Testing the Sensitivity of Terahertz Spectroscopy to Changes in

Testing the Sensitivity of Terahertz Spectroscopy to Changes in Molecular and Supramolecular Structure: A Study of Structurally Similar Cocrystals Edward P. J. Parrott,†,‡ J. Axel Zeitler,† Tomislav Frisˇcˇic´,§ Michael Pepper,‡ William Jones,§ Graeme M. Day,*,§ and Lynn F. Gladden*,†

CRYSTAL GROWTH & DESIGN 2009 VOL. 9, NO. 3 1452–1460

Department of Chemical Engineering and Biotechnology, UniVersity of Cambridge, Pembroke Street, Cambridge CB2 3RA, U.K., CaVendish Laboratory, UniVersity of Cambridge, J. J. Thomson AVenue, Cambridge CB3 0HE, U.K., and Department of Chemistry, UniVersity of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K. ReceiVed August 12, 2008; ReVised Manuscript ReceiVed December 8, 2008

ABSTRACT: Terahertz time-domain-spectroscopy (THz-TDS) has emerged as a versatile spectroscopic technique, and an alternative to powder X-ray diffraction in the characterization of molecular crystals. We tested the ability of terahertz spectroscopy to distinguish between chiral and racemic hydrogen-bonded cocrystals that are similar in molecular and supramolecular structure. Terahertz spectroscopy readily distinguished between the isostructural cocrystals of theophylline with chiral and racemic forms of malic acid which are almost identical in molecular structure and supramolecular architecture. Similarly, the cocrystals of theophylline with chiral and racemic forms of tartaric acid, which are similar at the molecular level but dissimilar in crystal packing, were distinguished unequivocally. The investigation of the same cocrystals using X-ray powder diffraction and Raman spectroscopy suggested that THz-TDS is comparable in sensitivity to diffraction methods and more sensitive than Raman spectroscopy to changes in cocrystal architecture. The differences in spectra acquired by THz-TDS could be further enhanced by cooling the samples to 109 K. Introduction In response to the need for fast and reliable solid-state analytical tools required for high-throughput solid-state screening technology, a rapid development of methods for the characterization of molecular materials has taken place in recent years. X-ray powder diffraction (XRPD),1 often considered as the gold standard for the characterization of pharmaceutical solids,2 has now been joined by solid-state NMR spectroscopy3 and terahertz time-domain-spectroscopy (THz-TDS).4,5 THz-TDS is a vibrational spectroscopic technique that probes the infrared active vibrational modes in the far-infrared and sub-millimeter region of the electromagnetic spectrum using ultrashort pulses of coherent terahertz radiation (0.1-4 THz ) 3-133 cm-1). The advantages of THz-TDS for analytical purposes are its nondestructive nature, the use of nonionizing radiation, short acquisition times, and simplicity of sample preparation. THz-TDS enables the characterization of solid-state materials through the excitation of soft intramolecular vibrational modes as well as intermolecular modes and hydrogen-bonding networks inherent to the molecular assembly in the solid state.6,7 In this way, THzTDS is attractive as a means to probe noncovalent interactions, such as hydrogen bonds and related supramolecular synthons. In this context, we have demonstrated how computational methods can be used to assign features in a terahertz spectrum to particular molecular movements,8,9 adding to our understanding of how differences in terahertz spectra reflect variations in the network of intermolecular interactions between different crystal structures. In a practical sense, THz-TDS is complementary to infrared (IR) and Raman spectroscopies, and is expected to have a strong potential for characterizing and * To whom correspondence should be addressed. (G.M.D.) Tel: +44 1223 336390. Fax: +44 1223 336362. E-mail: [email protected]. (L.F.G.) Tel: +44 1223 334762. Fax: +44 1223 334796. E-mail: [email protected]. † Department of Chemical Engineering and Biotechnology, University of Cambridge. ‡ Cavendish Laboratory, University of Cambridge. § Department of Chemistry, University of Cambridge.

