THz Fingerprints of Short-Range Correlations of Disordered Atoms in

Subscriber access provided by UNIV OF LOUISIANA

A: Spectroscopy, Molecular Structure, and Quantum Chemistry

THz Fingerprints of Short-Range Correlations of Disordered Atoms in Diflunisal Feng Zhang, Houng-Wei Wang, Keisuke Tominaga, Michitoshi Hayashi, and Tetsuo Sasaki J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00580 • Publication Date (Web): 30 Apr 2019 Downloaded from http://pubs.acs.org on April 30, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

THz Fingerprints of Short-Range Correlations of Disordered Atoms in Diflunisal

Feng Zhang,1 Houng-Wei Wang,2 Keisuke Tominaga,1* Michitoshi Hayashi,2* Tetsuo Sasaki3 1Molecular

Photoscience Research Center, Kobe University, Nada, Kobe, 657-0013,

Japan 2Center for Condensed Matter Sciences, National Taiwan University, 1 Roosevelt Rd., Sec. 4, Taipei, 10617, Taiwan 3Research Institute of Electronics, Shizuoka University, Hamamatsu, Shizuoka, 4328011, Japan

The corresponding authors’ email addresses: [email protected] (K. Tominaga) [email protected] (M. Hayashi)

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract This work proposes a THz spectroscopy approach to the investigation of one of the outstanding problems in crystallography—the structure analysis of a crystal with disorder. Form I of diflunisal, in which the two ortho-sites on one phenyl ring of diflunisal show occupational disorder, was used for an illustration. THz radiation interacts with the collective vibrations of correlated disorder, thus providing a promising tool to examine the symmetry of short-range correlations of disordered atoms. Through a thorough examination of the selection rule of THz vibrations in which the disordered atoms are involved to different extents, we deduced that only four short-range correlation possibilities of disorder exist and all of them display unambiguous fingerprint peaks in the 50-170 cm-1 frequency region. We finally proposed an alternating packing model in which the correlation lengths of disorder are on the nanometer scale.

2


Page 2 of 43

Page 3 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1. Introduction

For determining atomic positions of a molecular crystal, X-ray crystallography has been the mainstay for 100 years. Despite all the advances, two problems remain challenging. One is that hydrogen atoms are invisible owing to their weak interactions with X-ray.1 The other is that the determination of the distribution of disordered atoms is far from a routine task. The first problem is in fact limited to X-ray and electron beams since hydrogen atoms can be seen with recourse to neutron scattering. The second problem is, however, inherent in any form of the diffraction methodology. The central issue of the structural analysis of disorder is determining the correlations of disordered atoms. Since the diffraction methods collect signals as a time- and space-average, correlated disorder do not contribute to Bragg diffractions but give rise to diffuse scattering of X-ray. To our best knowledge, few schemes have been generally accepted for building a disorder model from the diffuse-scattering patterns.2-3 Shedding light on disorder in other experimental dimensions is of the essence.

THz spectroscopy is a promising complementary technique to X-ray. THz radiation excites the collective vibrations, typically in the 0.1-10 THz region, of a system.4-5 The collective excitations have two characteristics that can be exploited to tackle the foregoing 3



problems. First, structural information on the position of the hydrogen atoms in molecular or polymer crystals is completely reflected on account of the collective nature of the excitation. In a previous work,6 we have illustrated the capability of THz spectroscopy to determine the positions of hydrogen atoms that play a crucial role in leading to the breaking of the helical symmetry in a polymer crystal. Second, the selection rule of the collective excitation is determined by the symmetry associated with atoms’ long-range packing.5, 7-11 The most fundamental level of information on order/disorder of atomic arrangement can in principle be deduced via examining the selection rules of THz modes. By comparison, the FTIR and Raman spectroscopy measurements probe vibrations localized in functional groups or structural segments and thus do not reflect the direct structural information on the long-range packing. NMR spectroscopy has been another established approach for the study of disorder in solids.12-14 NMR measures the chemical shifts of atom probes sensitive to the local environment, while THz spectroscopy probes directly the spatially collective vibrational information. The THz approach therefore detects atomic information on a different scale from the NMR measurements.

Let us first presume the existence of a perfect crystal where long-range translational symmetry generates the momentum representation, phonon modes are consequently a well-defined physical property. The selection rule imposed by the conservation of energy 4


Page 4 of 43

Page 5 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and momentum in the interaction between phonons and light restricts that phonon modes at only gamma point are optically active; thus we call a set of both conditions as the gamma-point selection rule. If we perform THz measurements at temperature as low as possible (e.g. 10 K) to reduce the thermal-induced line shape broadening, we would often observe discrete and sharp THz peaks.15-18 We then consider to introduce disorder to a limited number of atomic sites of every molecule in the crystal, and the disordered sites are too few to affect the nature of all the vibrational modes in a significant way. Alternatively, the influence of the disorder to a certain THz mode depends on the extent to which it is relevant to this mode. The more the disordered atoms are involved in the motion of the THz mode, the more remarkable variations are expected to be caused to the frequency and line shape of this mode, and vice versa. Our previous works have revealed that THz modes of most molecular crystals have three sorts of origins, pure intermolecular vibrations (translation motion of the center of mass (COM) of each molecule and libration motions about the three principal axes of each molecule), pure intramolecular interactions, and the mixing between these two.19-24 Precisely, it is the translational symmetry of the potential surfaces associated with the three types of THz vibrations that dictates the gamma-point selection rule. The introduction of disorder to the positions of certain atoms, depending on the extents to which the atoms contribute to the intermolecular and 5



intramolecular interactions, will break or conserve the translational symmetry of the potential surfaces governing the three sorts of vibrations. THz spectroscopy in fact provides us with at least three different perspectives from which one can cast light on the spatial distributions of disordered atoms. This is an inherent advantage of THz spectroscopy as applied to the structure analysis of disorder.

We will adopt one of the simplest occupational disorder systems, Form I of diflunisal, as a demonstration. Diflunisal is a chiral molecule composed of a biphenyl backbone with 2,4-difluoro-substitutions on one phenyl-ring and 4-hydroxyl and 3-carboxylic-acid substitutions on another phenyl-ring. The previous X-ray studies 25-29 have reported that diflunisal has at least six polymorphs depending on the solvents used for crystallization. In a crystallization process from toluene leading to Form I of diflunisal, the fluorinecontaining ring can exist in two configurations related by the two-fold flipping freedom about the single bond connecting the two phenyl rings.29 The pair of hydrogen and fluorine, occupying the two 2, 6-ortho sites of the fluorine-containing ring, are disordered with an occupancy factor of 0.5 for each. The disordered ortho sites are highlighted in light blue in Fig. 1a and 1b. A pair of enantiomers forms an SR dimer via the carboxylic acid hydrogen-bond connection and composes the smallest building block. Each SR dimer has four disordered sties specified as 2S6S2R6R where the superscripts describe the 6


Page 6 of 43

Page 7 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


chirality of the subject enantiomer. The pairwise occupations of 2S6S and 2R6R by fluorine and hydrogen result in four configurations A, B, C, and D, corresponding to the combination of HFHF, HFFH, FHHF, and FHFH, respectively. Therefore, the essence of the structure analysis of disorder is to determine the spatial distributions of the four types of SR-dimers. SR-dimers are connected via the R22 (4) phenoxy hydrogen-bond motifs to form an SR-dimer column (H-bond chain) as indicated by the purple box in Fig. 1a. At the both vertical edges of the SR-dimer column, weak C-H…F-C hydrogen-bond (F and H in yellow and white, respectively) and dispersion-force connects this column with the neighboring SR-dimer columns, forming a sheet-like layer. The sheet-like layers further pile up via the inter-layer C-H … F-C hydrogen-bond and dispersion-force connections to form the 3D crystal structure as shown in Fig. 1b. We stress here that the disordered hydrogen and fluorine atoms do not participate in any inner-layer hydrogen bonds but play a determinate role in the formation of the inter-layer connections. Refer to Fig. S1 for the 10 inter-layer connection patterns formed via the mutual stacking of the four types of dimers.

