Resolving the Origins of Crystalline Anharmonicity Using Terahertz Time-Domain Spectroscopy and ab Initio Simulations

Terahertz time-domain transmission spectroscopy of water and hydrogel thin films: Extraction of optical parameters and application to agarose gel characterization

Terahertz time-domain spectroscopy (THz-TDS) is an emerging optical technique that has potential applications in the characterization of (bio)materials. However, the complicated extraction of optical parameters from multi-layered and optically thin samples is a barrier towards its acceptance by applied scientists. Therefore, the aim of this work is to provide a straightforward approach for the extraction of the THz absorption coefficient and index of refraction profiles of aqueous thin films in a window-sample-window configuration, which is ubiquitous in many laboratories (i.e., sample in a cuvette). A numerical approach-based methodology that accounts for multiple layers, Fabry-Pérot effect, and sample thickness is elaborated which involves an optical interference model based on a tri-layer structure and a simple thickness estimation technique. This method was validated on water samples where a good agreement was found with the THz optical parameters of water reported in the literature, while the use of a commercial software resulted in erroneous optical parameters estimates when used without due regard to its limitations. A case study was then performed to demonstrate the ability of the proposed method to characterize agarose hydrogels with varying degree of sulfation. It was demonstrated that THz-TDS can provide insight into the hydration state of the agarose hydrogels, including the relative number of the hydrogen bonds between the hydroxyl moieties of water and the polysaccharide network which is perturbed by the presence of sulfate. The trend in the index of refraction profiles suggested microstructural differences between the agarose hydrogels, which were confirmed by visualizing the agarose network morphology using cryo-SEM imaging.

Is Ortho-Terphenyl a Rigid Glass Former?

Ortho-terphenyl (OTP) has long been used as a model system to study the glass transition due to its apparent simplicity and a widespread assumption that it is a rigid molecule. Here, we employ terahertz time-domain spectroscopy and low-frequency Raman spectroscopy to investigate the rigidity of OTP by direct observation of the low-frequency vibrational dynamics. These terahertz phonons involve complex large-amplitude atomic motions where intramolecular and intermolecular displacements are often mixed. Comparison of experimental results with density functional theory and ab initio molecular dynamics simulations shows that the assumption of rigidity neglects important implications for the glass transition and must be revisited. These results highlight the significance of terahertz modes on elasticity, which will be even more critical in more complex systems such as biomolecules.

Investigating the function and design of molecular materials through terahertz vibrational spectroscopy

Terahertz spectroscopy has proved to be an essential tool for the study of condensed phase materials. Terahertz spectroscopy probes the low-frequency vibrational dynamics of atoms and molecules, usually in the condensed phase. These nuclear dynamics, which typically involve displacements of entire molecules, have been linked to bulk phenomena ranging from phase transformations to semiconducting efficiency. The terahertz region of the electromagnetic spectrum has historically been referred to as the 'terahertz gap', but this is a misnomer, as there exist a multitude of methods for accessing terahertz frequencies, and now there are cost-effective instruments that have made terahertz studies much more user-friendly. This Review highlights some of the most exciting applications of terahertz vibrational spectroscopy so far, and provides an in-depth overview of the methods of this technique and its utility to the study of the chemical sciences.

Chemical Modifications Suppress Anharmonic Effects in the Lattice Dynamics of Organic Semiconductors

The lattice dynamics of organic semiconductors has a significant role in determining their electronic and mechanical properties. A common technique to control these macroscopic properties is to chemically modify the molecular structure. These modifications are known to change the molecular packing, but their effect on the lattice dynamics is relatively unexplored. Therefore, we investigate how chemical modifications to a core [1]benzothieno[3,2-b]benzothiophene (BTBT) semiconducting crystal affect the evolution of the crystal structural dynamics with temperature. Our study combines temperature-dependent polarization-orientation (PO) low-frequency Raman measurements with first-principles calculations and single-crystal X-ray diffraction measurements. We show that chemical modifications can indeed suppress specific expressions of vibrational anharmonicity in the lattice dynamics. Specifically, we detect in BTBT a gradual change in the PO Raman response with temperature, indicating a unique anharmonic expression. This anharmonic expression is suppressed in all examined chemically modified crystals (ditBu-BTBT and diC8-BTBT, diPh-BTBT, and DNTT). In addition, we observe solid-solid phase transitions in the alkyl-modified BTBTs. Our findings indicate that π-conjugated chemical modifications are the most effective in suppressing these anharmonic effects.

