Symmetry and chirality in crystals

Chirality hierarchical transfer in homochiral polymer crystallization under high-pressure CO2

Ordered phase transitions are commonly correlated to symmetry breaking, while disordered phase transitions are characterized by symmetry restoration. Nevertheless, this study demonstrates that these correlation relations are not always applicable in chiral polymers under high-pressure Carbon Dioxide. Without racemization, homochiral Poly (lactide acid) can generate two vortex-shaped dendritic crystals with opposite spiral chirality, and snowflake-shaped dendritic crystals without spiral chirality. The transition from homochiral molecules to achiral crystals signifies the chiral symmetry restoration during the ordering process. The primary elements responsible for the various hierarchical transfers of homochiral Poly (lactide acid) are related to chain tilt, surface stress, and frustrated structures of Poly (lactide acid) crystals. Here, we show the entropy impact of Carbon Dioxide can be utilized to programmatically regulate the morphological chirality of crystal superstructure and crystal form of homochiral Poly (lactide acid).

Design and synthesis of S-citalopram-imprinted polymeric sorbent: Characterization and application in enantioselective separation

The current work describes the efficient creation and employment of a new S-citalopram selective polymeric sorbent, made from poly(divinylbenzene-maleic anhydride-styrene). The process began by using suspension polymerization technique in the synthesis of poly(styrene-maleic anhydride-divinylbenzene) microparticles. These were then modified with ethylenediamine, developing an amido-succinic acid-based polymer derivative. The S-citalopram, a cationic molecule, was loaded onto these developed anionic polymer particles. Subsequently, the particles were post-crosslinked using glyoxal, which reacts with the amino group residues of ethylenediamine. S-citalopram was extracted from this matrix using an acidic solution, which also left behind stereo-selective cavities in the S-citalopram imprinted polymer, allowing for the selective re-adsorption of S-citalopram. The attributes of the polymer were examined through methods such as 13C NMR, FTIR, thermogravemetric and elemental analyses. SEM was used to observe the shapes and structures of the particles. The imprinted polymers demonstrated a significant ability to adsorb S-citalopram, achieving a capacity of 878 mmol/g at a preferred pH level of 8. It proved efficient in separating enantiomers of (±)-citalopram via column methods, achieving an enantiomeric purity of 97 % for R-citalopram upon introduction and 92 % for S-citalopram upon release.

Nonlinear Optical Activity of a Chiral Organic-Inorganic ([(NH3CH2CH2)3NH])2[MnBr5]Br5 Photoluminescent and Piezoelectric Crystal

The family of Mn-based organic-inorganic hybrids has greatly expanded due to their advantages in applications. They also show superior bright and size-tunable photoluminescence and can be considered a perfect alternative to toxic lead-based compounds. In this work, we present the detailed structural, optical, and electrical characterization of ([(NH3CH2CH2)3NH])2[MnBr5]Br5. The title compound exhibits a unique type of inorganic arrangement created by the trigonal bipyramids. It crystallizes in noncentrosymmetric space group R32, indicating its optical activity, piezoelectricity, and second-order optical nonlinearity proven by the second harmonic of light measurements. The studied crystals exhibit intense photoluminescence originating from the Mn(II) ion 4T1(G) → 6A1 transition. The measured lifetime of the photoluminescence emission is ≤1.5 ms, while the measured quantum yield for both powder and crystal samples reaches ∼70%.

Chiral and Polar Duality Design of Heteroanionic Compounds: Sr18 Ge9 O5 S31 Based on [Sr3 OGeS3 ]2+ and [Sr3 SGeS3 ]2+ Groups

Chirality and polarity are the two most important and representative symmetry-dependent properties. For polar structures, all the twofold axes perpendicular to the principal axis of symmetry should be removed. For chiral structures, all the mirror-related symmetries and inversion axes should be removed. Especially for duality (polarity and chirality), all of the above symmetries should be broken and that also represents the highest-level challenge. Herein, a new symmetry-breaking strategy that employs heteroanionic groups to construct hourglass-like [Sr3 OGeS3 ]2+ and [Sr3 SGeS3 ]2+ groups to design and synthesize a new oxychalcogenide Sr18 Ge9 O5 S31 with chiral-polar duality is proposed. The presence of two enantiomers of Sr18 Ge9 O5 S31 is confirmed by the single-crystal X-ray diffraction. Its optical activity and ferroelectricity are also studied by solid-state circular dichroism spectroscopy and piezoresponse force microscopy, respectively. Further property measurements show that Sr18 Ge9 O5 S31 possesses excellent nonlinear optical properties, including the strong second harmonic generation efficiency (≈2.5 × AGS), large bandgap (3.61 eV), and wide mid-infrared transparent region (≈15.3 µm). These indicate that the unique microstructure groups of heteroanionic materials are conducive to realizing symmetry-breaking and are able to provide some inspiration for exploring the chiral-polar duality materials.

