Characteristics of Low-Frequency Molecular ... - ACS Publications

Subscriber access provided by UNIV OSNABRUECK

Article

Characteristics of Low-frequency Molecular Phonon Modes Studied by THz Spectroscopy and Solid-state Ab initio Theory: Polymorphs I and III of Diflunisal Feng Zhang, Houng-Wei Wang, Keisuke Tominaga, and Michitoshi Hayashi J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b08798 • Publication Date (Web): 25 Jan 2016 Downloaded from http://pubs.acs.org on February 2, 2016

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 free 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 accessible to all readers and 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.

The Journal of Physical Chemistry B 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 73

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

Characteristics of Low-frequency Molecular Phonon Modes Studied by THz Spectroscopy and Solid-state Ab initio Theory: Polymorphs I and III of Diflunisal

Feng Zhang,† Houng-Wei Wang,‡ Keisuke Tominaga, *, † and Michitoshi Hayashi, *, ‡ †

Molecular Photoscience Research Center, Kobe University, Kobe 657-8501, Japan

†

Center for Condensed Matter Sciences, National Taiwan University, 1 Roosevelt Rd. Sec.

4, Taipei 10617, Taiwan

Corresponding Authors: *E-mail: [email protected] (K. Tominaga). *Tel: 81-078-803-5684 *E-mail: [email protected] (M. Hayashi). *Tel: 886-2-33665250

1

ACS Paragon Plus Environment


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 THz absorption spectra of two polymorphs of diflunisal—form I and form III exhibit distinct features due to the influence of packing conformations on the frequency distributions and IR activities within 100 cm-1 region. In order to understand the origins of these THz modes, we perform a detailed mode analysis. The result shows that although the spectral features are different, these low-frequency phonon modes of the two molecular polymorphs have similar vibrational characteristics in terms of harmonic couplings of intermolecular and intramolecular vibrations.

2


Page 2 of 73

Page 3 of 73

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 Low-frequency vibrations are the major thermal source of condensed matter. Thermal energy at ambient temperature, e.g. 293 K, amounts to 204 cm-1. It means that merely vibrations below this frequency limit are able to be excited and make contributions to physical processes at ambient temperature. Low-frequency vibrations directly control thermal properties of materials such as heat capacity, thermal conductivity and thermal expansion, and form the heat bath for vibrational dynamics in higher frequency regions.1-3 Low-frequency vibrations also participate in many electrical processes via interactions with electrons, e.g. electrical conduction, and the formation of polarons.1-2, 4-5 Moreover lowfrequency vibrations play a crucial role in biological systems and these are believed to be the important reaction coordinates along which many biological functions such as cooperative effect, allosteric transition and intercalation of drugs into DNA and proteins take place.6-7 Compared with amorphous materials, crystalline materials provide an easy access to low-frequency vibrations from both theoretical and experimental aspects. In the crystalline systems the translation symmetry generates the momentum representation, in which atoms vibrate in the phonon form.1 The selection rule thereby imposed allows only the gammapoint phonons to interact with light, resulting in resolvable-band features of optical (terahertz (THz) and/or low-frequency Raman) spectra. On the other hand, theoretical models could be remarkably simplified by fully exploiting the translation symmetry.1 So far phonon modes in the simple systems such as ionic, metallic and covalent crystals have been 3



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

successfully interpreted.1-2 But the low-frequency phonons in the more complicated molecular systems have not been fully understood yet due to the challenges to represent the subtle nature of intermolecular interactions in theory.8-9 The advance of the solid-state density functional theory (DFT) in recent years has gradually opened the way to molecular phonon modes.10-12 The solid-state DFT methods, implementing the periodic boundary condition and modern DFT functionals including dispersion forces, have enabled a relatively accurate representation of electronic structures of molecular crystals. Under the harmonic assumption of a potential surface at the equilibrium geometry, normal mode simulations have proved reliable at least against the frequency criterion, to reproduce the experimentally observed THz bands of various molecular crystalline systems.13-24 Solid-state simulations use mass-weighted Cartesian coordinates because they are mathematically convenient for the Fourier transformation that is required by the Bloch’s theorem. However mass-weighted Cartesian coordinates are difficult to associate with specific intermolecular and intramolecular motions. Thus the physical meanings of simulated normal modes in mass-weighted Cartesian coordinates are not instantly clear. In order to characterize the nature of simulated normal modes, we need to interpret them on a basis of elementary intermolecular and intramolecular vibrations with firm origins. To this end, we have developed an effective mode analysis method that allows characterizing a phonon mode of interest in terms of a harmonic coupling between 4


