long-range interactions. [22] Recent work has shown that further empirical optimisation of the SEDC parameters specifically for NMR calculations can lead to improved accuracy of calculated 15 N, 17 O, and 35 Cl quadrupolar parameters, [23] although it is not clear if these parameters can improve the accuracy for other nuclei such as 27 Al.
In this work, we present a combined diffraction, DFT, and solid-state NMR study of Alq 3 polymorphs. We study two commercial samples and two further samples prepared through heat treatment. We find that the α-Alq 3 and ε-Alq 3 structures are closely related and that neither conform to the original α-Alq 3 structure proposed by Brinkmann et al. DFT calculations confirm that both structures contain complexes in the mer conformation, whereas the γ-Alq 3 and δ-Alq 3 polymorphs, which form as a mixture during heat treatment, contain the fac conformation. We also investigate the influence of the choice of method for dispersion correction during the DFT geometry optimisation that precedes the calculation of NMR parameters. We find that the method used influences the calculated NMR parameters, with the optimised SEDC approach tending to give quadrupolar parameters in slightly closer agreement with experiment. We also find that the distinction between mer and fac isomers on the basis of η Q that has been assumed in previous work is not always justified.

| Alq 3 samples
Two commercial samples of Alq 3 were purchased from Tokyo Chemical Industry UK Ltd. (product number T1527; referred to in this work as Alq 3 C1 ) and Alfa Aesar (product number H55656; referred to in this work as Alq 3 C2 ). To produce Alq 3 in the fac isomeric form, approximately 1 g of Alq 3 C1 was spread in the bottom of an alumina boat and placed in a tube furnace under N 2 gas flowing at 0.5 L min −1 . The temperature was ramped to 350 C at 10 C min −1 and then to 395 C at 1 C min −1 . The sample was held at 395 C for 5 min, before cooling to room temperature. This left a pale yellow powder in the alumina boat, which was collected and is referred to as Alq 3 heated . The annealing procedure also caused partial sublimation of the sample, resulting in the deposition of a light yellow fibrous material on the inside of the tube. This was collected and is denoted Alq 3 sublimed .

| X-ray diffraction
PXRD data were recorded at room temperature using a Smartlab diffractometer (Rigaku Corporation) equipped with a 9-kW Cu rotating anode (λ = 1.54056 Å) operating in reflection mode with parallel beam geometry. Data were collected in the 5-70 2θ range at a scan speed of 0.02 s −1 . For SCXRD measurements, a single crystal was mounted on a MiTeGen loop using Paratone-N oil. The mount was placed on a Rigaku Oxford Diffraction Super-Nova diffractometer equipped with an Atlas S2 CCD detector. Measurements were carried out at 100 K. Using Olex2, [24] the structure was solved with the ShelXT [25] structure solution program using Intrinsic Phasing and refined with the ShelXL [26] refinement package using least squares minimisation. The twin law was found using Platon software. [27] 2.3 | Solid-state NMR  3 ) powders were used as secondary references for 13 C and 27 Al, respectively. 13 C MAS NMR spectra were recorded at a magicangle spinning (MAS) rate of 12.5 kHz using cross polarisation (CP) to transfer magnetisation from 1 H with a contact time of 3 ms. The CP pulse was ramped linearly from 70% to 100% power. A recycle interval of 30 s was used. 1 H heteronuclear decoupling using two-pulse phase modulation (TPPM) [28] with a pulse length of 4.8 μs and a radiofrequency field strength of 100 kHz was applied during acquisition. 27 Al MAS NMR spectra were recorded using a singlepulse experiment with 100-kHz TPPM 1 H decoupling during acquisition. A recycle interval of 3 s was used. 27 Al multiple-quantum (MQ)MAS measurements were performed using a phase-modulated split-t 1 pulse sequence with whole-echo acquisition. 1 H TPPM decoupling was applied at a radiofrequency field strength of 100 kHz during the pulse sequence and acquisition.
