Racemization, chiral stability and weak interactions

We study, in the framework of the Schrödinger's equation, the effect of intermolecular interactions on tunneling racemization of the active molecule. This molecule is assumed as a two-level system and the left-right isomerism is viewed in terms of a double-bottomed harmonic potential well. The active molecule is assumed to be embedded in a gas, liquid or solid, submitted to a perturbing potential U created by the molecules of the sample. In our model we take into account the difference of energy (ε) between the left (L) and right (R) configurations due to the weak interactions. We show that when ε=0 and the perturbing potential U is due to random binary collisions, the optically active system inevitably racemizes. However, when ε≠0 there is chiral stability when ε⪢δ, where δ is the difference of energy, between left and right configurations, due to the natural tunneling effect. On the other hand, when ε≠0 and U is created by a cooperative effect between the interacting molecules we show that there is no racemization but it is possible to have chiral stability. This occurs when the heterochiral interaction (ULR) and δ are much smaller than ε. According to our estimates the stability occurs, for typical molecular parameters, only for fundamental harmonic oscillator frequencies ω>5.2×1013rad/s, that is, in the infrared and far-infrared regions. In our approach the weak interaction, which is responsible for the left-right symmetry breaking, plays a fundamental role in the optical stability.