Page 4 of 73

Page 5 of 73

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


elementary intermolecular and intramolecular vibrations.19,

22

Here harmonic coupling

refers to the linear superposition of elementary vibrations with distinct origins. We can then measure the root-mean-square mass-weighted displacement amplitudes (RMSMWDA) of all the intermolecular and intramolecular vibrational components, and calculate their percentage contributions in the normal mode under question. Relying on the percentage information, we will understand what parts of vibrations in a molecular system are thermally active at certain temperature, thereby making contributions to physical processes of interest. We have quantitatively revealed three new features of low-frequency molecular phonon modes through a systematic investigation in an array of prototype molecular systems.19-22 The three features can be categorized as follows: (1) a strong harmonic coupling occurs between intermolecular and intramolecular vibrations with similar characteristic frequency regions. This situation is allowed when the molecules become sufficiently flexible so that some intramolecular vibrations, such as conformational torsion and deformation, have low vibration energy comparable to intermolecular vibrations. This phenomenon is basically predictable from the classical perspective; (2) a weak harmonic coupling takes place between intermolecular and intramolecular vibrations with various characteristic frequency regions. This situation has been observed generally in many existing molecular crystal systems. It is contrary to the conventional viewpoint, and would be described as a non-classical phenomenon; and 5



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

(3) the harmonic couplings in (1) and (2) happen in a broad spectrum of phonon modes. This situation allows the undergoing intramolecular vibrations to have broad frequency distributions in the low-frequency region. This phenomenon cannot be intuitively understood as well, and the underlying mechanism remains unclear. Compared with the conventional oriented gas model25-26 and/or rigid body model27-28 which assumes the complete separation of dynamics of intermolecular and intramolecular vibrations, the above-mentioned three findings reveal a more delicate structure of the lowfrequency molecular phonon modes. We now understand that the low-frequency molecular phonons in most systems may contain not only intermolecular vibrations, but also a considerable part of intramolecular vibrations. More importantly, the intramolecular vibrations consist not only of motions having a similar vibrational energy as the intermolecular vibrations, but also of some motions conventionally regarded having much higher vibrational energy.20, 22 A more fundamental question can be raised as to what are the key physical factors determining the three new features. One may intuitively agree that the molecular flexibility plays a determinant role in the feature (1), which may not need further explanation. However, regarding the questions relevant to the features (2) and (3), we are currently unable to give clear answers. We are however able to firmly claim that intermolecular interactions are the determinant. The argument is self-evident—it is the intermolecular interaction that makes molecules condense in the solid state and gives rise to phonon mode 6


Page 6 of 73

Page 7 of 73

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


vibrations. Thus the intermolecular interaction must be the key to explain the vibrational characteristics of phonon modes. As to what properties of intermolecular interactions play a leading role, we may consider two aspects. The first is the physical essence of intermolecular interactions. Namely, do different intermolecular interaction systems show remarkable differences in terms of the features (2) and (3)? Within the scope of our previous investigations in five prototypes molecular systems: C60, anthracene, adenine, αglycine and L-alanine,19-22 we conclude the features (2) and (3) are common to most molecular systems. The only exception is C60 that shows bare coupling possibility between intermolecular and intramolecular vibrations. Therefore there must be a crucial property of intermolecular interactions that lead to this distinction between C60 and other molecular systems. The second aspect is the quantitative properties of intermolecular interactions. One may ask a question as to whether or not a variation in terms of the number of hydrogen bonds per molecule, the strengths and orientations of molecular dipole moments, and/or the strength of dispersion force per molecule results in remarkable changes of the features (2) and (3) for a certain molecular system. We will contribute this work to a particular discussion from the second aspect. To this end, molecular polymorphs, in particular the packing polymorphs, may provide an ideal system. Molecular packing polymorphism results from different packing possibilities of the same molecular units in crystals. In these systems, intermolecular interactions merely vary to a quantitative degree—the intermolecular interaction motifs. It allows us to specifically examine the impact of the quantitative variations of intermolecular-interaction motifs on 7



