Exposing Key Vibrational Contributions to Properties of Organic

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Exposing key vibrational contributions to properties of organic molecular solids with high signal, low frequency neutron spectroscopy and ab initio simulations Anup Pandey, Ada Sedova, Luke L. Daemen, Yongqiang Cheng, and Anibal J. Ramirez-Cuesta Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b00648 • Publication Date (Web): 03 Aug 2018 Downloaded from http://pubs.acs.org on August 13, 2018

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Crystal Growth & Design

Exposing key vibrational contributions to properties of organic molecular solids with high signal, low frequency neutron spectroscopy and ab initio simulations.

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Anup Pandey,∗,‡,§ Ada Sedova,∗,¶,§ Luke L. Daemen,‡ Yongqiang Cheng,‡ and Anibal J. Ramirez-Cuesta‡ ‡Neutron Scattering Division, and ¶National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA §These authors contributed equally and are listed alphabetically E-mail: [email protected]; [email protected]

Abstract Stability and response of supramolecular forms is important to many areas in materials science, and contributions from vibrations can be crucial. We have collected the first spectra of organic molecular crystals and polymorphic cocrystals using the next generation, high-signal VISION spectrometer in the far-infrared (FIR) and mid-infrared (MIR) †

Notice: “This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).”

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range. Unambiguously different spectral signatures were found for carbamazepine and two polymorphs of the carbamazepine-saccharin cocrystal, including numerous modes undetectable with optical methods. For FIR-range frequencies, in addition to correct calculation of peak positions, accurate line-shape features were reproducible by simulation using ab initio vibrational calculations. High confidence spectral assignments and thermochemical information for this region are thus expected, and a benchmark for vibrational ab initio calculations is provided, creating a significant addition to methods used in investigation and design of organic materials.

Polymorphism and co-crystallization are important to many applications, as different properties arise from changes in supramolecular morphology, and have been investigated in pharmaceutics as a means of altering and controlling drug pharmacokinetics. 1–3 Screening for polymorph and co-crystal formation 1,4 has been championed using both high-throughput experimental and computational methods. Successful in silico prediction can, in-turn, expand our basic understanding of the molecular details that drive supramolecular self-assembly. Despite extensive experimental characterization of polymorphs and cocrystals, a detailed molecular theory explaining how properties are altered by supramolecular configuration has not been attained, 1,5,6 although it is clear that a rigorous understanding of intermolecular interactions in the solid-state is essential. 5,7 In addition to potential energy calculations, information provided by vibrational dynamics, such as free energy, can help explain nonequilibrium phenomena such as response to environment. Supramolecular synthesis is not purely enthalpically driven but can involve entropic components including vibrations. 2,3,5,7,8 Characterizing the influence of intermolecular forces on dynamics requires an accurate description. Thus, an ability to test the accuracy of vibrational calculations is necessary; however, experimental settings may be different from computational models, and extrapolations, which may introduce uncertainty, may be required. Terahertz, low-wavenumber Raman and infrared spectroscopy have become popular methods for detection and analysis of molecular-crystal morphology. 9–11 The vibrational region