The general idea of a theoretical analysis of disorder consists of sampling a configurational space large enough to reflect as closely as possible all the possible local disorders and defining the energetically probable configuration(s).30-35 For the molecular 7



crystal systems, to treat the whole set of configurations at the ab initio level demands however an unsustainable computational cost. Building a model under the guidance of experimentation is therefore of the prime importance. Once such a model that captures the very essence of disorder is established, it can be refined against the X-ray diffuse patterns using various least-square or evolutionary algorithms that have been routinely available.3 It is worth noting that although THz spectroscopy has been employed to characterize several disordered molecular systems,36-44 almost all the works use THz spectroscopy as merely an experimental criterion to evaluate the proposed structural models of disorder. To our best knowledge, none of them has illustrated the possibility that unambiguous information about disorder, in addition to that revealed by X-ray crystallography or NMR spectroscopy, can be extracted directly from the experimental evidence reflected in THz spectroscopy.

The crucial point of the disordered model investigated in this work is to represent the spatial correlations of the four types of SR-dimers. By correlations, we mean that the SRdimers show ordered arrangements in certain manners. Despite of the infinite possibilities of correlations of the SR-dimers, we can categorize the correlations into three classes which are schematically illustrated using a one dimensional model in Fig. 2. Class a represents the self-correlation of a certain SR-dimer and features the repetitive 8


Page 8 of 43

Page 9 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


arrangement of a unit cell containing the SR-dimer. Class b stands for the intercorrelations of the four types of SR-dimers A, B, C, and D and characterizes the repetitive arrangement of a unit cell comprised of a combination of the SR-dimers. Clearly, there are only four correlation patterns in Class a but infinite possibilities in Class b. Class c denotes the zero-correlations of the four types of dimers. Namely, the arrangements of A, B, C, and D are rather random and no repeating packing patterns appear. We shall elucidate that THz spectroscopy, through an interplay with the solid-state density functional theory (DFT), is capable of providing discriminating evidence to judge the existence of the three classes of correlations and to determine the correlation dimensions.

2. Results and Discussion

2.1 Static disorder

The previous X-ray measurement was performed at room temperature.27, 29 Since the diffraction approach measures the space and time average of a statistical distribution of atoms, the observed disorder can be either static or dynamic. The static disorder refers to the spatial distributions of dimers A, B, C, and D in the crystal and is a predetermined property when diflunisal crystallizes from its mother solution. The dynamic disorder happens if the thermal energy is high enough to activate the 2-fold flipping motions of 9



the fluorine-containing rings, and every molecule in the crystal is swiftly sampling two configurational states. As we have reported,22 the internal mode of diflunisal featuring the relative torsional motions of the two phenyl rings falls in the THz region. THz spectroscopy is therefore a sensitive probe of the dynamic flipping of the fluorinecontaining rings.22 We expect to observe abrupt changes of the frequencies and line shapes of certain THz peaks when the critical temperature is reached. To this end, we first lowered temperature down to 10 K, at which the dynamic disorder is undoubtedly minimized. We then raised temperature gradually to examine the variations of THz peaks. As shown in Fig. S2, the frequencies of all the observed THz peaks shift smoothly towards the lower-frequency sides and their intensities decrease smoothly in the course of temperature rising, implying that the disorder is not dynamic but static.

2.2 Three frequency regions

THz spectra recorded at 10 K are shown in the upper panel of Fig. 3. According to the line shapes of the absorption peaks, the whole THz frequency region (10 cm-1 ~200 cm-1) divides into three parts, 10-50, 50-175, and 175-200 cm-1, being designated as Regions I, II, and III, respectively. Regions I and III feature discrete and sharp peaks a and b, and i, respectively, that can be perfectly fitted with Lorentzian line shapes as shown 10


Page 10 of 43

Page 11 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


by the red lines in the upper panel of Fig. 3. Characteristics of Region II are six broad peaks (c, d, e, f, g, and h) that cannot be satisfactorily fitted with Lorentzian line shapes as shown in Fig. S3. Note that the spectra’ base lines in the three frequency regions have been shifted for ease of clarity. In order to examine whether the disorder affects the baselines or not, we use the spectra of Form III of diflunisal as a reference because the occupational disorder does not exist in this polymorphs at all. Comparing the spectra of Forms I and III in Fig. S4, one can see that these spectra display almost overlapping baselines in the whole THz frequency region, implying that the occupational disorder does not make a notable contribution to the baselines and we can safely ignore the part of experimental information.45-48

Let us start with the structure analysis by discussing Regions I and III. The appearance of a well-defined Lorentzian peak implies the collective excitation of all molecules in a crystal grain at the center frequency and with a lifetime determined by the line width at the half maximum. As a result, certain symmetry must exist over distant molecules without direct interactions; in this case, the molecules vibrate with fixed phase relations and consequently the frequency dispersion does not happen. For the molecular solid under question, the symmetry is certainly translational invariance. The sharp Lorentzian shapes in Region I and III suggests that the disordered atoms must be of 11



Page 12 of 43

marginal importance to the forces giving rise to vibrations in both regions. Thus, the translational symmetry of the associated potential surfaces is conserved. In other words, we assume that the THz modes observed in Regions I and III should be reproduced if ignoring disorder, i.e. using a perfect crystal model. Note that the disorder results from the ortho fluorine. If we replace the fluorine atom with a hydrogen atom, the two 2,6ortho sites become equivalent with respect to the 2-fold flipping symmetry of the fluorinecontaining phenyl ring as shown in Fig. 1a. In this case, the disorder is eliminated and the translational symmetry over long range emerges. Consequently, the concept of phonon modes becomes well-defined and the gamma-point selection rule holds. It is worth stressing that we propose in this step a hydrogen substituted variant of diflunisal for generating a perfect packing structure in which the translational symmetry is conserved. Although the perfect crystal model simplifies the actual packing structures of this disordered system, it reflects the actual characteristics of the vibrational modes in Region I and III according to the information revealed directly from the experimental observation.

The gamma point corresponds to the long-wave limit and does not involve the translation operator. Thus, the gamma-point selection is determined by the symmetry (or the so-called factor-group symmetry) of the repetitive units.8,

11

On this account, the

crucial point of constructing a perfect crystal model is the determination of symmetry of 12


Page 13 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


its repetitive units. There are three cases to be considered. The first is a unit cell containing a dimer where the inversion symmetry Ci between the two enantiomers is conserved, and the crystal possesses P 1 space group symmetry. The Ci symmetry gives rise to two representations Au and Ag; the former is IR active and the latter is IR inactive. The second case represents a Ci-symmetry-breaking case of the first one; the crystal possesses in consequence P1 space-group symmetry. Because of the relaxation of the symmetric restriction, all the modes at the gamma point except for the three acoustic ones are IR active. The third is a unit cell composed of more than one dimer. The Ci symmetry is however not conserved in such a unit cell, since P 1 allows at most two molecules in each repetitive cell. The crystal possesses consequently P1 space-group symmetry.

