Biomolecular Homochirality and Electroweak Interactions. I. The Yamagata Hypothesis

Large vibrationally induced parity violation effects in CHDBrI. Chem Commun (Camb) 2023;59:14579-14582. [PMID: 37990542 DOI: 10.1039/d3cc03787h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

The isotopically chiral molecular ion CHDBrI+ is identified as an exceptionally promising candidate for the detection of parity violation in vibrational transitions. The largest predicted parity-violating frequency shift reaches 1.8 Hz for the hydrogen wagging mode which has a sub-Hz natural line width and its vibrational frequency auspiciously lies in the available laser range. In stark contrast to this result, the parent neutral molecule is two orders of magnitude less sensitive to parity violation. The origin of this effect is analyzed and explained. Precision vibrational spectroscopy of CHDBrI+ is feasible as it is amenable to preparation at internally low temperatures and resistant to predissociation, promoting long interrogation times (Landau et al., J. Chem. Phys., 2023, 159, 114307). The intersection of these properties in this molecular ion places the first observation of parity violation in chiral molecules within reach.

Possible chemical and physical scenarios towards biological homochirality

The single chirality of biological molecules in terrestrial biology raises more questions than certitudes about its origin. The emergence of biological homochirality (BH) and its connection with the appearance of life have elicited a large number of theories related to the generation, amplification and preservation of a chiral bias in molecules of life under prebiotically relevant conditions. However, a global scenario is still lacking. Here, the possibility of inducing a significant chiral bias "from scratch", i.e. in the absence of pre-existing enantiomerically-enriched chemical species, will be considered first. It includes phenomena that are inherent to the nature of matter itself, such as the infinitesimal energy difference between enantiomers as a result of violation of parity in certain fundamental interactions, and physicochemical processes related to interactions between chiral organic molecules and physical fields, polarized particles, polarized spins and chiral surfaces. The spontaneous emergence of chirality in the absence of detectable chiral physical and chemical sources has recently undergone significant advances thanks to the deracemization of conglomerates through Viedma ripening and asymmetric auto-catalysis with the Soai reaction. All these phenomena are commonly discussed as plausible sources of asymmetry under prebiotic conditions and are potentially accountable for the primeval chiral bias in molecules of life. Then, several scenarios will be discussed that are aimed to reflect the different debates about the emergence of BH: extra-terrestrial or terrestrial origin (where?), nature of the mechanisms leading to the propagation and enhancement of the primeval chiral bias (how?) and temporal sequence between chemical homochirality, BH and life emergence (when?). Intense and ongoing theories regarding the emergence of optically pure molecules at different moments of the evolution process towards life, i.e. at the levels of building blocks of Life, of the instructed or functional polymers, or even later at the stage of more elaborated chemical systems, will be critically discussed. The underlying principles and the experimental evidence will be commented for each scenario with particular attention on those leading to the induction and enhancement of enantiomeric excesses in proteinogenic amino acids, natural sugars, and their intermediates or derivatives. The aim of this review is to propose an updated and timely synopsis in order to stimulate new efforts in this interdisciplinary field.

Magnetars and Magnetic Separation of Chiral Radicals in Interstellar Space: Homochirality

Pasteur was the first to realize Earth's homochirality. Consequently, he attempted to design experiments revealing a mechanism that would expose life's chiral preference. Some of these experiments involved the application of magnetic fields to chemical reactions. His experiments failed, in part, because B-fields are pseudo-vectors and cannot couple preferentially to one handedness. However, extremely large magnetic fields cause the Maxwell equations to break down. This allows the motions of spin and charge densities in paramagnetic anion radicals to produce polarized axial B-fields that can undergo preferential coupling to one handedness. Hence, when a racemic mixture of paramagnetic organic molecules passes by an extremely large external gradated magnetic field, the enantiomers experience different torque forces and acquire different translational directions. B-fields of the required magnitude are unknown on this planet. In fact, they would be lethal, thereby eliminating any chance of Pasteur's success. On the other hand, Duncan and co-workers have recently discovered and garnered physical understanding of magnetars in interstellar space. Some of these neutron star systems produce B-fields greater than the quantum electrodynamic field strength, which is more than enough to generate the required torque for the interstellar enantiomeric separation. In space, chiralitically enriched materials can be deposited on planetesimals and result in homochiral "islands" on the planets. The formation of magnetars is a consequence of weak force events. We assert that, in interstellar space, a plethora of enantiomerically enriched dust clouds resulted from inter-magnetar-paramagnetic molecule force fields.

