Chiral symmetry breaking yields the I-Au60 perfect golden shell of singular rigidity

Fundamental Cause of Bio-Chirality: Space-Time Symmetry—Concept Review

The search for fundamental determinants of bio-molecular chirality is a hot topic in biology, clarifying the meaning of evolution and the enigma of life’s origin. The question of origin may be resolved assuming that non-biological and biological entities obey nature’s universal laws grounded on space-time symmetry (STS) and space-time relativity (SPR). The fabric of STS is our review’s primary subject. This symmetry, encompassing the behavior of elementary particles and galaxy structure, imposes its fundamental laws on all hierarchical levels of the biological world. From the perspective of STS, objects across spatial scales may be classified as chiral or achiral concerning a specific space-related symmetry transformation: mirror reflection. The chiral object is not identical (i.e., not superimposable) to its mirror image. In geometry, distinguish two kinds of chiral objects. The first one does not have any reflective symmetry elements (a point or plane of symmetry) but may have rotational symmetry axes (dissymmetry). The second one does not have any symmetry elements (asymmetry). As the form symmetry deficiency, Chirality is the critical structural feature of natural systems, including sub-atomic particles and living matter. According to the Standard Model (SM) theory and String Theory (StrT), elementary particles associated with the four fundamental forces of nature determine the existence of micro- and galaxy scales of nature. Therefore, the inheritance of molecular symmetry from the symmetry of elementary particles indicates a bi-directional (internal [(micro-scale) and external (galaxy sale)] causal pathway of prevalent bio-chirality. We assume that the laws of the physical world impact the biological matter’s appearance through both extremities of spatial dimensions. The extended network of multi-disciplinary experimental evidence supports this hypothesis. However, many experimental results are derived and interpreted based on the narrow-view prerogative and highly specific terminology. The current review promotes a holistic approach to experimental results in two fast-developing, seemingly unrelated, divergent branches of STS and biological chirality. The generalized view on the origin of prevalent bio-molecular chirality is necessary for understanding the link between a diverse range of biological events. The chain of chirality transfer links ribosomal protein synthesis, cell morphology, and neuronal signaling with the laterality of cognitive functions.

Modeling and measuring plasmonic excitations in hollow spherical gold nanoparticles

We investigate molecular plasmonic excitations sustained in hollow spherical gold nanoparticles using time-dependent density functional theory (TD-DFT). Specifically, we consider Au60 spherical, hollow molecules as a toy model for single-shell plasmonic molecules. To quantify the plasmonic character of the excitations obtained from TD-DFT, the energy-based plasmonicity index is generalized to the framework of DFT, validated on simple systems such as the sodium Na20 chain and the silver Ag20 compound, and subsequently successfully applied to more complex molecules. We also compare the quantum mechanical TD-DFT simulations to those obtained from a classical Mie theory that relies on macroscopic electrodynamics to model the light–matter interaction. This comparison allows us to distinguish those features that can be explained classically from those that require a quantum-mechanical treatment. Finally, a double-shell system obtained by placing a C60 buckyball inside the hollow spherical gold particle is further considered. It is found that the double-shell, while increasing the overall plasmonic character of the excitations, leads to significantly lowered absorption cross sections.

Robustness of the chiral-icosahedral golden shell I-Au60 in multi-shell structures

Motivated by the recent theoretical discovery [S.-M. Mullins et al., Nat. Commun. 9, 3352 (2018)] of a surprisingly contracted 60-atom hollow shell of chiral-icosahedral symmetry (I-Au₆₀) of remarkable rigidity and electronegativity, we have explored, via first-principles density functional theory calculations, its physico-chemical interactions with internal and external shells, enabling conclusions regarding its robustness and identifying composite forms in which an identifiable I-Au₆₀ structure may be realized as a product of natural or laboratory processes. The dimensions and rigidity of I-Au₆₀ suggest a templating approach; e.g., an I_h-C₆₀ fullerene fits nicely within its interior, as a nested cage. In this work, we have focused on its susceptibility, i.e., the extent to which the unique structural and electronic properties of I-Au₆₀ are modified by incorporation into selected multi-shell structures. Our results confirm that the I-Au₆₀ shell is robustly maintained and protected in various bilayer structures: I_h-C₆₀@I-Au₆₀, I_h-Au₃₂@I-Au₆₀ ²⁺, Au₆₀(MgCp)₁₂, and their silver analogs. A detailed analysis of the structural and electronic properties of the selected I-Au₆₀ shell-based nanostructures is presented. We found that the I-Au₆₀ shell structure is quite well retained in several robust forms. In all cases, the I-symmetry is preserved, and the I-Au₆₀ shell is slightly deformed only in the case of the I_h-C₆₀@I-Au₆₀ system. This analysis serves to stimulate and provide guidance toward the identification and isolation of various I-Au₆₀ shell-based nanostructures, with much potential for future applications. We conclude with a critical comparative discussion of these systems and of the implications for continuing theoretical and experimental investigations.