Fits to experimental data were performed using the Sola line shape analysis tool within Bruker Topspin software. For all spectra, fits reproducibly converged to the same parameters from different starting points. To estimate errors, the parameters for converged line shapes were manually adjusted until a discernible visual discrepancy with the experimental line shape was obtained.

| DFT calculations
Geometry optimisations and calculations of total energies and NMR parameters were carried out using the CASTEP DFT code (version 17.21), [29] employing the GIPAW algorithm, [30] which allows the reconstruction of the allelectron wave function in the presence of a magnetic field. Core-valence interactions were described by ultrasoft pseudopotentials. [31] Geometry optimisations and calculations of total energies and NMR parameters were performed using a planewave energy cut-off of 50 Ry (680 eV) and integrals over the Brillouin zone were performed using a k-point spacing of 0.05 Å −1 . Geometry optimisations were carried out as described in the main text, using either the generalised gradient approximation Perdew-Burke-Ernzerhof (PBE) [32] or revised PBE (rPBE) [33] exchange-correlation functionals and SEDC schemes available within CASTEP. The GIPAW calculations generate the absolute shielding tensor (σ) in the crystal frame. Diagonalisation of the symmetric part of σ yields the three principal components, σ XX , σ YY , and σ ZZ . The calculated isotropic shielding, σ iso calc , is given by  Tables S1  and S2). The quadrupolar coupling constant, C Q = eQV ZZ /h and asymmetry parameter, η Q = (V XX − V YY )/V ZZ are obtained directly from the principal components of the electric field gradient (EFG) tensor, which are ordered such that jV ZZ j ≥ jV YY j ≥ jV XX j, where Q, the nuclear quadrupole moment equal to 146.6 mb, was used for 27 Al. [34] In addition to the magnitude, the calculations also generate the sign of C Q . However, the sign of C Q cannot be determined from the experimental data presented in this work; therefore, when comparing calculated and experimental quadrupolar couplings, we refer only to the magnitude of the calculated C Q . shed structures that are available, best agreement is observed with a simulated pattern for ε-Alq 3 ( Figure 2b). It is noteworthy that the experimental pattern for Alq 3

C1
shows evidence of weak reflections between 9 and 11 2θ, which are a hallmark of ε-Alq 3 and distinguish it from the simulated patterns for α-Alq 3 . The PXRD pattern for Alq 3 C2 (Figure 2c) is very similar, although slightly broader peaks are observed and the weak features between 9 and 11 2θ are less pronounced. The pattern shows very close agreement with published experimental patterns for α-Alq 3 . [3,13] Simulated patterns for α-Alq 3 based on the structures proposed by Brinkmann et al. [3] and Rajeswaran et al. [14] are shown in Figure 2d,e. Both patterns are very similar, but minor differences are observed including the presence of a small peak at 12 2θ for the Brinkmann structure that is not observed in the pattern for the Rajeswaran structure, whereas the peak at 17 2θ in the Rajeswaran structure has a small shoulder that is not observed in the Brinkmann structure. However, when compared with the experimental pattern for Alq 3 C2 , the broader experimental peak width does not allow for the presence or absence of these features to be unambiguously determined, so it is not possible to assign the pattern to either the Brinkmann or Rajeswaran structures. Figure 2f shows a PXRD pattern of Alq 3 sublimed . The most prominent peaks at 6.4 , 7.3 , and 7.9 2θ are consistent with the simulated patterns for α-Alq 3 and ε-Alq 3 . However, the peak intensity reduces significantly with increasing 2θ angle, indicating reduced long-range order in the structure. The pattern also shows several peaks consistent with crystalline 8-hydroxyquinoline which can form during the sublimation process due to oxidative condensation in the presence of O 2 and H 2 O contaminants. [35][36][37] Indeed, several of the needle-shaped crystals extracted from Alq 3 sublimed gave very similar unit cell parameters to this phase (CCDC structure code HXQUIN13) by SCXRD. A small number of larger crystals were also present, which were found to be ε-Alq 3 by SCXRD. In addition, the sample contained a large number of small fibrous clusters, although these were too small to be analysed by SCXRD. Figure 2g shows a PXRD pattern for Alq 3 heated . Previous reports have shown that heating the sample under similar conditions results in a mixture of δ-Alq 3 and γ-Alq 3 . [4,13] Indeed, the pattern for Alq 3 heated shows good agreement with a simulated pattern for a 1:1 mixture of δ-Alq 3 and γ-Alq 3 based on structures proposed by Rajeswaran [15] and Muccini [4] (Figure 2h).

