Parity-Violating Interactions

We conclude this chapter with a look at some more exotic properties, at least from the point of view of mainstream chemistry. In a 1949 article celebrating Einstein s 70th birthday, Dirac (1949) suggested that the laws of nature might not be invariant with respect to space inversion or time reversal. Special relativity only requires that physical laws be invariant with respect to the position and velocity of the observer, and any change in these can be effected though a series of (infinitesimal) transformations that do not involve reflections of time or space. Experimental evidence for processes that do not conserve parity under space inversion, P-odd processes, was eventually observed in nuclear p decay, contributing in turn to the development of the standard model for 

Spatial inversion has an important position in chemistry as the operation that connects two different enantiomers of a chiral molecule. Biochemically it is observed that for living organisms only L-amino acids are present in proteins, and that DNA and RNA are built up from D-sugars. In the wake of the discovery of P-odd processes, suggestions have been made that there may be a connection between this type of interaction and the natural selection of only one enantiomeric form for biochemical processes. It is possible to envision some interaction between molecular structure and the weak force that would favor one of the enantiomers energetically. 

To see how this might occur, we look at the operator that would be responsible for breaking the energy degeneracy between two enantiomers. This has the form 

The chirality operator is odd under spatial inversion, exhibiting what is called pseudoscalar behavior, that is, it is a scalar with the transformation properties of a vector. For a molecule with two enantiomeric forms, A and B, with respective wave functions and 4 5, we expect space inversion, represented by the operator /, to connect the two forms such that 

For a matrix element of a many-electron chirality operator we have 

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Bakasov A, Ha T-K, Quack M (1995) Ab initio Calculation of molecular energies including parity violating interactions. In Chela-Flores J, Raulin F (eds) Chemical Evolution Physics of the Origin of Life. Kluwer, Dordrecht Boston London, p 287 Ball P (1994) Designing the Molecular World, Chemistry at the Frontier, Princeton University... 

A. Bakasov, T.-K. Ha, M. Quack, Ab initio calculation of molecular energies including parity violating interactions, J. Chem. Phys. 109 (1998) 7263-7285, 110 (1999) 6081. 

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. 

If we put all ingredients together, we arrive at the following effective Hamiltonian for the parity violating interaction between the n... 

The improved theoretical methods also invited to reinvestigate parity violating effects in biologically relevant systems [125,134,140,141,162,168, 169,178] and it could be demonstrated, that previous claims for a systematic stabilisation of amino acids in water, which based on lower level calculations, were not justified [140]. This finding gave again fresh impetus to the debate on possible relations between parity violating interaction and biochemical homochirality. 

This section on spectroscopically relevant molecules will be closed with camphor, for which early attempts to measure parity violating frequency shifts exist that provided an experimental upper bound of Aiz/i/ 10 [59]. As of yet, no calculations of the parity violating frequency shifts have been published, but Lazzeretti, Zanasi and Faglioni [136] computed the parity violating potential at the equilibrium structure of camphor within their one-component RPA method and predicted this potential to be of about —7 X 10 E h for the D-enantiomer, which would therefore be stabilised due to the parity violating interactions. This result has also been discussed in relation to the question of the origin of the biochemical homochirality, which will also be the main subject of the following section. 

By virtue of these results, it was repeatedly claimed that L-amino acids were systematically stabilised with respect to their D-counterparts due to parity violating weak interactions and this alleged stabilisation was frequently interpreted as evidence for a possible link between parity violating interactions and the observed biochemical homochirality in terrestrial organisms. 

A. Hennum, T. Helgaker, W. Klopper, Parity-violating interaction in H2O2 calculated from density-functional theory, Chem. Phys. Lett. 354 (2002) 274-282. 

J. Laerdahl, R. Wesendrup, P. Schwerdtfeger, Parity-violating interactions and biochemical homochirality, ChemPhysChem 1, 60-62. 

There are some physical factors which can be considered as possible candidates to cause biological asymmetry. The most often mentioned physical phenomenon is the weak parity violating interaction. It seems to be very appealing to explain biological asymmetry by the the general asymmetry of the physical world. 

