Symmetry Elements Research Articles

Synthesis, crystal structure, and intrinsic reactivity descriptors of coordination complexes of [(cis-PdCl2·L-proline) L-proline] and [trans-PdCl2·(glycine-OMe)2

This work describes the synthesis and structural characterization of two palladium (II) complexes elucidated by infrared spectroscopy, dispersive energy analysis (EDS) with Scanning Electron Microscopy (SEM) and X-ray single-crystal diffraction analysis. The first chiral complex is derivatized from l-proline amino acid, obtaining [Cis-PdCl2·L-proline(L-proline)] (1), in which the structure does not have symmetry elements and crystallized in a triclinic crystal system on a non-centrosymmetric space group P1. The comparison with the structural complex of [trans-PdCl2·(glycine-OMe)2] (3) becomes necessary due to the anticancer activity of its analog, cis-platinum, and the catalytic activity caused by Pd as a metallic center. Complex 1 is therefore made up of a free proline molecule linked by a single hydrogen bond to a PdCl2 molecule forming a 5-member chelate ring of the COO···Pd···NH type with another proline molecule and displaying distorted angles and bond sizes to the square planar geometry of the palladium (Pd) center. Ring formation generates a new stereogenic center chemically correlated with the induction caused by the absolute configuration S of the initial amino acid. The crystal results strongly indicate the confirmed configuration by the Flack parameter and its crystal packing stabilization by an intermolecular H-bond network, highlighting as a secondary mimicking structure the β sheets formed by hydrogen bonding interaction of the N—H···Cl type responsible for the disorder moldered on pyrrolidine ring.Furthermore, the Pd(II) complex obtained by the glycine was [trans-PdCl2·(glycine-OMe)2] (3). Regarding its chemical structure, this complex is constituted by the union of two glycine methyl ester molecules binding to a Pd in a trans disposition concerning the almost perfect square plane, which also contains a C2 axis of rotation. Complex 3 crystallized in a monoclinic system and centrosymmetric space group P21/c, the packing is favored by four strong hydrogen bond type interactions presenting helices with 90° rotations between each layer.Owing to their great interest and relevance in Pd—N amino acid in catalytic and medicinal chemistry, the electronic and global reactivity properties of complexes 1 and 3 were further explored by computational methods in the framework of Density Functional Theory, finding 1 as the most reactive complex due to the narrower E-LUMO/E-HOMO energy gap, having this band gap in agreement with the lowest hardness value compared to those shown for 3, in which band gap and hardness are higher with a tendency to kinetic stability and controlled reactivity.

Structure and Spectral Properties of Thianthrene and Its Benzoyl-Containing Derivatives

The IR absorption spectra of the recently synthesized series of benzoyl-containing thianthrene derivatives were studied in the context of their structural identification. Geometry optimizitation of the ground singlet state by density functional theory (DFT) calculations with the gradient and Hessian search were performed for thianthrene molecule in the framework of the C2v symmetry restriction. The excited singlet and triplet states of thianthrene were found to be distorted along the b3u vibrational mode of the D2h point group, as well as the ground state, which leads to the non-planar batterfly-like structure (C2v). But the excited states require additional symmetry reduction; they are closer to planarity but have no symmetry elements. Optimized ground states structure for the thianthrene-benzoyle molecule and its four derivatives with fluoro-substituents and different substitution positions were analyzed through complete assignment of all their vibrational modes and comparison with experimental infrared absorption spectra. A good agreement between experimental data and DFT calculated IR spectra provides additional structural support to results of the X-ray diffraction analysis of all synthesized compounds. The Hirshfeld surfaces analysis of the crystalline 3-fluorobenzoyl-thianthrene (T3F) was performed in order to analyze intermolecular interactions in T3F crystal. It indicates the presence of weak CH…F, CH…S and CH…O intermolecular contacts, stabilizing the crystal structure of T3F. The CH…O interactions appear in the IR spectrum of T3F crystal as two vibrational modes with frequencies 3084 and 3078 cm–1. The intermolecular interactions CH…F and CH…S do not affect the IR spectrum of T3F.

