True and false chirality and absolute enantioselection

Second-Order Nonlinear Circular Dichroism in Square Lattice Array of Germanium Nanohelices

Second-harmonic generation (SHG) is prohibited in centrosymmetric crystals such as silicon or germanium due to the presence of inversion symmetry. However, the structuring of such materials makes it possible to break the inversion symmetry, thus achieving generation of second-harmonic. Moreover, various symmetry properties of the resulting structure, such as chirality, also influence the SHG. In this work, we investigate second-harmonic generation from an array of nanohelices made of germanium. The intensity of the second-harmonic displayed a remarkable enhancement of over 100 times compared to a nonstructured Ge thin film, revealing the influence of interaction between nanohelices. In particular, nonlinear circular dichroism, characterized through the SHG anisotropy factor g SHG-CD, changed its sign not only with the helix handedness but also with its density as well. We believe that our discoveries will open up new paths for the development of nonlinear photonics based on metamaterials and metasurfaces made of centrosymmetric materials.

Chiral selectivity vs. noise in spontaneous mirror symmetry breaking

Mirror symmetry breaking bifurcations, that occur in nonlinear chemical systems leading to final chiral states with very large enantiomeric excess, can be exploited as an efficient chiral signal selector for even the smallest chiral polarizations. This effect of the chiral polarization requires the system's capacity for overcoming thermal noise, which is manifested as fluctuating reaction rate constants. Therefore, we investigate the chiral selectivity across a range of tiny parity-violating energy differences (PVED) in the presence of inevitable non-equilibrium temperature fluctuations. We use a stochastic differential equation simulation methodology (Ito process) that serves as a valuable tool in open systems for identifying the thresholds at which the chiral force induces chiral selectivity in the presence of non-equilibrium temperature fluctuations. This approach enables us to include and analyze chiral selectivity in the presence of other types of fluctuations, such as perturbations in the rate of fluid flow into and out of the reactor and in the clamped input concentrations. These concepts may be of practical interest (i.e., spontaneous deracemizations) but are also useful for a better understanding of the general principles governing the emergence of biological homochirality.

Chirality in Light-Matter Interaction

The scientific effort to control the interaction between light and matter has grown exponentially in the last 2 decades. This growth has been aided by the development of scientific and technological tools enabling the manipulation of light at deeply sub-wavelength scales, unlocking a large variety of novel phenomena spanning traditionally distant research areas. Here, the role of chirality in light-matter interactions is reviewed by providing a broad overview of its properties, materials, and applications. A perspective on future developments is highlighted, including the growing role of machine learning in designing advanced chiroptical materials to enhance and control light-matter interactions across several scales.

Enantioselectivity of discretized helical supramolecule consisting of achiral cobalt phthalocyanines via chiral-induced spin selectivity effect

Enantioselectivity of helical aggregation is conventionally directed either by its homochiral ingredients or by introduction of chiral catalysis. The fundamental question, then, is whether helical aggregation that consists only of achiral components can obtain enantioselectivity in the absence of chiral catalysis. Here, by exploiting enantiospecific interaction due to chiral-induced spin selectivity (CISS) that has been known to work to enantio-separate a racemic mixture of chiral molecules, we demonstrate the enantioselectivity in the assembly of mesoscale helical supramolecules consisting of achiral cobalt phthalocyanines. The helical nature in our supramolecules is revealed to be mesoscopically incorporated by dislocation-induced discretized twists, unlike the case of chiral molecules whose chirality are determined microscopically by chemical bond. The relevance of CISS effect in the discretized helical supramolecules is further confirmed by the appearance of spin-polarized current through the system. These observations mean that the application of CISS-based enantioselectivity is no longer limited to systems with microscopic chirality but is expanded to the one with mesoscopic chirality.