“fingerprinting” crystal structures, as it interacts with those vibrational modes directly related to the crystal packing. THzTDS has already been applied to differentiate between polymorphs, solvates, and amorphous forms of organic compounds8-13 and has also been used to monitor dynamic processes, such as polymorphic transitions, dehydration, and mechanochemical formation of multicomponent crystals (cocrystals).9,14-18 The development of terahertz spectroscopy is timely with the rapid growth of interest in cocrystals19,20 as functional (e.g., pharmaceutical,21,22 electronic,23 or photonic24,25) materials. The ability to use terahertz spectroscopy as a high-throughput analytical technique makes it particularly promising for rapid screening of pharmaceutical cocrystals.20 We consider this aspect of terahertz spectroscopy increasingly important with the development of efficient methods for cocrystal synthesis via mechanochemical and sonochemical methods.26-28 In order to investigate the potential of terahertz spectroscopy in differentiating molecular solids, we investigated the differences in spectra of cocrystal pairs having similar chemical composition and supramolecular architectures. In particular, we decided to challenge the ability of the technique to differentiate between chiral and racemic forms of two recently reported29,30 cocrystals of theophylline (tp) with malic acid (chiral form: L-mal and racemic form: DL-mal) and tartaric acid (chiral form: L-tart and racemic form: DL-tart) (Scheme 1). The cocrystals (tp) · (L-mal) and (tp) · (DL-mal) represent a suitable challenge to solid-state analytical tools, as the two cocrystals are crystallographically isostructural (Table 1) and display only minor structural differences in the architecture of intermolecular hydrogen bonds. The cocrystals (tp)2 · (L-tart) and (tp)2 · (DLtart) are not crystallographically isostructural (Table 1), but display highly similar hydrogen-bonded architectures. The comparison of tp cocrystals with optically different forms of malic acid and tartaric acid provides an opportunity to compare the abilities of THz-TDS and more routine solid-state analytical tools of XRPD and FT-Raman spectroscopy,31 to differentiate molecular materials with different levels of chemical and

10.1021/cg8008893 CCC: $40.75  2009 American Chemical Society Published on Web 02/04/2009

Sensitivity of Terahertz Spectroscopy to Structure

Crystal Growth & Design, Vol. 9, No. 3, 2009 1453

Scheme 1. Chemical Diagrams of Theophylline, Tartaric Acid, and Malic Acid

Table 1. Crystallographic Parameters for the Crystal Structures of Investigated Chiral and Racemic Cocrystals of tp29,30 cocrystal

(tp) · (L-mal)

(tp) · (DL-mal)

(tp)2 · (L-tart)

(tp)2 · (DL-tart)

crystal system space group a/Å b/Å c/Å R/o β/o γ/o V/Å3

monoclinic P21 15.8592(8) 6.0791(3) 14.6549(9) 90 108.589(2) 90 1339.2(2)

monoclinic P21/n 14.9572(8) 6.0716(3) 15.5163(6) 90 106.430(2) 90 1351.6(1)

monoclinic P21 8.9522(4) 6.7582(5) 18.876(1) 90 100.685(4) 90 1122.18

triclinic P1 7.3102(1) 8.3730(1) 17.9724(3) 98.294(1) 99.466(1) 94.527(1) 1067.78

supramolecular similarity. It was expected that THz-TDS would be particularly suited to distinguish between isostructural materials, such as (tp) · (L-mal) and (tp) · (DL-mal), due to its ability to probe intermolecular interactions, as opposed to atomic positions or intramolecular motions that are probed by XRPD and Raman spectroscopy, respectively. We have also made a preliminary attempt to understand the nature of the observed differences in terahertz spectra in these two pairs of cocrystals based on atom-atom model potential based lattice energy and lattice dynamics calculations. Experimental Section As described elsewhere,29,30 cocrystals of (tp) · (L-mal), (tp) · (DLmal), and (tp) · (L-tart) could not be easily obtained by cocrystallization from a solution. Consequently, all the cocrystals used in this investigation were prepared by liquid-assisted grinding.29,30 In a typical liquidassisted grinding experiment, 0.2 g of the mixture of solid reactants in the appropriate stoichiometric ratio was placed in a stainless steel grinding jar of 10 mL volume, along with 50 µL of nitromethane and two stainless steel grinding balls of 7 mm diameter. The mixtures were ground for 30 min using the MM200 grinding mill operating at 30 Hz. The (tp) · (DL-mal) cocrystal obtained this way always contained small amounts of tp and DL-mal as impurities.30 Measurement of THz-TDS spectra was performed using a setup similar to that described previously.9 For the acquisition of the terahertz spectra sub-picosecond coherent pulses of broadband terahertz radiation (0.1-4 THz) were generated by photoexcitation of a DC biased semiinsulating GaAs substrate by 12 fs pulses of a NIR laser (Femtolasers,