Recent developments in the chiroptical properties of chiral plasmonic gold nanostructures: bioanalytical applications

The presence of excess L-amino acid in the Murchison meteorite, circular polarization effect in the genesis of stars and existence of chirality in interstellar molecules contribute to the origin of life on earth. Chiral-sensitive techniques have been employed to untangle the secret of the symmetries of the universe, designing of effective secure drugs and investigation of chiral biomolecules. The relationship between light and chiral molecules was employed to probe and explore such molecules using spectroscopy techniques. The mutual interaction between electromagnetic spectrum and chirality of matter give rise to distinct optical response, which advances vital information contents in chiroptical spectroscopy. Chiral plasmonic gold nanoparticle exhibits distinctive circular dichroism peaks in broad wavelength range thereby crossing the limits of its characterization. The emergence of strong optical activity of gold nanosystem is related to its high polarizability, resulting in plasmonic and excitonic effects on incident photons. Inspired by the development of advanced chiral plasmonic nanomaterials and exploring its properties, this review gives an overview of various chiral gold nanostructures and the mechanism behind its chiroptical properties. Finally, we highlight the application of different chiral gold nanomaterials in the field of catalysis and medical applications with special emphasis to biosensing and biodetection.

Triskelion Structured Colloidal Quantum Dots

We show, using density functional theory and ab initio molecular dynamics, that certain small colloidal quantum dots with a mixed nanocrystal core capped with achiral surface ligands spontaneously form a triskelion (from the Greek, three-legged) structure with (approximate) C₃ symmetry that can be dynamically stable at room temperature when additionally capped with small amine ligands. Furthermore, the nanocrystal core also forms a triskelion structure. The focus of our study is a colloidal quantum dot with a Cd₁₆Se₇Te₃ core (and a charge of +12) capped with negatively charged surface ligands to achieve charge neutrality-in the simplest instance, 12 Cl^--to form the colloidal quantum dot Cd₁₆Se₇Te₃Cl₁₂. The small size of the core (for which almost all atoms are surface atoms), the high positive charge that destabilizes the core, the mixed (Cd/Te) composition that creates mechanical strain in the core, and the inclusion of precisely three Te atoms in the predominantly Se core all play critical roles in the spontaneous formation of the triskelion structure.

Effect of the charge state on the structure of the Au60 cluster

This manuscript outlines a DFT-D study of a neutral and charged Au60 cluster. The neutral structure features an I-symmetry, while 1-, 1+, and 2+ charge states result in a structure with Cs symmetry. The main difference among neutral and charged clusters is their compactness and we used a polyhedral approach to analyze their structure in terms of tetrahedral and octahedral building blocks. Moreover, we calculated their IR/Raman spectra to distinguish among them.

Enantiomeric Transitions in the Chiral Cluster Au15 Studied by a Reaction Coordinate Deduced from Molecular Dynamics Simulations