Observation of intrinsic chiral bound states in the continuum

Photons with spin angular momentum possess intrinsic chirality, which underpins many phenomena including nonlinear optics¹, quantum optics², topological photonics³ and chiroptics⁴. Intrinsic chirality is weak in natural materials, and recent theoretical proposals^5-7 aimed to enlarge circular dichroism by resonant metasurfaces supporting bound states in the continuum that enhance substantially chiral light-matter interactions. Those insightful works resort to three-dimensional sophisticated geometries, which are too challenging to be realized for optical frequencies⁸. Therefore, most of the experimental attempts^9-11 showing strong circular dichroism rely on false/extrinsic chirality by using either oblique incidence^9,10 or structural anisotropy¹¹. Here we report on the experimental realization of true/intrinsic chiral response with resonant metasurfaces in which the engineered slant geometry breaks both in-plane and out-of-plane symmetries. Our result marks, to our knowledge, the first observation of intrinsic chiral bound states in the continuum with near-unity circular dichroism of 0.93 and a high quality factor exceeding 2,663 for visible frequencies. Our chiral metasurfaces may lead to a plethora of applications in chiral light sources and detectors, chiral sensing, valleytronics and asymmetric photocatalysis.

Rotation, Electric-Field Responses, and Absolute Enantioselection in Chiral Crystals

The microscopic origin of chirality, possible electric-field induced static rotational lattice deformation, and rotation-field induced electric polarization are investigated. By building up a realistic tight-binding model for the elemental Te crystal in terms of a symmetry-adapted basis, we identify the microscopic origin of the chirality and essential couplings among polar and axial vectors with the same time-reversal properties. Based on this microscopic model, we elucidate quantitatively that an interband process, driven by nearest-neighbor spin-dependent imaginary hopping, is the key factor in the electric-field induced rotation and its inverse response. From the symmetry point of view, these couplings and responses are characteristic and common to any chiral material, leading to a possible experimental approach to achieve absolute enantioselection by simultaneously applied electric and rotation fields, or a magnetic field and electric current, and so on, as a conjugate field of the chirality.

Comments on "Molecular Chirality in Classical Spacetime: Solving the Controversy about the Spinning Cone Model of Rotating Molecules"

A recent mathematical analysis by Michel Petijean aimed at solving the Barron/Mislow controversy concerning the chirality or otherwise of a non-translating spinning cone concluded that both are right: the controversy is a matter of an arbitrary choice of a conversion factor. This reassessment highlights the different physicochemical properties of a stationary spinning cone and a chiral molecule and concludes that Petitjean's analysis is misleading.

Molecular Chirality in Classical Spacetime: Solving the Controversy about the Spinning Cone Model of Rotating Molecules

The spinning cone is a model of rotating molecules used by Barron in 1986 in relation to asymmetric synthesis and to parity violation. He considered that the non-translating cone spinning about its symmetry axis has false chirality (i.e., it is not chiral), whereas Mislow concluded in 1999 that it is indeed chiral and severely criticized the true versus false chirality nomenclature introduced by Barron, who still disagreed in 2013 with the conclusion of Mislow. Here, it is shown that this controversy comes from an ambiguity in the spinning cone model and that in fact both authors were right. Light is thrown on the true chirality versus false chirality controversy with a very recently published result, which was thus unavailable to both authors: this is a new definition of chirality that encompasses the one introduced by Lord Kelvin at the end of the 19th century.

False Chirality, Absolute Enantioselection and CP Violation: Pierre Curie’s Legacy

The 1884 suggestion of Pierre Curie (1859–1906) that the type of dissymmetry shown by collinear electric and magnetic fields may induce an enantiomeric excess, in a chemical reaction that would otherwise produce a racemic mixture, is explored in the context of fundamental symmetry arguments. Curie’s arrangement exhibits false chirality (time-noninvariant enantiomorphism), and so it may not induce absolute enantioselection (ae) in a process that has reached thermodynamic equilibrium, since it does not lift the degeneracy of chiral enantiomers. However, it may do so in far-from-equilibrium processes via a breakdown in microscopic reversibility analogous to that observed in elementary particle processes under the influence of CP violation, the associated force possessing false chirality with respect to CP enantiomorphism. In contrast, an influence like circularly polarized light exhibiting true chirality (time-invariant enantiomorphism) lifts the degeneracy of enantiomers, and so may induce ae in all circumstances. Although to date, ae has not been observed under the influence of Curie’s arrangement of collinear electric and magnetic fields, it is argued that two different experiments have now demonstrated ae under a falsely chiral influence in systems far from equilibrium, namely in a spinning sample under a gravitational field, and in the separation of enantiomers at a ferromagnetic surface.

Recent advances in studies on the magneto-chiral dichroism of organic compounds

Magneto-chiral dichroism is described in terms of devices and synthesis, and is a clue to explain the homochirality of life.