13
C CPMAS NMR spectra of the Alq 3 samples are shown in Figure 3. The spectrum for Alq 3 C1 (Figure 3a) shows sharp resonances indicative of an ordered structure, although there is considerable overlap due to the large number of resonances present. The resonances are divided into six main groups, although nine chemically distinct environments are expected from the 8-hydroxyquinolinate ligand, suggesting that there is overlap between some of the groups. The large number of observed resonances is consistent with the ε-Alq 3 structure, which comprises 81 crystallographically distinct carbon sites due to the presence of three distinct Alq 3 complexes in the asymmetric unit, each containing three crystallographically inequivalent ligands.

C1
; however, there is increased broadening indicating the presence of disorder. This is consistent with the slightly broader peaks observed in the PXRD pattern for this sample. The similarity of the 13 C CPMAS NMR spectrum of Alq 3 C2 to that of Alq 3 C1 helps to distinguish between the α-Alq 3 structures proposed by both Brinkmann et al. and Rajeswaran et al., for which simulated PXRD patterns both show reasonable agreement. The Brinkmann et al. structure contains just one complex in the asymmetric unit, resulting in 27 crystallographically distinct carbon sites. The Rajeswaran structure is based on a disordered analogue of ε-Alq 3 , therefore in principle containing 81 local carbon environments. Although the number of carbon sites is not fully resolved in the 13 C CPMAS NMR spectrum, the close resemblance to the spectrum Alq 3 C1 is consistent with significantly more than 27 local environments being present, suggesting that the Rajeswaran structure provides a better description of the local structure.
The spectrum for the Alq 3 sublimed (Figure 3c) is almost identical to that for Alq 3 C2 . There is no evidence of additional resonances corresponding to the crystalline 8-hydroxyquinoline ligand, which is known to be present in the sample from SCXRD. It is possible that the pure ligand has a much longer T 1 relaxation time and so was not observed. The 13 C CPMAS NMR data suggest that despite the increased disorder evident from the PXRD data, the local structure in Alq 3 sublimed and Alq 3 C2 is very similar. Furthermore, the close resemblance of the spectra for both samples to that of . The γ-Alq 3 structure proposed by Muccini et al. [4] contains a single Alq 3 complex in the asymmetric unit, and the 8-hydroxyquinoline ligands are crystallographically equivalent. Therefore, 10 13 C resonances are expected for this structure. The δ-Alq 3 structures proposed by Colle et al. [11] and Rajeswaran et al. [15] both contain a single crystallographic Alq 3 complex, but the 8-hydroxyquinoline ligands are crystallographically distinct, resulting in 27 crystallographic carbon sites. Therefore, for a mixture of γ-Alq 3 and δ-Alq 3 , 37 carbon resonances would be expected. Although the spectrum is not fully resolved, it is clear that significantly fewer resonances are present than in the spectrum for Alq 3 C1 .