A recently developed modified basin hopping (MBH) optimization algorithm, combined with an energy function calculated by the semiempirical density functional tight-binding (DFTB) theory, was applied to determine the lowest-energy structures of Au_n clusters with size n = 3-20. It was predicted from the DFTB/MBH optimization algorithm calculations that clusters Au₁₀, Au₁₅, and Au₁₈ exhibit chiral properties; i.e., each of these three clusters possesses the same energy value and associated with it are two nonsuperposable mirror-image clusters. In the potential energy landscape, there thus exist multidimensional barriers separating the two enantiomers, and this lowest-energy double-well morphology is surrounded by potential-energy minima of higher energies. In this paper, we have chosen to study the chiral cluster Au₁₅ by employing an isothermal Brownian-type molecular dynamics simulation to discern in greater detail its conformational transition from one enantiomer, say left, to its right counterpart. To facilitate our analysis of the simulation data, we transpose the multidimensional configurational space description to a lower dimensional collective variable (CV) space spanned by two geometry-relevant CVs. The thermally driven progression and mechanism of enantiomeric transitions between the left and right enantiomers will be our main focus, and the strategy is to dissect the time development of the CVs collected from different sets of independent simulation runs. From simulation data, we found that an understanding of the dynamics of enantiomeric transitions needs first to seek out the left and right enantiomers through a molecular modeling and visualizing program, then to ferret out and identify between the left and right enantiomers a symmetrical structure, and finally to define from the latter a reaction coordinate. We showed in this work that this single reaction coordinate is predictive in unraveling the left ⇌ right enantiomeric transition events, providing a specific inkling of the transition time span and its associated distribution which can be checked further for its reasonableness by the autocorrelation function and a vibrational analysis, all of which shed light on the mechanisms of transition.

Chirality and Surface Bonding Correlation in Atomically Precise Metal Nanoclusters

Chirality is ubiquitous in nature and occurs at all length scales. The development of applications for chiral nanostructures is rising rapidly. With the recent achievements of atomically precise nanochemistry, total structures of ligand-protected Au and other metal nanoclusters (NCs) are successfully obtained, and the origins of chirality are discovered to be associated with different parts of the cluster, including the surface ligands (e.g., swirl patterns), the organic-inorganic interface (e.g., helical stripes), and the kernel. Herein, a unified picture of metal-ligand surface bonding-induced chirality for the nanoclusters is proposed. The different bonding modes of M-X (where M = metal and X = the binding atom of ligand) lead to different surface structures on nanoclusters, which in turn give rise to various characteristic features of chirality. A comparison of Au-thiolate NCs with Au-phosphine ones further reveals the important roles of surface bonding. Compared to the Au-thiolate NCs, the Ag/Cu/Cd-thiolate systems exhibit different coordination modes between the metal and the thiolate. Other than thiolate and phosphine ligands, alkynyls are also briefly discussed. Several methods of obtaining chiroptically active nanoclusters are introduced, such as enantioseparation by high-performance liquid chromatography and enantioselective synthesis. Future perspectives on chiral NCs are also proposed.

Tetrahedral Geometry Induction of Stable Ag-Ti Nanoclusters by Flexible Trifurcate TiL3 Metalloligand

A series of increasingly large silver nanoclusters with a varied combination of Archimedean and/or Platonic solid arrangements was constructed using a flexible trifurcate TiL₃ (L = Salicylic acid or 5-fluorosalicylic acid) metalloligand: Ag₄@Ag₄@Ti₄ (PTC-85), Ag₁₂@Ti₄ (PTC-86), Ag₄@Ag₆@Ag₁₂@Ti₄ (PTC-87), Ag₆@Ag₂₄@Ag₁₂@Ti₄ (PTC-88), and Ag₁₂@Ag₂₄@Ti₄ (PTC-89). The silver nanoclusters are each capped by four TiL₃ moieties, thereby forming {Ti₄} supertetrahedra with average edge lengths ranging from ∼8.12 Å to ∼17.37 Å. Such {Ti₄} moieties further induce the tetrahedral geometry of the encapsulated silver nanoclusters. These atomically precise metallic clusters were found to be ultrastable with respect to air for several months, and to water for more than 3 days, due to the stabilizing effects of the TiL₃ metalloligand. Moreover, the obtained clusters exhibit nonlinear optical (NLO) effects in optical limiting tests and also temperature-dependent photoluminescent properties. This work provides an interesting metalloligand method not only to induce the spatial growth of metallic clusters to achieve highly symmetric structures, but also to enhance their stability which is crucial for future application.

