Molecular parity

Scheme 10 A pair of rod-like dialkylpolysilanes (33-SS and 33-RR) undergoing helix-helix transition at - 65 °C in isooctane used for molecular parity test experiment...

Molecular parity nonconservation caused by the parity violating property of the elec-troweak force is discussed. Different approaches to the computation of these parity violating influences are outlined and recent predictions for parity violating effects in spectroscopically and biologically relevant molecules are reviewed. 

Compared to atomic physics, the present situation in molecular physics is by far less comfortable The first detection of molecular parity violating effects is still lacking and calculations of parity non-conservation phenomena in molecules have not yet reached the accuracy of the corresponding atomic computations. Calculations of parity violating effects in chiral molecules, however, play currently more the decisive role of determining suitable molecular candidates for a successful or promising experiment, a task for which computational errors of more than 20 % may be perfectly acceptable. Some of these current uncertainties are due to difficulties in the... 

In early computational work on molecular parity violation, AEpy has been related to the parity violating potential Vpy computed at the equilibrium geometry of a chiral compound. jAE pv] was then reported as... 

Apart from spectroscopic properties it has also been considered to look at parity violating effects in the bulk (see for instance [31]). While this is possible in principle, this approach suffers from the enormous difficulty to attribute observed macroscopic effects unequivocally to molecular parity violation (see also discussion in [33]). 

Quite generally, however, all these experimental attempts to measure molecular parity violating effects depend on guidance from theory. In the initial stage, theory is needed to identify suitable molecular candidates with favourable properties for an experiment, while at a later stage, theory is needed to analyse and interpret the results of an experiment. In the fom th section, I will describe the methods currently available for the computation of molecular parity violating effects, but first I will outline briefly the way one has to go from the standard model of physics in order to arrive at the final working equations employed in these calculations. 

FROM THE STANDARD MODEL OF PHYSICS TO MOLECULAR PARITY VIOLATION... 

Here j is the electromagnetic four-current, and j are weak charged currents and finally j° is the weak neutral current that couples to the Z° boson. This neutral current deserves our particular attention when we are interested in molecular parity violating effects. 

The potentials (94) and (95) are already quite similar to the leading effective Hamiltonians that have been used so far in one- and four-component calculations of molecular parity violating eflFects. We have assumed above that the fermions are elementary particles. The effective potentials may, however, also be applied for the description of low energy weak neutral scattering events, in which heavy non-elementary fermions like the proton and the neutron or even entire atomic nuclei are involved, provided that properly adjusted vector and axial coupling coefficients py and for non-elementary fermions are used. 

We have finally arrived at those effective Hamiltonians, that have been employed in calculations of molecular parity violating effects either within a one-, two- or four-component scheme. In the following section I will outline the various strategies to include these Hamiltonians in perturbative computation of parity nonconservation effects in molecular systems. 

As discussed already in the introduction, the calculations of molecular parity nonconservation effects do at present not reeich the accuracy of the computations of atomic parity violating effects. This can mainly be attributed to additional difficulties due to vibrations and rotations of the molecule — complicating factors which are of course absent in atomic systems. At present, the rovibronic influences on parity violating effects in polyatomic molecules appear to be much more important than for instance radiative corrections and contributions from continuum states, which are vital to achieve the desired accuracy in calculations of parity violation in atoms. 

While the relativistically parameterised extended Hiickel approach to the calculation of molecular parity violating effects has the merit of simplicity, it suffers in particular from the non-self-consistent character of the extended Hiickel method. This problem is avoided in the four-component Dirac Hartree-Fock approaches to the computation of parity violating potentials in chiral molecules introduced by Quiney, Skaane and Grant [155] as well as Laerdahl and Schwerdtfeger [156]. These will be described in the following section. 

First attempts to calculate molecular parity violating potentials within a two-component framework have been undertaken by Kikuchi and coworkers [168,169]. They have added the Breit-Pauli spin-orbit coupling operator Hso to the usual non-relativistic Hamiltonian Hq... 

Since the first quantitative calculations on parity violating energy differences, which have been reported by Hegstrom, Rein and Sanders [25,107] almost two decades ago, about a dozen groups worldwide have performed calculations on various aspects of molecular parity violation. 

After this brief overview over the development in electroweak quantum chemistry in the last two decades, I will in the following subsections provide a list of the molecular systems and reactions studied computationally in relation to molecular parity violating effects. This list spans the range from benchmark systems to spectroscopically and biologically relevant molecules to chemical reactions. 

We leave now the benchmark, test and model systems and come to those compounds, that have either already been studied experimentally to determine molecular parity violating effects or which have been proposed as potential candidates for such measurements. 

As has been discussed in the introduction, the possibility of a relation between parity violating energy differences and the biochemical homochirality observed on earth has been noted by Yamagata [11] a decade after the discovery of parity violation in nuclear physics. Various different kinetic mechanisms have been proposed which could possibly amplify the tiny energy difference between enantiomeric structures to result in an almost exclusive chiral bias on a time scale relevant for the biochemical evolution. This aspect as well as other hypotheses regarding the origin of the biochemical homochirality have been discussed and reviewed multiple times (see for instance [33,37-39,190-193] and literature cited therein) so that we can concentrate here on the computational aspects of molecular parity violating effects in biochemical systems. 

This shall conclude the section on parity violating effects in chemical reactions and also this survey of the quantitative estimates of molecular parity violating effects. 

I am deeply indebted to Martin Quack for his stimulus, for sharing ideas and insight as well as for his support and help in various ways. Therefore, this chapter is dedicated to him on the occasion of his 55th birthday. I thank Jurgen Stohner for his comments on the manuscript and for stimulating discussions on various aspects of molecular parity violation. And last but not least I thank my student Guido Laubender for his dedicated work. 

R. Berger, Molecular parity violation in electronically excited states, Phys. Chem. Chem. Phys. 5 (2003) 12-17. 

Molecular Parity Violation and Chirality The Asymmetry of Life and the Symmetry Violations in Physics... 

Molecular Parity Violation and Chirality The Asymmetry of Life. 

Of all the observed asymmetries described here, the homochirality of biochemistry is perhaps the most relevant to the everyday life of the chemist, and it also could be the one enigma of the three for which a solution will first be found. An initial step toward solving this problem shall be discussed here in the framework of the theory of molecular parity violation and possible experiments on this phenomenon. 

The Theory of Molecular Parity Violation in Chiral Molecules... 

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