Fine-structure sensitive deep learning framework for predicting catalytic properties with high precision

The fine structure of a surface considerably affects its catalytic performance in structurally sensitive reactions. High-throughput (HT) screening and machine learning (ML) are considered efficient for exploring the hidden rules of impacts. However, no protocol for constructing an interpretable ML framework sensitive to fine structures has been reported thus far. Herein, we developed a data augmented convolutional neural network (CNN)-based ML framework called “global + local” convolutional neural network (GLCNN), which combines “global + local” features. This framework captures original fine structures without the use of complicated encoding methods by transforming the catalytic surfaces and adsorption sites into two-dimensional grids and one-dimensional descriptors, respectively. The GLCNN framework accurately predicted and distinguished the adsorption energies of OH on a set of analogous carbon-based transition-metal single-atom catalysts with a mean absolute error of less than 0.1 eV. Moreover, this model yields the best results among popular models trained on large datasets so far. Unlike conventional CNN and descriptor-based models with one-sided feature extraction, this fine-structure-sensitive ML framework can extract key factors that affect the catalytic performance from both geometric and chemical/electronic features, such as symmetry and coordination elements, through unbiased interpretable analysis. This framework provides a feasible solution for the high-precision HT screening of heterogeneous catalysts with a broad physical and chemical space.

Platonic and Archimedean bodies as the basis of the structure of self-accommodating complexes of martensite crystals in alloys with shape memory effects

The aim of the work is to analyze the relationship of the architecture of self-accommodation complexes (SC) with the lattice syngony of martensite crystals. Self-accommodating complexes consist of a set of pairwise twinned domains — crystals of martensite belonging to crystallographically equivalent variants of the orientation relationship between the lattices of austenite and martensite. The simplest SC are calculated for tetragonal, orthorhombic, rhombohedral and monoclinic distortion of the cubic lattice of austenite. It is shown that complete self-accommodation is possible only in complexes containing simultaneously all variants of the orientation relation. The issue of external faceting of complexes is discussed. The reason for the formation of SC is the minimization of elastic energy, i.e. the appearance regulated by the energy of the interphase boundary. On the other hand, if the outer surface of the SC is a polyhedron, then its symmetry should "fit"into the anisotropy of the elastic properties of austenite. For reasons of symmetry, it is clear that the polyhedron must be correct and have the same symmetry elements as the cubic lattice of austenite, while the axes of symmetry of the cubic lattice of austenite must coincide with the axes of symmetry of the polyhedron. Similar polyhedra are some of the bodies of Platon and Archimedes, which have axes of symmetry of the 2nd, 3rd and 4th order. A number of examples calculated in the work confirms the possibility of the existence of complexes in the form of these polyhedra.

SYMMETRY OF SYNTACTIC STRUCTURE IN THE QUR'ANIC EXPRESSION

Symmetry is considered as a linguistic tool that aims at illustrating the system of texts structures, from the smallest unit to the largest unit, which is referred to in the linguistics text as the "sentence of the text" as a whole. This tool aims at identifying the types and varieties of symmetries and to explore the methods of their rotation in texts construction. The Holy Quran is the only text in which the elements of symmetry have been integrated, as its chapters and verses were engineered in this miraculous structural pattern. It is the primary source for supplying this phenomenon with its diverse elements, which still need to be explored in all its dimensions and intricacies. The term "Symmetry" is a neologism coined by researcher Ayman Eid Al-Rawajfah, who used it in his research, such as "Symmetry in the Holy Qur'an: Theoretical Foundations and Applications" and "Summetry Grid Theory (Intonation) in the Holy Qur'an,", etc., It is synonymous with the term "proportion," which Arab scholars used in their studies of Qur'anic expression, such as Burhan al-Din (885 AH) in his book entitled "Nizam al-Durar fi Tanasub al-Ayat wa al-Surah," and al-Suyuti (911 AH) in his book "Al-Itqan fi Ulum alQur'an," where he included a titled section called "In the Proportion of Verses and Chapters," among many others. Symmetry in the Holy Quran is not limited to chapters and verses but it includes the arrangement of its language structures, vocabulary, and contexts. The research selected the level of structural elements because of their importance in shaping the intended meanings of verses and chapters and because their elements are interconnected in constructing the text. Therefore, the research aimed to elucidate the mechanism of structural symmetry and its effectiveness in engineering the intended meanings through the treatment of models from the Holy Quran