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 characteristics of low-frequency molecular phonon modes. A great number of THz spectroscopic studies of molecular packing polymorphs have been reported in both experiment and theory.13-17, 29-43 However, most works focus on a discussion in terms of phonon mode frequencies. For example, Taday et al.30-36 and Korter et al.13-17 have illustrated the distinctive ability of THz spectroscopy in terms of polymorph identification; very few works are concerned with a quantitative comparison between polymorphs in terms of origins of normal modes, probably because of a lack of an efficient mode-analysis method. We will in this work use two packing polymorphs—form I and III of diflunisal, a nonsteroidal anti-inflammatory medicine, as a case study.44 Form I has P 1 space group symmetry. Each unit cell contains two irreducible molecular units #1 and #2, which are related by an inversion symmetry through the point of inversion at (a/2, b/2, c/2) as shown in the left panel of Fig. 1 (a). An inversion symmetry is equivalent to a 2-fold rotationreflection symmetry. Because diflunisal is a chiral molecule, the two diflunisal in the unit cell are a pair of enantiomers. We designate the molecular unit #1 as L-diflunisal, and the molecular unit #2 as D-diflunisal, as shown in the right panel of Fig. 1 (a). Form III has

P212121 space group symmetry. Each unit cell contains four irreducible units, related by two-one screw symmetries as shown in the left panel of Fig. 2 (a). Each irreducible unit is comprised of a pair of enantiomers, designated as pairs of #1 and #5, #2 and #6, and so on. Molecules #1 to #4 adopt the “L” configuration, while molecules #2 to #8 the “D” configuration. The pair of #1 and #5 are displayed in the right panel of Fig. 2 (b) to show 8


Page 8 of 73

Page 9 of 73

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


their chiral relation. Different from form I, each pair of enantiomers in form III are in a pseudo-inversion symmetric relation, and thus symmetrically irreducible. Structure information of both forms is provided in Table (1). With respect to intermolecular connections, dimers form between enantiomers via the carboxylic-acid hydrogen-bond motifs, constructing the elementary interaction units in both polymorphic systems. Specifically, for form I, a L-diflunisal in one unit cell connects a Ddiflunisal in an adjacent unit cell, and vice versa; for form III, a L-diflunisal in one unit cell connects a D-diflunisal in the corresponding irreducible unit of an adjacent unit cell, and vice versa. Fig. 1 (b) and Fig. 2 (b)) show a dimer unit for form I and III, respectively. The difference between these two polymorphs are: dimers in form I are further connected via the R22 (4) phenoxy hydrogen-bond motif to form long chains. The long chains pack via mainly dispersion forces; while dimers in form III directly pack via mainly dispersion forces. In summary, diflunisal molecules in both polymorphic systems experience the same types of intermolecular interactions, which are merely different at a quantitative level— each diflunisal molecule in form I has one more hydrogen-bond connection than that in form III. The two polymorphs of diflunisal therefore provide an excellent system for the embedded purpose of this work: to examine the influence of quantitative variations of intermolecular interactions on the characteristics of low-frequency molecular phonon modes.

9



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

2. MATERIALS AND METHODS 2.1 Experiments Diflunisal was purchased from Sigma Aldrich and used without further purification. Polymorphs I and III of diflunisal were recrystallized from its solution in toluene and ethanol, respectively. Saturated solution of diflunisal in acetone and ethanol were first prepared at 50 ℃ and 70 ℃ in water bath, respectively, and then cooled in a refrigerator set at 4 ℃ over night. The obtained crystals were filtered under reduced pressure and dried over P2O5 in a desiccator at room temperature. The polymorphs of both samples were examined by using the powder X-ray diffraction method (Rigaku, Japan; 1.54 Å, Cu-Kα radiation) at room temperature, to ensure they are consistent with that determined by W. Cross, et al.44 THz spectra were recorded by using a THz-time domain spectrometer (Aispec, Japan).45 A pair of photoconductive antenna were used to generate and detect THz radiation by aligning femtosecond laser beams. The THz path was purged by dry air to prevent the vapor absorption. Transmittance THz spectra, acquired by averaging 10 scans, are able to cover a frequency region of 10-100 cm-1. A liquid nitrogen cryostat was used to create a 78 K environment for the low-temperature measurements. Sample powder was grounded in a mortar, and then uniformly mixed with fine polyethylene (PE) powder with proper ratios. The mixture was then pressed into around 2 mm thick pellets using a hydraulic press for THz measurements. A pure PE pellet with the same amount of PE 10


Page 10 of 73

Page 11 of 73

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


powder as in the sample pellets was used as a reference sample. Power spectra were obtained as the real parts of Fourier transformation of time-domain traces truncated slightly before the appearance of the first echo pulses. The same Fourier transformation range was used for all samples and the reference. The absorbance spectra Abs (ω ) were calculated according to the following formula:

Abs(ω ) = −2 log

E smp (ω ) E ref (ω )

where E smp (ω )

,

(1)

and E ref (ω ) refer to the power spectra of sample and reference,

respectively.