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below 200 cm−1 reports on lattice vibrations and thus provides important information about intermolecular interactions, which vary significantly between forms and are primarily responsible for differences in stability and response to environmental stimuli. For some spectroscopies this may be the only region where strong differences in spectra appear for polymorphs and other supramolecular variants; 12 modifications in lineshape in addition to peak positions in THz-spectroscopy 9 enhance discrimination. Spectroscopic studies of supramolecular assemblies have been performed with two intentions: to identify and differentiate forms, 10–13 and to characterize vibrations responsible for the spectra– a goal requiring computation. Gas-phase ab initio calculations are frequently used but neglect significant effects of intermolecular interactions in condensed phase 13,14 thus comparison to experiment can involve guesswork. In addition, instrument-related effects can further complicate assignment of the correct vibrational modes to spectral peaks. Incoherent, inelastic neutron vibrational spectroscopy (INS) complements optical spectroscopy. INS is not subject to selection rules and reports directly on all mass-weighted atomic motions; together with the high cross-section of hydrogen, it is ideal for studying dynamics of hydrogen bonds in condensed systems, and for large motions of hydrogenated molecules. 15,16 The next-generation VISION vibrational spectrometer at the Spallation Neutron Source user-facility at the Oak Ridge National Laboratory (ORNL), due to its design, can achieve a resolution of 0.5–2.0 (∆ E/E) in the range 16-4000 cm−1 , while simultaneously providing excellent signal-to-noise ratio in the THz and FIR regions. 16–18 Measurements are performed at temperatures as low as 5 K. The high signal allows for adequate spectra to be collected in under an hour, creating the potential for high-throughput data collection and subsequently, substantial data sets. Organic molecular crystals are bound by intermolecular forces weak enough to allow for high flexibility, while they can simultaneously be strong enough to induce significant static and correlational splitting and shifting of the gas-phase spectra. As a result, investigation of fluctuations in bonds primarily responsible for differences in behavior between morphological

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variants by solid-state spectroscopy is well-complemented by solid-state calculations. The relatively simple theory of INS, together with the predominance of harmonic quantum effects at temperatures near 0 K provides a near-exact match of simulation and experiment when spectra are collected at 5 K. This is attained using crystallographic structures, solid-state ab initio vibrational calculations, and the dedicated aCLIMAX code, 19 an ORNL version of which (Oclimax) is publicly available, and can include VISION instrumental parameters (pages S2-S3 describe the calculation and the components of lineshape for INS). In addition to calculation of peak locations, the relative intensity of each peak, which is a direct function of the amplitude of motion of that mode and is specified by the eigenvectors from the normal mode analysis, is more easily calculated than intensities of optical spectra. The VISION spectra of benzene, paracetamol, saccharine (SAC), carbamazepine (CBZ), and the two polymorphic forms of the carbamazepine-saccharin co-crystal (CBZ-SAC) were collected at 5 K. Figure 1 shows this spectral series in the THz region, displaying the characteristic fingerprint regions of the lattice modes and the differences in this region for the different patterns of intermolecular interactions. The SAC, CBZ, and CBZ-SAC systems contain the R22 (8) bimolecular ring synthon, a highly robust motif in supramolecular synthesis, and contain large, complex clusters of peaks that form a plateau-like pattern in this range. Figure S17 shows spectra through 1800 cm−1 for these molecules; PXRD and IR spectra are found on pages S18-S19. Pages S9-S11 display and characterize the different intermolecular-interaction geometries. To illustrate the high signal-to-noise ratio of the VISION spectrometer in the FIR range, Figure S18 shows unprocessed measurements compared to signal-processed spectra: data are typically re-binned and smoothed using parameters described in SI. It is clear that in this region processing serves primarily aesthetic purposes and that all features of the spectra, including splittings, shoulders, and other lineshape details, are clearly discernible from the raw data. Figure S18 also shows spectra with instrumentresolution error-bars, and duplicate measurements illustrating reproducibility of features. This high signal in the low-frequency region is unique for the VISION spectrometer and can

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provide unprecedented insight into vibrations of hydrogen bonds in organic materials.

Figure 1: VISION spectra for A) benzene, B) paracetamol, C) saccharin, D) carbamazepine Form III, E) CBZ-SAC I, and F) CBZ-SAC II.

