Parity-violating Energy Research Articles

Parity violation and the evolution of biomolecular homochirality.

Parity violation at the level of terrestrial biopolymers, as seen in proteins, DNAs, and RNAs, and parity violation at the level of nuclear processes, as evident in longitudinally polarized beta-particles and parity-violating energy differences (PVEDs), are discussed and their fundamental importances are emphasized. Attempts to find a causal connection between the unique homochirality of biopolymers and parity violation at the nuclear level, and speculations that the former is a consequence of the latter, are reviewed. Consideration of all lines of evidence leads to the conclusion that there is no substantiation for such a causal connection, and that the two levels of parity violation are entirely independent of each other.

Calculation of the parity-violating energy by using the generalized spin-orbitals obtained by the SCF calculation including the spin-orbit coupling interaction

Calculation of the parity-violating energy by using the generalized spin-orbitals obtained by the SCF calculation including the spin-orbit coupling interaction

Energetic stabilization of d-camphor via weak neutral currents.

It is shown via a series of numerical tests on the camphor molecule, C10H16O, that the naturally occurring d-enantiomer is energetically stabilized with respect to its mirror image by electroweak force. The calculated energy difference between enantiomers, about 1.5 x 10(-19) hartree, is roughly eight orders of magnitude smaller than the upper bound suggested by available spectroscopic investigations on the frequency of a spectroscopic transition. However, such a difference is about ten times larger than previous estimates of parity-violating energy contributions reported in the literature for other chiral molecules, which makes the idea of electroweak stabilization of one enantiomer more reliable than expected before.

Demonstration of the parity-violating energy difference between enantiomers.

Racemic mixtures of (+) and (-) sodium potassium tartrate, tris(1, 2-ethanediamine)cobalt(III), and tris(1,2-ethanediamine)iridium(III) molecules were crystallized, and the optical activities of the resulting crystalline materials, dissolved in water, were carefully measured to study the influence of the parity-violating energy difference in the crystallization process. Although no effect was found in the case of tartrate, enantiomeric excess appeared in the crystallization of the cobalt and iridium complexes. These investigations, performed in our laboratory, demonstrated the contribution of the parity-violating neutral weak current to the forces acting in molecules.

Theoretical results which strengthen the hypothesis of electroweak bioenantioselection

It is shown via a large series of numerical tests on two fundamental organic molecules, the $L\ensuremath{-}\ensuremath{\alpha}$-amino acid L-valine and the sugar precursor hydrated D-glyceraldheyde, that the ab initio calculation of the parity-violating energy shift, at the random-phase approximation level of accuracy, provides results that are about one order of magnitude larger than those obtained by means of less accurate methods employed previously. These findings would make more plausible the hypothesis of electroweak selection of natural enantiomers via the Kondepudi-Nelson scenario, or could imply that Salam phase-transition temperature is higher than previously inferred: accordingly, the hypothesis of terrestrial origin of life would become more realistic.

On the stabilization of natural L-enantiomers of α-amino acids via parity-violating effects

Rigorous calculations of the parity-violating energy difference between enantiomers of a few α-amino acids are presented, which strongly support the idea that weak nuclear forces are responsible for energy stabilization of natural L forms.

Calculation of contributions of one- and two-electron spin-orbit coupling terms to the parity-violating energy shifts for amino acids and helical alkanes

Rigorous calculations were performed for spin-orbit coupling terms of the Breit–Pauli Hamiltonian in the calculation of the parity-violating energy shifts Epν using the sum-over-state perturbation theory, and the role of one-electron and two-electron spin-orbit coupling terms was examined. Calculations on amino acids and helical n-alkanes have suggested that inclusion of one-center terms both of one- and two-electron spin couplings is sufficient to estimate the Epν values quantitatively.

On the calculation of parity-violating energies in hydrogen peroxide and hydrogen disulphide molecules within the random-phase approximation

It is shown via extended numerical tests that the ab initio calculation of a parity-violating energy term, at the random-phase approximation (or coupled Hartree-Fock perturbation theory) level of accuracy, gives results which are more than one order of magnitude larger than those usually obtained by means of less accurate methods employed so far. These findings make more plausible the hypothesis of electroweak selection of natural enantiomers.

Electroweak enantioselection and the origin of life.

All biomolecules are of one hand--but what determines which hand? Why is life based on L-amino acids and D-sugars rather than D-amino acids and L-sugars? We believe the symmetry-breaker could be the weak force, which causes enantiomers to differ very slightly in energy. In this paper we present our calculations of this parity-violating energy difference (PVED) for a range of important biomolecules, and in nearly all cases it is indeed the 'natural' enantiomer which is the more stable.

Possibilities to measure the parity-violating energy difference

Four methods: direct, polymerization, condensation and crystallization, are dicussed. that may be applied to measure the parity violating energy difference between enantiomers We find that the best possibility is the crystallization with element of high Z in the asymmetry center.

