Chiral Matrices Research Articles

Chiral random band matrices at zero energy

Chiral random band matrices at zero energy

Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case

We extend our recent study of winding number density statistics in Gaussian random matrix ensembles of the chiral unitary (AIII) and chiral symplectic (CII) classes. Here, we consider the chiral orthogonal (BDI) case which is the mathematically most demanding one. The key observation is that we can map the topological problem on a spectral one, rendering the toolbox of random matrix theory applicable. In particular, we employ a technique that exploits supersymmetry structures without reformulating the problem in superspace.

Biogenetic Chiral Deep Eutectic Solvents that Produce Self-Assembled Chiroptical Materials.

Deep eutectic solvents (DESs) show particular properties compared to ionic liquids and other traditional organic solvents. Controlled synthesis of chiral materials in DESs is unprecedented due to the complex interplays between DESs and solutes. In this work, all bio-derived chiral DESs were prepared using choline chloride or cyclodextrin as hydrogen bonding acceptors and natural chiral acids as donors, which performed as chiral matrices for the rational synthesis of chiroptical materials by taking advantage of the efficient chirality transfer between the DESs and solutes. In a very selective manner, building units with molecular pockets could facilitate strong binding affinity towards chiral acid components of DESs disregarding the presence of competitive hydrogen bonding acceptors. Chirality transfer from DESs to nanoassemblies leads to chirality amplification in the presence of minimal amounts of entrapped chiral acids, thanks to the spontaneous symmetry breaking of solutes during aggregation. This work utilizes chiral DESs to control supramolecular chirality, and illustrates the structural basis for the fabrication of DES-based chiral materials.

Biogenetic Chiral Deep Eutectic Solvents that Produce Self‐Assembled Chiroptical Materials

AbstractDeep eutectic solvents (DESs) show particular properties compared to ionic liquids and other traditional organic solvents. Controlled synthesis of chiral materials in DESs is unprecedented due to the complex interplays between DESs and solutes. In this work, all bio‐derived chiral DESs were prepared using choline chloride or cyclodextrin as hydrogen bonding acceptors and natural chiral acids as donors, which performed as chiral matrices for the rational synthesis of chiroptical materials by taking advantage of the efficient chirality transfer between the DESs and solutes. In a very selective manner, building units with molecular pockets could facilitate strong binding affinity towards chiral acid components of DESs disregarding the presence of competitive hydrogen bonding acceptors. Chirality transfer from DESs to nanoassemblies leads to chirality amplification in the presence of minimal amounts of entrapped chiral acids, thanks to the spontaneous symmetry breaking of solutes during aggregation. This work utilizes chiral DESs to control supramolecular chirality, and illustrates the structural basis for the fabrication of DES‐based chiral materials.

Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence

Topological invariance is a powerful concept in different branches of physics as they are particularly robust under perturbations. We generalize the ideas of computing the statistics of winding numbers for a specific parametric model of the chiral Gaussian unitary ensemble to other chiral random matrix ensembles. In particular, we address the two chiral symmetry classes, unitary (AIII) and symplectic (CII), and we analytically compute ensemble averages for ratios of determinants with parametric dependence. To this end, we employ a technique that exhibits reminiscent supersymmetric structures, while we never carry out any map to superspace.

Chiral molecular nanosilicas.

Molecular nanoparticles including polyoxometalates, proteins, fullerenes and polyhedral oligosiloxane (POSS) are nanosized objects with atomic precision, among which POSS derivatives are the smallest nanosilicas. Incorporation of molecular nanoparticles into chiral aggregates either by chiral matrices or self-assembly allows for the transfer of supramolecular chirality, yet the construction of intrinsic chirality with atomic precision in discrete molecules remains a great challenge. In this work, we present a molecular folding strategy to construct giant POSS molecules with inherent chirality. Ferrocenyl diamino acids are conjugated by two or four POSS segments. Hydrogen bonding-driven folding of diamino acid arms into parallel β-sheets facilitates the chirality transfer from amino acids to ferrocene and POSS respectively, disregarding the flexible alkyl spacers. Single crystal X-ray structures, density functional theory (DFT) calculations, circular dichroism and vibrational circular dichroism spectroscopy clearly verify the preferential formation of one enantiomer containing chiral molecular nanosilicas. The chiral orientation and chiroptical properties of POSS show pronounced dependence on the substituents of α-amino acids, affording an alternative way to control the folding behavior and POSS chirality in addition to the absolute configuration of amino acids. Through the kinetic nanoprecipitation protocol, one-dimensional aggregation enables chirality transfer from the molecular scale to the micrometer scale, self-assembling into helices in accordance with the packing propensity of POSS in a crystal phase. This work, by illustrating the construction of chiral molecular nanosilicas, paves a new way to obtain discrete chiral molecular nanoparticles for potential chiroptical applications.