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Carbamazepine is known for its ability to exist in numerous polymorphs. 9,20 It has been extensively studied by experiment, including spectroscopy, 9,11 and also by calculations: Day and coworkers 21 calculated lattice dynamics of four forms of CBZ using a high-level, periodic, rigid-molecule model, two additional studies 22,23 used ab initio methods on the gas-phase single molecule and dimer, and most recently, Brandenburg and coworkers calculated the vibrations at the solid-state ab initio level to obtain estimated lattice parameters and free energies, and experimentally determined lattice sizes for a large range of temperatures using PXRD. 20 CBZ-SAC has become a model of both co-crystallization and polymorphism: due to the low solubility of CBZ, many attempts to co-crystallize CBZ to improve solubility have been documented. 24,25 CBZ-SAC has been found in two monotropically related forms, Form I more stable and Form II metastable. 26 Although multiple experimental characterizations, including spectroscopic, exist in the literature, 26 we were unable to find computational work describing vibrational modes for any forms of this co-crystal. Highly featured, distinct INS signatures are obtained for each; the cocrystals and their isolated components have significantly different spectra as do the two polymorphs. This is true over the entire spectral range through 1800 cm−1 . Figure 2 compares spectra of two polymorphs of CBZ-SAC in FIR-range: shifting of peak positions and different lineshape features are found over the majority of the spectrum for the two forms. Previous work on two polymorphic forms of paracetamol using the FDS spectrometer at Los Alamos National Laboratory also found an ability of INS to distinguish polymorphs in the FIR range; 27 the signal, range, and high-throughput capabilities of the next-generation VISION instrument offer new possibilities for these types of studies to provide information for the crystal engineering community. Figure 3 displays calculated VISION spectra for SAC, CBZ, and CBZ-SAC I and II, computed with periodic density functional theory using a method that enables parallelization of the vibrational calculation. Calculations were performed on supercells with minimum dimensions of 10 Å, using a 600 eV PW cutoff, using the following crystal structures (CSD

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Figure 2: VISION spectra of CBZ-SAC. Form I: red solid line, and Form II, black dotted line. refcodes): SAC, SCCHRN02; CBZ, CBMZPN01; CBZ-SAC I, UNEZAO; CBZ-SAC II, UNEZAO01. Space groups, lattice information, and supercell sizes used in the calculations are listed in Tables S3-S4. No frequency scaling was performed. Calculated spectral lineshapes agree remarkably well with experiment in the FIR region: experimental peak positions, relative intensities, and peak broadening are reproduced by simulation with impressive accuracy in the regions 0-650 cm−1 . Differences between the two polymorphs of CBZ-SAC are also reproduced well (Figure S5). The effects of dispersion interactions for organic molecules, especially those containing aromatic rings such as are found in these four systems, are considered to be significant and are not described well by DFT functionals; thus, empirical corrections have been developed to correct values such as lattice energy. In Figure 3, bottom panel, we show results with and without the D3 correction 28 for the THz region. Additional computational details and results are provided in the SI, including the remaining range with and without D3. While D3 has been known to dramatically correct the values of calculated lattice energies, 29 for vibrational dynamics the D3 correction was found to minimally alter results, affecting the 7



FIR region only slightly, mostly in THz portions. Only for CBZ-SAC I does the D3 correction bring the THz region into better agreement with experiment. For this system, geometric characterization of the supramolecular assembly shows an extended pi-stacking network; for the other systems, stacked aromatic rings are found in dimers. This is characterized in detail on pages S10-S11. These results suggest that even better agreement with experiment can possibly be attained in the THz region through the use of different dispersion corrections.

Figure 3: VISION spectra, experimental: blue, top; calculated: red, middle panel, with D3 correction, and bottom panel, with and without D3 for THz region, for A) saccharin, B) carbamazepine Form III (monoclinic), C) CBZ-SAC I, and D) CBZ-SAC II. Computational optimization of lattice geometry to reflect experimental temperatures is a common procedure, as systems expand and contract, which can affect the nature of the intermolecular interactions. 7 All of the four systems studied by calculation have crystal structures obtained well above 5 K, the temperature at which our INS measurements were collected. 8