Low-Frequency Vibrational Spectroscopy and Quantum Mechanical Simulations of the Crystalline Polymorphs of the Antiviral Drug Ribavirin

Crystal polymorphism is a common phenomenon in pharmaceutical solids and a critical issue when considering the formulation of therapeutics since multiple polymorphs may form during drug manufacturing. Low-frequency vibrational spectroscopy is sensitive to polymorphic content, and in this work, terahertz time-domain spectroscopy and low-frequency Raman spectroscopy were utilized in the study of crystalline ribavirin, a widely applicable antiviral. Characteristic spectra with numerous peaks in the sub-200 cm^–1 region were obtained of the more common polymorph of ribavirin (Form II). Solid-state density functional theory (ss-DFT) simulations were then used to optimize the crystal structure of this polymorph and calculate the frequencies and spectral intensities of the lattice vibrations in the low-frequency region. The near-harmonic thermal behavior of the sample with cooling enabled excellent agreement between experiment and theory to be achieved, emphasizing the quality of the applied model, and the observed spectral peaks could be assigned to specific atomic motions in the solid. Form I and Form II polymorphs of ribavirin were both investigated with ss-DFT to understand the different aspects governing the relative stabilities of these solids. The ss-DFT simulations of the polymorph energies revealed that Form II is more stable at all temperatures due to a stronger cohesive energy than Form I; however, ribavirin in Form I has a significantly lower conformational energy. The finding of monotropism appears to conflict with the reported enantiotropism of the ribavirin polymorphs but ultimately confirms that crystal defects in the real samples greatly affect the thermodynamic relationship of the crystals.

In Situ Observation of the Structure of Crystallizing Magnesium Sulfate Heptahydrate Solutions with Terahertz Transmission Spectroscopy

Terahertz time-domain spectroscopy in a transmission geometry combined with visual analysis was used to investigate the crystallization process of MgSO₄ solution. Careful spectral analysis of both a feature at 1.6 THz and the overall magnitude of absorption allowed the extraction of information about the liquid phase before and during crystallization, aiding the investigation of solvation dynamics and the behavior of molecular species at phase boundaries. The method was reproducibly applied to a number of measurements on a series of solutions of three chosen concentrations at different temperatures. When increasing temperature at the end of the measurement, the dissolution of crystals was observed as well. The temperature-dependent absorption data of the semicrystalline systems were converted to the solvent concentrations using a recently developed method. Solutions of a series of concentrations were also investigated in the temperature range of 4-25 °C. The results were compared to the theoretical calculated values, and the consistent differences proved the existence of a hydration shell around the salt ions whose behavior is different from bulk water. Future work will focus on triggering nucleation at specific positions in order to study the very beginning of the crystallization process. MgSO₄ heptahydrate is used as a model system in this study, while the concept and the setup can be applied to other systems.

On the use of a volume constraint to account for thermal expansion effects on the low-frequency vibrations of molecular crystals