Adsorption Properties of Hybrid Metal–Mesogenic Silver–Cholesterol and Silver–Thiocholesterol Nanosystems

Silver nanoparticles (SNPs) are obtained from silver nitrate via borohydride reduction followed by stabilization with cholesterol and thiocholesterol in different molar ratios. According to TEM results, the average size of SNPs stabilized by cholesterol is 5.5 ± 0.8 nm. that the average size of those stabilized by thiocholesterol is 2.5 ± 0.4 nm. Calculations for a model interaction between silver and ligands shows that thiocholesterol is a stronger stabilizer of SNPs. SNPs stabilized by thiocholesterol are used as modifiers of silica gel surfaces. Adsorption isotherms are constructed and quantitative characteristics of SNP adsorption on silica gel are determined. The best quantitative characteristics of adsorption are obtained for the molar ratio SNP : thiocholesterol = 1 : 2. Hybrid metal-mesogenic SNP–thiocholesterol nanosystems are used as chiral matrices to separate a series of optically active test compounds using TLC with a selectivity coefficient of 1.6.

Formation of Chiral Structures in UV-Initiated Formose Reaction

It has been found that the UV-initiated formose reaction in an extremely concentrated aqueous solution of formaldehyde gives sugars and other biologically significant chiral compounds with sp3-hybridized carbon atom. The reaction leads to an optically active condensed phase, which is a result of the spontaneous spatial separation of enantiomers in the racemate into the antipodes, similarly to the separation of enantiomers of different chirality sign in the famous Pasteur experiments. In our opinion, such a scenario is as close as possible to the actually realized de novo scenario of synthesis of chiral prebiotic molecules and matrices.

Individual eigenvalue distributions of crossover chiral random matrices and low-energy constants of SU(2) × U(1) lattice gauge theory

We compute individual distributions of low-lying eigenvalues of a chiral random matrix ensemble interpolating symplectic and unitary symmetry classes by the Nystr\"om-type method of evaluating the Fredholm Pfaffian and resolvents of the quaternion kernel. The one-parameter family of these distributions are shown to fit excellently the Dirac spectra of SU(2) lattice gauge theory with a constant U(1) background or dynamically fluctuating U(1) gauge field, which weakly breaks the pseudo-reality of the unperturbed SU(2) Dirac operator. Observed linear dependence of the crossover parameter with the strength of U(1) perturbations leads to precise determination of the pseudo-scalar decay constant, as well as the chiral condensate in the effective chiral Lagrangian of AI class.

New chiral metal-mesogenic nanosystems “silver - thiocholesterol” and their adsorption properties

ABSTRACTNew chiral matrices for thin film chromatography were obtained using hybrid metal-mesogenic nanosystems «silver – thiocholesterol» with different metal to ligand ratio, immobilized on silica gel particles. It was shown, that heteroatomic derivative of cholesterol – thiocholesterol and its composition with small silver nanoparticles formed in the system by the chemical reduction of silver ions possess liquid crystalline cholesteric mesophase. Molar ratio between thiocholesterol ligand molecules (L) and silver (Ag) insignificantly influenced on the size of silver nanoparticles formed in the system: for molar ratio Ag : L = 1:5 the main diameter of nanoparticles was equal to (2,7 ± 0,4) nm, for molar ratio Ag : L = 1:2 – (2, 2 ± 0,4) nm, for molar ratio Ag : L = 1:0,5 – (2,1 ± 0,6) nm. The new chiral matrices for thin film chromatography possess enantioselectivity related to optical isomers of 2,2′-diamino-1,1′-binaphtol (DABN) and trifluoroantranylethanol (TFAE). We have succeeded to select optical isomers of TFAE with selecting factor equal to 1,56.

Circularly polarized laser emission induced in isotropic and achiral dye systems.

The production of efficient, tunable, and switchable circularly polarized laser emission would have far reaching implications in optical communications or biophotonics. In this work, it is demonstrated the direct generation of circularly polarized (CP) laser emission in achiral and isotropic dye laser systems without the use of extracavity polarizing elements, and without resorting to chiral dyes, chiral liquid crystal matrices, or interferometric methods. The origin of this ellipticity arises from the dynamic birefringence induced by the strong and polarized laser pumping and the subsequent orientation anisotropy of the excited molecular dipoles. A complete polarimetric characterization of the polarization state of conventional dye laser oscillators as a function of different experimental parameters is performed and it is shown that the generated light always possesses a certain level of circularity that changes in a distinctive way with pump energy and polarization. These results demonstrate that it is possible to generate and modulate CP laser light from efficient and photostable conventional laser dyes.