The 13 C CPMAS NMR data are consistent with the PXRD data, but the lack of resolution between crystallographically distinct sites does not allow the phases to be unambiguously characterised. To gain further insight, 27 Al solid-state NMR experiments were performed. The 27 Al MAS NMR spectrum of Alq 3 C1 (Figure 4a) shows what appears to be a second-order quadrupolar broadened lineshape, although the features suggest that several unresolved resonances are present. To separate the resonances, a 27 Al MQMAS NMR spectrum was recorded at 16.4 T (Figure 4b). This spectrum shows two main features centred around δ 1 = 19.75 and 20 ppm. However, the feature at δ 1 = 20 ppm is broadened, suggesting it is actually made up of two resonances. To confirm this, spectra were recorded at 20.0 T (Figure 4c,d). Although the MAS spectrum does not show significantly increased resolution, the MQMAS spectrum is more clearly resolved, confirming the presence of three crystallographically distinct sites in the material. Regarding the published crystal structures, the only proposed structure with three crystallographically distinct Al sites is ε-Alq 3 . This supports the good agreement of the PXRD with the simulated pattern for this polymorph. Quadrupolar  . 27 Al MAS and MQMAS NMR spectra of Alq 3 heated are shown in Figure 6. The MAS spectrum (Figure 6a) shows a second-order quadrupolar broadened lineshape that closely resembles a single site, except for the presence of a small feature on the right-hand side. As mentioned in Section 3.1, previous reports have shown that heating the sample under similar conditions results in a mixture of δ-Alq 3 and γ-Alq 3 , [4,13] and the PXRD (  Table 1). These agree well with experimental η Q of Kaji et al., [13] although C Q values were not reported in that study. In the MQMAS spectrum (Figure 6b), the lineshapes remain unresolved, highlighting the close similarity in the 27 Al NMR parameters of the two phases. The low η Q values are also consistent with the axial symmetry of the fac for δ-Alq 3 using the point charge model. [12] 3

.3 | DFT calculations
To link the solid-state NMR data to the proposed structures, first-principles DFT calculations were performed. Although β-Alq 3 was not studied experimentally in this work, DFT calculations were also performed on this structure for additional comparison. Prior to the calculation of NMR parameters, crystal structures were geometry optimised. As discussed in Section 1, for molecular crystalline structures, DFT often fails to adequately describe long-range nonbonding interactions as a result of the absence of van der Waals forces in commonly used exchange-correlation functionals. For this reason, geometry optimisations can lead to unrealistic unit cell expansions and atomic positions, which can significantly alter the calculated NMR parameters, in particular quadrupolar parameters that can be highly sensitive to small deviations in bond lengths and angles. One way to address this is to constrain the unit cell parameters to the experimental values during the geometry optimisation. However, in recent years a number of semiempirical dispersion correction (SEDC) schemes have been developed, which modify the DFT-calculated energy using an empirically-derived dispersion correction. [22] The inclusion of dispersion correction schemes such as those proposed by Grimme (G06) [38] and Tkatchenko and Scheffler (TS) [39] has been shown to give improved agreement for calculated 27 Al quadrupolar parameters in aluminophosphate frameworks containing organic structure-directing agents, [40] and they have also been applied the study of Al-containing flexible metal-organic frameworks. [41] For the case of Alq 3 , the complexes contain no external hydrogen-bonding groups, and therefore, their organisation within the crystal structure is expected to be highly dependent on weak intermolecular interactions such as π-π interactions between the ligands. Indeed, when preliminary geometry optimisations were performed with no dispersion correction or cell constraints, significant unit cell expansion was observed and the optimisations failed to converge to an energy minimum. For this reason, four different geometry optimisation procedures were explored in order to assess how well different methods account for dispersion interactions from the perspective of the calculated NMR parameters. The procedures used are summarised in Table 2. In Method A, the unit cell parameters were fixed to the experimental values, whereas all atomic positions were allowed to vary. In Method B, all atomic positions and the unit cell parameters were allowed to vary under the G06 SEDC scheme, whereas Method C employed the same approach under the TS SEDC scheme. Method D employed a modification to the G06 SEDC scheme recently proposed by Holmes et al., whereby the unit cell parameters are fixed, but the damping parameter is set to 3.25, and the rPBE exchange-correlation functional is used. [23] The damping parameter was empirically optimised on a training set of organic solids and was shown to give better agreement between calculated and experimental 14 N, 17 O, and 35 Cl quadrupolar parameters. Although here we only consider 27 Al quadrupolar parameters (which were not considered by Holmes et al.), this method was employed in order to investigate if the empirically optimised damping function together with the rPBE functional can be more generally employed. Figure 7a,b shows percentage changes in unit cell parameters and volumes for both of the optimisation methods where the unit cell was allowed to vary (Methods B and C). In all cases, a reduction in the unit cell volume is observed. For the G06 method, reductions are between 6% and 9% as compared with the experimental unit cell volume. For the TS method, smaller reductions of between 3% and 6% are observed. These results are consistent with previous calculations on aluminophosphate frameworks containing organic guest molecules where reductions of up to 2% were observed, with larger contractions in general for the G06 method. [40] The larger contractions observed for the Alq 3 structures likely reflects the greater contribution of nonbonding interactions to the crystal structure than in the previous work where the framework structures were determined by covalent interactions.