About Chirality in Minkowski Spacetime

In this paper, we show that Lorentz boosts are direct isometries according to the recent mathematical definitions of direct and indirect isometries and of chirality, working for any metric space. Here, these definitions are extended to the Minkowski spacetime. We also show that the composition of parity inversion and time reversal is an indirect isometry, which is the opposite of what could be expected in Euclidean spaces. It is expected that the extended mathematical definition of chirality presented here can contribute to the unification of several definitions of chirality in space and in spacetime, and that it helps clarify the ubiquitous concept of chirality.

Homochirality: A Perspective from Fundamental Physics

In this brief review, possible mechanisms which could lead to complete biological homochirality are discussed from the viewpoint of fundamental physics. In particular, the role played by electroweak parity violation, including neutrino-induced homochirality, and contributions from the gravitational interaction, will be emphasized.

Highlighting spin selectivity properties of chiral electrode surfaces from redox potential modulation of an achiral probe under an applied magnetic field

Impressive spin-related effects are observed in cyclic voltammetry (CV) experiments performed under an applied magnetic field on a non-ferromagnetic electrode modified with a thin electroactive oligothiophene film, either "inherently chiral" or featuring chiral pendants with stereogenic centres. When flipping the magnet's north/south orientation, the CV peaks of two achiral, chemically reversible Fe(iii)/Fe(ii) redox couples in aqueous or organic solution undergo impressive potential shifts (up to nearly 0.5 V depending on protocol conditions), specularly by changing the film's (R)- or (S)-configuration. The magnitude of the potential shift decreases upon increasing both the polymer film thickness and the distance between the permanent magnet and the electrode surface. Such unprecedented spin-related redox potential modulation, obtained in the absence of a magnetic electrode acting as a spin injector, provides striking evidence (as well as an attractive evaluation criterion) of the spin selectivity properties of chiral thin films.

Monosaccharides and Their Derivatives in Carbonaceous Meteorites: A Scenario for Their Synthesis and Onset of Enantiomeric Excesses

Carbonaceous meteorites provide the best glimpse into the solar system’s earliest physical and chemical processes. These ancient objects, ~4.56 billion years old, contain evidence of phenomena ranging from solar system formation to the synthesis of organic compounds by aqueous and (likely) low-temperature photolytic reactions. Collectively, chemical reactions resulted in an insoluble kerogen-like carbon phase and a complex mixture of discrete soluble compounds including amino acids, nucleobases, and monosaccharide (or “sugar”) derivatives. This review presents the documented search for sugars and their derivatives in carbonaceous meteorites. We examine early papers, published in the early 1960s, and note the analytical methods used for meteorite analysis as well as conclusions on the results. We then present the recent finding of sugar derivatives including sugar alcohols and several sugar acids: The latter compounds were found to possess unusual “d” enantiomeric (mirror-image) excesses. After discussions on the possible roles of interstellar grain chemistry and meteorite parent body aqueous activity in the synthesis of sugar derivatives, we present a scenario that suggests that most of Earth’s extraterrestrial sugar alcohols (e.g., glycerol) were synthesized by interstellar irradiation and/or cold grain chemistry and that the early solar disk was the location of the initial enantiomeric excesses in meteoritic sugar derivatives.

Chirality in molecular collision dynamics

Chirality is a phenomenon that permeates the natural world, with implications for atomic and molecular physics, for fundamental forces and for the mechanisms at the origin of the early evolution of life and biomolecular homochirality. The manifestations of chirality in chemistry and biochemistry are numerous, the striking ones being chiral recognition and asymmetric synthesis with important applications in molecular sciences and in industrial and pharmaceutical chemistry. Chiral discrimination phenomena, due to the existence of two enantiomeric forms, very well known in the case of interaction with light, but still nearly disregarded in molecular collision studies. Here we review some ideas and recent advances about the role of chirality in molecular collisions, designing and illustrating molecular beam experiments for the demonstration of chiral effects and suggesting a scenario for a stereo-directional origin of chiral selection.