Materials Established for Enantioselective Release of Chiral Compounds

The importance of chiral compounds has been widely recognized. Enantioselectively controlled release of the desired enantiomer from a racemate while retarding the other isomer provides a novel route toward practical applications of biologically chiral molecules. Such processes may maximize the efficacy while minimizing the dosage and frequency of chiral compounds. So far, exciting achievements have been made in enantioselective release (ESR), which can be classified into two main groups according to the essential strategy: (1) chiral interactions occurring between chiral compounds and chiral matrices (“enantioselective interaction” strategy); and (2) recognizing sites inside molecular-imprinting polymers (MIPs; “key-to-lock” strategy). The chiral compounds of interest are not limited to chiral drugs, but also include other biologically important chiral compounds (e.g., amino acids). Based on our studies, this article reviews the state-of-the-art techniques and materials systems toward ESR. The emphasis is...

Hydrodynamical spectral evolution for random matrices

The eigenvalues of the matrix structure where X is a random Gaussian Hermitian matrix and is non-random or random independent of X, are closely related to Dyson Brownian motion. Previous works have shown how an infinite hierarchy of equations satisfied by the dynamical correlations become triangular in the infinite density limit, and give rise to the complex Burgers equation for the Green’s function of the corresponding one-point density function. We show how this and analogous partial differential equations, for chiral, circular and Jacobi versions of Dyson Brownian motion follow from a macroscopic hydrodynamical description involving the current density and continuity equation. The method of characteristics gives a systematic approach to solving the PDEs, and in the chiral case we show how this efficiently reclaims the characterization of the global eigenvalue density for non-central Wishart matrices due to Dozier and Silverstein. Collective variables provide another approach to deriving the complex Burgers equation in the Gaussian case, and we show that this approach applies equally as well to chiral matrices. We relate both the Gaussian and chiral cases to the asymptotics of matrix integrals.

Production of chiral matrices with hybrid silver–thiocholesterol nanosystems and study of their properties

A new type of chiral matrix based on silver–thiocholesterol hybrid nanosystems adsorbed on silica gel has been proposed. The molar ratio of stabilized thiocholesterol (L) ligand and silver (Ag) was found to have little effect on the size of the resulting silver nanoparticles (SNPs). The average diameter of SNPs was 2.7 ± 0.4, 2.2 ± 0.4, and 2.1 ± 0.6 nm upon the ratios Ag: L = 1: 5, Ag: L = 1: 2, and Ag: L = 1: 0.5, respectively. The resulting chiral matrices possess enantioselectivity relative to the 1,1’-binaphthyl-2,2’-diamine (BNDA) and trifluoroanthranyl ethanol (TFAE) optical isomers. The TFAE optical isomers were successfully separated using thin layer chromatography (α = 1.56).

On the Form Factors of Local Operators in the Bazhanov–Stroganov and Chiral Potts Models

We consider general cyclic representations of the six-vertex Yang–Baxter algebra and analyze the associated quantum integrable systems, the Bazhanov–Stroganov model and the corresponding chiral Potts model on finite size lattices. We first determine the propagator operator in terms of the chiral Potts transfer matrices and we compute the scalar product of separate states (including the transfer matrix eigenstates) as a single determinant formulae in the framework of Sklyanin’s quantum separation of variables. Then, we solve the quantum inverse problem and reconstruct the local operators in terms of the separate variables. We also determine a basis of operators whose form factors are characterized by a single determinant formulae. This implies that the form factors of any local operator are expressed as finite sums of determinants. Among these form factors written in determinant form are in particular those which will reproduce the chiral Potts order parameters in the thermodynamic limit. The results presented here are the generalization to the present models associated to the most general cyclic representations of the six-vertex Yang–Baxter algebra of those we derived for the lattice sine–Gordon model.

Enantioselective recognition at mesoporous chiral metal surfaces.

Chirality is widespread in natural systems, and artificial reproduction of chiral recognition is a major scientific challenge, especially owing to various potential applications ranging from catalysis to sensing and separation science. In this context, molecular imprinting is a well-known approach for generating materials with enantioselective properties, and it has been successfully employed using polymers. However, it is particularly difficult to synthesize chiral metal matrices by this method. Here we report the fabrication of a chirally imprinted mesoporous metal, obtained by the electrochemical reduction of platinum salts in the presence of a liquid crystal phase and chiral template molecules. The porous platinum retains a chiral character after removal of the template molecules. A matrix obtained in this way exhibits a large active surface area due to its mesoporosity, and also shows a significant discrimination between two enantiomers, when they are probed using such materials as electrodes.

