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In this lesson, we delve into the role of ring conformation and its stability, which determines the spatial arrangement and, consequently, the molecular symmetry and stereoisomerism of cyclic compounds. 1,2-Dimethylcyclohexane is used as a case study to evaluate the possible number of stereoisomers. Here, given the multiple (n = 2) chiral centers, there are 2n = 4 possible configurations that lack a plane of symmetry, as the ring skeleton exists in a non-planar chair conformation. In addition,...
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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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Isomerism in Complexes
Isomers are different chemical species that have the same chemical formula.
Transition metal complexes often exist as geometric isomers, in which the same atoms are connected through the same types of bonds but with differences in their orientation in space. Coordination complexes with two different ligands in the cis and trans positions from a ligand of interest form isomers. For example, the octahedral [Co(NH3)4Cl2]+ ion has two isomers (Figure 1) In the cis...
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The Cope rearrangement is classified as a [3,3] sigmatropic shift in 1,5-dienes, leading to a more stable, isomeric 1,5-diene. The reaction involves a concerted movement of six electrons, four from two π bonds and two from a σ bond, via an energetically favorable chair-like transition state.
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Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are...
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The chair conformation is the most stable form of cyclohexane due to the absence of angle and torsional strain. The absence of angle strain is a result of cyclohexane’s bond angle being very close to the ideal tetrahedral bond angle of 109.5° in its chair conformer. Similarly, the torsional strain is also absent owing to the perfectly staggered arrangement of bonds.
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Area of Science:

  • Chemistry
  • Materials Science
  • Physics

Background:

  • Symmetry is a fundamental concept across science, with symmetry breaking driving many natural phenomena.
  • Organic cages, with their defined 3D structures and dynamic motions, serve as excellent models for studying symmetry and its breaking.
  • Understanding symmetry breaking is crucial for fields ranging from particle physics to molecular chirality in biology.

Purpose of the Study:

  • To elucidate the scale-dependency of symmetry and symmetry breaking using organic cages.
  • To investigate the thermodynamic driving forces behind spontaneous chiral resolution in crystallization.
  • To explore emergent properties arising from symmetry-broken molecular packing in organic cage crystals.

Main Methods:

  • Analysis of racemization processes in organic cages to determine time-scale dependency of symmetry.
  • Investigation of hierarchical self-assembled structures of racemic organic cages across different scales.
  • Thermodynamic analysis of spontaneous chiral resolution, focusing on enthalpy-entropy compensation in cage conglomerates.

Main Results:

  • Symmetry and symmetry breaking are shown to be time-scale dependent, influenced by molecular motion, hydrogen bonding, and framework rigidity.
  • Symmetry and asymmetry manifest differently across molecular, supramolecular, and macroscopic levels in self-assembled structures.
  • Racemic compounds are more entropy-favored than conglomerates; spontaneous chiral resolution requires favorable enthalpy to overcome unfavorable entropy, observed in cage conglomerates with strong intermolecular interactions.
  • Symmetry-broken molecular packing in cage racemates leads to unique properties like second-harmonic generation and piezoelectricity.

Conclusions:

  • Organic cages provide a versatile platform for understanding fundamental aspects of symmetry and symmetry breaking.
  • The study offers insights into the time and spatial scale dependency of symmetry, driving forces for chiral resolution, and properties of symmetry-broken materials.
  • Findings pave the way for designing novel organic materials with tailored optical and electronic properties.