On the asymmetric autocatalysis of aldol reactions: The case of 4-nitrobenzaldehyde and acetone. A critical appraisal with a focus on theory

Under neutral conditions, spontaneous mirror symmetry breaking has been occasionally reported for aldol reactions starting from achiral reagents and conditions. Chiral induction might be interpreted in terms of autocatalysis exerted by chiral mono-aldol or bis-aldol products as source of initial enantiomeric excesses, which may account for such experimental observations. We describe here a thorough Density Functional Theory (DFT) study on this complex and otherwise difficult problem, which provides some insights into this phenomenon. The picture adds further rationale to an in-depth analysis by Moyano et al, who showed the isolation and characterization of bis-aldol adducts and their participation in a complex network of reversible steps. However, the lack of enantiodiscrimination (ees vanish rapidly in solution) suggests, according to the present results, a weak association in complexes formed by the catalysts and substrates. The latter would also be consistent with almost flat transition states having similar heights for competitive catalyst-bound transition structures (actually, we were unable to locate them at the level explored). Overall, neither autocatalysis as once conjectured nor mutual inhibition of enantiomers appears to be operating mechanisms. Asymmetric amplification in early stages harnessing unavoidable enantiomeric imbalances in reaction mixtures of chiral products represents a plausible interpretation.

Chiral discrimination in nuclear magnetic resonance spectroscopy

Chirality is a fundamental property of molecules whose spatial symmetry is characterized by the absence of improper rotations, making them not superimposable to their mirror image. Chiral molecules constitute the elementary building blocks of living species and one enantiomer is favoured in general (e.g. L-aminoacids and D-sugars pervade terrestrial homochiral biochemistry) because most chemical reactions producing natural substances are enantioselective. Since the effect of chiral chemicals and drugs on living beings can be markedly different between enantiomers, the quest for practical spectroscopical methods to scrutinize chirality is an issue of great importance and interest. Nuclear magnetic resonance (NMR) is a topmost analytical technique, but spectrometers currently used are 'blind' to chirality, i.e. unable to discriminate the two mirror-image forms of a chiral molecule, because, in the absence of a chiral solvent, the spectral parameters, chemical shifts and spin-spin coupling constants are identical for enantiomers. Therefore, the development of new procedures for routine chiral recognition would offer basic support to scientists. However, in the presence of magnetic fields, a distinction between true and false chirality is mandatory. The former epitomizes natural optical activity, which is rationalized by a time-even pseudoscalar, i.e. the trace of a second-rank tensor, the mixed electric dipole/magnetic dipole polarizability. The Faraday effect, magnetic circular dichroism and magnetic optical activity are instead related to a time-odd axial vector. The present review summarizes recent theoretical and experimental efforts to discriminate enantiomers via NMR spectroscopy, with the focus on the deep connection between chirality and symmetry properties under the combined set of fundamental discrete operations, namely charge conjugation, parity (space inversion) and time (motion) reversal.

Molecular chirality in meteorites and interstellar ices, and the chirality experiment on board the ESA cometary Rosetta mission

Life, as it is known to us, uses exclusively L-amino acid and D-sugar enantiomers for the molecular architecture of proteins and nucleic acids. This Minireview explores current models of the original symmetry-breaking influence that led to the exogenic delivery to Earth of prebiotic molecules with a slight enantiomeric excess. We provide a short overview of enantiomeric enhancements detected in bodies of extraterrestrial origin, such as meteorites, and interstellar ices simulated in the laboratory. Data are interpreted from different points of view, namely, photochirogenesis, parity violation in the weak nuclear interaction, and enantioenrichment through phase transitions. Photochemically induced enantiomeric imbalances are discussed more specifically in the topical context of the "chirality module" on board the cometary Rosetta spacecraft of the ESA. This device will perform the first enantioselective in situ analyses of samples taken from a cometary nucleus.

Magnetoelectric effects in local light-matter interactions

We study the generic dipole interaction of a monochromatic free-space electromagnetic field with a bi-isotropic nanoparticle or a molecule. Contributions associated with the breaking of dual, P, and T symmetries are responsible for electric-magnetic asymmetry, chirality, and the nonreciprocal magnetoelectric effect, respectively. We calculate absorption rates, radiation forces, and radiation torques for the nanoparticle and introduce novel field characteristics quantifying the transfer of energy, momentum, and angular momentum due to the three symmetry-breaking effects. In particular, we put forward a concept of "magnetoelectric energy density," quantifying the local PT symmetry of the field. Akin to the "superchiral" light suggested recently for local probing of molecular chirality, here we suggest employing complex fields for a sensitive probing of the nonreciprocal magnetoelectric effect in nanoparticles or molecules.