Femtosource cM1, Vienna, Austria, centre wavelength 800 nm). Using two parabolic off-axis mirrors the terahertz pulses were focused onto the samples and the transmitted pulses were collected using an identical set of parabolic mirrors. A coherent detection scheme was used employing electro-optical sampling. This approach allows for the measurement of the terahertz electric field directly rather than just its amplitude. To increase the speed of data acquisition as well as to improve spectral resolution and signal-to-noise ratio, a 50 ps rapid optical delay was used. Between 200 and 300 scans were co-added at a scanning frequency of 0.5 Hz for each spectrum. The resulting timedomain waveform was apodized using a Hamming function. Power spectra of the time-domain signals were calculated using FFT resulting in a spectral resolution of 30 GHz (1 cm-1). Room temperature XRPD measurements were performed on samples mounted on a flat plate, using a Philips X′Pert Pro diffractometer equipped with Ni-filtered Mo KR radiation and a X′celerator CCD detector. Room temperature FT-Raman spectra were recorded on the Bruker RAM II system, equipped with a liquid-nitrogen cooled Ge detector, at the excitation wavelength of 1064 nm. For each spectrum, 64 scans were collected with the excitation laser power of 175 mW. Computational Methods. Lattice energy minimizations and lattice dynamics calculations were performed in the rigid-molecule approximation, using the crystal structure modeling program DMAREL.32 Molecular geometries taken from the experimentally determined crystal structures were partially optimized in isolated-molecule density functional theory (B3LYP/6-31G**) calculations, using the program Gaussian03.33 The tp molecular structure was fully optimized, while some torsion angles were constrained in the malic and tartaric acid optimizations to maintain the crystal structure conformation. The constrained torsion angles in malic acid were (referring to atom numbers in Scheme 1): C1-C2-C3-C4; O2-C1-C2-C3; O4-C4-C3-C2; and H3-O3-C2-C3 and those constrained in tartaric acid were C1-C2C3-C4; O2-C1-C2-C3; O5-C4-C3-C2; H3-O3-C2-C3; and H5-O4-C3-C2. Such partial molecular optimizations were performed for each independent acid molecule in each of the cocrystal structures and the X-ray determined molecular geometries were replaced by these optimized molecules to create our starting point for rigid-molecule lattice energy minimization and lattice dynamics. For analysis of the conformational energies of the acid molecules, full (unconstrained) geometry optimizations were also performed starting from each of the crystal structure conformations. An exp-6 atom-atom intermolecular model potential and atomic multipole electrostatic model was used for the lattice energy calculations. Parameters for the exp-6 potential were taken from Williams and co-workers 34-36 for C · · · C, O · · · O, N · · · N and HC · · · HC interactions (were HC are hydrogen atoms bonded to carbon), and Price and coworkers for HN · · · HN37 and HO · · · HO38 (HN being hydrogen bonded to nitrogen, and HO hydrogen bonded to oxygen). Parameters for heteroatomic interactions were determined using standard combining rules. Atomic multipoles, up to hexadecapole on each atom, were derived from the B3LYP/6-31G** wave functions via a distributed multipole analysis39,40 using the program GDMA.41 Ewald summation was used for all charge-charge and charge-dipole interactions and all other atom-atom interactions were summed to a 15 Å direct cutoff. Lattice energy minimizations were performed using a quasi-Newton-Raphson method, varying molecular positions, orientations and unit cell parameters to find the nearest local minimum. Relative stabilities of the cocrystals were assessed from total crystal energies, which are calculated as a sum of the B3LYP/6-31G** molecular energies and exp-6-DMA intermolecular energies. Implementation of the rigid-molecule lattice dynamics in DMAREL is described elsewhere.42 The vibrational frequencies were calculated at the lattice energy minima, and absorption intensities are estimated from the change in dipole in the unit cell along each eigenvector, assuming that the molecular dipoles remain constant. THz spectra were simulated assuming a Lorentzian peak shape with a full width at half-maximum of 0.1 THz.

Results and Discussion X-ray Powder Diffraction. The features in XRPD patterns (Figure 1) for the isostructural cocrystals (tp) · (L-mal) and (tp) · (DL-mal) are highly similar, preventing the two cocrystals from being readily distinguished by visual inspection of their patterns (Figure 1a). The similarity of the two diffraction patterns

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Figure 1. (a) XRPD patterns of (tp) · (DL-mal) (bottom), (tp) · (L-mal) (middle) and the difference pattern (top); (b) the hydrogen-bonded ring motif in (tp) · (DL-mal); (c) the hydrogen-bonded ring motif in (tp) · (L-mal). To visualize the difference in hydrogen-bonding properties of malic acid in the two structures, two sides of each malic acid molecule are shown in yellow (without alcohol functionality) and green (with the alcohol functionality).