Vaccine elicitation and structural basis for antibody protection against alphaviruses

Alphaviruses are RNA viruses that represent emerging public health threats. To identify protective antibodies, we immunized macaques with a mixture of western, eastern, and Venezuelan equine encephalitis virus-like particles (VLPs), a regimen that protects against aerosol challenge with all three viruses. Single- and triple-virus-specific antibodies were isolated, and we identified 21 unique binding groups. Cryo-EM structures revealed that broad VLP binding inversely correlated with sequence and conformational variability. One triple-specific antibody, SKT05, bound proximal to the fusion peptide and neutralized all three Env-pseudotyped encephalitic alphaviruses by using different symmetry elements for recognition across VLPs. Neutralization in other assays (e.g., chimeric Sindbis virus) yielded variable results. SKT05 bound backbone atoms of sequence-diverse residues, enabling broad recognition despite sequence variability; accordingly, SKT05 protected mice against Venezuelan equine encephalitis virus, chikungunya virus, and Ross River virus challenges. Thus, a single vaccine-elicited antibody can protect invivo against a broad range of alphaviruses.

Comment on “Comment on “Crystallographic and theoretical study of the atypical distorted octahedral geometry of the metal chromophore of zinc(II) bis((1R,2R)-1,2-diaminocyclohexane) dinitrate””

We defend argumentation that entitled compound (1) (CCDC 1576255) crystallizes into centrosymmetric space-group type P21/n as reported, previously [J. Mol. Struct. 1248 (2022) 131488]. Recent paper [J. Mol. Struct. 1284 (2023) 135362] supports negation of this statement, claiming that (1) is assigned to non-centrosymmetric P21 structure (CCDC 2226587). Inter-laboratory crystallographic experiments support opposite statements, regarding, space-group type. We must be able to argue what fails through experimentation or chemometrics, assessing validity of structural solutions. Single crystal 3D X-ray diffraction analysis is carried out via statistical tests, assessing whether measurands are used reliably. Results from work [J. Mol. Struct. 1284 (2023) 135362] fail to realize robust statistical tests of CheckCIF and PLATON, testing most serious problems of crystallographically determined structure. Major con-arguments against structural solution of CCDC 1576255 are based on our chemical synthesis, using presumably enantiopure analytes. Such argument fails to a significant extend, however. Many reports show that centrosymmetric crystals could contain either non- or centrosymmetric molecules. Moreover, study [J. Mol. Struct. 1284 (2023) 135362] does not provide neither spectroscopic nor chiral chromatographic or mass spectrometric experiments, evidencing chirality and purity of starting ligand and synthetic product (1), in addition to, a lack of data on elemental analysis and synthetic yield. The structural solution is argued only assessing Flack parameter of space-group type P21 (x(u)=0.078(17)) and R1=0.0316 factor. However, the x(u)-value is relatively high. When x(u)≈0 and its sd(yEr±)≈0, then absolute structure is likely considered to be correct one. There is a lack of comments on cases of chiral racemization, typical for ligands such as 1,2-diaminocyclohexane, when x(u)=0.5; and it cannot provide properly in a large number of cases unambiguous justification for correct space group assignment. Small R1-quantity is incapable of justifying unambiguously an absolute structure, as well. Our arguments against structure CCDC 2226587 focus on effect of temperature and energy of X-ray irradiation, in addition to chiral racemization processes. The study uses Mo Kα irradiation. Structural solution CCDC 2226587 does not meet robust test, considering symmetry elements as mentioned above. Conversely, structure CCDC 1576255 satisfies this criterion. The same is true for independent structural solutions of crystals of our sample (CCDC 2256980) examined in paper [J. Mol. Struct. 1248 (2022) 131488], which are presented, as well. Therefore, structure CCDC 1576255 is accurate and precise. It is obtained under repeatability and reproducibility conditions. This is not valid to work [J. Mol. Struct. 1284 (2023) 135362]. The robust capability of tests, considering symmetry elements of distinguishing among space-group types is illustrated via our new data on replicates of non-centrosymmetric P21 structure of (1) (CCDC 2256806) (a = 6.7580(14), b = 7.1970(14), and c = 21.385(4)Å, β=96.69(3)o; Z = 2, V = 1033.0(4) Å3; and R1=0.0770). Its space-group type is proven by the latter test. Comparative analysis with our resolving data on CCDC 2226587 in P21/n structure is also carried out. The latter structural resolving satisfies the test, considering symmetry elements. Chemometrics and high-resolution single crystal X-ray diffraction measurands are used.