For the β-, γ-, δ-, and ε-Alq 3 structures, the reductions in the unit cell volumes arise from broadly uniform contractions in the unit cell parameters. However, for the α-Alq 3 structure, [3] the cell contraction actually arises from two large and opposing changes in the a and c crystallographic axes. This shows that although the change in total unit cell volume is consistent with the other structures, the optimisation procedures have resulted in quite large structural changes as compared with the experimental structure. Figure 7c compares relative energies for the five polymorphs optimised by each method. For Methods A, B, and C, energies for the optimised β-, δ-, γ-, and ε-Alq 3 structures are very similar within a range of 0.17 eV, whereas Method D shows a larger range of 0.6 eV. However, for all the optimisation methods, the energy for the optimised α-Alq 3 structure is significantly higher. This suggests that despite the large variation in the unit cell parameters during the optimisation processes, the optimised α-Alq 3 structure only represents a local minimum and the other polymorphs sit significantly closer to the global minimum in total energy. Together with the large structural changes observed during the optimisations, this suggests that the structure proposed by Brinkmann et al. does not provide an accurate representation of the α-Alq 3 structure. Simulated 13 C MAS NMR spectra based on calculated 13 C chemical shifts are shown in Figure S1. The simulated spectra for α-Alq 3 show poor agreement with the experimental spectrum for Alq 3 C1 , as they contain fewer resonances due to the lower number of crystallographically distinct carbon sites in the structure as discussed above. Simulated spectra for ε-Alq 3 show better agreement in terms of the number of resonances, particularly for the carbonyl carbon, which is well separated from the rest of the resonances. However, the rest of the resonances show more overlap than is observed experimentally. In this respect, all optimisation methods give similar results, although Method D overestimates the separation between the carbonyl resonance and the rest of the resonances. Simulated spectra for a 1:1 mixture of γ-Alq 3 and δ-Alq 3 show reasonable agreement with the experimental spectrum for Alq 3 heated in terms of grouping of the chemical shifts, although the region between 100 and 115 ppm is divided into two groups whereas one group is observed experimentally. Method D again overestimates the separation of the carbonyl resonance from the rest of the spectrum. Due to the large number of resonances and overlap in the experimental spectra, it is not possible to make a full assignment for either of the samples. Calculated 27 Al NMR parameters for structures with the mer conformation are shown in Table 3. Considering the calculated chemical shifts, the values obtained from Method A (ε-Alq 3 ) are in good agreement with the experimental values for Alq 3 C1 . However, Methods B, C, and D overestimate the shifts in comparison with the experimental values. Despite this, the range of shifts for the three sites in ε-Alq 3 (less than 1 ppm) is consistent with the experiment. This suggests the discrepancy may originate from the choice of reference shielding. Chemical shieldings were referenced using calculations by the same four methods for AlPO-34, chosen due to its well-defined structure and accurately measured experimental chemical shift. [42] In these reference calculations, there is For each method, total energies are normalised relative to the lowest energy structure optimised by that method significant variation in the chemical shielding between four methods used, with Method A yielding values 5-8 ppm lower than the other methods (see Table S1). In contrast, for the Alq 3 polymorphs, the calculated shieldings are very similar for the Methods A-C, whereas values for Method D are consistently 2-4 ppm higher. This may be linked to the use of the rPBE functional or modified damping parameter; however, to fully understand the effects of these and the variation in reference shielding on the calculated chemical shift would require a more detailed analysis of a wider range of compounds. For α-Alq 3 , C Q values between 5.48 and 7.21 MHz are calculated by the four optimisation methods. Although this structure is inconsistent with the three Al sites observed for Alq 3

C1
, the calculated C Q values are broadly consistent with the experimental values of 5.6-6.3 MHz determined for the mer isomers in this structure. However, the calculated η Q values show a large variation; respective values of 0.25 and 0.23 are calculated for Methods A and D, whereas values of 0.81 and 0.94 are calculated for Methods B and C. In all of the optimised structures, the aluminium has a very similar local coordination environment in the mer conformation, but there are small differences in the relative orientations of the ligands ( Figure S3). Because η Q is highly sensitive to small variations in the relative magnitudes of the quadrupolar tensor parameters, the variation η Q may be attributed to these structural differences.
For β-Alq 3 , the NMR parameters are less sensitive to the optimisation method, with calculated C Q and η Q values falling in the respective ranges of 4.95-6.45 and 0.81-0.91. These values are qualitatively consistent with a previously published 27 Al MAS NMR spectrum for this polymorph, which showed a single quadrupolar lineshape with η Q close to 1 and C Q of approximately 6 MHz. [15] For ε-Alq 3 , all four methods underestimate the C Q and η Q values in comparison with the experimental values for Alq 3 C1 . However, overall the calculated values are qualitatively consistent with the experimental observation of two sites with similar C Q and η Q values, and a third site with lower C Q and η Q values. However, Method A significantly underestimates η Q for Site 1, with a calculated value of 0.22 in comparison with the experimental values of 0.59. Closest overall agreement is obtained with Method D, which gives slightly higher η Q values than the other methods, but these values are still slightly underestimated compared with experiment. Calculated 27 Al NMR parameters for structures with the fac conformation are shown in Table 4. As was observed for the mer-containing polymorphs, Method A gives good agreement with the experimental shifts for Alq 3 heated , whereas Methods B-D overestimate the shift by 5-6 ppm. The calculated C Q values are also very similar between 4.52 and 4.81 MHz, although there is no clear correlation with the polymorphic form. The most distinct correlation is given by the calculated η Q values, for which γ-Alq 3 is consistently calculated to be 0.00, where η Q for γ-Alq 3 falls between 0.27 and 0.37. The consistent calculation of η Q = 0.00 for γ-Alq 3 shows that the structure optimises to a perfectly axially symmetric Al environment by all methods. Examination of the optimised structures (Table S4) shows that this is indeed the case. In contrast, the intermolecular arrangement in δ-Alq 3 distorts the ligands around the central Al site, resulting in a slight deviation from an axially symmetric structure. Compared with the experimental values for Alq 3 heated , the calculated values agree well with the experimental values for two sites observed, confirming that the samples is a mixture of γ-Alq 3 and δ-Alq 3 . In particular, the perfect axial symmetry of the Al environment in γ-Alq 3 is well reproduced.