Molecular chirality in meteorites and interstellar ices, and the chirality experiment on board the ESA cometary Rosetta mission

Life, as it is known to us, uses exclusively L-amino acid and D-sugar enantiomers for the molecular architecture of proteins and nucleic acids. This Minireview explores current models of the original symmetry-breaking influence that led to the exogenic delivery to Earth of prebiotic molecules with a slight enantiomeric excess. We provide a short overview of enantiomeric enhancements detected in bodies of extraterrestrial origin, such as meteorites, and interstellar ices simulated in the laboratory. Data are interpreted from different points of view, namely, photochirogenesis, parity violation in the weak nuclear interaction, and enantioenrichment through phase transitions. Photochemically induced enantiomeric imbalances are discussed more specifically in the topical context of the "chirality module" on board the cometary Rosetta spacecraft of the ESA. This device will perform the first enantioselective in situ analyses of samples taken from a cometary nucleus.

High-resolution spectroscopy of the chiral metal complex [CpRe(CH₃)(CO)(NO)]: a potential candidate for probing parity violation

Heavy-metal containing chiral compounds have been suggested as promising candidates for studying parity-violation effects. We report herein the broadband rotational spectroscopy study of the chiral complex [CpRe(CH3)(CO)(NO)] in the gas phase. The spectra obtained are very rich due to the two rhenium isotopologues ((185)Re and (187)Re), hyperfine structure arising from the rhenium and nitrogen nuclei, and the asymmetry of the chiral complex. Since rhenium is located very close to the molecular center of mass, the rotational constants for the two rhenium isotopologues are very similar. However they can be differentiated by their characteristic nuclear quadrupole hyperfine splitting patterns. Comparison with calculated nuclear quadrupole coupling constants shows that all-electron relativistic basis sets are necessary for a correct description of the rhenium atom in this type of complex. The present study is an important step towards future precision studies on chiral molecules.

Emergence of molecular chirality due to chiral interactions in a biological environment

We explore the interplay between tunneling process and chiral interactions in the discrimination of chiral states for an ensemble of molecules in a biological environment. Each molecule is described by an asymmetric double-well potential and the environment is modeled as a bath of harmonic oscillators. We carefully analyze different time-scales appearing in the resulting master equation at both weak- and strong-coupling limits. The corresponding results are accompanied by a set of coupled differential equations characterizing optical activity of the molecules. We show that, at the weak-coupling limit, chiral interactions prohibit the coherent racemization induced by decoherence effects and thus preserve the initial chiral state. At the strong-coupling limit, considering the memory effects of the environment, Markovian behavior is observed at long times.

Space asymmetry as a possible global feature

A series of reports in the literature indicated symmetry breaking in assemblies of chiral molecules of opposite handedness. These unexpected observations could be accounted for as being generated by the "parity violation" of the nuclear weak force, combined with an autocatalytic amplification process. However, in many such cases, in particular of chiral fluids, this putative mechanism is far from providing a reasonable explanation for such discrimination. In this article it is suggested that space may have deviated a priori from absolute symmetry, a possibility which complies with observations in atoms and molecules and may even be implicated in the asymmetrical configuration of spiral galaxies. Space asymmetry can be extrapolated to a difference between the relative statistical weights of the "right" versus the "left" directions with respect to Euclidian coordinates or, analogously, to a difference between the clockwise and anticlockwise orientations in polar coordinates. The difference in weights of these directions in space is estimated to be around 1%, based on the differences observed in density values of chiral fluids and chiral crystals of NaClO3. The implied asymmetry of time, as the conjugated fourth dimension, suggests a similar difference in magnitude of the time coordinate in a right-handed versus left-handed space, which is feasible for experimental verification.

