Understanding the Terahertz Spectra of Crystalline Pharmaceuticals: Terahertz Spectroscopy and Solid-State Density Functional Theory Study of (S)-(+)-Ibuprofen and (RS)-Ibuprofen

First-Principles Models of Polymorphism of Pharmaceuticals: Maximizing the Accuracy-to-Cost Ratio

Accuracy and sophistication of in silico models of structure, internal dynamics, and cohesion of molecular materials at finite temperatures increase over time. Applicability limits of ab initio polymorph ranking that would be feasible at reasonable costs currently represent crystals of moderately sized molecules (less than 20 nonhydrogen atoms) and simple unit cells (containing rather only one symmetry-irreducible molecule). Extending the applicability range of the underlying first-principles methods to larger systems with a real-life significance, and enabling to perform such computations in a high-throughput regime represent additional challenges to be tackled in computational chemistry. This work presents a novel composite method that combines the computational efficiency of density-functional tight-binding (DFTB) methods with the accuracy of density-functional theory (DFT). Being rooted in the quasi-harmonic approximation, it uses a cheap method to perform all of the costly scans of how static and dynamic characteristics of the crystal vary with respect to its volume. Such data are subsequently corrected to agree with a higher-level model, which must be evaluated only at a single volume of the crystal. It thus enables predictions of structural, cohesive, and thermodynamic properties of complex molecular materials, such as pharmaceuticals or organic semiconductors, at a fraction of the original computational cost. As the composite model retains the solid physical background, it suffers from a minimum accuracy deterioration compared to the full treatment with the costly approach. The novel methodology is demonstrated to provide consistent results for the structural and thermodynamic properties of real-life molecular crystals and their polymorph ranking.

At-line porosity sensing for non-destructive disintegration testing in immediate release tablets

Fully automated at-line terahertz time-domain spectroscopy in transmission mode is used to measure tablet porosity for thousands of immediate release tablets. The measurements are rapid and non-destructive. Both laboratory prepared tablets and commercial samples are studied. Multiple measurements on individual tablets quantify the random errors in the terahertz results. These show that the measurements of refractive index are precise, with the standard deviation on a single tablet being about 0.002, with variation between measurements being due to small errors in thickness measurement and from the resolution of the instrument. Six batches of 1000 tablets each were directly compressed using a rotary press. The tabletting turret speed (10 and 30 rpm) and compaction pressure (50, 100 and 200 MPa) were varied between the batches. As expected, the tablets compacted at the highest pressure have far lower porosity than those compacted at the lowest pressure. The turret rotation speed also has a significant effect on porosity. This variation in process parameters resulted in batches of tablets with an average porosity between 5.5 and 26.5%. Within each batch, there is a distribution of porosity values, the standard deviation of which is in the range 1.1 to 1.9%. Destructive measurements of disintegration time were performed in order to develop a predictive model correlating disintegration time and tablet porosity. Testing of the model suggested it was reasonable though there may be some small systematic errors in disintegration time measurement. The terahertz measurements further showed that there are changes in tablet properties after storage for nine months in ambient conditions.

Optimal estimated standard uncertainties of reflection intensities for kinematical refinement from 3D electron diffraction data

Estimating the error in the merged reflection intensities requires a full understanding of all the possible sources of error arising from the measurements. Most diffraction-spot integration methods focus mainly on errors arising from counting statistics for the estimation of uncertainties associated with the reflection intensities. This treatment may be incomplete and partly inadequate. In an attempt to fully understand and identify all the contributions to these errors, three methods are examined for the correction of estimated errors of reflection intensities in electron diffraction data. For a direct comparison, the three methods are applied to a set of organic and inorganic test cases. It is demonstrated that applying the corrections of a specific model that include terms dependent on the original uncertainty and the largest intensity of the symmetry-related reflections improves the overall structure quality of the given data set and improves the final Rall factor. This error model is implemented in the data reduction software PETS2.

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.