| DISCUSSION
Despite the numerous structural studies of Alq 3 polymorphs, the structure of α-Alq 3 has remained contentious and has never been conclusively determined. Furthermore, the distinction between α-Alq 3 and the subsequently discovered ε-Alq 3 is not fully understood. The PXRD and solid-state NMR measurements in this work strongly suggest that Alq 3 C1 corresponds to the ε-Alq 3 structure. In particular, the 27 Al MQMAS NMR spectra unambiguously confirm the presence of three crystallographically distinct Al sites, which are only present in the ε-Alq 3 structure. For Alq 3 C2 , the PXRD data give better agreement with the published structures for α-Alq 3 , although it does not unambiguously distinguish between them. However, the 13 C and 27 Al solid-state NMR measurements clearly show that the local structure of this material is very similar to Alq 3 C1 with three distinct Al sites but with increased disorder. For Alq 3 sublimed , the PXRD data are also inconclusive, with the loss of intensity at high 2θ angle suggesting a reduction in long-range order in the structure. From the point of view of solid-state NMR, the local structure in Alq 3 sublimed looks almost identical to , showing that the local structures are very similar to each other and to ε-Alq 3 . This suggests that the distinction between the α-Alq 3 and ε-Alq 3 polymorphs is very subtle, and both structures are characterised by the same local ordering of Alq 3 complexes with different degrees of disorder. Importantly, the experimental data conclusively rule out the structure originally proposed by Brinkmann et al., which contains only a single crystallographic Al site. This is also supported by the significantly higher total energy of this structure determined by DFT calculations, as well as the large structural changes seen during structural optimisation. For Alq 3 heated , the PXRD data are consistent with a mixture of γ-Alq 3 and δ-Alq 3 according to the structures published by Rajeswaran et al. [15] and Muccini et al. [4] The experimental 27 Al MAS NMR data are also consistent with this and show two low-η Q lineshapes consistent with the fac isomeric form. The comparison of optimisation methods reveals that the way in which dispersion interactions are accounted for during geometry optimisations can influence the calculated 27 Al NMR parameters. In general, Method A gives best agreement between calculated and experimental chemical shifts, although a significant factor in this is the choice of shielding reference, which has not been studied in detail. Notably, all methods are similar in terms of the range of chemical shifts for ε-Alq 3 , suggesting that they should perform similarly providing a suitable reference shielding is used. Future work on a wider set of model compounds is required to better estimate reference shieldings for particular optimisation methods, as well as to understand how the rPBE functional and modified damping parameter influence the calculated shielding.
Considering quadrupolar parameters, slightly larger C Q values are calculated in general for structures containing the mer conformation (although this is not always the case); this pattern is consistent with the experimental C Q values of around 6 MHz for Alq 3 C1 (mer) compared with 5 MHz for Alq 3 heated (fac). There is also a tendency for the calculated C Q values to be underestimated, particularly for Methods A and B. It is noteworthy that in general, Method D predicts the highest C Q values, giving better agreement with experiment (although still slightly underestimated). The better agreement of Method D may be expected because the SEDC damping parameter in this method was specifically optimised for the accurate calculation of C Q values. However, the damping parameter was optimised through consideration of calculated 14 N, 17 O, and 35 Cl quadrupole parameters for a set of organic solids where hydrogen bonds are the dominant structure determining interactions. For the Alq 3 complexes studied here, hydrogen bonding is absent and the structures are dominated by Al-O and Al-N bonding and π-π interactions between the ligands. It is possible that empirical optimisation of the damping parameter for structurally similar compounds could further improve the accuracy of the calculated 27 Al C Q values.