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However, the results of our calculations are not affected dramatically by this discrepancy. Strongly hydrogen-bonded systems do not seem to show a large volume change with temperature. 7,20 For rigorous benchmarking of DFT methods, the correct lattice geometry for the experimental temperature should be found; however, it has been shown that this is a highly non-trivial task as it involves the calculation of the vibrational contributions to the free energy at every volume tested. 7,20 This is a subject of our current work. For an understanding of the experimental behavior of the system, however, the structure used for calculation should reflect experimental conditions. The shifting of frequencies in response to temperature is known to affect the THz-region modes most significantly. 30 Experimental temperature response of volume of the CBZ lattice from 300-12 K was determined recently, 20 and the total volume change was found to be below 3 %. Calculated Grüneisen parameters were also reported in this study, based on quasi-harmonic calculations. These translate to a mean frequency change of about 2.1 cm−1 , with a minimum of shift of -11.6 cm−1 and a maximum of 6.1cm

−1

, with most of the larger

shifts in the lower-frequency regions. We measured the INS spectra of benzene and CBZ at temperatures of 50, 100, 150, and 200 K, in addition to 5 K to study the temperature response of frequencies. We found similar magnitudes of shifting in the THz regions as predicted by Brandenburg and coworkers’ calculations, and very little shifting in the region 200 cm−1 and above. These results are displayed in Figure 4. It is possible that strong hydrogen bonds in these systems provide a structural stability sufficient for the crystal lattice to vibrate mostly as a single harmonic oscillator at lower frequencies, which is required for the normal mode formalism. On the other hand, some of the larger (5-9 cm−1 ) shifts in the THz region can explain some discrepancies between calculation and experiment. Extended analysis of the changes in frequency with temperature and volume for CBZ (pages S11-S13) shows that effects of “pure" anharmonicity are negligible for modes of high INS intensity expected to be activated at room temperature (below 210 cm−1 ), especially when properly considering smaller temperature ranges individually (pages

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Figure 4: Temperature response of INS frequencies for CBZ and benzene. A) VISION spectra of benzene measured at a range of temperatures. B) VISION spectra of CBZ, Form III (monoclinic), measured at a range of temperatures. C) Close up of THz region of (B). D), E), F): INS spectra of CBZ in FIR, MIR, and THz regions, respectively, for three temperatures, overlaid with DFT calculations using PBE-D3.

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S12-S13). Above 650 cm−1 , there is more discrepancy between calculation and experiment for all four systems, involving shifts of frequencies as high as 28 cm−1 , see Figure 4 and page S8. Other components of the lineshape are mostly unchanged, suggesting that the magnitude and forms of the modes are mostly correct, and corresponding peaks are thus mappable. Comparison to temperature studies on CBZ and benzene shown in Figure 4 rules out the possibility that these shifts are due to temperature effects, as this region shows very little shifting of frequencies with temperature, even for a less strongly-bound system such as benzene. This region consists of modes involving bending of hydrogen-containing groups such as C-H and N-H bonds, and possibly may involve anharmonic or only locally-harmonic dynamics. Alternately, these errors may indicate problems with the description of the forces calculated by the PBE functional or the dispersion correction. This suggests a method of benchmarking DFT methods. Benchmarking the Hessian will report not only on minimum energy but also on the shape of the potential energy surface, which is important to dynamics. The MIR-region frequencies may possibly be corrected in the future following such benchmarking studies, and/or any corrections due to anharmonicity. Figure S1 shows gas-phase calculations of VISION spectra for CBZ, for comparison to solid-state results. Gas-phase calculations are unable to achieve good agreement with experiment, and comparison of gas-phase-calculated atomic motions at various frequencies with solid-state calculations shows the modes are not the same. In fact, we found that many similar modes are shifted towards a higher frequency by about 20-30 cm−1 in the solid state, while some motions seen in the gas phase calculation are not found in the solid state, and vice versa (page S5). Peak assignments for CBZ and CBZ-SAC I and II based on the solid-state calculations are displayed in Tables S1, S8 and S9. For CBZ we find numerous modes (Table 1 and Figure S7) with high INS intensity that were not detectable by THz-spectroscopy. 21 Molecular modes combine with lattice modes even for low frequencies, reducing the accuracy of rigid-molecule