A volume-constraint method is presented as a means to capture the influence of thermal expansion on the low-frequency vibrations in molecular crystals. In particular, the room-temperature terahertz absorption spectra of L-tartaric acid, α-lactose monohydrate, and α-para-aminobenzoic acid (PABA) have been simulated using dispersion-corrected, solid-state density functional theory (DFT-D). By comparing the normal modes obtained with a unit cell optimised without constraints to those obtained with a unit cell optimised while constrained to keep its experimental volume, wholesale improvements to the resultant spectrum is achieved when using the constrained geometry by inhibiting cell contraction. These improvements are demonstrated over a range of popular density functionals and basis sets up to triple-zeta complexity. A correlation method is then presented as a means to quantitatively compare the vibrational pattern of normal modes obtained from both unit cells. This analysis reveals that thermal expansion can effect the character and relative frequency of normal modes, with the choice of geometry ultimately affecting the assignment of the experimental absorptions. The sensibility of using the experimental volume as an approximation is then discussed, where it is speculated that large basis sets or hybrid functionals are necessary to ensure that the thermal expansion effect is not overestimated. The low-frequency absorption spectrum of PABA is then fully characterised using the PBE-D3BJ/6-311G(2d,2p) method.

Low-frequency vibrational spectroscopy: a new tool for revealing crystalline magnetic structures in iron phosphate crystals

In this report, the strong-dependence of low-frequency (terahertz) vibrational dynamics on weak and long-range forces in crystals is leveraged to determine the bulk magnetic configuration of iron phosphate - a promising material for cathodes in lithium ion batteries. We demonstrate that terahertz time-domain spectroscopy - coupled with quantum mechanical simulations - can discern between various spin configurations in FePO₄. Furthermore, the results of this work unambiguously show that the well-accepted space group symmetry for FePO₄ is incorrect, and the low-frequency spectroscopic measurements provide a clearer picture of the correct structure over the gold-standard of X-ray diffraction. This work opens the door for characterizing, predicting, and interpreting crystalline magnetic ordering using low-frequency vibrational spectroscopy.

The necessity of periodic boundary conditions for the accurate calculation of crystalline terahertz spectra

Terahertz vibrational spectroscopy has emerged as a powerful spectroscopic technique, providing valuable information regarding long-range interactions - and associated collective dynamics - occurring in solids. However, the terahertz sciences are relatively nascent, and there have been significant advances over the last several decades that have profoundly influenced the interpretation and assignment of experimental terahertz spectra. Specifically, because there do not exist any functional group or material-specific terahertz transitions, it is not possible to interpret experimental spectra without additional analysis, specifically, computational simulations. Over the years simulations utilizing periodic boundary conditions have proven to be most successful for reproducing experimental terahertz dynamics, due to the ability of the calculations to accurately take long-range forces into account. On the other hand, there are numerous reports in the literature that utilize gas phase cluster geometries, to varying levels of apparent success. This perspective will provide a concise introduction into the terahertz sciences, specifically terahertz spectroscopy, followed by an evaluation of gas phase and periodic simulations for the assignment of crystalline terahertz spectra, highlighting potential pitfalls and good practice for future endeavors.

A study of plant growth regulators detection based on terahertz time-domain spectroscopy and density functional theory

Terahertz technology is receiving increasing attention for its use as an efficient non-destructive, non-contact and label-free optical method for qualitative and quantitative detection. The aim of this study was to develop a chemical analysis methodology based on terahertz time-domain spectra that could be used to detect plant growth regulators, such as glyphosine, naphthaleneacetic acid, daminozide and gibberellic acid. The THz fingerprint spectra of these four PGRs were located in the 0.3–1.8 THz, with the peaks of glyphosine at 0.32, 0.49, 0.74, 0.87, 0.96, and 1.49 THz; daminozide at 0.33, 0.39, 0.55, 0.67, and 1.17 THz; gibberellic acid at 0.46, 0.58, 0.92, and 1.38 THz and naphthaleneacetic acid at 0.43, 0.57, 0.73, and 0.90 THz. The results showed that these four plant growth regulators exhibited numerous distinct spectral features in frequency-dependent absorption spectra, which demonstrated the qualitative capacity of terahertz time-domain. The origin of the observed terahertz absorption peaks of these four plant growth regulators was determined through density functional theory calculations and analysis of absorption spectra. Discriminant analysis method was used to evaluate the classification trends of the four plant growth regulators based on their THz absorbance spectra. Generally, this study provides a reference for the rapid detection of plant growth regulators in fruits and vegetables by using terahertz spectroscopy technology.