Role of core-shell energetics on anti-Mackay, chiral stacking in AgCu nanoalloys and thermally induced transition to chiral stacking

In AgCu nanoalloys a size-dependent transition to the chiral stacking from the anti-Mackay stacking has been predicted previously. This trend is explained by considering the interplay between the core-shell energetics. Results indicate that the energy changes in the Ag shell alone is not sufficient to explain the stability of the chiral stacking and the energy changes in the Cu core also need to be considered. In addition to this, thermally induced transition to chiral stacking was observed at sizes where anti-Mackay stacking is energetically favourable. On transition to the chiral stacking, the Ag-Ag, Ag-Cu and Cu-Cu bond lengths change significantly. These observations are also applicable for AgCu nanoalloys with incomplete Ag shells.

How metallic are noble-metal clusters? Static screening and polarizability in quantum-sized silver and gold nanoparticles

Metallicity of nanoparticles can be defined in different ways. One possibility is to look at the degree to which external fields are screened inside the object. This screening would be complete in a classical perfect metal where surface charges arrange on the classical -i.e., abrupt - surface such that no internal fields exist. However, it is obvious that this situation is modified for very small clusters: the surface charges are "smeared out" at the surface, and the screening might be less complete. In the present work we ask the question as to how close small noble-metal clusters are to a classical metal. We show that, indeed, the screening is almost complete (≈96%) already for as little as one atomic layer of the coinage metals, silver and gold alike. At the same time, we show that quantum effects, viz., electronic shell closings and the Friedel-like oscillations of the density, play a role, meaning that the clusters cannot be described solely using the concept of screening in a classical metal.

Chiral-Icosahedral ( I) Symmetry in Ubiquitous Metallic Cluster Compounds (145A,60X): Structure and Bonding Principles

There exists a special kind of perfection-in symmetry, simplicity, and stability-attainable for structures generated from precisely 60 ligands (all of a single type) that protect 145 metal-atom sites. The symmetry in question is icosahedral ( I_h), generally, and chiral icosahedral ( I) in particular. A 60-fold equivalence of the ligands is the smallest number to allow this kind of perfection. Known cluster compounds that approximate this structural ideal include palladium-carbonyls, I_h-Pd₁₄₅(CO)₆₀; gold-thiolates, I-Au₁₄₄(SR)₆₀; and gold-alkynyls, I-Au₁₄₄(C₂R)₆₀. Many other variants are suspected. The Pd₁₄₅ compound established the basic achiral structure-type. However, the Au₁₄₄-thiolate archetype is prominent, historically in its abundance and ease of preparation and handling, in its proliferation in many laboratories and application areas, and ultimately in the intrinsic chirality of its geometrical structure and organization of its bonding network or connectivity. As discovered by mass spectrometry (the "30-k anomaly") in 1995, it appeared as a broad single peak, as solitary and symmetrical as Mount Fuji, centered near 30 kDa (∼150 Au atoms), provoking these thoughts: Surely this phenomenon requires a unique explanation. It appears to be the Buckminsterfullerene (carbon-60) of gold-cluster chemistry. Herein we provide an elementary account of the unexpected discovery, in which the Pd₁₄₅-structure played a critical role, that led to the identification and prediction, in 2008, of a fascinating new molecular structure-type, evidently the first one of chiral icosahedral symmetry. Rigorous confirmation of this prediction occurred in early spring 2018, when two single-crystal X-ray crystallography reports were submitted, each one distinguishing both enantiomeric structures and noting profound chirality for the surface (ligand) layer. The emphasis here is on the structure and bonding principles and how these have been elucidated. Our aim has been to present this story in simplest terms, consistent with the radical simplicity of the structure itself. Because it combines intrinsic profound chirality, at several levels, with the highest possible symmetry-type (icosahedral), the structure may attract broader interest also from educators, especially if studied in tandem with the analysis of hollow (shell) metallic systems that exhibit the same chirality and symmetry. Because the shortest (stiffest) bonds follow the chiral 3-way weave pattern of the traditional South-Asian reed football, this cultural artifact may be used to introduce chiral-icosahedral symmetry in a pleasant and memorable way. One may also appreciate easily the bonding and excitations in I-symmetry metallic nanostructures via the golden fullerenes, that is, the proposed hollow Au₆₀,₇₂ spheres. Beyond any aesthetic or pedagogical value, we aim that our Account may provide a firm foundation upon which others may address open questions and the opportunities they present. This Account can scarcely hint at the prospects for further fundamental understanding of these compounds, as well as a widening sphere of applications (chemical, electronic, imaging). The compounds remain crucial to a wider field presently under intense development.