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What are the current theories of computational chemistry for studying homochirality (for example the phenomenon discussed here, here and in many other places)?

Electroweak chemistry has been developed to answer such questions on a more physical level, but do we have significant results or understanding of chirality from this theory?

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    $\begingroup$ +1. I'll send this to my friend Emil Zak who is an expert on chirality. We will have to decide if this is best asked as 2 separate questions or just one. $\endgroup$ Aug 1 '20 at 17:35
  • $\begingroup$ Martin Quack at ETH Zurich does some research in this area: ir.ethz.ch/research.htm $\endgroup$
    – Tyberius
    Aug 1 '20 at 19:01
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Relating to the question about electroweak chemistry: the parity violation effect of the weak force on chiral asymmetry has been considered for quite a while now. A good accessible introduction to the problem can be found here: Molecular Parity Violation and Chirality: The Asymmetry of Life and the Symmetry Violations in Physics, by Martin Quack. Another rather early papers on electroweak chemistry can be found here: Electroweak Quantum Chemistry of Alanine: Parity Violation in Gas and Condensed Phases - more literature can be pulled out from the citations metric to the above papers.

Several candidate molecules have been proposed, such as CHBrClF, HSSH and derivatives of the latter, in which this asymmetry could be measured spectroscopically. So far however, such an observation is still elusive, due to weakness of this naturally occurring interaction, which may be causing only very small shift between the sets of rotational-vibrational energy levels of the left-handed and right-handed forms of a chiral species.

Some recent attempts to measure parity violation in chiral molecules have been reported here: High-resolution FTIR spectroscopy of trisulfane HSSSH: a candidate for detecting parity violation in chiral molecules. A rather intriguing recent result reporting plausible 'electroweak interference' in asymmetric synthesis can be found here: Energy threshold for chiral symmetry breaking in molecular self-replication.

Next, relating more to the first question: apart from natural possible sources of chiral asymmetry, some people proposed ways to synthetically induce and study this chiral asymmetry with appropriately tailored electromagnetic fields. Excellent frontier studies in this field are conducted in the O. Smirnova's group, see, for instance: Synthetic chiral light for efficient control of chiral light–matter interaction.

Not to mention one, there are a bunch of approaches to achieve enantio-selective chiral response or dynamical discrimination (parity breaking) in chiral species. These approaches are largely based on the fact that a mixed product of some molecular properties, such as the electric dipole moment: $\vec{\mu}_a(R) \cdot \vec{\mu}_b(R) \times \vec{\mu}_c(R) = - \vec{\mu}_a(S) \cdot \vec{\mu}_b(S) \times \vec{\mu}_c(S)$ changes sign between enantiomers (R/S) (this mixed product is time-even and parity-odd). M. Schnell's group is perhaps leading the way in enantio-sensitive spectroscopy, which utilizes the sign-change property of the mixed-dipole moment product: Enantiomer-specific detection of chiral molecules via microwave spectroscopy. Suitable molecules must therefore have three significant components of the electric dipole moment and the interacting radiation must be resonant with three rotational transitions. This is however not enough to induce any dissymetry in populations of left- and right- enantiomers, only enantio-specific signal can be measured.

For chiral discrimination to be possible a chiral molecule must interact with another chiral field. One proposal for such a discriminatory interaction is given here: Field-Induced Diastereomers for Chiral Separation, which is based on a more general quantity which is parity-odd and time-even: mixed product of the electronic polarisability and the electric dipole moment: $\alpha_{xz}\mu_y$, which in the presence of a chiral field is responsible for discrimination in rotational-vibrational populations in a wider class of chiral molecules. Only off-resonant lasers and a dc electric field are needed in this case to induce asymmetry in the populations of left- and right- enantiomers. Some natural environments can possibly create instances of similar conditions.

I'm sure there are many other approaches, which I ignorantly omitted, and which more specifically target the problem of homochirality of life. Please feel encouraged to update and edit with more references. So far, to the best of my knowledge a commonly considered mechanism for homochirality involve the weak interaction (parity violation). An interesting research path leads along the interactions of parity-odd molecular properties (mixed products of electronic polarisability and the electric dipole moment, or even nuclear quadrupole moment) with chiral electromagnetic fields.

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