Study on the crystallization behavior and conformation adjustment scale of poly(lactic acid) in the terahertz frequency range

The observed properties of crystalline polymers are determined by their internal structure, which in turn is the result of their different crystallization behaviors. Here, we investigate the crystallization behavior of poly(lactic acid) (PLA) by terahertz time-domain spectroscopy (THz-TDS) at varied temperatures. We find that the changes in the chain packing and conformation of PLA are characterized by THz spectroscopy. Combining X-ray diffraction (XRD) and infrared spectroscopy (IR), we attributed the blue-shift of the THz peak to the tightness of the chain packing, while its absorption enhancement is caused by the conformation transition. The effects of chain packing and chain conformation on the characteristic peak are phased. Furthermore, absorption discontinuities of the characteristic peaks of PLA crystallized at different temperatures are observed, which originated from differences in the degree of conformational transition caused by different thermal energies. We find that the crystallization temperature at which the absorption mutation of PLA occurs corresponds to the temperature at which the motion of the segment and molecular chain is excited, respectively. At these two temperatures, PLA exhibits different scales of conformational transitions leading to stronger absorption and larger absorption changes at higher crystallization temperatures. The results demonstrate that the driving force of PLA crystallization is indeed from changes in chain packing and chain conformation, and the molecular motion scale can also be characterized by THz spectroscopy.

New Insights into the Crystallographic Disorder in the Polymorphic Forms of Aspirin from Low-Frequency Vibrational Analysis

Terahertz time-domain spectroscopy (THz-TDS) is applied to two polymorphs of acetylsalicylic acid (aspirin), and the experimental spectra are compared to lattice dynamical calculations using high accuracy density functional theory. The calculations confirm that forms I and II have very close energetic and thermodynamic properties and also that they show similar spectral features in the far-infrared region, reflecting the high degree of similarity in their crystal structures. Unique vibrational modes are identified for each polymorph which allow them to be distinguished using THz-TDS measurements. The observation of spectral features attributable to both polymorphic forms in a single sample, however, provides further evidence to support the hypothesis that crystalline aspirin typically comprises intergrown domains of forms I and II. Differences observed in the baseline of the measured THz-TDS spectra indicate a greater degree of structural disorder in the samples of form II. Calculated Gibbs free-energy curves show a turning point at 75 K, inferring that form II is expected to be more stable than form I above this temperature as a result of its greater vibrational entropy. The calculations do not account for any differences in configurational entropy that may arise from expected structural defects. Further computational work on these structures, such as ab initio molecular dynamics, would be very useful to further explore this perspective. Here, aspirin is a model system to show how the additional insight from the low-frequency vibrational information complements the structural data and allows for quantitative thermodynamic information of pharmaceutical polymorphs to be extracted. The methodology is directly applicable to other polymorphic systems.

Scalemic mixtures preparation for optimized composition of ibuprofen solid dosage forms

The stable and metastable phase diagrams between the sinister and the rectus ibuprofen enantiomers were established by means of thermal analysis and X-ray powder diffraction experiments as a function of temperature. The results obtained allow proving for the first time the existence, for the stable system, of a solid solution by mixing the racemic ibuprofen with one of its enantiomers for low concentration of the enantiomer. Since the rectus ibuprofen is a non-active pharmaceutical agent which can be partially bio-converted into the sinister enantiomer, the present work offers a new approach for scalemic mixtures preparation in order to improve the benefit/risk ratio related to ibuprofen solid dosage form administration.

