Asymmetry of electron chirality between enantiomeric pair molecules and the origin of homochirality in nature

Abstract

We propose the difference of reaction rates of the weak interaction between enantiomers produces the small imbalance of the number density between pairs of enantiomers, which may be the origin of the homochirality in nature. Since left-handed particles have larger reaction rate of the weak interaction than right-handed particles, the nonzero total electron chirality in a chiral molecule, which is the integrated chirality density over the whole molecule, induces different reaction rate of the weak interaction between an enantiomeric pair. Due to this difference of reaction rates, one of the enantiomeric pair is more destroyed than the other by interactions with astronomical particles in space, such as cosmic rays and neutrinos emitted by nuclear fusion in star cores. It is numerically shown that chiral molecules generally have nonzero total electron chirality in addition to parity-violating energy shift, for ${\mathrm{H}}_{2}{X}_{2}$ ($X=\text{O}$, S, Se, Te) molecules as a typical sample of chiral molecules. This total chirality is shown to be related to the dihedral angle of ${\mathrm{H}}_{2}{X}_{2}$ molecules and is the result of the cancellation between large contributions from some highest occupied molecular orbitals. It is shown that the value of total chirality in a chiral molecule is drastically enhanced if the molecule is ionized or excited, since this cancellation is broken. The parity-violating energy shift has this property also though the enhancement is smaller for ${\mathrm{H}}_{2}{X}_{2}$ molecules.