Molecules chiral, parity violation

J. K. Laerdahl, P. Schwerdtfeger, Fully relativistic o5 initio calculations of the energies of chiral molecules including parity-violating weak interactions, Phys. Rev. A 60 (1999) 4439-4453. 

The traditional treatment of molecules relies upon a molecular Hamiltonian that is invariant under inversion of all particle coordinates through the center of mass. For such a molecular Hamiltonian, the energy levels possess a well-defined parity. Time-dependent states conserve their parity in time provided that the parity is well defined initially. Such states cannot be chiral. Nevertheless, chiral states can be defined as time-dependent states that change so slowly, owing to tunneling processes, that they are stationary on the time scale of normal chemical events. [22] The discovery of parity violation in weak nuclear interactions drastically changes this simple picture, [14, 23-28] For a recent review, see Bouchiat and Bouchiat. [29]... 

I would like to draw attention here to some work on chiral molecules, which allows very fundamental tests of symmetries in physics and chemistry. The experiment outlined in Scheme 2 [4] allows us to generate, by laser control, states of well-defined parity in molecules, which are ordinarily left handed (L) or right handed (R) chiral in their ground states. By watching the time evolution of parity, one can test for parity violation and I have discussed in detail [4-6] how parity violating potentials AEpv might be measured, even if as... 

Physical applications An early application of relativistic molecular theory was to heavy atom collisions, and the production of supercritical fields involving highly stripped ions [234-237]. Studies have been made of parity- and time-reversal symmetry violation in diatomic molecules [74,238,239], and of parity violation in small chiral molecules [240-242]. 

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... 

How does de lege parity violation affect chiral molecules In order to illustrate this we restrict ourselves to a two-level system with two chiral or handed states called L) and R). In classical terms these shall correspond to the equilibrimn structures of the left-handed and the right-handed enantiomer. For the quantum mechanical viewpoint we employ here for convenience the Born-Oppenheimer approximation although the discussion is also possible in quite general terms without this approximation. We assume that the ordinary — that is purely electrostatic — multidimensional Born-Oppenheimer potential energy hypersurface (PES) exhibits two minima corresponding to the left-handed and the right-handed structure which are... 

If we consider, instead of a two-level system, the multiple levels of ordinary chiral molecules, the states of well defined parity will in the low-energy region still come in almost degenerate pairs which are energetically separated from other states. Therefore the main contribution to parity violating effects will still be due to interpair coupling. In this limit A py can essentially be identified with 2 x fpvl-... 

In special chiral molecules one may as well search for circular polarisations induced by parity violating interactions [47] and also other spectroscopic techniques where one might observe signatures of parity violation in chiral systems have been discussed (see for instance [68,69]), but these techniques have received less attention. 

The first four-component calculations on parity violating effects in chiral molecules were performed in 1988 by Barra, Robert and Wiesenfeld [54] within an extended Hiickel framework. Interestingly, this study was on parity violating chemical shift differences in the nuclear magnetic resonance (NMR) spectra of chiral compounds and hence focused as well on the nuclear spin-dependent term of Hpv. Shortly later, however, also the first four-component results on parity violating potentials obtained with an extended Hiickel method were published by Wiesenfeld [150]. 

Four component all-electron ab initio approaches to parity violating potentials in chiral molecules have been presented by Quiney, Skaane and... 

The parity violating potential in chiral molecules, on the other hand, has been computed by Wiesenfeld [150] within the four-component... 

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. 

Recently, hydrogen peroxide also served as a test system for ab initio calculations of parity violating chemical shift in chiral molecules [56]. 

G. Laubender, R. Berger, Ab initio calculation of parity violating chemical shifts in nuclear magnetic resonance spectra of chiral molecules, ChemPhysChem 4 (2003) 395-399. 

M. Quack, J. Stohner, Influence of parity violating weak nuclear potentials on vibrational and rotational frequencies in chiral molecules, Phys. Rev. Lett. 84 (2000) 3807-3810. 

J. Laerdahl, P. Schwerdtfeger, H. Quiney, Theoretical analysis of parity-violating energy differences between the enantiomers of chiral molecules, Phys. Rev. Lett 84 (2000) 3811-3814. 

R. Harris, L. Stodolski, The effect of the parity violating electron-nucleus interaction on the spin-spin coupling Hamiltonian of chiral molecules, J. Chem. Phys. 73 (1980) 3862-3863. 

T. Kitayama, H. Kiyonaga, K. Morihashi, O. Takahashi, O. Kikuchi, Ab initio spin-orbit coupling SCF calculations of parity-violating energy of chiral molecules, J. Mol. Struct. 589-590 (2002) 183-193. 

C. Chardonnet, C. Daussy, T. Marrel, A. Amy-Klein, C. Nguyen, C. Borde, Parity violation test in chiral molecules by laser spectroscopy, in B. Frois, M. Bouchiat (Eds.), Parity violation in atoms and polarized electron scattering. World Scientific, Singapore, 1999, pp. 325-355. 

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