Chiral Crystals, Jack, Conductivity and Magnetism

AbstractRecently, the application of magnetic fields to chiral chemical systems has been rewarding. In a forward‐looking 1986 paper, ‘Chiral Metals?’, Wallis, Karrer, and Jack D. Dunitz forecast ‘that the limitation to proper symmetry elements in a chiral conductor could be associated with the emergence of new properties, those connected with interactions between applied electric and magnetic fields and their internal counterparts.’ This was a prescient remark, but it has become manifest in ways that would not have been foreseen in its details by the authors. Here are reviewed the development of chiral conductors broadly imagined by Dunitz and coworkers, based on enantiopure tetrathiafulvalene derivatives that restrict space groups to those that have only symmetry operations of the first kind, as well as the new emergent properties associated with the transport of electrons when magnetic fields are applied to chiral crystals among other systems. These include electrical magnetochiral anisotropy (eMChA), inverse electrical magnetochiral anisotropy (ieMChA), helimagnetism and chirality induced spin selectivity (CISS). The conclusion discussing the circumstances under which achiral TTF crystals becomes chiral, only seems to introduce an oxymoron.

Updates on moleculARweb, the Swiss Portal for Chemistry and Structural Biology Education Using Augmented and now also Virtual Reality

We present a new activity on the moleculARweb platform on molecular symmetry elements, two more languages, a new marker-less augmented reality mode, and a new virtual reality tool for VR headsets.

Programming Motion of Platinum Microparticles: From Linear to Orbital

Self-powered catalytic micromotors that swim through a fluid by harvesting energy from their environment have received increasing attention because of their potential applications in nanomachinery, nanoscale assembly, and robotics. However, persistent directional motion is required for micromotors to perform useful work. Herein, through modeling and experiments, we demonstrate the general design strategy for single-component platinum micromotors that, in the presence of hydrogen peroxide, can execute a variety of motion trajectories from extremely linear to orbital. This is achieved via a simple shape design wherein the speed and directionality of a particle are determined by overall symmetry elements. Shape design gives high reproducibility and allows a wide range of adjustments to fine-tune the desired particle motion. We observe strong agreement between experimental data and numerical predictions, indicating that our model can serve to predict directionality and speed of a particle prior to fabrication. Shape programming works on an individual-particle basis, thus enabling complex systems which require different modes of motion for the individual parts.

Predicting neutrino mixing angles using group presentations

By assuming there exist three massive nondegenerate Majorana neutrinos, it is possible to describe neutrino mixing with a residual, unbroken discrete Klein subgroup of a larger spontaneously broken flavor symmetry group. Motivated by forthcoming measurements of leptonic CP violation, we revisit this framework by applying group presentation rules to it. We develop a method that is able to reproduce all previous results in the literature and may also hint at a possible group theoretical origin of CP violation in the Klein symmetry elements. This is due to the explicit appearance of a phase in them. However, for the cases considered in this analysis, it turns out that this phase can be removed. Still, this new method warrants further study.