2.3 Exclusion of Classes b and c

We consider first the crystal model with the highest order of symmetry— P 1 . The unit-cell structure determined by X-ray was adopted to construct the initial geometry,29 in which all the four ortho sites 2S6S2R6R are occupied by hydrogen. The geometry was optimized under the periodic boundary condition and by conserving the P 1 space group symmetry. We compare the optimized crystal structure with that determined in experimentation against five criteria: unit cell parameters, covalent bond lengths and 13



corresponding angles, intramolecular and intermolecular H-bond lengths, weak CH …F bond lengths formed between ordered atoms, and layer-layer stacking distance. As shown in Table S1, the perfect-crystal model consistently reproduces the crystals structure in all the five respects with deviations tolerated by experimentation. The calculated IR active modes are shown in the lower panel of Fig. 3. One may immediately agree that the two peaks a and b in Regions I and the one peak i in Region III have all been satisfactorily reproduced against the criteria of frequency and intensity (note that we are concerned with the reproduction of the relative intensities of the THz peaks in the examined frequency region). Refer to Fig. 3b and 3c for the direct comparisons of experiment and theory with respect to frequency and intensity, respectively. Note that the calculation underestimates the frequency of peak i by 7.7 cm-1. The relative error against the experimental value is about 4.1%, which is tolerated by experimentation.

We then consider a crystal model in which the P 1 symmetry is not conserved. The initial unit-cell geometry was optimized under the periodic boundary condition and with P1 space group symmetry, i.e. conserving the translational symmetry but relaxing the Ci factor-group symmetry. As shown in the left-lower panel of Fig. S5, an additional peak appears in Region I. It is reasonable to predict that the third case, which permits the inclusion of more than one dimer in one unit cell, would allow more peaks appearing in 14


Page 14 of 43

Page 15 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Region I and III because of the involvement of more vibrational freedoms in one unit cell. The result provides firm evidence that the conservation of P 1 space-group symmetry is an indispensable element if the disorder is ignored. In the absence of disorder, the dimers A, B, C, and D have the identical configuration and the two enantiomers involved conserve Ci inversion symmetry. Hence, the symmetry of Class a, representing the repetitive arrangement of the dimers, conforms to

P1

space-group symmetry.

Nevertheless, P 1 space-group symmetry allows the accommodation of at most two molecules in each repetitive cell. Class b, representing the packing of unit cells that contain more than two molecules, is thereby forbidden. And Class c, representing the random arrangement of the dimers A, B, C, and D, is excluded for the same reason.

We discuss the marginal importance of the disorder to vibrations in Regions I and III and justify the perfect-crystal model employed in both regions. Using a previously developed mode-analysis method, 19, 23 we characterize each mode in the THz region as a combination of three forms of vibrations with distinct origins: intermolecular translation of the COM of each constituent molecule and librations around the principal axes of each molecule, and intramolecular vibration. The percentage contributions of the three components to the vibrational energies of THz modes in Regions I and III are shown in the left and right panels of Fig. 4, respectively. The peaks a and b in Region I feature 15



predominately intermolecular librations (note intermolecular translations in the

Page 16 of 43

P1

space group do not have IR activities11), while the peak i in Region III an intramolecular vibration. At gamma point, all the unit cells in the lattice vibrate in phase. Within each unit cell, the two enantiomers, R and S, undergo the relative, precisely, in-phase and outof-phase, vibrations. THz modes in Region I are therefore controlled by the intermolecular interactions between the two types of molecules with opposite chiralities in the lattice. As shown in Fig. 1a, the enantiomers are connected via the inner-layer strong hydrogen bonds and week C-H…F-C bonds. Clearly, the disordered atoms do not participate in the two types of interactions at all, and they are involved in only the interlayer C-H…F-C bonds which connect molecules with identical chirality (Fig. S1). We thereby conclude that disorder does not contribute to the hydrogen-bond interactions important to Region I. Regarding the dispersion interactions between the enantiomers, the contribution of the disordered atoms to the total dispersion force is on average 4/52 (~7%,) where the “4” is the number of the disordered atoms in one diflunisal molecule and the “52” the total number of atoms. We would argue that this small contribution to the overall intermolecular interactions (including hydrogen bonds, dipole-dipole interactions, dispersion force, and so on) is trivial. Peak i in Region III represents the out-of-phase vibrations of an internal mode 16


Page 17 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


whose vibrational pattern is shown in Fig. 5.

We concern the extent to which the

hydrogen atoms on the 2,6-ortho sites are involved in this mode. To this end, we analyze the relative strengths of the displacement amplitudes  m of the hydrogen atoms on the two disordered sites with respect to the root-mean-square displacements (RMSD) of all atoms in one molecule according to Equation (1), respectively.

m

releative strength  1 26

 i1 i2 26

,

(1)

where the subscript m represents the hydrogen atoms on either the 2- or 6- ortho site.

 i is the displacement vector of the ith atoms in the internal mode, and 26 is the number of the atoms in one diflunisal molecule. The analysis shows that the relative strengths of

 ’s of the two 2- and 6-hydrogen are 0.82 and 0.45, respectively, both lower than the average 1, indicating their marginal importance to this motion. On this account, introducing disorder to these sites barely affect the nature of this mode. In summary, we conclude that the atoms on both the 2- and 6-ortho sites have trivial contributions to the potential surface that defines the vibrations in Regions I and III. Introducing disorder to the pairs of the two sites marginally changes the origins of vibrations, and thus, the perfect-crystal model is justified.

17



Page 18 of 43

2.4 Coexistence of the four correlation patterns in Class a

We next examine the applicability of the perfect-crystal model to reproducing the THz-spectral features in Region II. As shown in the middle-lower panel of Fig. S5, the perfect-crystal model with P 1 space-group symmetry predicts six IR active modes in this Region, all of them can find one-to-one correspondence with the resolved THz peaks c, d, e, f, g, and h. Thus we assume that the perfect-crystal model has reproduced the peak positions in Region II. Our concerns are nevertheless that the peak-broadening feature has not been reproduced by using the perfect-crystal model. As shown in Fig. S6, the modes predicted by the perfect-crystal model result from the mixing between intermolecular

and

intramolecular

vibrations,

although

the

contributions

of

intermolecular motions decrease rapidly with the increase of frequency. According to the discussion in the last section, disorder is barely correlated with the intermolecular vibrations at gamma point. We then focus on the analysis of the relative strengths of the hydrogen atoms on the 2- and 6-ortho sites to the intramolecular component of every mode according to Equation (1). As shown in Fig. S7, the 2-ortho site has large relative strengths (generally beyond the average—1) in modes c, d, e, and f, and the 6-ortho site has large relative strengths in modes c and f.

Therefore, these modes are sensitive to the

substitution atoms in both the 2- and 6-ortho sites. Replacing any hydrogen atom in the 18


Page 19 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


two site with one fluorine atom will notably change the frequency of the corresponding molecule and destroys the collective nature of a phonon mode predicted by the perfectcrystal model. Disorder is therefore a non-ignorable factor for discussing vibrations in Region II, and we have to take into account the real correlations of disorder in theory.