Terahertz technology is receiving increasing attention for its use as an efficient non-destructive, non-contact and label-free optical method for qualitative and quantitative detection.

Prediction of the terahertz absorption features with a straightforward molecular dynamics method

In this paper, we provide a straightforward method to predict the terahertz absorption spectrum based on a fixed charge model with classic molecular dynamics calculations. The absorption features in the frequency range between 1 and 3.4 THz of stearic acid B-form and between 1 and 2.7 THz of C-form were successfully calculated. Most of the absorption peaks from the simulation correspond well with those from the measurements. By calculating the spatial and time-dependent energy accumulation in the molecular system, the core idea of our calculation method is further validated. Compared with the ab initio calculations, our method provides a computationally inexpensive way to accurately predict the locations of absorption features. With regard to the traditional molecular dynamic simulations, our method is able to extract the spatial distribution of the energy accumulation as well as the local motions in the molecular system.

Low-temperature dependence on the THz spectrum of CL-20/TNT energetic cocrystal by molecular dynamics simulations

Based on the unique advantages of terahertz (THz) spectrum on the detection of energetic cocrystals, the low-temperature dependent THz spectra of CL-20/TNT cocrystal were investigated by using molecular dynamics (MD) simulations from 5 to 296 K, as well as three different crystal faces, (001), (120), and (010). When the temperature decreases below 95 K, we have observed two new peaks for CL-20/TNT cocrystal, at 4.58 and 5.99 THz, respectively. Also, the THz peaks below 1.5 THz gradually disappear under cooling from 296 to 5 K, and they should originate from the lattice thermal vibrations. THz absorption peaks of CL-20/TNT cocrystal reveal frequency shifting, linearly dependent on temperature. Four of them are red shift and other two are blue shift of THz vibrational peaks of CL-20/TNT cocrystal with the temperature increase. The frequency shifts can be attributed to the effects of lattice thermal expansion on inter-/intramolecular vibrational modes as well as their coupling. From the temperature-dependent THz spectra of different crystal faces, we further confirm the response of different kinds of intermolecular interactions on the THz spectrum of CL-20/TNT cocrystal. Graphical abstractThe intermolecular interactions and peak positions of THz spectra of CL-20/TNT cocrystal in the range of 0-6 THz versus temperature.

Effects of Solvent Stabilization on Pharmaceutical Crystallization: Investigating Conformational Polymorphism of Probucol Using Combined Solid-State Density Functional Theory, Molecular Dynamics, and Terahertz Spectroscopy

Solid-state density functional theory (DFT), molecular dynamics (MD), and terahertz (THz) spectroscopy were used to study the formation of enantiotropically related conformational Form I and Form II polymorphs of the pharmaceutical compound, probucol. DFT calculations were performed on the crystal systems to compare relative lattice energies and the solvent stabilization of the metastable Form II structure. The thermodynamics of solvent inclusion in the Form II·MeOH crystal system were determined from MD simulations, as was the favored conformation of molecular probucol in methanol and ethanol solutions. The findings from both solid-state DFT and MD calculations suggest that the preferred molecular orientations of the probucol molecule in solution and the probable inclusion of methanol in the crystal lattice during the crystallization process lead to the solvent selectivity of the probucol polymorph formation. The additional stabilization energy provided by the crystallization solvent facilitates the nucleation and growth of the Form II polymorph under conditions that favor this metastable crystal form over the thermodynamically stable Form I, despite the higher energy molecular and crystalline configurations of probucol Form II. We demonstrate the influence of solvent on the formation of pharmaceutical polymorphs and provide a molecular-level view of complex interactions leading to polymorphism using a combination of computational methods and THz spectral data.

