Chirality Measure Research Articles

Spin-orbit Interaction-mediated Measurement of Surface Chirality

Spin-orbit Interaction-mediated Measurement of Surface Chirality

Seed-Mediated Growth and Advanced Characterization of Chiral Gold Nanorods.

The controlled growth of gold nanostructures with complex shapes and reduced symmetry, exemplified by chiral gold nanorods and nanoparticles, is one of the most dynamic fields of nanochemistry. A timely summary of underlying concepts, including growth mechanisms and redefined chirality measures, would further promote this research area. In this perspective, we aim to establish qualitative connections between the chiral shapes and growth conditions, specifically for the seed-mediated synthesis of chiral gold nanorods as a convenient case of chiral morphogenesis. The crystallographic and morphological features of achiral nanorods used as seeds, the experimental conditions during chiral growth, and the symmetry of the chiral inducers, can all be exploited to obtain nanorods with intricate chiral shapes. Chirality characterization (such as electron tomography techniques) and quantification (including chirality measures) emerge as critical aspects to comprehensively explore and understand such structures, enabling optimization of their geometric and optical features. We conclude by discussing relevant challenges to be addressed toward a better controlled synthesis of chiral plasmonic nanostructures.

X-ray circular dichroism measured by cross-polarization x-ray transient grating

Abstract Measuring natural circular dichroism in the x-ray regime to extract stereochemical information from chiral molecules in solution remains a challenge. This is primarily due to technical limitations of the existing synchrotron sources, which hinder access to measurements of local chirality by exploiting core hole electronic transitions. In response to this challenge, we propose an alternative approach: utilizing XFEL-based cross-polarization x-ray transient grating (XTG). This method provides an indirect means to measure x-ray circular dichroism (XCD). Notably, our findings reveal that the signal emerges only once the excited cores have undergone dephasing through relaxation. XTG is now routinely measured in the XUV regime and has recently been made available for hard x-rays. Free electron lasers now offer polarization controls, and XTG can be extended to various polarization states for the two pump beams, making XCD measured by XTG feasible with the current state-of-the-art technology.

Time-Dependent Extension of Grimme's Continuous Chirality Measure for Electronic Chirality Flips in Femto- and Attosecond Time Domains.

Grimme's Continuous Chirality Measure ( ) was developed for comparisons of the chirality of the electronic wave functions of molecules, typically in their ground states. For example, , and for alanine, hydrogen-peroxide, and for achiral molecules, respectively. Well-designed laser pulses can excite achiral molecules from the electronic ground state to time-dependent chiral superposition states, with chirality flips in the femto- or even attosecond (fs or as) time domains. Here we provide a time-dependent extension of Grimme's for trailing the electronic chirality flips. As examples, we consider two laser driven electronic wavefunctions which represent flips between opposite electronic enantiomers of oriented NaK within and . The corresponding vary respectively from or from to , and back.

Precise measurement of chiral spectrum in the ultraviolet band using weak measurement and a deep neural network model.

Circular dichroism (CD) spectrum and optical rotation (OR) spectrum, crucial for understanding molecular properties and configurations, present challenges due to limited testing methods and equipment accuracy in the ultraviolet (UV) region. This study proposes a weak measurement system for chiral signals in varying concentrations in the ultraviolet range, optimized using a deep neural network (DNN) model. Introducing different post-selections to detect the circular dichroism spectrum and optical rotation spectrum separately, with contrast as a probe, it achieves a detection resolution of up to 10-6 rad. Moreover, the fitted value of the training data can reach 0.9989, enhancing the prediction accuracy of chiral molecule concentrations. This method exhibits considerable promise for applications in chiral measurement and sensor technologies.

CSM Software: Continuous Symmetry and Chirality Measures for Quantitative Structural Analysis.

We present a comprehensive and updated Python-based open software to calculate continuous symmetry measures (CSMs) and their related continuous chirality measure (CCM) of molecules across chemistry. These descriptors are used to quantify distortion levels of molecular structures on a continuous scale and were proven insightful in numerous studies. The input information includes the coordinates of the molecular geometry and a desired cyclic symmetry point group (i.e., Cs, Ci, Cn, or Sn). The results include the coordinates of the nearest symmetric structure that belong to the desired symmetry point group, the permutation that defines the symmetry operation, the direction of the symmetry element in space, and a number, between zero and 100, representing the level of symmetry or chirality. Rather than treating symmetry as a binary property by which a structure is either symmetric or asymmetric, the CSM approach quantifies the level of gray between black and white and allows one to follow the course of change. The software can be downloaded from https://github.com/continuous-symmetry-measure/csm or used online at https://csm.ouproj.org.il.