2.2 Simulations Solid-state DFT calculations were performed using the CRYSTAL 14 software package.10,

46

The periodic boundary condition was implemented to account for the

translational symmetry of molecular crystals. Electron density matrices were expressed in the representation of Bloch waves. Full geometry optimizations, in which both unit cell parameters and atomic coordinates were full relaxed, were carried out prior to frequency calculations to look for the most stable structure at 0 K for each polymorph. The crystal structures at room temperature of form I and III, reported by W. Cross, et al.44 using the Xray diffraction method, were used as the starting points. The mass-weighted Hessian matrix of each system is diagonalized at the gamma point for normal mode simulations. Mode frequencies are determined by the eigenvalue matrices, and normal mode coordinates are

11



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 12 of 73

obtained by transforming the atomic Cartesian displacement coordinates via the eigenvector matrices. IR intensities of normal modes were calculated through the Berry phase approach.47-48 Pople’s double zeta basis set 6-31G(d,p) with polarization functions was used to construct electronic wave functions.49-50 Grimme’s dispersion correction term D*

51-53

was

implemented to augment the PBE functional54-55 for constructing a PBE-D* method. The correction strength was optimized by adjusting a global scaling factor s6 , and the unit cell volume was used as the scaling criterion. Once a small shrinking of the unit cell volume compared with the experimental value was achieved, we assumed the correction term has reached a balance with the PBE functional. The total energy convergence criteria for geometry optimizations and frequency calculations were set to 10-9 and 10-11 hartree, respectively. The accuracy of atomic integration grids are controlled by a pruned (75, 974) grid having 75 radial distribution points and a maximum number of 974 angular distribution points. The integration accuracy in the reciprocal space, namely the size of the commensurate grid and the sampling rate of k points, is controlled by shrinking factors (4, 4) and (3, 3) for the form I and form III systems, respectively. The accuracy of the bielectronic integral series was control by a set of parameter of 10-8, 10-8, 10-8, 10-8 and 1016

, for the overlap threshold for Coulomb integrals, the penetration threshold for Coulomb

integrals, the overlap threshold for Hartree-Fock exchange integrals, and the two pseudooverlap thresholds of the Hartree-Fock exchange series, respectively.10 All other numerical accuracy controls are used as the default settings of CRYSTAL14. 12


Page 13 of 73

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


Gas phase normal mode simulations are performed using CRYSTAL 14 as well.10, 46 Single irreducible molecule unit(s) were extracted from the optimized unit cell structure for each polymorphic system. The same calculation strategy (functional and basis set) as well as the same set of accuracy control parameters used for solid-state normal mode simulations were applied.

3. RESULTS AND DISCUSSIONS 3.1 Geometry optimization The X-ray diffraction method has revealed the F2 atoms in form I are at room temperature disordered over two sites related by a two-fold rotational symmetry around the single bond connecting the two aromatic rings, each site has an occupancy factor of 0.5.44 It indicates diflunisal molecules in form I have two configurations, as a result of thermal flipping of the F-atom containing aromatic rings. At 0 K when thermal motions are frozen, every diflunisal molecule should adopts a unique configuration. We in this work assume that the P1 space group symmetry persists at 0 K, thus the unit cell has two possible configurations with F2 atoms either pointing away from the carboxylic groups or pointing towards the carboxylic groups as shown in Fig. S1. Regarding form III, the F2 atoms are found completely ordered at room temperature, so would do at low temperature. We first perform a geometry optimization for form III. The global scaling factor s 6 of the Grimme’s dispersion-correction term was adjusted to 0.186 to produce a shrinking -0.36% of the unit cell volume compared with the experimental value determined at room temperature (Table 13



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). We regard the same dispersion-correction strength is suitable for form I as well, and apply the s6 scaling factor 0.186 to the geometry optimizations for the two candidate configurations of form I. It turned out that the geometry optimization for the molecular configuration with the F2 atoms pointing towards the carboxylic groups diverged, while that with the F2 atoms pointing away from the carboxylic groups converged (Table S1). It indicates the latter structure (Fig. 1) is the most stable geometry of form I at 0 K. The optimized structure produces a shrinking -1.10% of the unit cell volume compared with the experimental value determined at room temperature (Table 1). Accuracy of geometry optimizations are assessed from both aspects of intramolecular and intermolecular structures. With respect to intramolecular structures, three criteria are employed: lengths and angles of covalent bonds, lengths of intramolecular H-bonds, and dihedral angles of the two aromatic rings. The first two are used for assessing the reproducibility of local structures, and the last one for the back-bone configurations. With respect to intermolecular structures, lengths of intermolecular H-bonds are employed as the criterion. The reproducibility of bond lengths and angles of covalent bonds is measured by the root mean square deviation (RMSD) of the simulated values from the experimental values. The reproducibility of lengths of intramolecular hydrogen bonds, dihedral angles of the two aromatic rings, and lengths of intermolecular hydrogen bonds are directly measured by deviations of the simulated values from the experimental values. As shown in Table 2 and Table 3, the geometry optimizations, against all criteria, have arrived at an accuracy level tolerated by experiment. In general the reproducibility of form III appears better than 14