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models. Table 1: Comparison of intensities for some low-frequency modes of carbamazepine, for THz spectroscopy and VISION INS, described with respect to carboxamide hydrogen bonds at the homosynthon dimer. THz intensity values from Day and coworkers. 21 Frequency ranges given include frequencies at which the same motion was found to occur in both calculations. Frequency (cm−1 ) 35-38 39-43 44-46 49-53 53-62

Distortion of dimer Out-of plane bend with translation In-plane shear, libration of dimer Translation/libration of dimer Symmetric stretch and libration of dimer Large out-of-plane shear

THz Intensity INS Intensity 0.001 0.87 0, 0 1, 0.76 0 0.6 0 0.7 0 0.75

D3 correction did not significantly affect the forms of the modes, although motions were slightly damped and sometimes involved small differences in groups of atoms comprising the direction of highest magnitude displacement. Figure 5 displays regions for the two CBZ-SAC polymorphs that are compared in detail in Table S10, and illustrates two representative differences in the spectra, labeled by blue arrows, one from the THz region and one from the FIR region. The large peak cluster at 38-45 cm−1 for Form II involves translation of CBZ and cooperative tilting of saccharin stacks, with out-of-plane bending at the heterosynthon-dimer contacts. For Form I, translation of CBZ occurs in the region 47-60 cm−1 , but homosynthon-dimer bonds retain planarity. Form II undergoes out-of-plane twisting of the CBZ rings caused by bending and stretching of C–C bonds at 470-491 cm−1 with an shearing of the heterosynthon-dimer contacts due to immobility of the saccharin, and Form I at 454-475 cm−1 , with a cooperative scissoring of amide hydrogens of the carboxamide group in the homosynthon, and flexible preservation of dimer contacts, due to symmetry about the dimer. Cooperative symmetric vibrations thus are shown to maintain key intermolecular interactions, while non-cooperative vibrations may act in a destabilizing manner. The Debye temperature range for the latter mode is 653.2-706.5 K, so these differences can be expected to be unaltered and to influence the materials at ambient conditions. The same is true for all frequencies over about 220 cm−1 . Many modes in the FIR region demonstrate these types of changes due to symmetry differences, and two examples are provided as animations in the 12


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SI.

Figure 5: A) VISION spectra for polymorphs I and II of CBZ-SAC co-crystal in THz range, and B) in FIR range. Arrows in A and B show modes illustrated in C and D.

Using D3, the total calculated electronic energies of the two forms are very close, as is common for many organic polymorphs. 2 Form II is within 0.7 kJ/mol of Form I, with Form I having the lowest energy, as found in experiment. 26 Although experimental values report free energy, the total electronic energies (Elattice ) of -275.9 kJ/mol (Form I) and 275.2 kJ/mol (Form II), without vibrational additions, are already close to the experimental values of -295.4 kJ/mol and -287.8 kJ/mol, respectively. Without the D3 correction, the difference between the two forms is greater, and Form I is estimated to be less stable, which is incorrect, while the values for the energies are much too low compared to experiment (Table 2). The remaining vibrational contributions should slightly increase the energy by about 13-20 kJ/mol while further separating the forms, favoring Form I. However, we see from Table 2 that the reverse is found by calculation, and Form II is calculated to be more stable after vibrational additions which contribute to the Helmholtz free energy (HFE). The estimated energy of formation (Ef orm ) for CBZ-SAC I from its coformers is calculated to be positive when vibrational contributions are added, but is expected to be negative. Further details about these calculations are documented on pages S3-S4. 13