Parity-violating energy shift of helical n-alkanes

The parity-violating energy shift, E pv, was calculated for right-handed helical n-alkanes C n H 2 n+2 ( n = 4−11) and the dependence of the E pv value on molecular evolution was examined. It was shown that the right-handed n-alkane helix is more stable than its mirror image, and the energy difference between the mirror-image molecules increases constantly as the chain length increases.

The search for large parity-violating energy differences finds fruit in thiosubstituted DNA analogues

Earlier calculations of parity-violating energy differences between enantiomers (PVEDs) have produced values for typical biomolecules no larger than 10 −20 hartree, corresponding to 10 −17 kT at 298 K, but in this paper we report PVEDs of 10 −17 hartree, corresponding to 10 −14 kT, for thiosubstituted DNA analogues.

Parity-Violating Energy Shift of Glycine, Alanine, and Serine in the Zwitterionic Forms: Calculation Using HFO-NG Basis Sets

Abstract The parity-violating energy shift, Epv, was calculated for glycine, alanine, and serine using the HFO-5G and -6G minimal basis sets, which were determined so as to well reproduce the behavior of an atomic orbital near the nucleus. A clear basis set dependence was observed in both the sign and magnitude of Epv. For the zwitterionic form of glycine, the HFO-5G and -6G calculations gave an Epv similar to that obtained by the (14,14/10) minimal basis set. For the most stable conformation of l-alanine, these basis set gave a negative Epv, indicating that l-alanine is more stable than d-alanine, while the split-valence basis sets gave positive values. It was shown that l-serine is lower in energy than d-serine due to the parity-violating interaction for almost the entire range of the C–C rotation angle.

The search for large parity-violating energy differences between enantiomers

Earlier reports of unusually large parity-violating energy differences between enantiomers in sugar precursors are shown to be wrong, but interesting new results for phosphates and silica are presented which point the way to systems with larger values.

Effect of atomic number on parity-violating energy differences between enantiomers

Within a relativistic framework, the ground-state energy difference between left and right isomers of a chiral molecule is calculated. This energy difference is due to parity non conserving, electron-nucleus interaction. The influence of high-Z atoms, up to lead (Z=82) is investigated, for elements belonging to to groups 14 and 16, as well as Pt. Electron-nucleus overlaps are systematically calculated in a Dirac-Hartree-Fock scheme, showing a relativistic increase of the overlap of the order of 10 for Z∼80.

Parity violation and the origins of biomolecular handedness

The violation of parity by the weak interactions ensures that enantiomeric chiral molecules have inequivalent energies, one being inherently stabilized with respect to the other. These parity-violating energy differences have been calculated for a number of fundamental biomolecules including a series of a-amino acids, polypeptide structures, and a representative of the sugar series together with its variation over a possible prebiotic reaction path leading to α-amino acids. In each case the natural enantiomer found in terrestrial biochemistry was shown to be intrinsically stabilized and preferred over its unnatural enantiomer. The significance of these results in accounting for the prebiotic origins of the terrestrial biomolecular homochirality is discussed and the possible consequences of parity-violating energy differences in mineral catalysts during the prebiotic era considered.

On the measurement of the parity violating energy difference between enantiomers

An experiment is outlined for measuring the small energy difference between two enantiomers due to the parity-violating weak neutral current perturbation. The method is based on the violation of the selection rules for the time evolution of states of well defined initial parity in isolated molecules. It could confirm or reject recent quantitative theoretical estimates of parity-violating energy differences.

Parity-violating energy differences and the origin of biomolecular homochirality

The violation of parity by the weak interactions ensures that enantiomeric chiral molecules have inequivalent energies. These parity-violating energy differences have been calculated, using ab initio methods, for the series of α -amino acids glycine, alanine, valine, serine and aspartic acid, and for a set of polypeptide/protein fragments in both the α -helix and β -sheet secondary structures. In each case the energy differences are found to favour the existence of the natural left-handed l -enantiomers over their unnatural mirror-image right-handed d -enantiomers. The variation of the parity-violating energy difference along a prebiotic reaction path leading to the formation of a possible precursor of alanine has also been determined. Under equilibrium conditions the energy difference is found to preferentially select the stereochemical reaction channel corresponding to the eventual formation of l -alanine rather than that for its unnatural d -enantiomer. The significance of these results in accounting for the prebiotic origins of the terrestrial biomolecular homochirality are discussed.

The effects of parity violation of molecular structure

Through the action of the parity-violating weak interactions, a chiral molecule and its enantiomer are expected to have equilibrium structures which slightly deviate from an exact mirror-image relationship. It is found that such deviations, and the resulting small differences in the electromagnetic interactions within enantiomeric molecules, are insufficient to perturb significantly or counteract the inherent parity-violating energy differences between enantiomers.

The parity-violating energy differences between the enantiomers of α-amino acids

The parity-violating weak neutral current perturbation of the electronic energy has been calculated, using ab initio methods, for a series of α-amino acids. The WNC energy shifts for these fundamental biomolecules consistently favour the existence of the natural L-enantiomers in preference to the unnatural mirror-image D-enantiomers.