Figure 2. (a) XRPD patterns of (tp)2 · (DL-tart) (bottom), (tp)2 · (L-tart) (middle), and the difference pattern (top); (b) view along the [212] diffracting plane in (tp)2 · (L-tart) and (c) along the [12j3] diffracting plane in (tp)2 · (DL-tart). The two planes (red) adopt an identical orientation with respect to the supramolecular motifs that are analogous between the two cocrystals. This is visualized through shaded circles that delineate the hydrogenbonded rings in (tp)2 · (DL-tart) and analogous portions of the hydrogen-bonded helix in (tp)2 · (L-tart).

is illustrated by the resulting difference pattern, which reveals that patterns of both cocrystals exhibit the same features but slightly shifted in the 2θ diffraction angle. In almost all cases the shift is below 0.2°, and the largest observed shifts are 0.2°, 0.2°, 0.4°, and 0.6° for [202j] (2θ ) 14.3°), [113] (2θ ) 26.3°), [213] (2θ ) 29.6°), and [202] (2θ ) 20.0°) reflections, respectively. The difficulty43 in differentiating the two cocrystals using XRPD is understandable, as the method probes the average positions of heavy atoms (C, N, O) within the unit cell; that is, the positioning of the heavy atoms in the two cocrystals is highly similar. The similarity of the structures is made possible by the conformational flexibility of malic acid, which allows an L-malic acid molecule in (tp) · (L-mal) to play the same role as a D-malic acid molecule in (tp) · (DL-mal). The most significant difference between (tp) · (L-mal) and (tp) · (DL-mal) structures is in the organization of hydrogen bonds and related hydrogen atoms, which are difficult to probe via X-ray diffraction (Figure 1b,c). In particular, both cocrystals exhibit hydrogen-bonded ring motifs involving two malic acid and two tp molecules. However, in (tp) · (L-mal) one-half of the malic acid molecules utilize a different combination of hydrogen-bonding functionalities to form the ring motif than the malic acid molecules (in tp) · (DLmal). As a result, (tp) · (DL-mal) is based on R44(18) and (tp) · (Lmal) on R44(19) hydrogen-bonded motifs. For the chiral and racemic forms of tp cocrystals with tartaric acid, differentiation via XRPD is expected to be facilitated by

the absence of isostructurality. However, the inspection of the difference XRPD pattern for (tp)2 · (L-tart) and (tp)2 · (DL-tart) revealed more similarities than expected. Whereas it is possible to identify certain reflections in the XRPD patterns that are unique to each cocrystal as isolated positive or negative features, most reflections appear to be simply shifted in the 2θ diffraction angle (Figure 2a). Again, the shifts in the features are not very large, for example, 0.2° for the reflection at the 2θ angle 14.5° (indexed as the [003] and [102] reflections for (tp)2 · (D-tart) and (tp)2 · (DL-tart), respectively), 0.4 ° for the reflection at 2θ ) 25.4° (indexed as the [211] and [121j] reflections for (tp)2 · (Dtart) and (tp)2 · (DL-tart), respectively) and 0.3° for the reflection with 2θ ) 27.4° (indexed as [212] and [12j3] reflections in (tp)2 · (D-tart) and (tp)2 · (DL-tart), respectively). Although the similarity in XRPD patterns is not immediately expected considering the differences in crystal system and unit cell parameters, it can be explained by the similarity in supramolecular architectures of (tp)2 · (L-tart) and (tp)2 · (DL-tart). Namely, the organization of molecules in the two cocrystals is highly similar, with interlocked hydrogen-bonded helices in (tp)2 · (L-tart) replaced by interwoven hydrogen-bonded rings in (tp)2 · (DL-tart). Consequently, the strongly diffracting planes are expected to be structurally similar for the two cocrystals, albeit the corresponding Miller indices are different by virtue of different crystallographic properties. This is illustrated by the similarity of the [212] plane in (tp)2 · (L-tart) and the [12j3]


Figure 3. Raman spectra of (tp) · (DL-mal) (bottom), (tp) · (L-mal) (middle), and the resulting difference spectrum (top).