The comparison between calculated and experimental η Q values reveals larger discrepancies, which is important because this parameter has been proposed as a way to distinguish between the mer and fac isomers. Using a point charge model, Utz et al. proposed that the mer conformation should be characterised by a high η Q value (calculated value of 0.91) whereas the axially symmetric fac conformation should have η Q close to 0. [12] Considering the polymorphs containing the mer isomer, the calculated η Q for β-Alq 3 is generally close to the point charge value. However, for the α-Alq 3 and ε-Alq 3 , several calculated η Q values are significantly lower than 0.91. In DFT calculations, η Q is usually one of the least accurately reproduced parameters due to its high sensitivity to small relative variations in the individual components of the quadrupolar tensor. However, the calculations do suggest that low η Q values can be obtained for structures in the mer conformation. The experimental η Q values for Alq 3 C1 , which contains the mer conformation, are also lower than this 0.91. This highlights the limitations of the simple point charge model, which does not take into account ionic polarizability and orbital overlap effects. Indeed, these are likely to be significant in Al-O and Al-N bonds, which have a significant degree of covalent character. Nevertheless, the relative magnitudes of η Q could still provide a useful indicator of the isomeric form even if the point charge model is only qualitatively correct. However, the DFT calculations also show a large variation in η Q for the mer conformation depending on the optimisation method used. For example, for ε-Alq 3 optimised according to Method A, the calculated η Q value for Site 1 is 0.22, which is lower than all calculated η Q values for δ-Alq 3 containing the fac conformation. Using Method D, the calculated η Q of 0.50 for Site 1 in ε-Alq 3 is closer to the experimental value of 0.59. The local Al coordination environment is very similar in the two cases, and also similar to β-Alq 3 , and there is no clear structural relationship between η Q and the local coordination environment. Rather, the relative magnitudes of the V XX and V YY quadrupolar tensor components appear to be very sensitive to small variations in bond length and angle between the structures, resulting in a range of η Q values for subtly different structures. Therefore, although the relative sizes of the experimental η Q values for Alq 3 C1 and Alq 3 heated are broadly in line with the predictions of the point charge model, the DFT calculations show that η Q is not necessarily a reliable indicator of the isomeric conformation of the Alq 3 complex.

| CONCLUSIONS
In this work, 13 C and 27 Al solid-state NMR measurements have been used to provide new insights into the structures of Alq 3 polymorphs. For two commercial samples, Alq 3 C1 and Alq 3 C2 , PXRD data identifies them as the ε-Alq 3 and α-Alq 3 polymorphs, respectively, although the different proposed structures for α-Alq 3 cannot be easily distinguished. 27 Al MQMAS NMR unambiguously shows that a crystal structure comprising a single crystallographic Al site proposed by Brinkmann et al. does not describe the structure well and this is further supported by DFT calculations, which show it is a highenergy structure. Instead, both samples contain three crystallographic Al sites, in agreement with the crystal structure for ε-Alq 3 proposed by Rajeswaran et al. The similarity between the spectra and increased disorder evident in Alq 3 C2 supports the α-Alq 3 structure also proposed by Rajeswaran et al., which is based upon a disordered analogue of ε-Alq 3 . Alq 3 sublimed appears significantly more disordered by PXRD, but the solid-state NMR data show local ordering of the Alq 3 complexes, very similar to Alq 3 C1 and Alq 3

C2
. This suggests that α-Alq 3 is highly prone to disorder in varying degrees, which may have contributed to the difficulties in accurately characterising this structure in previous studies. In contrast, the experimental data for Alq 3 heated are consistent with the proposed structures for γ-Alq 3 and δ-Alq 3 , each of which appear fully ordered by both PXRD and solid-state NMR. DFT calculations show that the use of SEDC schemes in geometry optimisations can influence the 27 Al C Q in Alq 3 polymorphs, and a recently proposed modification to the G06 scheme which is optimised for the calculations of quadrupolar parameters gives good agreement with experiment. The previously proposed relationship between the isomeric conformation of the Alq 3 complex and the η Q value based on a point charge model is found to be valid to some extent in terms of the experimental NMR parameters. However, the DFT calculations show that η Q is very sensitive to the geometry of the Al local coordination environment, and this relationship should not necessarily be relied upon as an indicator of the isomeric conformation, particularly if any further polymorphs are discovered. computational resources, which is partially funded by the EPSRC (EP/P020194). The UK 850 MHz solid-state NMR Facility used in this research was funded by EPSRC and BBSRC (contract reference PR140003), as well as the University of Warwick including via part funding through Birmingham Science City Advanced Materials Projects 1 and 2 supported by Advantage West Midlands (AWM) and the European Regional Development Fund (ERDF).