Parity-Violation Effects in Molecules

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. 

Indeed, the restriction to purely electromagnetic interactions for the description of atomic and molecular systems appears to be a very good first approximation. The weak force gives, nevertheless, rise to significant effects that would be absent if parity would be a conserved quantity. Zel dovich 

Z exchange (middle diagram) and scattering of a myon-antineutrino (i ) at an electron (right diagram). Only the last process does not interfere with the (usual) photon exchange. 

Indeed, around 1980, first experimental results on atomic parity violation have been reported, in particular measurements of the optical activity of bismuth, thallium and lead vapours as well as measurements of an induced electric dipole (El) amplitude to a highly forbidden magnetic dipole transition (Ml) in caesium. These experiments have nowadays reached very high resolution so that even effects from the nuclear anapole moment, which results from weak interactions within the nucleus, have been observed in caesium. The electronic structure calculations for caesium are progressing to a sub-percent accuracy for atomic parity violating effects and the reader is referred to chapter 9 of the first part of this book [12]. 

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 

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A couple of heteronuclear diatomic radicals with either a Ei/2 or a IIi/2 ground state have been suggested for experimental attempts to detect parity violating effects in molecules. With his semi-empirical method, Kozlov [149] studied numerically the parity violating effective constant Wpy of the heavy nuclei in and and obtained a value of about 2 kHz... 

Berger R (2004) Parity-violation effects in molecules. In Schwerdtfeger P (ed) Relativistic electronic structure theory, vol. Part 2. Elsevier, Amsterdam, pp 188-288... 

P,T-PARITY VIOLATION EFFECTS IN POLAR HEAVY-ATOM MOLECULES... 

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. 

Early four-component numerical calculations of parity-violating effects in diatomic molecules which contain only one heavy nucleus and which possess a Si/2 ground state have been performed by Kozlov in 1985 [149] within a semi-empirical framework. This approach takes advantage of the similarity between the matrix elements of the parity violating spin-dependent term e-nuci,2) equation (114)) and the matrix elements of the hyperfine interaction operator. Kozlov assumed the molecular orbital occupied by the unpaired electron to be essentially determined by the si/2, P1/2 and P3/2 spinor of the heavy nucleus and he employed the matrix elements of e-nuci,2) nSi/2 and n Pi/2 spinors, for which an analytical expres-... 

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]. 

A. Soncini, A. Ligabue, P. Lazzeretti, R. Zanasi, Parity-violating effects in asymmetric chemical reactions A theoretical study on the CHFClBr molecule, Phys. Rev. E 62 (2000) 8395-8399. 

D. Figgen, T. Saue, P. Schwerdtfeger. Relativistic four- and two-component calculations of parity violation effects in chiral tungsten molecules of the form NWXYZ (X, Y, Z=H, F, Cl, Br, or I). /. Chem. Phys., 132 (2010) 234310. 

Crassous, J., Chardonnet, C., Saue, T. and Sdiwerdtfeger, P. (2005) Recent e q)erimental and theoretical developments towards the observation of parity violation (PV) effects in molecules by spectroscopy. Organic and Biomolecular Chemistry, 3, 2218—2224. 

In particular, the consideration of relativistic and QED effects of electronic systems (i.e. free electrons, electronic ions, atoms or molecules) in strong external electromagnetic fields provides various appropriate scenarios for sensitive tests of our understanding of the underlying interactions. Theories of fundamental interactions, such as quantum electrodynamics (QED) or the standard model of electroweak interactions can be tested conclusively by studying QED radiative corrections and parity-violating effects (PNC) in the presence of strong fields. 

I note in passing that apart from the effects due to parity nonconservation, also effects that arise from nonconservation of the symmetry with respect to simultaneous spatial and temporal inversion, so-called VT-odd effects, or to simultaneous charge conjugation and spatial inversion, denoted CT -violating effects, received particular attention especially for diatomic molecules. Readers interested in VT- or CP-violating effects in molecular systems are referred to the book of Khriplovich [42] and to the reviews [32,43]. 

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-... 

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. 

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. 

By virtue of the results obtained for BaF, these error margins appear to be somewhat too narrow. With empirical data extracted from molecular beam experiments, Kozlov [149] obtained in 1985 a value for the parity violating effective constant Wpy of 212 Hz and a value of 180 Hz with data derived from electron paramagnetic resonance (EPR) spectra of the matrix-isolated molecule. With a different method for the treatment of the spin-orbit interaction, Kozlov and Labzowsky [32] obtained in 1995 Wpy = 240 Hz and 210 Hz, respectively. The ab initio calculations performed by Kozlov, Titov, Mosyagin and Souchko [171] with RECPs, however, resulted in Wpv = 111 Hz on the self-consistent field (SCF) level and Wpy = 181 Hz on the SCF level with an effective operator technique designed to take... 

Parity violating effective constants W y, for the heavy nucleus in heteronu-clear diatomic molecules as obtained with various different approaches (see text). 

The influence of the weak interaction on chemical reactions can be calculated since it favours left-handedness, it has an effect on the energy content of molecules and thus on their stability. In the case of the amino acids, the L-form would be more stable than the corresponding D-form to a very small extent. Theoretical calculations (using ab initio methods), in particular by Mason and Tranter (1983), indicated that the energy difference between two enantiomers due to the parity violation is close to 10 14J/mol (Buschmann et al., 2000). More recent evidence suggests that the... 

Since the historical PV weak force origin /3-decay experiment of 60Co [ 106], theoreticians presumed that the tiny parity violating WNC at molecular and subatomic levels may also allow a distinction between mirror image molecules at the macroscopic level as well. This is because PV-WNC at the molecular level may be a candidate for the homochiral scenario under terrestrial and extraterrestrial conditions [1,2,104,109-118]. The WNC, however, did not induce any observable PV effects between enantiomers in their ground states because of the minuscule PV energy difference (PVED) of 10 19 eV and/or negligibly small 10 - % ee in racemates. Theoreticians also proposed several possible amplification mechanisms at reproducible detection levels within laboratory time scales and at terrestrial locations [113,117,118]. 

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