A Relationship between the Molecular Parity-Violation Energy and the Electronic Chirality Measure

When the weak forces producing parity-violating effects are taken into account, there is a tiny energy difference between the total electronic energies of two enantiomers (ΔEPV), which might be the key to understanding the evolution of the biological homochirality. We focus on the electronic chirality measure (ECM), a powerful descriptor based on the electronic charge density, for quantifying the chirality degree of a molecule, in a representative set of chiral molecules, together with their EPV energies. Our results show a novel, strong, and positive correlation between ΔEPV and ECM, supporting a subtle interplay between the weak forces acting within the nuclei of a given molecule and its chirality. These findings suggest that experimental investigations for molecular parity violation detection should consider molecules with ECM values as large as possible and may support that a chiral signature is imprinted on life by fundamental physics via the parity-violating weak interactions.

A workflow for deriving chemical entities from crystallographic data and its application to the Crystallography Open Database

Knowledge about the 3-dimensional structure, orientation and interaction of chemical compounds is important in many areas of science and technology. X-ray crystallography is one of the experimental techniques capable of providing a large amount of structural information for a given compound, and it is widely used for characterisation of organic and metal-organic molecules. The method provides precise 3D coordinates of atoms inside crystals, however, it does not directly deliver information about certain chemical characteristics such as bond orders, delocalization, charges, lone electron pairs or lone electrons. These aspects of a molecular model have to be derived from crystallographic data using refined information about interatomic distances and atom types as well as employing general chemical knowledge. This publication describes a curated automatic pipeline for the derivation of chemical attributes of molecules from crystallographic models. The method is applied to build a catalogue of chemical entities in an open-access crystallographic database, the Crystallography Open Database (COD). The catalogue of such chemical entities is provided openly as a derived database. The content of this catalogue and the problems arising in the fully automated pipeline are discussed, along with the possibilities to introduce manual data curation into the process.

Continuous symmetry and chirality measures: approximate algorithms for large molecular structures

Quantifying imperfect symmetry of molecules can help explore the sources, roles and extent of structural distortion. Based on the established methodology of continuous symmetry and chirality measures, we develop a set of three-dimensional molecular descriptors to estimate distortion of large structures. These three-dimensional geometrical descriptors quantify the gap between the desirable symmetry (or chirality) and the actual one. They are global parameters of the molecular geometry, intuitively defined, and have the ability to detect even minute structural changes of a given molecule across chemistry, including organic, inorganic, and biochemical systems. Application of these methods to large structures is challenging due to countless permutations that are involved in the symmetry operations and have to be accounted for. Our approach focuses on iteratively finding the approximate direction of the symmetry element in the three-dimensional space, and the relevant permutation. Major algorithmic improvements over previous versions are described, showing increased accuracy, reliability and structure preservation. The new algorithms are tested for three sets of molecular structures including pillar[5]arene complexes with Li+, C100 fullerenes, and large unit cells of metal organic frameworks. These developments complement our recent algorithms for calculating continuous symmetry and chirality measures for small molecules as well as protein homomers, and simplify the usage of the full set of measures for various research goals, in molecular modeling, QSAR and cheminformatics.

Vibrational Circular Dichroism Spectroscopy of Chiral Molecular Crystals: Insights from Theory

Chirality is a curious phenomenon that appears in various forms. While the concept of molecular (RS-)chirality is ubiquitous in chemistry, there are also more intricate forms of structural chirality. One of them is the enantiomorphism of crystals, especially molecular crystals, that describes the lack of mirror symmetry in the unit cell. Its relation to molecular chirality is not obvious, but still an open question, which can be addressed with chiroptical tools. Vibrational circular dichroism (VCD) denotes chiral infrared (IR) spectroscopy that is susceptible to both, the molecular as well as the intermolecular space by means of vibrational transitions. When carried out in the solid state, VCD delivers a very rich set of non-local contributions that are determined by crystal packing and collective motion. Since its discovery in the 1970s, VCD has become the method of choice for the determination of absolute configurations, but its applicability reaches beyond towards the study of different crystal forms and polymorphism. This brief review summarises the theoretical concepts of crystal chirality and how computations of solid-state VCD can shed light into the intimate connection of chiral structure and vibrational optical activity.