Recognition of Symmetry as a Powerful Tool in Natural Product Synthesis

AbstractThe design of concise and efficient synthetic strategies to access naturally occurring, pharmaceutically active complex molecules is of utmost importance in current chemistry. It not only enables rapid access to these molecules and their analogues but also provides sufficient quantities for their biological evaluation. Identification of any symmetric or pseudosymmetric synthetic intermediates upon retrosynthetic bond disconnection of the target molecule holds the promise to significantly streamline the route towards the compound of interest. This review will highlight recent examples of successful natural product syntheses reported within the past five years that benefited from the recognition of symmetry elements during the retrosynthetic design.1 Introduction2 Examples2.1 Chondrosterin I and J2.2 (–)-Bilobalide A2.3 Delavatine A2.4 Oxycodone2.5 (–)-20-epi-vincamine and (–)-20-epi-eburnamonine2.6 Reserpine2.7 (–)-Berkeleyone A2.8 (–)-Maximiscin2.9 Aplysiasecosterol A2.10 (–)-Batrachotoxinin A2.11 (–)-Mitrephorone A3 Conclusions

Predicting single-phase solid solutions in as-sputtered high entropy alloys: High-throughput screening with machine-learning model

Searching for single-phase solid solutions (SPSSs) in high-entropy alloys (HEAs) is a prerequisite for the intentional design and manipulation of microstructures of alloys in vast composition space. However, to date, reported SPSS HEAs are still rare due to the lack of reliable guiding principles for the synthesis of new SPSS HEAs. Here, we demonstrate an ensemble machine-learning method capable of discovering SPSS HEAs by directly predicting quinary phase diagrams based only on atomic composition. A total of 2198 experimental structure data are extracted from as-sputtered quinary HEAs in the literature and used to train a random forest classifier (termed AS-RF) utilizing bagging, achieving a prediction accuracy of 94.6% compared with experimental results. The AS-RF model is then utilized to predict 224 quinary phase diagrams including ∼32,000 SPSS HEAs in Cr-Co-Fe-Ni-Mn-Cu-Al composition space. The extrapolation capability of the AS-RF model is then validated by performing first-principle calculations using density functional theory as a benchmark for the predicted phase transition of newly predicted HEAs. Finally, interpretation of the AS-RF model weighting of the input parameters also sheds light on the driving forces behind HEA formation in sputtered systems with the main contributors being: valance electron concentration, work function, atomic radius difference and elementary symmetries.

A Pair of Interconverting Cages Formed from Achiral Precursors Spontaneously Resolve into Homochiral Conformers.

Without chiral induction the emergence of homochirality from achiral molecules is rather serendipitous, as the rationale is somewhat ambiguous. We herein provide a plausible solution. From achiral precursors are formed a pair of interconverting cage conformers that exhibit a C3 -axis as the only symmetry element. When their interconversion is impeded with intramolecular H-bonding, each conformer self-sorts into a homochiral crystal, which is driven by a helical network of multivalent intermolecular interactions during the self-assembly of homochiral cage conformers. As no chiral induction is involved throughout, we believe our study could enlighten the rational design for the emergence of homochirality with several criteria: 1) formation of a molecule without inversion center or mirror plane; 2) suppression of the enantiomeric interconversion, and introduction of multivalent interactions along the helical trajectory of screw symmetry within the resulting superstructure.

A Pair of Interconverting Cages Formed from Achiral Precursors Spontaneously Resolve into Homochiral Conformers

AbstractWithout chiral induction the emergence of homochirality from achiral molecules is rather serendipitous, as the rationale is somewhat ambiguous. We herein provide a plausible solution. From achiral precursors are formed a pair of interconverting cage conformers that exhibit a C3‐axis as the only symmetry element. When their interconversion is impeded with intramolecular H‐bonding, each conformer self‐sorts into a homochiral crystal, which is driven by a helical network of multivalent intermolecular interactions during the self‐assembly of homochiral cage conformers. As no chiral induction is involved throughout, we believe our study could enlighten the rational design for the emergence of homochirality with several criteria: 1) formation of a molecule without inversion center or mirror plane; 2) suppression of the enantiomeric interconversion, and introduction of multivalent interactions along the helical trajectory of screw symmetry within the resulting superstructure.