Qualitative and quantitative recognition of chiral drugs based on terahertz spectroscopy

Chiral drugs are drugs with chiral or asymmetric centres in their molecular structure. Different enantiomers of the same chiral drug have noticeably different pharmacological activities and pharmacokinetic properties. However, its distinction has been perplexing scholars for many years in the qualitative and quantitative detection of antagonistic drugs. Conventional detection methods, such as polarimetry, circular dichroism, and high-performance liquid chromatography, are time consuming, cause sample loss and have cumbersome operations, and they can be applied only to the sampling method. In this paper, we propose a fast, accurate, qualitative and quantitative method for the study of chiral drugs based on linearly polarized terahertz (THz) spectroscopy and imaging technology. Taking ibuprofen as an example, based on the THz absorption spectra of the enantiomers RS-ibuprofen, (R)-(-)-ibuprofen, and (S)-(+)-ibuprofen, their characteristic peak frequencies, peak amplitude differences and peak area differences were extracted to qualitatively and quantitatively distinguish and identify the three substances. THz spectral imaging provides more intuitive results than those obtained from previous methods. In quantitative identification, the stability and detection accuracy of THz spectroscopy are much greater than those of Raman spectroscopy (88.8-99.8% vs. 21.42-94.62%, respectively). The qualitative recognition accuracy was 100%, and the quantitative recognition standard deviation was less than 0.01, and it is also a non-destructive testing method. Furthermore, the above method combined with principal component analysis (PCA) and the support vector machine (SVM) neural network classification algorithm was applied to the analysis of other chiral drugs. These results are significant for the rapid, accurate and non-destructive identification of chiral drugs.

Broadband terahertz signatures and vibrations of dopamine

Dopamine (DA) is an essential neurotransmitter and hormone of the nervous system, its structural and conformational properties play critical roles in biological functions and signal transmission processes. Although this neuroactive molecule has been studied extensively, the low-frequency vibration features that are closely related to the conformation and molecular interactions in the terahertz (THz) band still remain unclear. In this study, a broadband THz time-domain spectroscopy (THz-TDS) system in the frequency band of 0.5-18 THz was used to characterize the unique THz fingerprint of DA. In addition, density functional theory (DFT) calculations were performed to analyze the vibrational properties of DA. The results suggest that each THz resonant absorption peak of DA corresponds to specific vibrational modes, and the collective vibration also exists in the broadband THz range. Moreover, the interactions between the DA ligand and the D2 and D3 receptors were investigated by docking, and the simulated THz spectra were obtained. The results indicate the dominant role of hydrogen bonding interactions and the specificity of molecular conformation. This work may help to understand the resonance coupling between THz electromagnetic waves and neurotransmitters.

Reducing crystal structure overprediction of ibuprofen with large scale molecular dynamics simulations

Reduction of a large dataset of computationally predicted structures of ibuprofen by employing molecular dynamics and biased simulations at finite temperature and pressure.

Terahertz circular dichroism spectroscopy of biomaterials enabled by kirigami polarization modulators

Terahertz circular dichroism (TCD) offers multifaceted spectroscopic capabilities for understanding the mesoscale chiral architecture and low-energy vibrations of macromolecules in (bio)materials^1-5. However, the lack of dynamic polarization modulators comparable to polarization optics for other parts of the electromagnetic spectrum is impeding the proliferation of TCD spectroscopy^6-11. Here we show that tunable optical elements fabricated from patterned plasmonic sheets with periodic kirigami cuts make possible the polarization modulation of terahertz radiation under application of mechanical strain. A herringbone pattern of microscale metal stripes enables a dynamic range of polarization rotation modulation exceeding 80° over thousands of cycles. Following out-of-plane buckling, the plasmonic stripes function as reconfigurable semi-helices of variable pitch aligned along the terahertz propagation direction. Several biomaterials, exemplified by an elytron of the Chrysina gloriosa, revealed distinct TCD fingerprints associated with the helical substructure in the biocomposite. Analogous kirigami modulators will also enable other applications in terahertz optics, such as polarization-based terahertz imaging, line-of-sight telecommunication, information encryption and space exploration.

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.