The discussion about Regions I and III has excluded the correlation possibilities in Class b and c. We verify this conclusion by specifically examining a case in Class b which represents a periodic packing of a supercell constructed through a lateral arrangement of the four dimers A, B, C, and D (Fig. S8a). As shown in Fig. S8b, this packing model reproduces an overwhelming number of characteristic THz peaks in Region II, especially in the 160-175 cm-1 frequency region, than that appear in the experimental spectrum. We thus consider only the four correlation patterns in Class a. When these correlation patterns coexist in a crystal, they reduce the correlation length of each other and result in the shortrange order. Using the one-dimension packing as an illustration, one prototype is CCCCCAAAAABBBBBDDDDD. For a certain phonon mode in Region II, its characteristic frequency in one segment, i.e. AAAAA, is notably different from others, owing to the influence of the distinct substitutions on the disordered sites of the unit cell. The phonon mode meets a boundary at the interfaces of the segments and is effectively confined within a dimension of d, which defines the length of the segment under question. 19



As a result, an uncertainty is caused to the wave vector of the phonon through the relationship

k 

1

2

d . This situation implies the relaxation of the gamma-point

selective rule and all the phonon modes in the vicinity k of the gamma point become optically active.49-52 This mechanism explains the observed broad line shapes in Region II.

According to picture depicted above, we examine the gamma-point IR modes of the four correlation patterns in Class a under PBC. As shown in Table S1, all the four models satisfactorily reproduce the unit cell parameters, covalent bonds, dihedral angles of the biphenyl backbone, intramolecular and intermolecular H-bonds, weak CH … F bonds formed between ordered atoms, and layer-layer stacking distance. It implies that the variation of the four correlation patterns does not induce significant changes to either intramolecular or intermolecular interactions. As a result, all the atoms, expect for the disordered hydrogen and fluorine, display determined positions in the X-ray observation. The normal mode simulation results are shown in the lower panel of Fig. 3. By averaging the intensities of the THz modes of the four correlation patterns, one may agree that, the six resolved peaks in Region II have been reproduced against the criteria of both frequency and intensity. We can unambiguously assign the peaks d, e, and f to unit cells A, B and C, and D, respectively, and we can explain the other three peaks c, g, and h as 20


Page 20 of 43

Page 21 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the average results of the four unit cells. The characteristics of all the simulated THz modes are shown in the middle panel of Fig. 4, and the vibrational pattern of the intramolecular component of each mode is shown in Fig. 5. In the 80-105 cm-1 frequency region where the three peaks d, e, and f are located, the four unit-cell configurations give rise to vibrations with completely distinct origins in terms of the mixing ratios of the intermolecular and intramolecular vibrations. Furthermore, regarding the intramolecular vibrations, the hydrogen atoms in the 2- or 6-ortho sites of the unit cells A, B and C, and D all have extraordinary relative strengths as shown in Fig. 6. The disordered atoms therefore play an important role in the determination of the nature of normal modes in the 80-105 cm-1 frequency region. This frequency region shows the fingerprint peaks for justifying the existence of the four correlation patterns in Class a. For the other frequency regions where the peaks c, g, and h are located, the corresponding vibrations of the four correlation patterns have very similar origins (Fig. 4). The disorder however induces notable frequency dispersions between them.

Owing to the strong influence of disorder on vibrations in Region II, it is not possible to excite collective vibrations throughout a whole crystal grain but within each segment of short-range order. Phonon wave-vectors are herein relaxed. An observed line shape in fact represents a superposition of phonon modes predicted by a perfect crystal model in a 21



certain area of the gamma point. Since an optical phonon mode has normally negative frequency dispersion,53-55 the additional optical transitions away from the gamma point obviously lead to a red shift of its mean position and concomitant broadening of the line shape (Fig. 3).

2.5 Dimensions of correlation

The dimensions of the phonon-confinement have three possibilities: one-, two-, and three-dimensions. The first two cases are anisotropic in space, while the last one isotropic. The one dimensional case corresponds to the thin film confinement in which the layer(s) composed of a certain type of unit cells is confined in the normal direction of layer; the two dimensional case corresponds to the column confinement in which the H-bond chain(s) is confined in the radical direction. If the one and two dimensional confinements exist, the gamma-point selection rule holds for the phonon modes whose vectors lay either within the layer plane or along the column direction. Sharp peaks are therefore expected to appear in Region II. The absence of such phenomena implies that the low dimensional confinements are ignorable and the three dimensional confinement is the dominant presence.

As the four correlation patterns in Class a are mutually confined in three dimensions, 22


Page 22 of 43

Page 23 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


they would adopt an alternating packing model as shown in Fig. 7. The horizontal direction represents the direction of H-bond chains, and the vertical direction is one of the other two directions—either the layer-extending or layer-stacking direction. A segment in a certain color represents the short-range periodic packing of a certain unit cell out of A, B, C, and D. These segments alternate along the H-bond-chain direction and are connected without intervals via the R22 (4) phenoxy hydrogen-bond motifs, they also alternate in other two directions via the weak C-H…F-C hydrogen-bond and dispersion force connections (Figs. 1a and S1). This alternating packing model, we propose, would represent the essence of disorder in this crystal. Regarding the average length of the four correlation patterns, it should be considerably shorter than the typical wavelength  of the THz wave transmitting in the crystal grain. The refractive index of Form I of diflunisal is around 1.68 (Fig. S9). Taking the THz radiation at 3 THz for example,  is around 60

. Based on the previous study49-52 of inorganic nanocrystals where the phonon-

confinement model is applicable, we estimate the average correlation length is in the order of several or tens of nanometers. In fact, one can quantitatively reproduce the dispersion relations of phonons of the four correlation patterns under PBC and obtain their vibrational densities of state in the vicinity k of gamma point through the relation

k  1 2 d . One is then allowed to deduce the distributions of the average lengths d of the 23



four correlation patterns by fitting the THz absorption outlines in Region II. The computational demand to reproduce the dispersion relationships of phonons at the accuracy level adopted in this work is nevertheless unaffordable. It is rather realistic to work out the problem in the real space, i.e. to fit the X-ray diffuse patterns on the basis of this packing model. One can in this way finally present a detailed picture of the spatial distributions of the four correlation patterns.

3. Methods

3.1 Experiment

THz spectra were recorded with using two spectrometers. One is a THz time-domain system (Aispec, Japan). A pair of photoconductive antennas were used for generating and detecting THz pulses. This spectrometer covers a 12-80 cm-1 frequency region with significant signal/noise ratio and a 0.3 cm-1 frequency resolution. A cryostat (OptistatDN, Oxford Instruments, UK) was used to generate a temperature-variable environment from 78 to 300 K by cooling with liquid nitrogen and heating with an electric heater. Temperature stability was better than ±0.1 K. The other is a continuous-wave (CW) GaP THz spectrometer that uses the difference frequency generation (DFG) in a GaP crystal for the generation of THz radiation and uses a niobium transition-edge superconductor 24


Page 24 of 43

Page 25 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(TES) bolometer, cooled with a low vibration pulse tube cooler (QMC Instruments QNbB/PTC), for the detection. Detailed information about this system has been provided somewhere else.17-18, 56-57 The measurement frequency range was 0.6–6.0 THz. Frequency accuracy was adjusted to be better than 100 MHz at each point, although the highest absolute frequency accuracy and resolution reach 3.0 and 8.0 MHz, respectively. A cryostat (Microstat He2, Oxford instruments, UK) was used to control the temperature from 5 to 300 K by cooling with liquid helium/nitrogen and heating with an electric heater. Temperature stability was better than ±0.05 K.