Emergence of chirality from electron spins, physical fields, and material-field composites

In this work, chirality in spin-active electronic states is explained clearly to address confusion about chiral effects recently discovered in materials science. We stress that the electronic toroidal monopole G0 can serve as a measure of chirality. By using the symmetry classification in terms of four distinct types of multipole bases, we extend the concept of chirality from materials to physical fields and material-field composites. Additionally, we illustrate specific examples from physics and chemistry that demonstrate the process of acquiring chirality through the combination of seemingly achiral degrees of freedom, which we term the emergence of chirality. Interference between multiple chiralities exhibiting phenomena specific to handedness is also discussed.

Chiral Kirigami for Bend-Tolerant Reconfigurable Hologram with Continuously Variable Chirality Measures.

Despite the commonality of static holograms, the holography with multiple information layers and reconfigurable grey-scale images at communication frequencies remain a confluence of scientific challenges. One well-known difficulty is the simultaneous modulation of phase and amplitude of electromagnetic wavefronts with a high modulation depth. A less appreciated challenge is scrambling of the information and images with hologram bending. Here, this work shows that chirality-guided pixelation of plasmonic kirigami sheets enables tunable multiplexed holography at terahertz (THz) frequencies. The convex and concave structures with slanted Au strips exhibit gradual variations in geometries facilitating modulation of light ellipticity reaching 40deg. Real-time switching of 3D images of the letter "M" and the Mona Lisa demonstrates the possibility of complex grey-scale information content and importance of continuously variable mirror asymmetry. Microscale chirality measures of each pixel experiences little change with bending while retaining controllable reconfigurability upon stretching, which translates to remarkable resilience of chiral holograms to bending. Simplicity of their design with local chirality measures opens the door to information technologies with fault-tolerant THz encryption, wearable holographic devices, and new communication technologies.

Quantum Mechanical Quantitative Nuclear Magnetic Resonance Enables Digital Reference Standards at All Magnetic Fields and Enhances qNMR Sustainability.

Quantum mechanics (QM)-driven 1H iterative functionalized spin analysis produces HifSA profiles, which encode the complete 1H spin parameters ("nuclear genotype") of analytes of interest. HifSA profiles enable the establishment of digital reference standards (dRS) that are portable, FAIR (findable - accessible - interoperable - reusable), and fit for the purpose of quantitative 1H NMR (qHNMR) analysis at any magnetic field. This approach enhances the sustainability of analytical standards. Moreover, the analyte-specific complete chemical shift and J-coupling information in HifSA-based dRS enable computational quantitation of substances in mixtures via QM-total-line-shape fitting (QM-qHNMR). We present the proof of concept for HifSA-based dRS by resolving the highly overlapping NMR resonances in the experimental spectra ("nuclear phenotypes") of the diastereomeric mixture of (2RS, 4RS)- and (2RS, 4SR)-difenoconazole (DFZ), a widely used antifouling food additive. The underlying 1H spin parameters are highly conserved in various solvents, are robust against variation in measurement temperature, and work across a wide range of magnetic fields. QM-qHNMR analysis of DFZ samples at 80, 400, 600, and 800 MHz showed high congruence with metrological reference values. Furthermore, this study introduces QM-qHNMR combined with chiral shift reagents for the analysis of all four DFZ stereoisomers: (2R, 4R)-, (2S, 4S)-, (2R, 4S)-, and (2S, 4R)-DFZ to perform chiral qHNMR measurements.

Graph‐theoretical chirality measure and chirality–property relations for chemical structures with multiscale mirror asymmetries

AbstractChirality is an essential geometric property unifying small molecules, biological macromolecules, inorganic nanomaterials, biological microparticles, and many other chemical structures. Numerous chirality measures have attempted to quantify this geometric property of mirror asymmetry and to correlate these measures with physical and chemical properties. However, their utility has been widely limited because these correlations have been largely notional. Furthermore, chirality measures also require prohibitively demanding computations, especially for chiral structures comprised of thousands of atoms. Acknowledging the fundamental problems with quantification of mirror asymmetry, including the ambiguity of sign‐variable pseudoscalar chirality measures, we revisit this subject because of the significance of quantifying chirality for quantitative biomimetics and describing the chirality of nanoscale materials that display chirality continuum and scale‐dependent mirror asymmetry. We apply the concept of torsion within the framework of differential geometry to the graph theoretical representation of chiral molecules and nanostructures to address some of the fundamental problems and practical limitations of other chirality measures. Chiral gold clusters and other chiral structures are used as models to elaborate a graph‐theoretical chirality (GTC) measure, demonstrating its applicability to chiral materials with different degrees of chirality at different scales. For specific cases, we show that GTC provides an adequate description of both the sign and magnitude of mirror asymmetry. The direct correlations with macroscopic properties, such as chiroptical spectra, are enhanced by using the hybrid chirality measures combining parameters from discrete mathematics and physics. Taking molecular helices as an example, we established a direct relation between GTC and optical activity, indicating that this chirality measure can be applied to chiral metamaterials and complex chiral constructs.