Terahertz Spectroscopy of Tetrameric Peptides

Determining the sequence and structure of peptides is crucial for understanding their structure-property relationships. Among many techniques, structures are typically elucidated using nuclear magnetic resonance spectroscopy and single crystal X-ray diffraction measurements. In this study, we present terahertz time-domain spectroscopy (THz-TDS) as a complementary, nondestructive technique that is sensitive to both the primary and secondary structures of tetrapeptides. Using only a few milligrams of peptide, THz-TDS spectra have been measured, some of which have been supported by density functional theory (DFT) calculations, to distinguish six tetrameric peptides with similar primary and secondary structures.

Correlation between saturated fatty acid chain-length and intermolecular forces determined with terahertz spectroscopy

We measured crystalline (C-form) saturated fatty acids with even carbon numbers ranging from 12 to 20 using temperature dependent terahertz time-domain spectroscopy (THz-TDS). Absorption features between 0.5 and 3 THz were identified at temperatures from 96 K to 293 K, and a systematic red-shift was obvserved with the increasing carbon chain length. The origins of these absorption bands were uncovered using state-of-the-art ab initio density functional theory (DFT) calculations. Similar vibrational motions in the absorption bands of the different materials highlight the unique role that THz-TDS has for probing weak non-covalent interactions in these materials. Our results showcase the utility of the terahertz region, which is beyond the scope of related vibrational techniques, providing direct evidence of the effect of chain length on the intermolecular interactions of these molecules.

Chiral Purity of Crystals Using Low-Frequency Raman Spectroscopy

The pharmaceutical industry is in need of new techniques to identify the chirality of solids due to regulatory and safety concerns regarding the biological activity of enantiomers. In this study, we present for the first time the application of low-frequency Raman spectroscopy as a new and sensitive method for analyzing the chiral purity of crystals. Using this method, we were able to identify small amounts, as low as 1 % w/w, of an enantiomer in racemic crystals. To demonstrate the capabilities of the method, we used a model system based on chiral crystals of enantiopure, racemic crystals and their mixtures in various ratios. We found that the low-frequency Raman spectra of racemic and enantiopure crystals are significantly different, reflecting the different hydrogen bond networks. Moreover, a comparison of the sensitivity of enantiomeric excess in chiral crystals to that of circular dichroism and X-ray diffraction measurements showed that low-frequency Raman attains high sensitivity comparable to chiral optical methods used for solutions. Overall, our proposed approach of using Raman spectroscopy for determining enantiomeric excess in crystals is simple, fast, and offers a high degree of chiral sensitivity.

Terahertz and infrared characteristic absorption spectra of aqueous glucose and fructose solutions

In this paper, the terahertz (THz) and infrared (IR) characteristic absorption spectra of aqueous glucose solutions and aqueous fructose solutions with different concentrations were measured and studied. The absorption spectra of these two molecules in solid-state and in aqueous solutions were compared and analyzed, the significant effect of molecular adjacent environment on the molecular structure and vibrational mode was revealed. In addition, the THz and IR absorption spectra of these two isomers' aqueous solutions were also compared and explored. No obvious differences were found from their IR absorption features measured at room temperature, while their THz absorption spectra do have the differences, indicating THz characteristic absorption spectra more suitable for the detection and identification of aqueous glucose and fructose solutions. The results are helpful to understand the influence of aqueous solutions environment on the molecular structures and vibrational modes of the materials, and also provide a theoretical reference for the quantum chemical calculation of biological macromolecules.

Exploring the solid state phase transition in dl-norvaline with terahertz spectroscopy

Experimental and theoretical demonstration of the power of terahertz spectroscopy to provide novel insights into solid-state phase-transformations in organic materials.

Terahertz spectra of l-phenylalanine and its monohydrate

The low-frequency vibrational property of l-phenylalanine (l-Phe) and l-phenylalanine monohydrate (l-Phe·H₂O) has been investigated by terahertz time-domain spectroscopy (THz-TDS) at room and low temperature ranging from 0.5 to 4.5THz. Distinctive THz absorption spectra of the two compounds were observed. Density functional theory (DFT) calculations based on the crystal structures have been performed to simulate the vibrational modes of l-Phe and l-Phe·H₂O and the results agree well with the experimental observations. The study indicates that the characterized features of l-Phe mainly originate from the collective vibration of molecules. And the characterized features of l-Phe·H₂O mainly come from hydrogen bond interactions between l-Phe and water molecules. l-Phe and l-Phe·H₂O were also verified by differential scanning calorimetry and thermogravimetry (DSC-TG) and powder X-ray diffraction (PXRD) examinations.