Page 14 of 73

Page 15 of 73

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


that of form I, expect for the two dihedral angles of the D-diflunisal unit, whose reproduction errors are notably larger than that of form I. In addition, apart from the lengths and bonds of covalent bonds, the other three observables have been generally underestimated in both polymorphic systems. Exceptions are found regarding the intramolecular H-bond of L-diflunisal of form III, and the intermolecular hydrogen bond O5(H16)…O3 in the pseudosymmetric carboxylic-acid hydrogen-bond motif of form III. Both have been slightly overestimated.

3.2 Frequency calculations THz spectra of form I and III measured at 78 K are shown in the upper panels of Fig. 3 (a) and Fig. 4, respectively. The frequency regions with reduced signal/noise ratios are shadowed in gray. Despite being constructed from the same molecular units, form I and III exhibit dramatically different profiles in THz spectra. This difference can be explained as follows. THz radiation resonates with the optical phonon modes in the low-frequency region. Qualitatively speaking, the primary origin of the low-frequency molecular phonon modes is the intermolecular vibrations, which is fundamentally related to molecular packing structures. Molecular packing structures with distinct space group symmetries will impose distinct restrictions on the number and optical activity of gamma-point phonon modes, resulting in distinct resonant features with THz radiation. This attribute makes THz spectroscopy have a distinctive capability in terms of polymorph identifications, as having been massively demonstrated in the past.13-17, 29-43

15



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 simulated IR-active phonon modes are shown in the middle panels of Fig. 3 (a) and Fig. 4 for form I and III, respectively. Lorentzian line shapes with FWHM=2.0 cm-1 are convolved into all modes to provide a visual guide. Mode distributions, including Ramanactive modes (red), are shown in the lower panels of Fig. 3 (a) and Fig. 4 for form I and III, respectively. The frequency and symmetry information of all modes in both polymorphic systems is provided in Table S5. One can readily find fairly well correspondences between the experimental peaks and the simulated IR modes for both systems. For a quantitative examination, THz bands of form I are resolved through a multi-peak fit with a Lorentzian line shape function, as shown in the upper panel of Fig. 3 (a). Figure 3 (b) shows a comparison between frequencies of the six resolved bands and the corresponding simulated modes. A very good correlation has been observed, indicating the reliability of frequency calculation. It ensures us that the normal mode eigenvectors would be accuracy to represent atomic motions at 0 K. One may also notice that some of the mode frequencies in form I are slightly overestimated, so do in form III. This is partially due to the anharmonicityinduced red-shifts of frequencies at the experimental temperature 78 K. The frequency reproduction would be improved by recording THz spectra at much lower temperatures to reduce the anharmonic effects on atomic motions. Because each unit cell contains four times more molecules in form III than in form I, form III have a larger frequency density. IR intensities of normal modes in form III appear also stronger than that in form I, due to more molecules contributing to the unit-cell transition dipole moments.

16


Page 16 of 73

Page 17 of 73

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


Despite the relatively satisfactory frequency reproduction in both systems, appreciable discrepancies between simulation and experiment appear in terms of IR intensities. For example, remarkable IR-intensity overestimations are observed for the 9th modes at 79.8 cm-1 in form I, and for the 42th modes at 73.8 in form III. According to the mode-analysis results in section 3.3, these two modes feature strong harmonic coupling between intermolecular and intramolecular vibrations. Such insufficiencies are primarily induced by the numerical derivative approaches employed in IR intensity calculations—the Berry phase approach in this work.47-48 In contrast, analytical derivatives would provide a better option in terms of both the accuracy and efficiency concerns.56-57 A revisit to the current simulation works would be necessary when such sophisticated analytical derivative approaches become available in the solid-state simulation methods. It is also worth noting that current spectra were taken at 78 K, and the possibility of excitations of overtone bands and combination bands could still not be eliminated. Another experiments performed at very low temperature (

Characteristics of Low-Frequency Molecular ... - ACS Publications

Recommend Documents