Symmetry

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Open AccessEditorial

Acknowledgement to Reviewers of Symmetry in 2015

by Symmetry Editorial Office

Symmetry 2016, 8(1), 6; https://doi.org/10.3390/sym8010006 - 21 Jan 2016

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The editors of Symmetry would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...] Full article

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Open AccessArticle

Symmetry in Sphere-Based Assembly Configuration Spaces

by Meera Sitharam, Andrew Vince, Menghan Wang and Miklós Bóna

Symmetry 2016, 8(1), 5; https://doi.org/10.3390/sym8010005 - 21 Jan 2016

Cited by 4 | Viewed by 4894

Abstract

Many remarkably robust, rapid and spontaneous self-assembly phenomena occurring in nature can be modeled geometrically, starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly processes. Since spheres within bunches could be identical and bunches could be identical, as well, the underlying symmetry groups could be of large order that grows with the number of participating spheres and bunches. Thus, understanding symmetries and associated isomorphism classes of microstates that correspond to various types of macrostates can significantly increase efficiency and accuracy, i.e., reduce the notorious complexity of computing entropy and free energy, as well as paths and kinetics, in high dimensional configuration spaces. In addition, a precise understanding of symmetries is crucial for giving provable guarantees of algorithmic accuracy and efficiency, as well as accuracy vs. efficiency trade-offs in such computations. In particular, this may aid in predicting crucial assembly-driving interactions. This is a primarily expository paper that develops a novel, original framework for dealing with symmetries in configuration spaces of assembling spheres, with the following goals. (1) We give new, formal definitions of various concepts relevant to the sphere-based assembly setting that occur in previous work and, in turn, formal definitions of their relevant symmetry groups leading to the main theorem concerning their symmetries. These previously-developed concepts include, for example: (i) assembly configuration spaces; (ii) stratification of assembly configuration space into configurational regions defined by active constraint graphs; (iii) paths through the configurational regions; and (iv) coarse assembly pathways. (2) We then demonstrate the new symmetry concepts to compute the sizes and numbers of orbits in two example settings appearing in previous work. (3) Finally, we give formal statements of a variety of open problems and challenges using the new conceptual definitions. Full article

(This article belongs to the Special Issue Rigidity and Symmetry)

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Open AccessReview

Synthesis of Chiral Cyclic Carbonates via Kinetic Resolution of Racemic Epoxides and Carbon Dioxide

by Xiao Wu, José A. Castro-Osma and Michael North

Symmetry 2016, 8(1), 4; https://doi.org/10.3390/sym8010004 - 14 Jan 2016

Cited by 23 | Viewed by 8251

Abstract

The catalytic synthesis of cyclic carbonates using carbon dioxide as a C1-building block is a highly active area of research. Here, we review the catalytic production of enantiomerically enriched cyclic carbonates via kinetic resolution of racemic epoxides catalysed by metal-containing catalyst systems. Full article

(This article belongs to the Special Issue Asymmetric Catalysis)

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10117 KiB

Open AccessArticle

Organocatalytic Asymmetric α-Chlorination of 1,3-Dicarbonyl Compounds Catalyzed by 2-Aminobenzimidazole Derivatives

by Daniel Serrano Sánchez, Alejandro Baeza and Diego A. Alonso

Symmetry 2016, 8(1), 3; https://doi.org/10.3390/sym8010003 - 13 Jan 2016

Cited by 11 | Viewed by 6225

Abstract

Bifunctional chiral 2-aminobenzimidazole derivatives 1 and 2 catalyze the enantioselective stereodivergent α-chlorination of β-ketoesters and 1,3-diketone derivatives with up to 50% ee using N-chlorosuccinimide (NCS) or 2,3,4,4,5,6-hexachloro-2,5-cyclohexadien-1-one as electrophilic chlorine sources. Full article

(This article belongs to the Special Issue Asymmetric Catalysis)

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Open AccessArticle

Natural Abundance Isotopic Chirality in the Reagents of the Soai Reaction

by Béla Barabás, Róbert Kurdi and Gyula Pályi

Symmetry 2016, 8(1), 2; https://doi.org/10.3390/sym8010002 - 08 Jan 2016

Cited by 13 | Viewed by 5299

Abstract

Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocatalysis. Therefore magnitude and eventual effects of isotopic chirality caused by natural abundance isotopic substitution (H, C, O, Zn) in the reagents of the Soai reaction were analyzed by combinatorics and probability calculations. Expectable enantiomeric excesses were calculated by the Pars–Mills equation. It has been found that the chiral isotopic species formed by substitution in the otherwise achiral reagents provide enantiomeric excess (e.e.) levels that are higher than the sensitivity threshold of the Soai autocatalysis towards chiral induction. Consequently, possible chiral induction exerted by these e.e. values should be taken into account in considerations regarding the molecular events and the mechanism of the chiral induction in the Soai reaction. Full article

(This article belongs to the Special Issue Asymmetric Catalysis)

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2637 KiB

Open AccessArticle

Structural Properties and Biological Prediction of ({[(1E)-3-(1H-Imidazol-1-yl)-1-phenylpropylidene] amino}oxy)(4-methylphenyl)methanone: An In Silico Approach

by Maha S. Almutairi, Devarasu Manimaran, Issac Hubert Joe, Ola A. Saleh and Mohamed I. Attia

Symmetry 2016, 8(1), 1; https://doi.org/10.3390/sym8010001 - 28 Dec 2015

Cited by 2 | Viewed by 4125

Abstract

Bioactive molecules are playing essential role in the field of drug discovery and various pharmaceutical applications. Vibrational spectral investigations of the anti-Candida agent ({[(1E)-3-(1H-imidazol-1-yl)-1-phenylpropylidene]amino}oxy)(4-methylphenyl)methanone ((1E)-IPMM) have been recorded and analyzed to understand its structural geometry, inter- and intra-molecular interactions. The equilibrium geometry, harmonic vibrational wavenumber, natural bond orbital (NBO) and Frontier orbital energy analyses have been carried out with the help of density functional theory with B3LYP/6-311++G(d,p) level of theory. The detailed vibrational assignments for the title molecule were performed on the basis of potential energy distribution analysis in order to unambiguously predict its modes. The calculated wavenumbers had good agreement with the experimental values. NBO analysis has confirmed the intramolecular charge transfer interactions. The predicted docking binding energy gave insight into the possible biological activity of the title molecule. Full article

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Symmetry, Volume 8, Issue 1 (January 2016) – 6 articles

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