Molecular Dynamics Simulations of Macromolecular Crystals

The structures of biological macromolecules would not be known to their present extent without X-ray crystallography. Most simulations of globular proteins in solution begin by surrounding the crystal structure of the monomer in a bath of water molecules, but the standard simulation employing periodic boundary conditions is already close to a crystal lattice environment. With simple protocols, the same software and molecular models can perform simulations of the crystal lattice, including all asymmetric units and solvent to fill the box. Throughout the history of molecular dynamics, studies of crystal lattices have served to investigate the quality of the underlying force fields, correlate the simulated ensembles to experimental structure factors, and extrapolate the behavior in lattices to behavior in solution. Powerful new computers are enabling molecular simulations with greater realism and statistical convergence. Meanwhile, the advent of exciting new methods in crystallography, including femtosecond free-electron lasers and image reconstruction for time-resolved crystallography on slurries of small crystals, is expanding the range of structures accessible to X-ray diffraction. We review past fusions of simulations and crystallography, then look ahead to the ways that simulations of crystal structures will enhance structural biology in the future.

Optical Properties of Meloxicam in the Far-Infrared Spectral Region

One of the most commonly used nonsteroidal anti-inflammatory active pharmaceutical ingredient called Meloxicam has been characterized spectroscopically both by Terahertz (THz) time domain spectroscopy (THz-TDS) and by Fourier Transform Infrared (FTIR) spectroscopy in far-IR regions of electromagnetic spectrum; 0.2 THz to 20 THz. While many relatively sharp features are observed in the far-IR range between 2 THz to 20 THz as expected for being an organic substance, very distinct and relatively strong absorption bands are also observed at 1.00, 1.66, 2.07 and 2.57 THz in the THz range. These well separated, defined, and fairly strong spectral features can be used for discrimination and quantification of Meloxicam in drug analysis. Frequency dependent refractive index of the drug was determined in a range of 0.2 THz and 2.7 THz, where an almost constant index was observed with an average index of 1.75. Powder XRD, and solid-state Density Functional Theory (SS-DFT) calculations were utilized to determine the crystalline form of the Meloxicam sample in its enolic crystalline form. Single molecule DFT calculations were also performed in all four possible structures of Meloxicam. In addition, the capability of THz waves transmission through common packaging materials is demonstrated for possibility of future on-site analysis. The results suggest that drug analysis will be possible to perform not only at every stage of manufacturing without destruction but also directly at the shelf of a market after development of portable THz technologies.

Uncovering the Connection Between Low-Frequency Dynamics and Phase Transformation Phenomena in Molecular Solids

The low-frequency motions of molecules in the condensed phase have been shown to be vital to a large number of physical properties and processes. However, in the case of disordered systems, it is often difficult to elucidate the atomic-level details surrounding these phenomena. In this work, we have performed an extensive experimental and computational study on the molecular solid camphor, which exhibits a rich and complex structure-dynamics relationship, and undergoes an order-disorder transition near ambient conditions. The combination of x-ray diffraction, variable temperature and pressure terahertz time-domain spectroscopy, ab initio molecular dynamics, and periodic density functional theory calculations enables a complete picture of the phase transition to be obtained, inclusive of mechanistic, structural, and thermodynamic phenomena. Additionally, the low-frequency vibrations of a disordered solid are characterized for the first time with atomic-level precision, uncovering a clear link between such motions and the phase transformation. Overall, this combination of methods allows for significant details to be obtained for disordered solids and the associated transformations, providing a framework that can be directly applied for a wide range of similar systems.

Predicting the structures and associated phase transition mechanisms in disordered crystals via a combination of experimental and theoretical methods

Experimental terahertz time-domain spectroscopy and theoretical solid-state ab initio density functional theory and molecular dynamics simulations are used to elucidate the structures, dynamics, and phase transformation processes of molecular crystals undergoing a solid-state order–disorder transition.

The significance of the amorphous potential energy landscape for dictating glassy dynamics and driving solid-state crystallisation

We show clear evidence for a theory proposing that the shape and structure of the PES is the fundamental factor underlying the dynamics at temperatures below the glass transition.

Intermolecular anharmonicity in molecular crystals: interplay between experimental low-frequency dynamics and quantum quasi-harmonic simulations of solid purine

A combined experimental spectroscopic and theoretical quasi-harmonic investigation of intermolecular anharmonicity in crystalline purine.