From Outside In: Stretching Students’ Conceptual Understanding of Molecular Symmetry with 2D and 3D Manipulatives

The main difficulty in studying molecular symmetry is the mental manipulation of molecules when searching for symmetry. Numerous methods of teaching molecular symmetry require students to identify symmetry elements of objects or molecules. As an alternative, we propose activity that identifies symmetry using elements outside the objects, together with accompanying worksheets containing guiding questions to help them distinguish between transforming symmetrical and asymmetrical objects across/around these elements. This novel activity can be used as a supplement to molecular symmetry instruction at the tertiary level.

Leveraging cognitive resources to investigate the impact of molecular orientation on students’ activation of symmetry resources

This study investigates students’ cognitive resources for identifying symmetry elements using survey data collected from 39 inorganic chemistry students from twelve undergraduate inorganic classes at universities across the United States. We propose a framework that leverages students’ knowledge of symmetry elements as a manifold of cognitive resources that can be productive or unproductive in certain contexts. This cognitive resources framework was paired with an asset-based perspective to advance work in this area beyond a deficit-framed study of “correctness”. Herein, we present findings from a qualitative analysis of the rotation and reflection symmetry elements activated for students by four select molecules. Each molecule was presented in two different static orientations to determine the impact of orientation on students’ cognitive resource activation. Our findings suggest that the orientation of static molecular images impacts the types of resources activated for students. Additionally, this study serves as an example for how to advance assessment of this topic beyond a binary approach (i.e. correct or incorrect).

Ring Silicates Cs4Tm2[Si4O12](OH)2 and Cs4(Tm,Tb)2[Si4O12](OH)2 As Merohedral Twins

New ring silicates Cs4Tm2[Si4O12](OH)2 and Cs4(Tm,Tb)2[Si4O12](OH)2 have been synthesized by the hydrothermal method. A structural analogy is revealed between them and the previously studied silicates K4Sc2(OH)2(Si4O12) and K2Sc[Si2O6]F. Their crystal structures are identified as orthorhombic merohedral twins by the lost element of tetragonal symmetry. The structures of new ring silicates are related to those of fresnoite and tetragonal melilite.

Polymorphism in carboxamide compounds with high-Z′ crystal structures

Repetitivity of 21-axis symmetry element in three polymorphic crystal structures of carboxamide compound with highZ′ packing problem.

A local point of view of the Cu(100) → NiTPP charge transfer at the NiTPP/Cu(100) interface.

A precise understanding, at the molecular level, of the massive substrate → adsorbate charge transfer at the NiTPP/Cu(100) interface has been gained through the application of elementary symmetry arguments to the structural determination of the NiTPP adsorption site by photoelectron diffraction (PED) measurements and Amsterdam density functional calculations of the free D4h NiTPP electronic structure. In particular, the PED analysis precisely determines that, among the diverse NiTPP chemisorption sites herein considered (fourfold hollow, atop, and bridge), the fourfold hollow one is the most favorable, with the Ni atom located at 1.93 Å from the surface and at an internuclear distance of 2.66 Å from the nearest-neighbors of the substrate. The use of elementary symmetry considerations enabled us to provide a convincing modeling of the NiTPP-Cu(100) anchoring configuration and an atomistic view of the previously revealed interfacial charge transfer through the unambiguous identification of the adsorbate π* and σ* low-lying virtual orbitals, of the substrate surface atoms, and of the linear combinations of the Cu 4s atomic orbitals involved in the substrate → adsorbate charge transfer. In addition, the same considerations revealed that the experimentally reported Ni(II) → Ni(I) reduction at the interface corresponds to the fingerprint of the chemisorption site of the NiTPP on Cu(100).