Circular dichroism study of the interaction between mutagens and bilirubin bound to different binding sites of serum albumins

Although recent investigations have shown that bilirubin not only has a negative role in the organism but also exhibits significant antimutagenic properties, the mechanisms of interactions between bilirubin and mutagens are not clear. In this study, interaction between bilirubin bound to different binding sites of mammalian serum albumins with structural analogues of the mutagens 2-aminofluorene, 2,7-diaminofluorene and mutagen 2,4,7-trinitrofluorenone were investigated by circular dichroism and absorption spectroscopy. Homological human and bovine serum albumins were used as chiral matrices, which preferentially bind different conformers of bilirubin in the primary binding sites and make it observable by circular dichroism. These molecular systems approximated a real system for the study of mutagens in blood serum. Differences between the interaction of bilirubin bound to primary and to secondary binding sites of serum albumins with mutagens were shown. For bilirubin bound to secondary binding sites with low affinity, partial displacement and the formation of self-associates were observed in all studied mutagens. The associates of bilirubin bound to primary binding sites of serum albumins are formed with 2-aminofluorene and 2,4,7-trinitrofluorenone. It was proposed that 2,7-diaminofluorene does not interact with bilirubin bound to primary sites of human and bovine serum albumins due to the spatial hindrance of the albumins binding domains. The spatial arrangement of the bilirubin bound to serum albumin along with the studied mutagens was modelled using ligand docking, which revealed a possibility of an arrangement of the both bilirubin and 2-aminofluorene and 2,4,7-trinitrofluorenone in the primary binding site of human serum albumin.

Three Types of Induced Tryptophan Optical Activity Compared in Model Dipeptides: Theory and Experiment

The tryptophan (Trp) aromatic residue in chiral matrices often exhibits a large optical activity and thus provides valuable structural information. However, it can also obscure spectral contributions from other peptide parts. To better understand the induced chirality, electronic circular dichroism (ECD), vibrational circular dichroism (VCD), and Raman optical activity (ROA) spectra of Trp-containing cyclic dipeptides c-(Trp-X) (where X = Gly, Ala, Trp, Leu, nLeu, and Pro) are analyzed on the basis of experimental spectra and density functional theory (DFT) computations. The results provide valuable insight into the molecular conformational and spectroscopic behavior of Trp. Whereas the ECD is dominated by Trp π-π* transitions, VCD is dominated by the amide modes, well separated from minor Trp contributions. The ROA signal is the most complex. However, an ROA marker band at 1554 cm(-1) indicates the local χ(2) angle value in this residue, in accordance with previous theoretical predictions. The spectra and computations also indicate that the peptide ring is nonplanar, with a shallow potential so that the nonplanarity is primarily induced by the side chains. Dispersion-corrected DFT calculations provide better results than plain DFT, but comparison with experiment suggests that they overestimate the stability of the folded conformers. Molecular dynamics simulations and NMR results also confirm a limited accuracy of the dispersion-DFT model in nonaqueous solvents. Combination of chiral spectroscopies with theoretical analysis thus significantly enhances the information that can be obtained from the induced chirality of the Trp aromatic residue.

Advances in synthetic optically active condensation polymers - A review

The study of optically active polymers is a very active research field, and these materials have exhibited a num- ber of interesting properties. Much of the attention in chiral polymers results from the potential of these materials for sev- eral specialized utilizations that are chiral matrices for asymmetric synthesis, chiral stationary phases for the separation of racemic mixtures, synthetic molecular receptors and chiral liquid crystals for ferroelectric and nonlinear optical applica- tions. Recently, highly efficient methodologies and catalysts have been developed to synthesize various kinds of optically active compounds. Some of them can be applied to chiral polymer synthesis. In a few synthetic approaches for optically active polymers, chiral monomer polymerization has essential advantages in applicability of monomer, apart from both asymmetric polymerization of achiral or prochiral monomers and enantioselective polymerization of a racemic monomer mixture. The following are the up to date successful approaches to the chiral synthetic polymers by condensation polymer- ization reaction of chiral monomers.

Quantum loop subalgebra and eigenvectors of the superintegrable chiral Potts transfer matrices

It has been shown in earlier works that for Q = 0 and L a multiple of N, the ground state sector eigenspace of the superintegrable τ2(tq) model is highly degenerate and is generated by a quantum loop algebra . Furthermore, this loop algebra can be decomposed into r = (N − 1)L/N simple algebras. For Q ≠ 0, we shall show here that the corresponding eigenspace of τ2(tq) is still highly degenerate, but splits into two spaces, each containing 2r − 1 independent eigenvectors. The generators for the subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q = 0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q ≠ 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.