plane in (tp)2 · (DL-tart). Despite different Miller indices, the two correspond to the same orientation of related supramolecular motifs in the two cocrystals (the hydrogen-bonded helix and the chain of interwoven rings) and, consequently, exhibit similar 2θ diffraction angle and intensity (Figure 2b,c). Raman Spectra. The Raman spectra of isostructural (tp) · (Lmal) and (tp) · (DL-mal) were recorded at mid-infrared frequencies of 4000 to 400 cm-1 and a resolution of 4 cm-1, typically used for the differentiation of solid forms. Since Raman spectroscopy primarily detects differences in molecular structure, the two cocrystals were not anticipated to show any significant differences in the Raman spectra (Figure 3), except in the spectral region of 3000 cm-1, corresponding to the vibrations of O-H bonds involved in hydrogen bonding. Indeed, the difference spectrum demonstrates that the two Raman spectra


are almost identical. All features in the difference spectrum are very low in intensity and appear to result from a slight shift of spectral features between the two cocrystals. These shifts are mostly at the limit of the resolution in typical Raman experiments: 6 (565 cm-1), 5 (685 cm-1), 8 (1330 cm-1), and 6 (1615 cm-1). Surprisingly, the largest features in the difference spectrum are not located in the region affected by hydrogen bonding, but at wavenumbers between 600 and 1300 cm-1 that are related to intramolecular vibrations. This can tentatively be explained by the broadness of absorption bands corresponding to O-H groups that participate in hydrogen bonding, as well as by a significant difference in conformations of malic acid molecules in (tp) · (L-mal) and (tp) · (DL-mal). However, the low intensity of features in the difference spectrum makes any such assignment difficult and highly speculative. The Raman spectra exhibit more pronounced differences for the two cocrystals of tp with tartaric acid, particularly in the region around 3000 cm-1 where a shift of 15 cm-1 is observed for the feature near 2963 cm-1 (Figure 4a), tentatively assigned to an N-H bond stretching vibration. The shift is large in comparison to the ones observed in (tp) · (L-mal) and (tp) · (DLmal), and can be attributed to significant differences in the structure in the hydrogen-bonded network. In particular, the neighboring chains of interwoven rings in (tp)2 · (DL-tart) are connected via a pair of N-H · · · O bonds between coplanar tp molecules, whereas the analogous spiral motifs of (tp)2 · (L-tart) are connected via a single N-H · · · O bond between two tp molecules mutually inclined at an angle of 63° (Figure 4b,c). Other significant differences in the Raman spectra of (tp)2 · (Ltart) and (tp)2 · (DL-tart) appear to be caused by subtle shifts in spectral features of the two optical forms, typically close to the resolution of the experiment, for example, 4 (678 cm-1), 7 (1181 cm-1), 8 (1329 cm-1), and 7 (1430 cm-1). In order to completely assess the significance of observed differences between Raman spectra of chiral and racemic cocrystals, the Raman spectra of cocrystals that are similar in symmetry but different in chemical composition were compared (Figure 5). The Raman spectra of chiral cocrystals (tp) · (L-mal) and (tp)2 · (L-tart) exhibit obvious differences in the region of the

Figure 4. (a) Raman spectra of (tp)2 · (DL-tart) (bottom), (tp)2 · (L-tart) (middle), and the difference spectrum (top); (b) the hydrogen-bonding interaction between two neighboring hydrogen-bonded helices in (tp)2 · (L-tart); and (c) the analogous interaction between two neighboring hydrogenbonded rings in (tp)2 · (DL-tart).


Parrott et al.

Figure 5. Raman spectra of (a) (tp)2 · (L-tart) (bottom), (tp) · (L-mal) (middle), and the difference pattern (top); (b) (tp)2 · (DL-tart) (bottom), (tp) · (DL-mal) (middle), and the difference pattern (top).

spectrum that corresponds to hydrogen-bonding interactions, as well as in the fingerprint region. The differences are illustrated by the high intensities of shift-related features and the appearance of isolated absorption peaks in the difference spectrum (Figure 5a). Similar large differences are observed in the comparison of the racemic cocrystals (tp) · (DL-mal) and (tp)2 · (DLtart) (Figure 5b). Consequently, FT-Raman spectra can readily detect minor differences in chemical composition (i.e., replacement of malic acid with tartaric acid), but cannot readily distinguish between structurally similar cocrystals that exhibit only subtle differences in the structure of the hydrogen-bonded architecture (i.e., (tp)2 · (L-tart) and (tp)2 · (DL-tart) cocrystals) or isostructural cocrystals that differ predominantly in the conformation of constituent molecules (i.e., (tp) · (L-mal) and (tp) · (DL-mal) cocrystals). THz Spectra. The terahertz spectra of the two malic acid cocrystals, (tp) · (DL-mal) and (tp) · (L-mal), are clearly different at room temperature, although the features are fairly broad and poorly resolved (Figure 6a).44 Cooling resolves these differences further, and at 109 K the chiral cocrystal exhibits five distinct features in the central region of the THz spectrum, between 1.0 and 2.2 THz, while only three vibrational modes are detected for the racemic system (Figure 6b). Of these three features the peak at 1.28 THz in the racemic cocrystal originates from malic acid impurity in the sample, the presence of which is supported