Chiroptical signatures of life and fundamental physics

This paper aims to inspire experimentalists to carry out proposed new chiroptical experiments springing from the theoretical study of the role of parity violation in the origin of biomolecular homochirality and to provide a brief update on the current status of calculations of the electroweak parity-violating energy difference (PVED) between enantiomers. If the PVED did select life's handedness, we would expect to find life on other planets consistently using the same hand as terrestrial biochemistry. Much more importantly, even finding the "wrong" hand (rather than a racemic mixture) on another planet could be the homochiral signature of life, and we discuss our proposal for chiroptical detection of life on extra-solar planets. The PVED may also have an exciting future as a "molecular footprint" of fundamental physics: comparison of calculated PVEDs with measured values could one day allow chemists to do "table-top particle physics" more cheaply with improved chiroptical techniques instead of ever larger particle accelerators. We discuss our proposed chiroptical method to measure the PVED by using molecular beams. To our knowledge, optical rotation has not yet been measured in molecular beams, but the rewards of doing so include a host of other "first ever" results in addition to measurement of the PVED.

Chirality, photochemistry and the detection of amino acids in interstellar ice analogues and comets

The primordial appearance of chiral amino acids was an essential component of the asymmetric evolution of life on Earth. In this tutorial review we will explore the original life-generating, symmetry-breaking event and summarise recent thoughts on the origin of enantiomeric excess in the universe. We will then highlight the transfer of asymmetry from chiral photons to racemic amino acids and elucidate current experimental data on the photochemical synthesis of amino and diamino acid structures in simulated interstellar and circumstellar ice environments. The chirality inherent within actual interstellar (cometary) ice environments will be considered in this discussion: in 2014 the Rosetta Lander Philae onboard the Rosetta space probe is planned to detach from the orbiter and soft-land on the surface of the nucleus of comet 67P/Churyumov-Gerasimenko. It is equipped for the in situ enantioselective analysis of chiral prebiotic organic species in cometary ices. The scientific design of this mission will therefore be presented in the context of analysing the formation of amino acid structures within interstellar ice analogues as a means towards furthering understanding of the origin of asymmetric biological molecules.

Progress toward the first observation of parity violation in chiral molecules by high-resolution laser spectroscopy

Parity violation (PV) effects in chiral molecules have so far never been experimentally observed. To take up this challenge, a consortium of physicists, chemists, theoreticians, and spectroscopists has been established and aims at measuring PV energy differences between two enantiomers by using high-resolution laser spectroscopy. In this article, we present our common strategy to reach this goal, the progress accomplished in the diverse areas, and point out directions for future PV observations. The work of André Collet on bromochlorofluoromethane (1) enantiomers, their synthesis, and their chiral recognition by cryptophanes made feasible the first generation of experiments presented in this article.

Analysis of parity violation in chiral molecules

In order to guide the experimental search for parity violation in molecular systems, in part motivated by the possible link to biomolecular homochirality, we present a detailed analysis in a relativistic framework of the mechanism behind the tiny energy difference between enantiomers induced by the weak force. A decomposition of the molecular expectation value into atomic contributions reveals that the effect can be thought of as arising from a specific mixing of valence s(1/2) and p(1/2) orbitals on a single center induced by a chiral molecular field. The intra-atomic nature of the effect is further illustrated by visualization of the electron chirality density and suggests that a simple model for parity violation in molecules may be constructed by combining pre-calculated atomic quantities with simple bonding models. A 2-component relativistic computational procedure is proposed which bridges the relativistic and non-relativistic approaches to the calculation of parity violation in chiral molecules and allows us to explore the single-center theorem in a variational setting.

Theoretical investigations into the enantiomeric and racemic forms of α-(trifluoromethyl)lactic acid

There are many different hypotheses on the origin of biomolecular homochirality. One possible scenario concerns the enantiomeric enrichment of a nearly racemic solid via self-disproportionation of enantiomers. In particular, in a recent paper Soloshonok and co-workers showed a first example of optical self-purification of α-(trifluoromethyl)lactic acid by sublimation [V. A. Soloshonok et al., J. Am. Chem. Soc. 2007, 129, 12112]. Here we present detailed theoretical studies of α-(trifluoromethyl)lactic acid in the solid state as well as in the gas-phase dimeric form. The calculations of energy differences between dimers show that in the solid state the enantiomeric pure compound is energetically preferred, while in the gas phase the equilibrium shifts towards the racemic mixture although thermodynamic corrections cannot be neglected, thus providing a detailed microscopic explanation for the enantio-purification process for the first time.