Characteristics of Low-Frequency Molecular Phonon Modes Studied by THz Spectroscopy and Solid-State ab Initio Theory: Polymorphs I and III of Diflunisal

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 of gamma point phonon modes within the 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.

Intramolecular vibrations in low-frequency normal modes of amino acids: L-alanine in the neat solid state

This paper presents a theoretical analysis of the low-frequency phonons of L-alanine by using the solid-state density functional theory at the Γ point. We are particularly interested in the intramolecular vibrations accessing low-frequency phonons via harmonic coupling with intermolecular vibrations. A new mode-analysis method is introduced to quantify the vibrational characteristics of such intramolecular vibrations. We find that the torsional motions of COO(-) are involved in low-frequency phonons, although COO(-) is conventionally assumed to undergo localized torsion. We also find the broad distributions of intramolecular vibrations relevant to important functional groups of amino acids, e.g., the COO(-) and NH3(+) torsions, in the low-frequency phonons. The latter finding is illustrated by the concept of frequency distribution of vibrations. These findings may lead to immediate implications in other amino acid systems.

First principles investigation of L-alanine in terahertz region

Terahertz absorption spectrum (0.5-4.0 THz) of L-alanine in the solid phase was measured by terahertz time-domain spectroscopy at room temperature. Simulations utilizing gaseous-state and solid-state theory were performed to determine the origins of the observed vibrational features. Our calculations showed that the measured features in solid-state materials could be well understood by considering the crystal packing interactions in a solid-state density functional theory calculation. Furthermore, intermolecular vibrations of L-alanine are found to be the dominating contributions to these measured spectral features in the range of 0.5-4.0 THz, except that located at 3.11 THz.

Terahertz spectroscopy: a powerful new tool for the chemical sciences?

Terahertz spectroscopy is only now beginning to make its transition from initial development by physicists and engineers to broader use by chemists, materials scientists and biologists, thanks to the increasing availability of commercial terahertz spectrometers. With the unique insights that terahertz spectroscopy can provide into intermolecular bonding and crystalline matter, it could prove to be an invaluable addition to the chemist's analytical toolset. This tutorial review aims to give an introduction to terahertz spectroscopy, its techniques, equipment, current applications and potential for the chemical sciences to a broad readership.

Revealing the true crystal structure of L-phenylalanine using solid-state density functional theory

Solid-state density functional theory can be used for crystal structure determination from powder X-ray diffraction data of molecular crystals that are too large and complex for conventional refinement methods.

Noncovalent interactions between modified cytosine and guanine DNA base pair mimics investigated by terahertz spectroscopy and solid-state density functional theory

Modified cytosine and guanine nucleobases cocrystallize in a hydrogen bonding configuration similar to that observed in native DNA. The noncovalent interactions binding these base pairs in the crystalline solid were investigated using terahertz (THz) spectroscopy and solid-state density functional theory (DFT). While stronger hydrogen bonding interactions are responsible for the general molecular orientations in the crystalline state, it is the weaker dipole-dipole and dispersion forces that determine the overall packing arrangement. The inclusion of dispersion interactions in the DFT calculations was found to be necessary to accurately simulate the unit cell structure and THz vibrational spectrum. Using properly modeled intermolecular potentials, the lattice vibrational motions of the cytosine and guanine derivatives were calculated. The vibrational characters of the modes exhibited by the DNA base pair mimic in the THz region were primarily rotational motions and are indicative of the energies and the nature of vibrations that would likely be observed between similar base pairs in DNA molecules.