Figure 6. Terahertz spectra of (tp) · (DL-mal) and (tp) · (L-mal): (a) recorded at room temperature; (b) recorded at 109 K and (c) calculated spectra.

by DSC and XRPD data. The difference in the number of spectral features attributable to each cocrystal reflects the influence of space group symmetry on THz spectra. The structure of each cocrystal contains eight molecules per unit cell, leading to 45 intermolecular optical vibrational modes, whose frequencies are expected to fall in the range from ∼0.5 to 6 THz. Whereas all of these can in theory be observed in the


Figure 7. Terahertz spectra of (tp)2 · (DL-tart) and (tp)2 · (L-tart): (a) recorded at room temperature; (b) recorded at 109 K; and (c) calculated spectra.

THz spectrum for (tp) · (L-mal), only 21 are allowed by the selection rules for (tp) · (DL-mal). Clearly, only a fraction of the allowed intermolecular vibrational modes are observed in practice, due to small absorption intensities, overlapping peaks, and the limited frequency range of the actual THz-TDS experiment. However, the influence of symmetry is nevertheless apparent, with fewer observed features in the spectrum of (tp) · (DL-mal) than (tp) · (L-mal). Although the structural differences between (tp)2 · (L-tart) and (tp)2 · (DL-tart) are greater than in the malic acid systems, differences in the THz spectra are less pronounced here. The terahertz spectra of L- and DL-tart cocrystals acquired at room temperature (Figure 7a) show that the two cocrystal systems


can be distinguished by THz-TDS: the chiral form, (tp)2 · (Ltart), exhibits an additional spectral feature at 0.84 THz, which is not present in the spectrum of (tp)2 · (DL-tart). As with the malic acid systems, a sharpening of the spectral features is observed in the terahertz spectra as the temperature is lowered to 109 K (Figure 7b). The extra peak in the chiral cocrystal is at 0.90 THz in the low temperature spectrum, while the spectrum of its racemic analogue still lacks any distinct features in this region. Both cocrystals exhibit a similar pattern of absorption features in the range 1.2-1.7 THz. In (tp)2 · (L-tart) this pattern comprises two absorption peaks at 1.28 THz and 1.57 THz, that appear blueshifted in (tp)2 · (DL-tart) at 1.37 THz and 1.68 THz. At slightly higher frequencies, we observe absorptions at 1.78 THz and 1.85 THz in the (tp)2 · (DL-tart) and (tp)2 · (Ltart) spectra, respectively; this absorption is much stronger in the (tp)2 · (L-tart) spectrum. In order to understand the differences in the terahertz spectra, lattice energy minimization, and lattice dynamics calculations were performed for the two pairs of cocrystals. We used rigid molecule calculations here so that a high quality intermolecular model potential could be applied. Rigid molecule lattice dynamics would not be suitable if we were interested in fully characterizing the THz spectra, because of the likely importance of the mixing of inter- and intramolecular motions. However, to give a qualitative understanding of the differences in the observed spectra, we are only looking for differences in the types of vibrational modes. For (tp) · (DL-mal) and (tp) · (L-mal), the 45 rigid molecule vibrational modes are calculated to fall in the range from 1.15 to 5.15 THz (38.5 to 171.9 cm-1) and 0.90 to 5.87 THz (30.1 to 195.8 cm-1), respectively. For (tp)2 · (DLtart) and (tp)2 · (L-tart), the six molecules in the unit cell give 33 lattice modes, whose calculated frequencies are in the range from 0.95 to 5.87 THz (31.7 to 195.8 cm-1) and 1.01 to 5.39 THz (33.7 to 179.8 cm-1), respectively: all of these are THz active for the chiral cocrystal, but only 15 of these are THz active for the racemic form (Figures 6c and 7c). The best agreement between calculated and observed spectra is seen for (tp)2 · (L-tart) (Figure 7). The relative frequencies and intensities of the calculated features are in reasonable agreement with the 109 K observed spectrum, but there is an overall shift of the calculated features to higher frequencies, by between 0.1 and 0.4 THz. The THz spectra of the other three crystals are less well reproduced in the calculations. The calculations for (tp)2 · (DLtart) do produce modes at the same frequencies as the strongest features in the calculated (tp)2 · (L-tart) spectrum, one just below 2 THz, and another feature centered on 2.25 THz (which results from two overlapping calculated modes at 2.21 THz and 2.28 THz). Assuming the same shift to higher frequency in the calculations as seen for (tp)2 · (L-tart), we might provisionally associate these calculated features with the observed peaks at 1.68 and 1.78 THz (at 109 K). However, the calculated feature at 1.48 THz would then have to be associated with the observed 1.37 THz feature, but with a badly overestimated absorption intensity. Given the level of agreement between calculations and the observed spectrum, these assignments are clearly only tentative. Nevertheless, it is still informative to investigate the nature of the molecular motions associated with the calculated modes. In particular, we examined the calculated modes tentatively assigned to those observed in the 1.2-1.7 THz range. From the similarity in patterns of the observed spectra, and given that the cocrystals display similar hydrogen-bond architectures, it would be tempting to assume that the molecular motions


