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arXiv:0910.4133

Weak Interactions ,Tunneling Racemization and Chiral Stability

M. Cattani, José Maria Filardo Bassalo

Published Oct 21, 2009• 0 citations
arXivHTMLPDF

Abstract

We study in the framework of the Schrodinger equation the effect of intermolecular interactions on the tunneling racemization of the active molecule. The active 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 E due to the weak interactions between the left (L) and right (R) configurations. We have shown that when E is equal to zero the system cannot be optically stable: the optical activity tends asymptotically to zero in the case of dilute gases or compressed gases and liquids or oscillates periodically around zero when the molecules are isolated or submitted to a static potential. Only when E is different of zero the system can be optically stable depending on the strength parameters of the potential U and on the magnitude of the spontaneous tunneling.

DOI
10.48550/arxiv.0910.4133

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We study in the framework of the Schrodinger equation the effect of intermolecular interactions on the tunneling racemization of the active molecule. The active 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 E due to the weak interactions between the left (L) and right (R) configurations. We have shown that when E is equal to zero the system cannot be optically stable: the optical activity tends asymptotically to zero in the case of dilute gases or compressed gases and liquids or oscillates periodically around zero when the molecules are isolated or submitted to a static potential. Only when E is different of zero the system can be optically stable depending on the strength parameters of the potential U and on the magnitude of the spontaneous tunneling.
We study the tunnel dynamics of a chiral molecule between its left (L) and right (R) conformations, under the global effect of collisional decoherence together with the effect of a mean-field generated by the environment where an energetic difference, K, between homochiral and heterochiral interactions is assumed. We show that this decoherence leads unavoidably to equal populations of the L and R chiral conformations even for a high enough value of K which tends to keep localized an initial chiral state. However, we also show that K contributes to the stabilization of an initial L or R state for times that could be many orders of magnitude larger than the tunneling time, in the case the decoherence rate is much greater than the tunneling rate. In this case, an estimation of this stabilization time and a critical tunneling time is made. Even in the case in which the tunneling rate is greater than the decoherence rate, the effect of K is to keep localized the initial chiral state for times greater than the tunneling time. A possible slight chiral asymmetry is also considered.
We consider the effects of multistate transitions on the tunneling racemization of chiral molecules. This requires going beyond simple two-state models of enantiomers and to include transitions within a multiple-level quantum-mechanical system. We derive an effective two-level description which accounts for transitions from the enantiomers to an arbitrary number of excited states as an application of the Weisskopf-Wigner approximation scheme. Modifications to the optical activity from these additional states are considered in general terms under the assumption of CPT invariance and then under TTT invariance. Some formal dynamical analogies between enantiomers and the neutral KKK-meson system are discussed.
In this review, the concepts of quantum tunneling and parity violation are introduced in the context of chiral molecules. A particle moving in a double well potential provides a good model to study the behavior of chiral molecules, where the left well and right well represent the L and R enantiomers, respectively. If the model considers the quantum behavior of matter, the concept of quantum tunneling emerges, giving place to stereomutation dynamics between left- and right-handed chiral molecules. Parity-violating interactions, like the electroweak one, can be also considered, making possible the existence of an energy difference between the L and R enantiomers, the so-called parity-violating energy difference (PVED). Here we provide a brief account of some theoretical methods usually employed to calculate this PVED, also commenting on relevant experiments devoted to experimentally detect the aforementioned PVED in chiral molecules. Finally, we comment on some ways of solving the so-called Hund’s paradox, with emphasis on mean-field theory and decoherence.
Abstract We examine the dynamics of the chiral states of chiral molecules with high tunneling rates in dilute and condensed phases in the context of time-dependent perturbation theory. The chiral molecule is effectively described by an asymmetric double-well potential, whose asymmetry is a measure of chiral interactions. The dilute and condensed phases are conjointly described by a collection of harmonic oscillators but with temperature-dependent sub-ohmic and temperature-independent ohmic spectral densities, respectively. We examine our method quantitatively by applying the dynamics to an isotopic ammonia molecule, NHDT, in an inert background gas (as the dilute phase) and in water (as the condensed phase). As the different spectral densities imply, the extension of the dynamics from the dilute phase to the condensed phase is not trivial. While the dynamics in the dilute phase leads to racemization, the chiral interactions in the condensed phase induce the quantum Zeno effect. Moreover, contrary to the condensed phase, the short-time dynamics in the dilute phase is sensitive to the initial state of the chiral molecule and to the strength of the coupling between the molecule and the environment.
In order to explore parity violating effects in chiral molecules, of interest in some models of evolution towards homochirality, quantum stochastic resonance (QSR) is studied for the population difference between the two enantiomers of a chiral molecule (hence for the optical activity of the sample), under low viscous friction and in the deep quantum regime. The molecule is described by a two-state model in an asymmetric double well potential where the asymmetry is given by the known predicted parity violating energy difference (PVED) between enantiomers. In the linear response to an external driving field that lowers and rises alternatively each one of the minima of the well, a signal of QSR is predicted only in the case that the PVED is different from zero, the resonance condition being independent on tunneling between the two enantiomers. It is shown that, at resonance, the fluctuations of the first order contribution to the internal energy are zero. Due to the small value of the PVED, the resonance would occur in the ultracold regime. Some proposals concerning the external driving field are suggested.