Zel dovich, Ya.B. (1958) Electromagnetic interaction with parity violation, Sov. Phys. JETP, 6, 1184-1186. 

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... 

Parity violating electron scattering. Recently it has been proposed to use the (parity violating) weak interaction to probe the neutron distribution. This is probably the least model dependent approach [31]. The weak potential between electron and a nucleus... 

More than forty years ago, Lee and Yang [8] observed anomalies in the decay patterns of theta and tau mesons, which suggested to them that parity was not conserved for certain weak interactions involved in the (3-decay of radioactive nuclei. This Nobel-prize-winning prediction was experimentally validated by Wu et al., [9] who found that the longitudinally polarized electrons emitted during the (3-decay of Co nuclei had a notable (40%) left-handed bias, i.e., their spins were predominantly antiparallel to their directions of motion. These experiments established that parity violation and symmetry breaking occurred at the nuclear level. 

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]... 

After discovery of the combined charge and space parity violation, or CP-violation, in iT°-meson decay [7], the search for the electric dipole moments (EDMs) of elementary particles has become one of the most fundamental problems in physics [6, 8, 9, 10, 1]. A permanent EDM is induced by the weak interaction that breaks both the space symmetry inversion and time-reversal invariance [11]. Considerable experimental effort has been invested in probing for atomic EDMs induced by EDMs of the proton, neutron and electron, and by P,T-odd interactions between them. The best available restriction for the electron EDM, de, was obtained in the atomic T1 experiment [12], which established an upper limit of de < 1.6 X 10 e-cm, where e is the charge of the electron. The benchmark upper limit on a nuclear EDM is obtained in atomic experiment on i99Hg [13], ]dHgl < 2.1 X 10 e-cm, from which the best restriction on the proton EDM, dp < 5.4 x 10 " e-cm, was also recently obtained by Dmitriev Sen kov [14] (the previous upper limit on the proton EDM was obtained in the TIE experiment, see below). 

The prediction of a heavy boson has received preliminary empirical support [92,96] from an anomaly in Z decay widths that points toward the existence of Z bosons with a mass of 812 GeV 1 33j [92,96] within the SO(l) grand unified field model, and a Higgs mechanism of 145 GeV4gj3. This suggests that a new massive neutral boson has been detected. Analysis of the hadronic peak cross sections obtained at LEP [96] implies a small amount of missing invisible width in Z decays. The effective number of massless neutrinos is 2.985 0.008, which is below the prediction of 3 by the standard model of electroweak interactions. The weak charge Qw in atomic parity violation can be interpreted as a measurement of the S parameter. This indicates a new Qw = 72.06 0.44, which is found to be above the standard model pre-... 

The Sachs theory [1] is able to describe parity violation and spin-spin interactions from first principles [6] on a classical level it can also explain... 

Weak Interactions were treated by Pais who, starting from Fermi s original theory, discussed the discovery by Lee and Yang,74 almost 5 years before, of the parity violation by weak interactions, its experimental confirmation,75 the muon-electron universality,76 the idea of an intermediate boson as a mediator of weak interaction, and the two-neutrinos question. 77... 

Abstract Understanding the origin of chirality in nature has been an active area of research since the time of Pasteur. In this chapter we examine one possible route by which this asymmetry could have arisen, namely chiral-specific chemistry induced by spin-polarized electrons. The various sources of spin-polarized electrons (parity violation, photoemission, and secondary processes) are discussed. Experiments aimed at exploring these interactions are reviewed starting with those based on the Vester-Ulbricht hypothesis through recent studies of spin polarized secondary electrons from a magnetic substrate. We will conclude with a discussion of possible new avenues of research that could impact this area. 

In the "nonrigid symmetric-top rotors" (such as NH ), the second-order Stark effect is observed under normal circumstances. Indeed, field strengths of the order of 1 600 000 [V/m] are required to bring the interaction into the first-order regime in this case [18]. In contrast, very weak interactions suffice to make the mixed-parity states and appropriate for the description of optically active systems. Parity-violating neutral currents have been proposed as the interaction missing from the molecular Hamiltonian [Eq.(1)] that is responsible for the existence of enantiomers [14,19]. At present, this hypothesis is still awaiting experimental verification. 

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