Parity-violating energy difference

These experimental results could not be confirmed by Lahav and co-workers they suggest that impurities in the starting materials have a much greater effect on the crystallisation process than the PVED (Parity Violating Energy Difference). Extensive experimental studies indicate the importance of small quantities of impurities, particularly in early phases of crystallisation nucleus formation. Amino acids from various sources were used, and the analyses were carried out using the enan-tioselective gas chromatography technique (M. Lahav et al 2006). 

Tranter, G. E. 1985a. The Parity Violating Energy Differences Between the Enantiomers of a-amino Acids. Mol. Phys. 56, 825-838. 

Tranter, G. E. 1986. Parity-violating Energy Differences and the Origin of Biomolecular Homochirality. J. Theor. Biol. 119, 467-479. 

In the 45 years since its proposal, Frank s autocatalytic mechanism (Section 11.3, above) has spawned numerous theoretical refinements including consideration of such factors as reversibility, racemization, environmental noise, and parity-violating energy differences. [100,101] In contrast to the above examples of stereospecific autocatalysis by the SRURC, however, none of these theoretical refinements is supported by experimental evidence. While earlier attempts to validate the Frank mechanism for the autocatalytic amplification of small e.e.s in other experimental systems have generally been unsuccessful, several recent attempts have shown more promising results. [102,104]... 

Mason, S. F. and Tranter, G. E. (1983). The parity violating energy difference between enantiomeric molecules. Chem. Phys. Lett., 94, 34. 

The parity violating energy difference between enantiomeric molecules. Mol Phys., 53, 1091-111. 

The most common form of TOT clathrate crystallises as discrete C2 symmetric cavities in the chiral space group 1, implying that the (—)-(M) and (+)-(/") forms separate spontaneously as crystallisation occurs. This property of TOT has been used in an ambitious model experiment designed to test the theory that the parity-violating energy difference (the violation of parity or symmetry in elementary particles), with autocatalytic amplification (in the case of TOT during crystallisation) is responsible for the observed chirality of modern biomolecules. The experiment did not find any evidence to support the theory, with equal amounts of each enantiomeric crystal being isolated.26... 

A. Szab6-Nagy, L. Keszthely i, Demonstration of the Parity-Violating Energy Difference Between Enantiomers. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 4252-4255. 

G. E. Tranter. Parity-violating energy differences of chiral minerals and the origin of biomoiecular homochirality. Nature, 318 (1985), 172. 

J. K. Laerdahl, P. Schwerdtfeger, H. M. Quiney, Theoretical Analysis of Parity-Violating Energy Differences between Enantiomers of Chiral Molecules, Phys. Rev. Lett. 84 (2000) 3811-3814. 

For completeness it should be emphasised that various definitions of the parity violating energy difference A pv can be found in the literature. 

Others have related the parity violating energy difference to the spectroscopically measurable molar standard reaction enthalpy ApyH° of the reaction R according to... 

One might also consider to relate AEpy to the coupling matrix elements between pairs of tunneling states. This leads then to vibrational state dependent parity violating energy differences. 

Historically, the era of electroweak quantum chemistry began with the calculation of parity violating energy differences between enantiomers of chiral compounds within one-component frameworks. Traditionally the emphasis was on closed shell chiral systems, although systems in electronically excited states have received attention recently, both in one- and four-component approaches [47,100]. 

Since the one-component approaches employ the efi ective Hamiltonian (113) or various further approximations to it, the expectation value of this Hamiltonian for a system in a closed shell singlet state vanishes. This is due to the scalar product between either the spin and the momentum operator of the electron or the scalar product of the electron momentum with the nuclear spin. In the absence of a coupling mechanism between spin and coordinate space, the scalar product must therefore vanish. For the parity violating energy difference between enantiomers the main coupling contribution is expected to be due to spin-orbit coupling. The corresponding... 

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