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A Relationship between the Molecular Parity-Violation Energy and the Electronic Chirality Measure

Juan J. Aucar, Alessandro Stroppa, Gustavo A. Aucar

Abstract

When the weak-forces producing parity-violating effects are taken into account, there is a tiny energy difference between the total electronic energies of two enantiomers ($ΔE_{PV}$), which might be the key to understand the evolution of the biological homochirality. We focus on the electronic chirality measure ($ECM$), a powerful descriptor based on the electronic charge density, for quantifying the chirality degree of a molecule, for a representative set of chiral molecules, together with their E$_{PV}$ energies. Our results show a novel, strong and \textit{positive} correlation between $ΔE_{PV}$ and $ECM$, supporting a subtle interplay between the weak-forces acting within the nuclei of a given molecule and its chirality. These findings suggest that experimental investigations for molecular parity violation detection should consider molecules with as large $ECM$ values as possible, and may support that a chiral signature is imprinted on life by fundamental physics via the parity-violating weak interactions.

A Relationship between the Molecular Parity-Violation Energy and the Electronic Chirality Measure

Abstract

When the weak-forces producing parity-violating effects are taken into account, there is a tiny energy difference between the total electronic energies of two enantiomers (), which might be the key to understand the evolution of the biological homochirality. We focus on the electronic chirality measure (), a powerful descriptor based on the electronic charge density, for quantifying the chirality degree of a molecule, for a representative set of chiral molecules, together with their E energies. Our results show a novel, strong and \textit{positive} correlation between and , supporting a subtle interplay between the weak-forces acting within the nuclei of a given molecule and its chirality. These findings suggest that experimental investigations for molecular parity violation detection should consider molecules with as large values as possible, and may support that a chiral signature is imprinted on life by fundamental physics via the parity-violating weak interactions.
Paper Structure (8 sections, 12 equations, 11 figures, 1 table)

This paper contains 8 sections, 12 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical Approach
  3. Calculation of parity-violation energies in molecules
  4. The electronic descriptor of chirality, ECM
  5. Computational Details
  6. Results and Discussion
  7. Conclusions
  8. Supporting Information

Figures (11)

  • Figure 3: Correlation between $\Delta E_{PV}$ and $ECM$ for the following molecules: alanine a), glyceraldehyde b). The substituted atoms whose atomic numbers were taken as a parameter are shown in the ESI file. Calculations were performed at DHF/dyall.cv2z and 4C-B3LYP/dyall.cv2z levels of theory.
  • Figure : TOC Graphic.
  • Figure : a)
  • Figure : a)
  • Figure : a)
  • ...and 6 more figures