Chirality Measures for Vectors, Matrices, Operators and Functions

Dryzun, Chaim; Avnir, David

doi:10.1002/cphc.201000715

Cited by 21 publications

(9 citation statements)

References 137 publications

(54 reference statements)

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“…Quantification of Chirality. We have previously shown that introducing an absolute, rather than a relative to a reference 81 (such as the Hausdorff chirality measure 82,83 ), pseudoscalar chirality indicator derived from the geometry of a chiral molecule 67,84,85 or a nanoscale particle 86,87 decorated with chiral molecules gives values for a chirality index, G oa a , that matches extraordinarily well with the experimental data and trends of the calculated values for HTP. In particular, G oa a allowed us to make comparisons and predictions and draw conclusions about the chiral induction potential of chiral organic molecules as well as GNRs and polyhedral (quasispherical) Au NPs decorated with these exact chiral molecules.…”

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confidence: 60%

Highly Sensitive, Tunable Chirality Amplification through Space Visualized for Gold Nanorods Capped with Axially Chiral Binaphthyl Derivatives

et al. 2019

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The creation and transmission of chirality in molecular systems is a well-known, widely applied notion. Our understanding of how the chirality of nanomaterials can be controlled, measured, transmitted through space, and applied is less well understood. Dynamic assemblies for chiral sensing or metamaterials engineered from chiral nanomaterials require exact methods to determine transmission and amplification of nanomaterial chirality through space. We report the synthesis of a series of gold nanorods (GNRs) with a constant aspect ratio of ∼4.3 capped with C 2 -symmetric, axially chiral binaphthyl thiols, preparation of dispersions in the nematic liquid crystal 5CB, measurements of the helical pitch, and the determination of the helical twisting power as well as the average distance between the chiral nanomaterial additives. By comparison to the neat organic chiral derivatives, we demonstrate how the amplification of chirality facilitated by GNRs decorated with chiral molecules can be used to clearly distinguish the chiral induction strength of a homologous series of binaphthyl derivatives, differing only in the length of the nontethered aliphatic chain, in the induced chiral nematic liquid crystal phase. Considering systematic errors in sample preparation and optical measurements, these chiral molecules would otherwise be deemed identical with respect to chiral induction. Notably, we find some of the highest ever-reported values of the helical twisting power. We further support our experimentally derived arguments of a more comprehensive understanding of chirality transfer by calculations of a suitable pseudoscalar chirality indicator.

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confidence: 60%

Highly Sensitive, Tunable Chirality Amplification through Space Visualized for Gold Nanorods Capped with Axially Chiral Binaphthyl Derivatives

et al. 2019

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“…A number of different metrics have been proposed in the literature attempting to quantify the chirality of a molecule or a certain object. Some of these are based on the distance between a given structure and the closest achiral structure 39 or on the Hausdorff distance between the sets of points representing two specular images 40 . Here we employ another approach that introduces an absolute, rather than relative to a reference, pseudoscalar indicator derived from the molecule (or more generally object) geometry 41 – 43 .…”

Section: Resultsmentioning

confidence: 99%

Chirality amplification by desymmetrization of chiral ligand-capped nanoparticles to nanorods quantified in soft condensed matter

et al. 2018

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Induction, transmission, and manipulation of chirality in molecular systems are well known, widely applied concepts. However, our understanding of how chirality of nanoscale entities can be controlled, measured, and transmitted to the environment is considerably lacking behind. Future discoveries of dynamic assemblies engineered from chiral nanomaterials, with a specific focus on shape and size effects, require exact methods to assess transmission and amplification of nanoscale chirality through space. Here we present a remarkably powerful chirality amplification approach by desymmetrization of plasmonic nanoparticles to nanorods. When bound to gold nanorods, a one order of magnitude lower number of chiral molecules induces a tighter helical distortion in the surrounding liquid crystal–a remarkable amplification of chirality through space. The change in helical distortion is consistent with a quantification of the change in overall chirality of the chiral ligand decorated nanomaterials differing in shape and size as calculated from a suitable pseudoscalar chirality indicator.

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“…The factor 100 expands the scale for convenience, so that the value of the measure ranges from zero to an upper bound which is lower than 100 (the 100 limit is obtained in the more general Continuous Symmetry Measure). For a more detailed description of the CCM computational methods see refs − for examples of its applications across chemistry see refs − …”

Section: The Studied Clusters and The Quantitative Computational Methodsmentioning

confidence: 99%

Chirality in Copper Nanoalloy Clusters

et al. 2011

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It is shown that chirality is common in bimetallic clusters. Specifically, a detailed computational study of two copper clusters, Cun + (n = 9,11), demonstrates that exchange of one copper atom with another metal atom (Ni, Zn, Ag, or Au) at various locations, leads, in most cases, to chirality in the a priori achiral cluster (n = 9) and always preserves it in the a priori chiral one (n = 11). Chirality was evaluated on a quantitative level, employing the Continuous Chirality Measure methodology, in two versions: a purely geometric structure analysis, and an analysis which takes into account the different nature of the atoms. Physical aspects of chirality were demonstrated by emergence of vibrational circular dichroism signals and by the emergence of parity violation (PV) energy difference, which is calculated by employing a quasi-relativistic approach. In the case of AgCu10 +(p9), the PV energy splitting value is about ∼10–15 Hartree, bringing this nanoalloy close to the range of systems that have been discussed as promising candidates for a measurement of this phenomenon on the molecular level.

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Chirality Measures for Vectors, Matrices, Operators and Functions

Cited by 21 publications

References 137 publications

Highly Sensitive, Tunable Chirality Amplification through Space Visualized for Gold Nanorods Capped with Axially Chiral Binaphthyl Derivatives

Highly Sensitive, Tunable Chirality Amplification through Space Visualized for Gold Nanorods Capped with Axially Chiral Binaphthyl Derivatives

Chirality amplification by desymmetrization of chiral ligand-capped nanoparticles to nanorods quantified in soft condensed matter

Chirality in Copper Nanoalloy Clusters

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