The powder samples of Forms I and III of diflunisal were purchased from SigmaAldrich. Forms I and III was recrystallized from the hot solutions of diflunisal in toluene and ethanol, respectively. The collected powder was ground and then uniformly mixed with fine polyethylene (PE) powder with proper ratios for THz measurements in different frequency regions. The mixtures were pressed into pellets using a hydraulic press. A pure PE pellet was used as the reference for the THz-TDS measurements, and empty space (vacuum) was for the CW-THz measurements. Refer to Fig. A1-A5 for the original data. The obtained spectra by the THz-TDS system were not smoothed at all, while that by the CW-GaP system were smoothed using the moving average. All the spectra were finally scaled and combined in Fig. 3. 25



3.2 Solid-state ab initio calculations

DFT calculations for the perfect crystal models were performed with using the CRYSTAL14 software package. The periodic boundary condition was implemented to account for the long-range translational symmetry in all the calculations. The B3LYP functional58-59 augmented by Grimme’s dispersion term60 (B3LYP-D*) was used for all calculations. All the parameters of the correction term adopted the values re-optimized by Civalleri et al.61 Gaussian-type 6-311G(2df,2pd) basis set was employed.62-63

The geometry optimizations were carried out under the full relaxation condition, namely, atomic coordinates and unit cell parameters were all allowed to relax. The convergence of geometry optimization was evaluated against a default criterion of CRYSTAL14, i.e. the root mean square (RMS) and the absolute value of the largest component of the gradients, and the RMS and the absolute value of the largest components of the estimated displacements should meet a threshold of 0.0003, 0.0045, 0.0012, and 0.0018 a.u., respectively.64 The frequencies were calculated through diagonalizing the Hessian matrix under the harmonic approximation and at gamma point. The IR intensities were calculated through a periodic coupled-perturbed Kohn-Sham (CPKS) analytical approach.65-66 The radial and angular distributions of points in atomic 26


Page 26 of 43

Page 27 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


integrations were defined by a default pruned (75, 943) grid in normal space. The commensurate grid and sampling rate of k points were defined by a shrinking factor (6, 6) in reciprocal space, which corresponds to 32 k-points in the first Brillouin zone. The truncation criteria for bielectronic integrals, i.e. the overlap threshold for Coulomb integrals, the penetration threshold for Coulomb integrals, and the overlap threshold for HF exchange integrals were set to 10-8, 10-8, and 10-8 hartree, respectively. The two pseudo-overlap thresholds of HF exchange series were set to 10-8 and 10-16 hartree, respectively. The SCF convergent threshold on total energy was set to 10-9, 10-11 hartree for the geometry and frequency calculation, respectively.64

Supporting Information Statement Supporting Information Available: Ten possible inter-layer connections between the four types of SR-dimers, A, B, C, and D (Figure S1). Temperature dependent THz spectra (Figure S2). Fitting result of Region II with using Lorentzian line shapes (Figure S3). Comparison between THz spectra of Form I and III of diflunisal (Figure S4). Comparison between experimental THz spectra and THz modes simulated with using the perfect-crystal models (Figure S5). Characteristics of the simulated THz modes in Region I, II, and III with using the perfect-crystal model 27



which conserves P-1 space group symmetry (Figure S6). The relative strengths of the hydrogen atoms in the two 2,6-disordered ortho sites of the perfect-crystal model which conserves P-1 space group symmetry (Figure S7). IR-active Modes predicted by a supercell packing model (Figure S8). The refractive index of Form I of diflunisal obtained by the THz-TDS measurement (Figure S9). Schematic representation of intermolecular and intramolecular interactions of one diflunisal molecule in the crystal (Figure S10). Comparison between the crystal structures predicted by experimentation and theoretical models (Table S1). The original experimental data of the THz spectra (Figure A1-A5). This material is available free of charge via the Internet at http://pubs.acs.org/

Acknowledgments All the authors thank Dr. Kaoru Ohta for his intriguing discussions. F.Z. acknowledges the support of the JSPS Grant-In-Aid project (18K05034). M.H. thanks the financial support from the Ministry of Science and Technology (MOST) of Taiwan under MOST 107-2113-M-002-012. A part of this research is based on the Cooperative Research Project of Research Center for Biomedical Engineering. The calculations were performed by using the supercomputers at the Research Center for Computational Science in Okazaki. 28


Page 28 of 43

Page 29 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


References 1. Palatinus, L.; Brázda, P.; Boullay, P.; Perez, O.; Klementová, M.; Petit, S.; Eigner, V.; Zaarour, M.; Mintova, S., Hydrogen Positions in Single Nanocrystals Revealed by Electron Diffraction. Science 2017, 355, 166-169. 2. Keen, D. A.; Goodwin, A. L., The Crystallography of Correlated Disorder. Nature 2015, 521, 303-309. 3. Welberry, T. R.; Weber, T., One Hundred Years of Diffuse Scattering. Crystallography Reviews 2016, 22, 2-78. 4. Born, M.; Huang, K., Dynamical Theory of Crystal Lattice Clarendon Press, Oxford, 1998. 5. Davydov, A. S., Theory of Light Absorption in Molecular Crystals, Translated from Acad. Sci. Of Ukrssr, Kiev, 1951 (in Russian); McGRAW-Hill Book COMPANY, INC, 1962. 6. Zhang, F.; Wang, H.-W.; Tominaga, K.; Hayashi, M.; Lee, S.; Nishino, T., Elucidation of Chiral Symmetry Breaking in a Racemic Polymer System with Terahertz Vibrational Spectroscopy and Crystal Orbital Density Functional Theory. The Journal of Physical Chemistry Letters 2016, 7, 4671-4676. 7. Davydov, A. S., The Theory of Molecular Excitons. Soviet Physics Uspekhi 1964, 7, 145. 8. Bhagavantam, S.; Venkatarayudu, T., Theory of Groups and Its Application to Physical Problems; Academic Press, 1969. 9. Halford, R. S., Motions of Molecules in Condensed Systems: I. Selection Rules, Relative Intensities, and Orientation Effects for Raman and Infra‐Red Spectra. J. Chem. Phys. 1946, 14, 8-15. 10. Hornig, D. F., The Vibrational Spectra of Molecules and Complex Ions in Crystals. I. General Theory. J. Chem. Phys. 1948, 16, 1063-1076. 11. Rousseau, D. L.; Bauman, R. P.; Porto, S. P. S., Normal Mode Determination in Crystals. J. Raman Spectrosc. 1981, 10, 253-290. 12. Ashbrook, S. E.; Dawson, D. M., Exploiting Periodic First-Principles Calculations in Nmr Spectroscopy of Disordered Solids. Acc. Chem. Res. 2013, 46, 1964-1974. 13. Moran, R. F.; Dawson, D. M.; Ashbrook, S. E., Exploiting Nmr Spectroscopy for the Study of Disorder in Solids. Int. Rev. Phys. Chem. 2017, 36, 39-115. 29