Molecular chirality quantification: Tools and benchmarks.

Molecular chirality has traditionally been viewed as a binary property where a molecule is classified as either chiral or achiral, yet in recent decades, mathematical methods for quantifying chirality have been explored. Here, we use toy molecular systems to systematically compare the performance of two state-of-the-art chirality measures: (1) the Continuous Chirality Measure (CCM) and (2) the Chirality Characteristic (χ). We find that both methods exhibit qualitatively similar behavior when applied to simple molecular systems such as a four-site molecule or the polymer double-helix, but we show that the CCM may be more suitable for evaluating the chirality of arbitrary molecules or abstract structures such as normal vibrational modes. We discuss a range of considerations for applying these methods to molecular systems in general, and we provide links to user-friendly codes for both methods. We aim for this paper to serve as a concise resource for scientists attempting to familiarize themselves with these chirality measures or attempting to implement chirality measures in their own work.

Continuous-wave cavity ringdown for high-sensitivity polarimetry and magnetometry measurements.

We report the development of a novel variant of cavity ringdown polarimetry using a continuous-wave laser operating at 532nm for highly precise chiroptical activity and magnetometry measurements. The key methodology of the apparatus relies upon the external modulation of the laser frequency at the frequency splitting between non-degenerate left- and right-circularly polarized cavity modes. The method is demonstrated by the evaluation of the Verdet constants of crystalline CeF3 and fused silica, in addition to the observation of gas- and solution-phase optical rotations of selected chiral molecules. Specifically, optical rotations of (i) vapors of α-pinene and R-(+)-limonene, (ii) mutarotating D-glucose in water, and (iii) acidified L-histidine solutions are determined. The detection sensitivities for the gas- and solution-phase chiral activity measurements are ∼30 and ∼120μdeg over a 30s detection period per cavity round trip pass, respectively. Furthermore, the measured optical rotations for R-(+)-limonene are compared with computations performed using the TURBOMOLE quantum chemistry package. The experimentally observed optically rotatory dispersion of this cyclic monoterpene was thus rationalized via a consideration of its room temperature conformer distribution as determined by the aforementioned single-point energy calculations.

Mapping electric field components of superchiral field with photo-induced force.

Circular dichroism (CD) of materials, difference in absorbance of left- and right-circularly polarized light, is a standard measure of chirality. Detection of the chirality for individual molecules is a frontier in analytical chemistry and optical science. The usage of a superchiral electromagnetic field near metallic structure is one promising way because it boosts the molecular far-field CD signal. However, it is still elusive as to how such a field actually interacts with the molecules. The cause is that the distribution of the electric field vector is unclear in the vicinity of the metal surface. In particular, it is difficult to directly measure the localized field, e.g., using aperture-type scanning near-field optical microscope. Here, we calculate the three-dimensional (3D) electric field vector, including the longitudinal field, and reveal the whole figure of the near-field CD on a two-dimensional (2D) plane just above the metal surface. Moreover, we propose a method to measure the near-field CD of the whole superchiral field by photo-induced force microscopy (PiFM), where the optical force distribution is mapped in a scanning 2D plane. We numerically demonstrate that, although the presence of the metallic probe tip affects the 3D electric field distribution, the PiFM is sufficiently capable to evaluate the superchiral field. Unveiling the whole figure of near-field is significantly beneficial in obtaining rich information of single molecules with multiple orientations and in analyzing the boosted far-field CD signals.

Chiral measure of chiral polyhedrons.

To quantify chiral shape, a tensor describing the particle shape has been proposed. This tensor, named the shape tensor (S-tensor), is an analog of the hydrodynamic tensor that relates the rotational and translational motions of particles in a liquid. The determinant of the S-tensor, named chirality measure density (CMD), was calculated for chiral tetrahedrons and octahedrons. It was found that CMD is opposite in sign when the mirror images are chiral to each other and vanishes when they are achiral. Therefore, the CMD is a good measure to distinguish the mirror images. The interaction between chiral particles was discussed in terms of the CMD.