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Due to the shifted MIR region discussed above, the vibrational contributions, Fvib , to the free energy are incorrect, with the zero-point vibrational energy (ZPVE) more affected than the thermal contribution (TC), due to increased weight of lower-frequency modes in the latter. A rough correction to that region was applied, based on average shifts in the region as compared to frequencies with maximum INS intensity. With this correction, shown in Table 3, numbers begin to approach experimental and physically realistic values. Corrections affect some systems more than others: for SAC and CBZ-SAC I, both positive and negative shifts occurred, and resulted in some cancellation of errors, while the other two systems only shifted in the negative direction. Thus when ranking of polymorph stability and prediction of cocrystal formation is attempted with addition of vibrational contributions, 3 inaccuracies in the MIR region could distort results enough to flip the prediction in the wrong direction, and without a consistent pattern between systems, as can be seen from the results of the sixth blind test of organic crystal structure prediction methods. 31 Table 2: Calculated Thermochemical Values, kJ/mol Elattice ZPVE TC Fvib HFE Ef orm * system PBE PBE-D3 PBE PBE-D3 PBE PBE-D3 PBE PBE-D3 PBE PBE-D3 PBE PBE-D3 SAC -44.6 -126.4 5.3 4.9 -14.3 -14.7 -9.0 -8.4 -53.6 -134.8 – – CBZ -26.7 -146.1 6.8 5.7 -13.4 -14.2 -6.6 -9.8 -33.3 -155.9 – – CBZ-SAC I -72.6 -275.9 13.1 12.5 -27.6 -25.7 -14.5 -13.2 -87.0 -289.1 -0.04 1.6 CBZ-SAC II -78.7 -275.2 11.7 10.1 -28.7 -30.4 -16.9 -20.3 -95.6 -295.5 -8.6 -4.8 Elattice : total electronic lattice energy; ZPVE: zero-point vibrational energy; TC: thermal contribution; Fvib : vibrational contribution to HFE; HFE: Helmholtz free energy; Ef orm : energy of formation of cocrystal fro its units. *Calculated using HFE with vibrational contributions.

Table 3: Corrected Thermochemical Values, kJ/mol system HFE-corr ZPVE-corr TC-corr Fvib -corr Ef orm -corr* SAC -134.5 4.6 -12.7 -8.1 – CBZ -150.1 8.7 -12.7 -4.0 – CBZ-SAC I -288.8 11.2 -24.1 -12.9 -4.2 CBZ-SAC II -290.5 15.8 -31.1 -15.3 -5.9 All values calculated using corrected MIR region based on INS frequencies. Only calculations using D3 are shown. *Calculated using HFE with (corrected) vibrational contributions.

We have demonstrated, in summary, that high-signal, low-frequency VISION INS spectra of organic solids, along with ab initio simulations, can provide an important additional method with which to extract detailed vibrational information for supramolecular assemblies, and to benchmark ab initio free energy calculations. We are beginning the collection 14


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of a dataset of these spectra and associated analyses, made possible by the high-throughput capabilities of this instrument. This provides information that can be crucial to the understanding, prediction and design of novel materials based on supramolecular synthesis.

Acknowledgement The authors thank Jerry Parks and Dmytro Bykov for helpful discussions. This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725, was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Award DE-SC0010419, and made use of the VISION beamline at ORNL’s Spallation Neutron Source, which is supported by the Scientific User Facilities Division, Office of Basic Energy Sciences (BES), U.S. Department of Energy (DOE), under Contract DE-AC05-00OR22725 with UT Battelle, LLC.

Supporting Information Available An extended computational results section, extended experimental results section, and materials and methods sections, lists of gamma-point frequencies for the four computed systems, and two animation files are found in the Supplementary Information (SI).

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For Table of Contents Use Only Exposing key vibrational contributions to properties of organic molecular solids with high signal, low frequency neutron spectroscopy and ab initio simulations. Authors: Anup Pandey*, Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Ada Sedova*, National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA *These authors contributed equally and are listed alphabetically Luke L. Daemen, Yongqiang Cheng, Anibal J. Ramirez-Cuesta: Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

Synopsis: The first spectra of organic molecular crystals and polymorphic cocrystals using the next generation, high-signal VISION spectrometer shows excellent differentiation of polymorphs, and numerous modes in the THz region undetectable with optical methods. For FIR-range frequencies, spectra are accurately reproducible by simulation using ab initio calculations, providing high-confidence spectral assignments and thermochemical information, and a means to benchmark ab initio methods.

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Exposing Key Vibrational Contributions to Properties of Organic

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