14. Sakellariou, D.; Brown, S. P.; Lesage, A.; Hediger, S.; Bardet, M.; Meriles, C. A.; Pines, A.; Emsley, L., High-Resolution Nmr Correlation Spectra of Disordered Solids. J. Am. Chem. Soc. 2003, 125, 4376-4380. 15. Shen, S. C.; Santo, L.; Genzel, L., Thz Spectra for Some Bio-Molecules. J Infrared Millim. Terahertz Waves 2007, 28, 595-610. 16. Walther, M.; Fischer, B. M.; Uhd Jepsen, P., Noncovalent Intermolecular Forces in Polycrystalline and Amorphous Saccharides in the Far Infrared. Chem. Phys. 2003, 288, 261-268. 17. Sasaki, T.; Sakamoto, T.; Otsuka, M., Detection of Impurities in Organic Crystals by High-Accuracy Terahertz Absorption Spectroscopy. Anal. Chem. 2018, 90, 1677-1682. 18. Sasaki, T.; Sakamoto, T.; Otsuka, M., Sharp Absorption Peaks in Thz Spectra Valuable for Crystal Quality Evaluation of Middle Molecular Weight Pharmaceuticals. J Infrared Milli Terahz Waves 2018. 19. Zhang, F.; Hayashi, M.; Wang, H.-W.; Tominaga, K.; Kambara, O.; Nishizawa, J.-i.; Sasaki, T., Terahertz Spectroscopy and Solid-State Density Functional Theory Calculation of Anthracene: Effect of Dispersion Force on the Vibrational Modes. J. Chem. Phys. 2014, 140, 174509. 20. Zhang, F.; Kambara, O.; Tominaga, K.; Nishizawa, J.-i.; Sasaki, T.; Wang, H.W.; Hayashi, M., Analysis of Vibrational Spectra of Solid-State Adenine and Adenosine in the Terahertz Region. RSC Adv. 2014, 4, 269-278. 21. Zhang, F.; Wang, H.-W.; Tominaga, K.; Hayashi, M., Intramolecular Vibrations in Low-Frequency Normal Modes of Amino Acids: L-Alanine in the Neat Solid State. J. Phys. Chem. A 2015, 119, 3008-3022. 22. Zhang, F.; Wang, H.-W.; Tominaga, K.; Hayashi, M., Characteristics of LowFrequency Molecular Phonon Modes Studied by Thz Spectroscopy and Solid-State Ab Initio Theory: Polymorphs I and Iii of Diflunisal. J. Phys. Chem. B 2016, 120, 16981710. 23. Zhang, F.; Wang, H.-W.; Tominaga, K.; Hayashi, M., Mixing of Intermolecular and Intramolecular Vibrations in Optical Phonon Modes: Terahertz Spectroscopy and Solid-State Density Functional Theory. Wiley Interdisciplinary Reviews: Computational Molecular Science 2016, 6, 386-409. 24. Zhang, F.; Wang, H.-W.; Tominaga, K.; Hayashi, M.; Hasunuma, T.; Kondo, A., Application of Thz Vibrational Spectroscopy to Molecular Characterization and the Theoretical Fundamentals: An Illustration Using Saccharide Molecules. Chemistry – An Asian Journal 2017, 12, 324-331. 30


Page 30 of 43

Page 31 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25. Cotton, M. L.; Hux, R. A., Diflunisal. In Analytical Profiles of Drug Substances, Florey, K., Ed. Academic Press: 1985; Vol. 14, pp 491-526. 26. Martínez-Ohárriz, M. C.; Martín, C.; Goñi, M. M.; Rodríguez-Espinosa, C.; Tros De Ilarduya-Apaolaza, M. C.; Sánchez, M., Polymorphism of Diflunisal: Isolation and Solid-State Characteristics of a New Crystal Form. J. Pharm. Sci. 1994, 83, 174177. 27. Kim, Y. B.; Park, I.-Y., Disordered Crystal Structure of Diflunisal. Journal of Pharmaceutical Investigation 1996, 26, 55-59. 28. Perlovich, G. L.; Hansen, L. K.; Bauer-Brandl, A., Interrelation between Thermochemical and Structural Data of Polymorphs Exemplified by Diflunisal. J. Pharm. Sci. 2002, 91, 1036-1045. 29. Cross, W. I.; Blagden, N.; Davey, R. J.; Pritchard, R. G.; Neumann, M. A.; Roberts, R. J.; Rowe, R. C., A Whole Output Strategy for Polymorph Screening: Combining Crystal Structure Prediction, Graph Set Analysis, and Targeted Crystallization Experiments in the Case of Diflunisal. Crystal Growth & Design 2003, 3, 151-158. 30. Kh, E. E.-K.; Erba, A.; Carbonnière, P.; Rérat, M., Piezoelectric, Elastic, Structural and Dielectric Properties of the Si 1− X Ge X O 2 Solid Solution: A Theoretical Study. J. Phys.: Condens. Matter 2014, 26, 205401. 31. Mustapha, S.; D'Arco, P.; De La Pierre, M.; Noel, Y.; Ferrabone, M.; Dovesi, R., On the Use of Symmetry in Configurational Analysis for the Simulation of Disordered Solids. Journal of Physics-Condensed Matter 2013, 25. 32. Okhotnikov, K.; Charpentier, T.; Cadars, S., Supercell Program: A Combinatorial Structure-Generation Approach for the Local-Level Modeling of Atomic Substitutions and Partial Occupancies in Crystals. Journal of Cheminformatics 2016, 8, 17. 33. Singer, S. J.; Kuo, J.-L.; Hirsch, T. K.; Knight, C.; Ojamäe, L.; Klein, M. L., Hydrogen-Bond Topology and the Ice $\Mathrm{Vii}/\Mathrm{Viii}$ and Ice $\Mathrm{I}H/\Mathrm{Xi}$ Proton-Ordering Phase Transitions. Phys. Rev. Lett. 2005, 94, 135701. 34. Kuo, J.-L.; Kuhs, W. F., A First Principles Study on the Structure of Ice-Vi: Static Distortion, Molecular Geometry, and Proton Ordering. J. Phys. Chem. B 2006, 110, 3697-3703. 35. Umemoto, K.; Wentzcovitch, R. M.; de Gironcoli, S.; Baroni, S., Order– Disorder Phase Boundary between Ice Vii and Viii Obtained by First Principles. Chem. Phys. Lett. 2010, 499, 236-240. 31



36. Li, R.; Zeitler, J. A.; Tomerini, D.; Parrott, E. P. J.; Gladden, L. F.; Day, G. M., A Study into the Effect of Subtle Structural Details and Disorder on the Terahertz Spectrum of Crystalline Benzoic Acid. PCCP 2010, 12, 5329-5340. 37. Nickel, D. V.; Delaney, S. P.; Bian, H. T.; Zheng, J. R.; Korter, T. M.; Mittleman, D. M., Terahertz Vibrational Modes of the Rigid Crystal Phase of Succinonitrile. J. Phys. Chem. A 2014, 118, 2442-2446. 38. Nickel, D. V.; Ruggiero, M. T.; Korter, T. M.; Mittleman, D. M., Terahertz Disorder-Localized Rotational Modes and Lattice Vibrational Modes in the Orientationally-Disordered and Ordered Phases of Camphor. PCCP 2015, 17, 67346740. 39. Delaney, S. P.; Pan, D. H.; Galella, M.; Yin, S. X.; Korter, T. M., Understanding the Origins of Conformational Disorder in the Crystalline Polymorphs of Irbesartan. Crystal Growth & Design 2012, 12, 5017-5024. 40. Delaney, S. P.; Korter, T. M., Terahertz Spectroscopy and Computational Investigation of the Flufenamic Acid/Nicotinamide Cocrystal. J. Phys. Chem. A 2015, 119, 3269-3276. 41. Neu, J.; Nemes, C. T.; Regan, K. P.; Williams, M. R. C.; Schmuttenmaer, C. A., Exploring the Solid State Phase Transition in Dl-Norvaline with Terahertz Spectroscopy. PCCP 2018, 20, 276-283. 42. Ruggiero, M. T.; Krynski, M.; Kissi, E. O.; Sibik, J.; Markl, D.; Tan, N. Y.; Arslanov, D.; van der Zande, W.; Redlich, B.; Korter, T. M.; et al. The Significance of the Amorphous Potential Energy Landscape for Dictating Glassy Dynamics and Driving Solid-State Crystallisation. PCCP 2017, 19, 30039-30047. 43. Ruggiero, M. T.; Zhang, W.; Bond, A. D.; Mittleman, D. M.; Zeitler, J. A., Uncovering the Connection between Low-Frequency Dynamics and Phase Transformation Phenomena in Molecular Solids. Phys. Rev. Lett. 2018, 120. 44. Ruggiero, M. T.; Kölbel, J.; Li, Q.; Zeitler, J. A., Predicting the Structures and Associated Phase Transition Mechanisms in Disordered Crystals Via a Combination of Experimental and Theoretical Methods. Faraday Discuss. 2018, 211, 425-439. 45. Schlömann, E., Dielectric Losses in Ionic Crystals with Disordered Charge Distributions. Phys. Rev. 1964, 135, A413-A419. 46. Bagdad, W.; Stolen, R., Far Infrared Absorption in Fused Quartz and Soft Glass. J. Phys. Chem. Solids 1968, 29, 2001-2008. 47. Strom, U.; Taylor, P. C., Temperature and Frequency Dependences of the FarInfrared and Microwave Optical Absorption in Amorphous Materials. Phys. Rev. B 1977, 16, 5512-5522. 32