Current State of Computational Modeling of Nanohelicenes

This review considers the works that focus on various aspects of the theoretical description of nanohelicenes (other equivalent names are graphene spirals, graphene helicoid, helical graphene nanoribbon, or helical graphene)-a promising class of one-dimensional nanostructures. The intrinsic helical topology and continuous π-system lead to the manifestation of unique optical, electronic, and magnetic properties that are also highly dependent on axial and torsion strains. In this paper, it was shown that the properties of nanohelicenes are mainly associated with the peripheral modification of the nanohelicene ribbon. We have proposed a nomenclature that enables the classification of all nanohelicenes as modifications of some prototype classes.

Revisiting Homochiral versus Heterochiral Interactions through a Long Detective Story of a Useful Azobis-Nitrile and Puzzling Racemate

This paper documents and reinvestigates the solid-state and crystal structures of 4,4'-azobis-4-cyanopentanoic acid (ACPA), a water-soluble azobis-nitrile of immense utility as a radical initiator in living polymerizations and a labile mechanophore that can be embedded within long polymer chains to undergo selective scission under mechanical activation. Surprisingly, for such applications, both the commercially available reagent and their derivatives are used as "single initiators" when this azonitrile is actually a mixture of stereoisomers. Although the racemate and meso compounds were identified more than half a century ago and their enantiomers were separated by classical resolution, there have been confusing narratives dealing with their characterization, the existence of a conglomeratic phase, and fractional crystallization. Our results report on the X-ray crystal structures of all stereoisomers for the first time, along with further details on enantiodiscrimination and the always intriguing arguments accounting for the stability of homochiral versus heterochiral crystal aggregates. To this end, metadynamic (MTD) simulations on stereoisomer molecular aggregates were performed to capture the incipient nucleation events at the picosecond time scale. This analysis sheds light on the driving homochiral aggregation of ACPA enantiomers.

NaRb6(B4O5(OH)4)3(BO2) Featuring Noncentrosymmetry, Chirality, and the Linear Anionic Group BO2. J Am Chem Soc 2023;145:4928-4933. [PMID: 36811389 DOI: 10.1021/jacs.2c12069]

Noncentrosymmetric (NCS) structures are of particular interest owing to their symmetry-dependent physical properties, e.g., pyroelectricity, ferroelectricity, piezoelectricity, and nonlinear optical (NLO) behavior. Among them, chiral materials exhibit polarization rotation and host topological properties. Borates often contribute to NCS and chiral structures via their triangular [BO₃] and tetrahedral [BO₄] units and their numerous superstructure motifs. However, no chiral compound with the linear [BO₂] unit has been reported to date. Herein, an NCS and chiral mixed-alkali-metal borate, NaRb₆(B₄O₅(OH)₄)₃(BO₂), with a linear BO₂^- unit in the structure was synthesized and characterized. The structure features a combination of three types of basic building units (BBUs), [BO₂], [BO₃], and [BO₄] with sp-, sp²-, and sp³-hybridization of boron atoms, respectively. It crystallizes in the trigonal space group R32 (No. 155), one of the 65 Sohncke space groups. Two enantiomers of NaRb₆(B₄O₅(OH)₄)₃(BO₂) were found, and their crystallographic relationships are discussed. These results not only expand the small family of NCS structures with the rare linear BO₂^- unit but also prompt recognition to the fact that NLO materials have generally overlooked the existence of two enantiomers in achiral Sohncke space groups.

Graph isomorphism-based algorithm for cross-checking chemical and crystallographic descriptions

Published reports of chemical compounds often contain multiple machine-readable descriptions which may supplement each other in order to yield coherent and complete chemical representations. This publication presents a method to cross-check such descriptions using a canonical representation and isomorphism of molecular graphs. If immediate agreement between compound descriptions is not found, the algorithm derives the minimal set of simplifications required for both descriptions to arrive to a matching form (if any). The proposed algorithm is used to cross-check chemical descriptions from the Crystallography Open Database to identify coherently described entries as well as those requiring further curation.