Photo-acoustic spectroscopy with widely tuneable laser enables circular dichroism mapping

Sensitive and reliable characterization of chirality in nanostructures and molecules is of great importance in multidisciplinary research combining physics, chemistry and nanotechnology, with potential applications in pharmaceutical and agrochemical industry. Chirality is connected to circular dichroism (CD) - the absorption difference when the chiral medium is excited with circular polarizations of opposite handedness. Hence, measuring chirality by direct absorption measurements is of great interest in nanophotonics and plasmonics community, where the nanostructured media can enhance chiro-optical effects. Here we present a recently constructed photo-acoustic spectroscopy (PAS) set-up, which offers many degrees of freedom in characterization. We use a laser which is widely tuneable in the near-infrared (680-1080 nm) and visible (340-540 nm) ranges. The laser output is modulated with a mechanical chopper, where its frequency defines the penetration depth of the thermal signal. The input polarization is controlled by a linear polarizer and a quarter-wave plate, and the laser can be focused before impinging on the sample in the tightly closed photo-acoustic cell. The cell is placed on translational and rotational stages, which allows for the spatial mapping and extrinsic chirality measurements. Finally, a sensitive microphone measures the pressure changes in the cell, enabling scattering-free measurement of absorption and CD.

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.

Determination of Enantiomeric Excess by Optofluidic Microlaser near Exceptional Point.

Enantiomeric excess (ee) is an essential indicator of chiral drug purification in the pharmaceutical industry. However, to date the ee determination of unknown concentration enantiomers generally involves two separate techniques for chirality and concentration measurement. Here, a whispering-gallery mode (WGM) based optofluidic microlaser near exceptional point to achieve the ee determination under unknown concentration with a single technique is proposed. Exceptional point induces the unidirectional WGM lasing, providing the optofluidic microlaser with the novel capability to measure chirality by polarization, in addition to wavelength-based concentration detection. The dual-parameters detection of optofluidic microlaser empowers it to achieve ee determination of various unknown enantiomers without additional concentration measurements, a feat that is challenging to accomplish with other methods. Featuring the sensitivity enhancement and miniature structure of the WGM sensors, the obtained chiroptical response of the present approach is ≈30-fold higher than that of the conventional optical rotation-based polarimeter, and the reagent consumption is reduced by three orders of magnitude.

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.

Heat transport with a twist.

Despite the desirability of polymers for use in many products due to their flexibility, light weight, and durability, their status as thermal insulators has precluded their use in applications where thermal conductors are required. However, recent results suggest that the thermal conductance of polymers can be enhanced and that their heat transport behaviors may be highly sensitive to nanoscale control. Here we use non-equilibrium molecular dynamics simulations to study the effect of mechanical twist on the steady-state thermal conductance across multi-stranded polyethylene wires. We find that a highly twisted double-helical polyethylene wire can display a thermal conductance up to three times that of its untwisted form, an effect which can be attributed to a structural transition in the strands of the double helix. We also find that in thicker wires composed of many parallel strands, adding just one twist can increase its thermal conductance by over 30%. However, we find that unlike stretching a polymer wire, which causes a monotonic increase in thermal conductance, the effect of twist is highly non-monotonic, and certain amounts of twist can actually decrease the thermal conductance. Finally, we apply the Continuous Chirality Measure (CCM) in an attempt to explore the correlation between heat conductance and chirality. The CCM is found to correlate with twist as expected, but we attribute the observed heat transport behaviors to structural factors other than chirality.

Coherent multipolar amplification of chiroptical scattering and absorption from a magnetoelectric nanoparticle

Background-free detection of inherently weak chiroptical signals remains one of the great challenges in research communities and industries. We demonstrate coherent multipolar amplification of chiroptical responses via a magnetoelectric nanoparticle capped with an optically active monolayer encapsulated in a lossless background medium. Such an achiral nanoparticle can simultaneously support both electric and magnetic Mie-type resonances. We show how the combined excitation of orthogonal multipolar modes of the same order boosts the magnetoelectric coupling induced by the adsorbed chiral molecules, thus enabling coherently enhanced chiroptical responses from the ligand-capped magnetoelectric nanoparticle and allowing for absolute chirality measurements, in comparison with non-magnetoelectric nanoparticles. Furthermore, we develop rigorous expressions to separate relative contributions of chiral and nonchiral portions of circular differential absorption cross section, and analyzed the chirality-dependent far-field radiation patterns at different overlapped multipolar modes, providing a theoretical framework to understand the underlying enhancement mechanism of the magnetoelectric-assisted sensing of molecular chirality.