Page 32 of 43

Page 33 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


48. Shen, Y. C.; Taday, P. F.; Pepper, M., Elimination of Scattering Effects in Spectral Measurement of Granulated Materials Using Terahertz Pulsed Spectroscopy. Appl. Phys. Lett. 2008, 92, 051103. 49. Arora, A. K.; Rajalakshmi, M.; Ravindran, T. R., Phonon Confinement in Nanostructured Materials. In Encyclopedia of Nanoscience and Nanotechnology, Nalwa, H. S., Ed. American Scientific Publishers: 2004; pp 499-512. 50. Beecher, A. N.; Dziatko, R. A.; Steigerwald, M. L.; Owen, J. S.; Crowther, A. C., Transition from Molecular Vibrations to Phonons in Atomically Precise Cadmium Selenide Quantum Dots. J. Am. Chem. Soc. 2016, 138, 16754-16763. 51. Campbell, I. H.; Fauchet, P. M., The Effects of Microcrystal Size and Shape on the One Phonon Raman Spectra of Crystalline Semiconductors. Solid State Commun. 1986, 58, 739-741. 52. Richter, H.; Wang, Z. P.; Ley, L., The One Phonon Raman Spectrum in Microcrystalline Silicon. Solid State Commun. 1981, 39, 625-629. 53. Natkaniec, I.; Bokhenkov, E. L.; Dorner, B.; Kalus, J.; Mackenzie, G. A.; Pawley, G. S.; Schmelzer, U.; Sheka, E. F., Phonon Dispersion in D 8 -Naphthalene Crystal at 6k. Journal of Physics C: Solid State Physics 1980, 13, 4265. 54. Dorner, B.; Bokhenkov, E. L.; Chaplot, S. L.; Kalus, J.; Natkaniec, I.; Pawley, G. S.; Schmelzer, U.; Sheka, E. F., The 12 External and the 4 Lowest Internal Phonon Dispersion Branches in D 10 -Anthracene at 12k. Journal of Physics C: Solid State Physics 1982, 15, 2353. 55. Chaplot, S. L.; Mierzejewski, A.; Pawley, G. S.; Lefebvre, J.; Luty, T., Phonon Dispersion of the External and Low-Frequency Internal Vibrations in Monoclinic Tetracyanoethylene at 5k. Journal of Physics C: Solid State Physics 1983, 16, 625. 56. Sasaki, T.; Tanabe, T.; Nishizawa, J.-i., Frequency Stabilized Gap ContinuousWave Terahertz Signal Generator for High-Resolution Spectroscopy. Optics and Photonics Journal 2014, 4, 8-13. 57. Sasaki, T.; Tanabe, T.; Nishizawa, J.-i., Development of Continuous Wave Terahertz Signal Generator Based on Difference Frequency Generation in Gallium Phosphide Crystal. Journal of the Japan Society of Infrared Science and Technolog 2016, 26, 74-81. 58. Lee, C.; Yang, W.; Parr, R. G., Development of the Colle-Salvetti CorrelationEnergy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785789.

33



59.

Becke, A. D., Density‐Functional Thermochemistry. Iii. The Role of Exact

Exchange. J. Chem. Phys. 1993, 98, 5648-5652. 60. Grimme, S., Accurate Description of Van Der Waals Complexes by Density Functional Theory Including Empirical Corrections. J. Comput. Chem. 2004, 25, 14631473. 61. Civalleri, B.; Zicovich-Wilson, C. M.; Valenzano, L.; Ugliengo, P., B3lyp Augmented with an Empirical Dispersion Term (B3lyp-D*) as Applied to Molecular Crystals. Crystengcomm 2008, 10, 405-410. 62.

Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A., Self‐Consistent

Molecular Orbital Methods. Xx. A Basis Set for Correlated Wave Functions. J. Chem. Phys. 1980, 72, 650-654. 63.

Frisch, M. J.; Pople, J. A.; Binkley, J. S., Self‐Consistent Molecular Orbital

Methods 25. Supplementary Functions for Gaussian Basis Sets. J. Chem. Phys. 1984, 80, 3265-3269. 64. R. Dovesi; V. R. Saunders; C. Roetti; R. Orlando; C. M. Zicovich-Wilson; F. Pascale; B. Civalleri; K. Doll; N. M. Harrison; I. J. Bush, Crystal14 User's Manual; University of Torino: Torino, 2014. 65. Maschio, L.; Kirtman, B.; Orlando, R.; Rèrat, M., Ab Initio Analytical Infrared Intensities for Periodic Systems through a Coupled Perturbed Hartree-Fock/Kohn-Sham Method. J. Chem. Phys. 2012, 137, 204113. 66. Ferrero, M.; Rérat, M.; Kirtman, B.; Dovesi, R., Calculation of First and Second Static Hyperpolarizabilities of One- to Three-Dimensional Periodic Compounds. Implementation in the Crystal Code. J. Chem. Phys. 2008, 129, 244110.

34


Page 34 of 43

Page 35 of 43

a

b

•••

6

S

2

R

2 6

•••

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


H-bond chain

Fig. 1. Intermolecular bonding patterns of diflunisal in Form I. The three unit cell axes a, b, and c are shown in red, green, and blue, respectively. Panel a shows a front view of the molecular layers along the a axis, and the dotted lines indicate the strong H-bond (OH…O-C) and weak H-bond (C-H…F-C) connections of one SR-dimer. One SR-dimer 2 column forming via the R2 (4) phenoxy H-bonds is highlighted in a purple frame. The

two disordered 2,6-ortho sites in each enantiomer R or S are highlighted in light blue, and the ordered fluorine atoms in the 4-para sites are shown in yellow. Panel b shows a sideview of the layers along the c axis. The disorder results in four SR-dimer configurations A, B, C, and D.

35



ABABABABABAB AABAABAABAAB

BBBBBBBBBBBB

AAABAAABAAAB

CCCCCCCCCCCC

ABBABBABBABB

DDDDDDDDDDDD

ABCABCABCABC

ABCABDBCDACD •••

AAAAAAAAAAAA

ABCDABCDABCD •••

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 43

(a)

(b)

(c)

Fig. 2. Schematic representation of the three classes of correlation patterns of dimers A, B, C, and D. For ease of illustration, we consider the one dimensional arrangement. Panel a represents the self-correlations of dimers and features the repetitive arrangement of unit cells. Panel b represents the correlations of the four or fewer types of dimers and features the repetitive arrangement of unit cells composed of a combination of dimers. Panel c represents the zero correlations, i.e. the random disorder of the dimers.

