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

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 ($\Delta E_{PV}$), 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 $\Delta E_{PV}$ 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.