Parrott et al. Table 2. Calculated Intermolecular (Einter), Intramolecular (Eintra) and Total (Etotal) Energies (all in kJ mol-1) for Cocrystals of tp Eintera

Eintrab

Etotalc

(tp) · (L-mal)

-247.5

-210.4

(tp) · (DL-mal) (tp)2 · (L-tart) (tp)2 · (DL-tart)

-249.9 -361.5 -369.8

molecule 1: +31.9 molecule 2: +42.2 +32.0 +18.0 +2.9

cocrystal

-217.9 -343.5 -366.9

a The intermolecular contribution to the crystal lattice energy, calculated from the exp-6 + distributed multipoles model. b The acid molecule intramolecular energy, given relative to the overall lowest energy fully optimized conformation. The theophylline molecular energy is assumed to be the same in all cocrystals. c The total energies are the sum of inter- and intramolecular energies (column 2 + column 3).

Figure 8. Calculated lattice modes for (a) (tp)2 · (L-tart) at 1.93 THz and (b) (tp)2 · (DL-tart) at 1.97 THz. The equilibrium structures are shown in color, with displacements along lattice modes in grayscale. Dashed lines indicate hydrogen bonds.

corresponding to these modes are similar in the chiral and racemic cocrystal. However, the calculated lattice modes in this region reveal that the absorption bands constituting the pattern belong to very different molecular movements in each cocrystal, examples of which are depicted in Figure 8. In the case of (tp)2 · (L-tart), the three modes involve O-H · · · O hydrogen bond stretching between tart molecules, along with stretching (1.71 THz), twisting (1.93 THz), and bending (1.99 THz) of hydrogen bonds between tp and tart (Figure 8a). For (tp)2 · (DL-tart) the calculated features between 1.4 and 2.4 THz result from a 1.48 THz vibration involving rotation of tp molecules and bending of their hydrogen bonds to tart, and higher frequency features (at 1.97 THz and overlapping modes at 2.21 and 2.28 THz) that are dominated by bending and stretching of hydrogen-bonded tp-tp dimers (Figure 8b). Thus, the calculations suggest that the similarity of patterns in THz spectra of (tp)2 · (L-tart) and (tp)2 · (DL-tart) is accidental and that, without the lattice dynamics calculations, we might have misinterpreted similarities in the spectra as resulting from related lattice modes in the two crystals. Indeed, previous studies have highlighted the difficulties in making direct links between structure and THz spectra: vibrations involving similar distortions of intermolecular interactions (e.g., stretching of hydrogen bonds) do not have characteristic frequencies, but are strongly influenced by the secondary interactions in the crystal.8 At the lowest frequencies, the calculated spectrum for (tp)2 · (L-tart) shows a strong peak centered at 1.05 THz, which results from the overlap of three THz active modes: one strongly absorbing mode at 1.04 THz between two weaker modes at 1.02 and 1.10 THz. Visualization of the calculated molecular displacements revealed motions of the tp and tartaric acid molecules combining to produce bending of the hydrogen bonds connecting the molecules of tp and L-tart. A similar motion of

