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Continuous Local Symmetry: Connection to Reactivity and Recognition

Duc Anh Lai, Devin A. Matthews

Abstract

Symmetry is one of the most beautiful yet mysterious concepts in science. In chemical systems, presence of local symmetries at specific fragments often serve as driving forces behind many physicochemical properties, including stability, spectroscopy, and reactivity. Moreover, degree of symmetry varies continuously with molecular dynamics and intermolecular interactions, making it a hidden but decisive factor. In this study, we propose a theoretical framework to quantify continuous degrees of symmetry and chirality localized within constrained regions of a molecular environment. Application of this method to reaction sites of dendralene molecules reveals strong correlations between local symmetry and molecular stability, parity-dependent behavior, and Diels-Alder reactivity. Additionally, representations of local chirality fields in porphyrins uncover unique signatures accounting for the chirality recognition power. Overall, these findings highlight the potentials of local symmetries within a molecular framework on predicting chemical properties.

Continuous Local Symmetry: Connection to Reactivity and Recognition

Abstract

Symmetry is one of the most beautiful yet mysterious concepts in science. In chemical systems, presence of local symmetries at specific fragments often serve as driving forces behind many physicochemical properties, including stability, spectroscopy, and reactivity. Moreover, degree of symmetry varies continuously with molecular dynamics and intermolecular interactions, making it a hidden but decisive factor. In this study, we propose a theoretical framework to quantify continuous degrees of symmetry and chirality localized within constrained regions of a molecular environment. Application of this method to reaction sites of dendralene molecules reveals strong correlations between local symmetry and molecular stability, parity-dependent behavior, and Diels-Alder reactivity. Additionally, representations of local chirality fields in porphyrins uncover unique signatures accounting for the chirality recognition power. Overall, these findings highlight the potentials of local symmetries within a molecular framework on predicting chemical properties.
Paper Structure (6 sections, 2 equations, 6 figures)

This paper contains 6 sections, 2 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Theoretical Methods
  3. Results
  4. Local symmetry: A predictor of dendralene reactivity and stability
  5. Chiral microenvironment: A hidden factor behind chiral recognition phenomena
  6. Conclusion

Figures (6)

  • Figure 1: [3--8]Dendralenes and derivatives.
  • Figure 2: a) Local quasi-$C_{2v}$ symmetry elements in [4]dendralene. b) Local symmetry measures of [3--8]dendralenes. c) Correlation of local reflection symmetry ($\sigma_v$) with monoadduct Diels--Alder reactivity. Linear regression (solid line) yields a coefficient of determination of $R^2 = 0.77$.
  • Figure 3: Difference in local reflection symmetry ($\sigma_v$) of substituted dendralenes with respect to [3]dendralene (1a). Dendralenes with lower reflection symmetry are more stable than 1a (blue), while those with higher reflection symmetry are more stable (orange). Note that species are arranged in order of local symmetry.
  • Figure 4: Tetraphenyloctamethylporphyrin and dimethoxyphenyl-substituted derivatives. The diprotonated structures are depicted in accordance with the carboxylic acid-complexed crystal structure.
  • Figure 5: Chirotopicity field in unsubstitubed porphyrin (1b)
  • ...and 1 more figures