36


Page 37 of 43

I

II

III i

1.0

0.5 0.0

c

Intensity (km/mol)

20 75 30

a

A

100 50

125 75

B 1.0 C

2

b

0.1

100 150 160 170 180 190 200 10 20 30 40 50

0.1

160 100 170

0.0 180 190 125 160200 170

f

e

h f

d

e 0.5

g

c

c

1.0

2

b

2

f d

a

0.2

1

i

i

1

g

ch

0.0

0 0.0 20 30

20 75 30

100 50

125 75

160 170 100

e

1

0.5g

100

160 170 180 190 200

Wavenumber (cm ) 0.0

180 190 200

-1

(a) i i

g

150

100

d

e

Calculated intensity (km/mol)

-1

h

f

c 50

a

b

0

2

1

a,b 0

0

50

100

150

200

0

-1

Experimental frequency (cm )

(b)

1 2 Experimental intensity

(c)

Fig. 3. Comparison between experiment and simulation in Region I, II and III. The upper part in panel (a) shows the THz spectra recorded with the 100 MHz resolution at 10 K. 37


B C

Wavenumber (cm ) Wavenumber (cm )

200

A

0

180 190 125 160200 170

-1

i

-1

0

0.0

50

2

h

0 2030 50

0.0

180 190 200

-1

D

d

a 1

0.5

0.0 -1

g c

0.0 0

h

Wavenumber (cm ) Wavenumber (cm )

1

be

0.5 g

h

0.0

50

bfi d

d

c

h 0.2 a

Absorbance

1.0

Intensity (km/mol)

1.5

0.2

302

g

0.5

0.0 0.0 20

2.0

d

a

0.5

1.0

f

e

Intensity (km/mol)

Absorbance

a

f

b e

i

1.0

1.0 0.1

Absorbance

b

0.1

0.0

Calculated frequency (cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


D


The two THz peaks a and b in Region I and the one peak i in Region III are fitted with using Lorentzian line shapes (red lines). The lower part in panel (a) shows the simulated THz modes. Lorentzian line shapes with full-width-at-half-maximum of 1.1, 3.5, and 2.5 cm-1 are convolved into the modes in Regions I, II, and III, respectively, to provide a visual guide. The intensities of all the line shapes are magnified by a factor of 3.14. Panel (b) shows the comparison between experiment and theory in terms of frequencies for THz peaks a, b, c, d, e, f, g and i. Panel (c) shows the comparison between experimental and theory in terms of intensity for THz peaks a, b, and i. The black lines in both panels have a slope of 1 and pass the origins.

38


Page 38 of 43

I

100 0 50 100 0

a

b Percentage (%)

50

A 100

c

50

d

B

II

C

e

D

g

f

Percentage (%)

100

Percentage (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


100 0 50 100 0

100 50

h

100 0 50 100 0

50

50

50

0

0

0

10 20 30

57 58 5980 -1

Wavenumber (cm )

90

100

III

100

Percentage (%)

Page 39 of 43

50

i

Trans.

100 0

A B

50

Lib.

C

100 0 50

Intra. Vib.

D

0 75 100 160 170 180 125200 128132 16550 170 175 -1

Wavenumber (cm )

-1

Wavenumber (cm )(cm-1) Wavenumber

Fig. 4. Characteristics of the simulated THz modes in Region I, II, and III. All the modes are decomposed into intermolecular translations and librations, and intramolecular vibrations. The percentage contributions of the three components to the vibrational energy of each modes are shown in the upper, middle and lower panels, respectively.

39



Mode c

Mode d

Mode f

Mode g

Page 40 of 43

Modes e

Mode h

Mode i

Fig. 5 Representations of the vibrational patterns of the intramolecular components of the seven THz modes in Region II and III. Modes d, g, and h are represented by the vibrations of a left-hand diflunisal in the SR dimer A. Modes c and f are indicated by the vibrations of a left-hand diflunisal in the SR dimer D. Modes e is represented by the vibrations of both the left-hand and right-hand diflunisal in the SR dimer B (upper panel) and that in the SR dimer C (lower panel). Mode i is represented by the vibration of diflunisal whose ortho fluorine is substituted by a hydrogen atom.

40


Page 41 of 43

22

11

11

0

00

2 1

c d e f g

2

0

2

75

1

h

h

A

A

0

2

75

1

100

D

D 50

125

75

100

125

150

175

180

-1

180 200 (cm ) 175 Wavenumber

150

B

200

C

F

0

2

180 200

-1 -1 175 -1 180 -1 200 -1 100 Wavenumber 125 150 Wavenumber Wavenumber ) ) (cm ) (cm ) (cm(cm )(cm Wavenumber Wavenumber 1 -1 C Wavenumber (cm )

0

50

c d e f g

1

100 125100 125 150 150 175 180 200 175180150 7575 10050 100 125 150 180 175 50 5050 75 50 200200 75 100 125 175 75 125 150 180 175 B

50

Relative strength

Relative strengthRelative strength

22

0

h

H Relative strength

Relative strength Relative strength strength

Relative strength

Relative strength

c cdc ded e cf e fg df gecgh fd hhge fh g

Relative strength

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


200

A D B

-1

Wavenumber (cm )

C 0 50

75

100

125

150

175

180

200

-1

Wavenumber (cm )

Fig. 6. The relative strengths of the disordered fluorine and hydrogen atoms with respect to the root-mean-square displacement of all atoms in the intramolecular vibrational components of the simulated THz modes. The upper and lower panels show the results for the fluorine and hydrogen atoms, respectively. Regions II and III represent the analysis results for all the THz modes simulated with using the four packing models A, B, C, and D.

41



Page 42 of 43

Direction of H-bond chains

14

A

B

C

D

H-bonds

Fig. 7. A proposed alternating-packing model for Form I of diflunisal. Bars in a certain color represent the H-bond columns composed of continuous distribution of the corresponding unit cell configuration. In the column direction, bars in different colors are connected via H-bonds.

42


Page 43 of 43

b

0.1 a

0.5

b

0.2

a

a

b

0.0 0.0 203030 20

D

THz

atoms show ambiguous fingerprint peaks in the THz frequency region.

A

a

0.5

0.5

0.0 20 30 50

Intensity (km/mol)

0.2

B,C

i 1.0 Short-range correlations of disordered 1.0

0.5

C C

20 30

0.1

1.0

b

0.1

0.0 0.0

0.0

0.1

i

1.0 Absorbance

Absorbance

TOC

Intensity Intensity(km/mol) (km/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


B B B B B C C C D B 0.0

125 160 170190200 200 75 50 100 75 125100 160170 180 B 190 B 180 D D D A A -1 -1 Wavenumber (cm ) Wavenumber (cm ) i b

2 0.2

0.0

B B B B B B C C

2 A

2

a

1 0.1 1

1

0.0 00

0

D

DFT

2

B,C

1

0

2

1

i

D D D

D D Di D A A A A A A 2

C C A A A A A A C C A C C A A A A A A D 1

D C C C D D D D B B 0

D 0C C C C D D D D A

20 30 75 5050 75

50 75 100 160 170 160170125 180 190200 180190200 100100 125 125 160170 180190 200 -1 -1 -1 Wavenumber (cm ) Wavenumber ) Wavenumber (cm (cm )

43


THz Fingerprints of Short-Range Correlations of Disordered Atoms in

Recommend Documents