molecules in (tp)2 · (DL-tart) provides a calculated mode at 0.96 THz, having a much lower predicted absorption intensity. Thus, the computational results provide a rationalization of the observed differences in the measured spectra; the dipole change related to this hydrogen bond bending is too small for the mode to stand out from the baseline in the spectrum of the racemic (tp)2 · (DL-tart), but the combination of three modes in the less symmetric chiral cocrystal produces the visible peak near 1 THz. There is more limited agreement of the calculated and observed spectra of the malic acid cocrystals (Figure 6). For (tp) · (DL-mal), the positions of the strongest observed features (at 109 K) do reasonably match the two strongest calculated features: one peak at 1.15 THz and a strongly absorbing set of four modes between 1.7 and 2.0 THz. The calculations clearly show many more vibrational modes contributing to the observed spectrum of (tp) · (L-mal) than (tp) · (DL-mal), although there is otherwise poor agreement between the calculated and observed spectra of (tp) · (L-mal). The poor modeling of the dynamics in (tp) · (L-mal) is perhaps due to the conformational strain of the malic acid molecules in the chiral cocrystal.30 The strained molecular conformation, which must be stabilized by intermolecular interactions, would amplify the limitations of the rigidmolecule approach taken in these calculations. Coupling of the lattice modes with intramolecular modes (specifically those around the strained torsion angles in malic acid) is probably quite important here. The computational results allowed us to further analyze the importance of the conformational strain in the cocrystals and provide insight into the balance between inter- and intramolecular energies. The results indicate that one of the two crystallographically independent L-malic acid molecules in (tp) · (L-mal) is distorted to a high energy conformation so that it can fill the role of the D-malic acid in (tp) · (DL-mal). As a result, the intermolecular contributions to the lattice energies were found to be only slightly different for the two malic acid cocrystals (Table 2). However, there is an important difference in intramolecular energies: the energy of one of the L-malic acid molecules in (tp) · (L-mal) is +10.20 kJ mol-1 higher than the conformation found in (tp) · (DL-mal). Overall, the calculations indicate that the (tp) · (L-mal) structure is 7.52 kJ mol-1 less stable than the (tp) · (DL-mal) structure. In the tartaric acid systems, the racemic cocrystal is again more stable, but the difference in stability is more evenly distributed between interand intramolecular contributions; the acid adopts a higher energy confirmation in the chiral cocrystal and the resulting intermolecular interactions are less stable than those in the racemic structure. Conclusions Our work has highlighted the difficulties of well-established solid-state characterization techniques such as XRPD and


vibrational spectroscopy in the mid-infrared region of the electromagnetic spectrum to differentiate between chemically and structurally similar molecular cocrystals. Due to the sensitivity to structures over length-scales greater than intramolecular bond distances THz-TDS is able to reveal clear differences between the racemic and chiral cocrystals despite their isostructurality, especially at lower temperatures. In the cocrystals of tp and malic acid the pronounced differences in the terahertz spectra were tentatively attributed to symmetry breaking in the chiral cocrystal due to the conformational stress in one of the L-mal acid molecules. The differences in the results of the characterization of the theophylline and malic acid cocrystals by XRPD and Raman were less pronounced compared to the THz-TDS experiments. However, both established techniques were very good in distinguishing between the cocrystals formed by tartaric acid and tp. Our results confirm that while there is no single technique for a conclusive solidstate characterization of organic molecular crystals THz-TDS has a strong potential to cover a broad range of characterization challenges due to its inherent sensitivity to crystal structure. Lattice dynamics calculations using a rigid molecule approximation gave some insight into the differences in lattice vibrational modes between the structures. The agreement of the simulated spectra with experiment is not convincing enough to confidently assign specific molecular motions to the observed THz features. The discrepancies are probably due in large part to coupling of the intramolecular modes (specifically those around the strained torsion angles in malic acid) to the lattice modes, which is not treated in these calculations. Nevertheless, the computational results do agree with some of the observed differences in the THz spectra, and analysis of the calculated vibrational modes gives an idea of the types of motion involved in the observed spectral features. One thing that the calculations show is that interpretation of differences in the spectra is not straightforward; the types of molecular motions are complex and the molecular motions are quite dissimilar in the different crystal forms. There is a clear need for advances in both the computation methods and in ways to analyze the resulting modes. The much more computationally demanding periodic density functional theory lattice dynamics approach is one route to improved computational results.45,46 A combination of the THz-TDS results with reliable computational simulation could help elucidate a better understanding of solid-state molecular dynamics. Indeed, the ability to probe directly lattice dynamics which represent vibrations of the whole molecule, rather than just the vibrations of single functional moieties within molecules, as is the case in IR-spectroscopy, makes THz-TDS a very powerful tool for the analysis of the structure of complex solid-state materials with potential advantages over existing techniques. We believe that the ability to differentiate crystalline molecular solids that exhibit only subtle differences in crystal structure will become increasingly important with the increasing interest in applications of multicomponent crystals, as the propensity of such materials to form isostructural solids appears to be higher than typically observed for single-component molecular crystals.47,48 Acknowledgment. G.M.D. thanks the Royal Society for funding via a University Research Fellowship. T.F. and W.J. thank the Pfizer Institute for Pharmaceutical Materials Science for funding. E.P.J.P., J.A.Z., and L.F.G. would like to acknowledge EPSRC and RCUK Basic Technology Grant EP/E048811/1 for funding.


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