Chiral oxorhenium(V) complexes as candidates for the experimental observation of molecular parity violation: a structural, synthetic and theoretical study

We report the synthesis and resolution of a series of new chiral "3 + 1" oxorhenium(V) complexes, designed for high-resolution laser spectroscopy experiments probing molecular parity-violation (PV) effects in the Re=O stretching mode frequency. These complexes display a particularly simple chemical structure, with the rhenium atom as the stereogenic center, and show large PV energy differences according to our calculations. They were obtained in the racemic and enantioenriched forms, in the latter case by using either semi-preparative chiral HPLC resolution or enantioselective synthesis. The vibrational transition frequency differences between the enantiomeric pairs due to PV have been calculated with two- and four-component relativistic Hamiltonians using Hartree-Fock (HF) and density functional theory (DFT). For three complexes, including one synthesized in enantioenriched form, our HF calculations predict frequency differences above the present resolution limit of 1 Hz. These results confirm the order of magnitude for the calculated HF PV vibrational frequency differences reported earlier for this class of compounds [P. Schwerdtfeger and R. Bast, J. Am. Chem. Soc., 2004, 126, 1652]. However, at the DFT level the PV vibrational frequency differences are in some cases reduced by an order of magnitude, but are still within the sensitivity of 0.01 Hz, which is the anticipated sensitivity in a new proposed experiment. We therefore believe that the present study represents an important step towards the experimental observation of PV in molecular systems, and emphasizes the extreme sensitivity of the PV vibrational frequency difference to the chemical environment around the rhenium center.

Electroweak parity-violating energy shifts of amino acids: the "conformation problem"

The preceding paper described our coupled-perturbed Hartree-Fock (CPHF) and density functional theory (DFT) methods of computing the parity-violating energy shift (PVES). This paper addresses the "conformation problem"-the difficulty determining which hand of amino acids in solution is favoured by the weak force due to the difficulty determining the solution conformation. We attempt to resolve this by using the methods of the preceding paper to compute the PVES of solution and gas-phase amino acid structures determined by other groups from high level optimizations that include solvation. We conclude that the conformational hypersensitivity of the PVES still precludes a definite conclusion as to the sign of the PVES of L-alanine in solution, but that there is no problem in the gas phase: the PVES of gas-phase L-alanine is decisively negative. We show that the PVES is very sensitive to certain torsion angles, but is not hypersensitive to bondlengths or bond angles. In determining structures for PVES computations, there is therefore no need for expensive full optimizations: one can just optimize the crucial torsion angles. We present new computations of gas-phase amino acids PVESs, using partial optimizations with small basis sets, and the results agree well with those from higher level techniques. In the following paper we apply these less costly techniques to larger amino acids. The "conformation problem" has led some to dismiss the PVES as the source of life's handedness, but we believe this is premature: we show here that amino acids are a special case because their favoured conformations are almost achiral.

Evaluation of coupled perturbed and density functional methods of computing the parity-violating energy difference between enantiomers

We present new coupled-perturbed Hartree-Fock (CPHF) and density functional theory (DFT) computations of the parity-violating energy difference (PVED) between enantiomers for H(2)O(2) and H(2)S(2). Our DFT PVED computations are the first for H(2)S(2) and the first with the new HCTH and OLYP functionals. Like other "second generation" PVED computations, our results are an order of magnitude larger than the original "first generation" uncoupled-perturbed Hartree-Fock computations of Mason and Tranter. We offer an explanation for the dramatically larger size in terms of cancellation of contributions of opposing signs, which also explains the basis set sensitivity of the PVED, and its conformational hypersensitivity (addressed in the following paper). This paper also serves as a review of the different types of "second generation" PVED computations: we set our work in context, comparing our results with those of four other groups, and noting the good agreement between results obtained by very different methods. DFT PVEDs tend to be somewhat inflated compared to the CPHF values, but this is not a problem when only sign and order of magnitude are required. Our results with the new OLYP functional are less inflated than those with other functionals, and OLYP is also more efficient computationally. We therefore conclude that DFT computation offers a promising approach for low-cost extension to larger biosystems, especially polymers. The following two papers extend to terrestrial and extra-terrestrial amino acids respectively, and later work will extend to polymers.

Parity-violating energy shifts of Murchison L-amino acids are consistent with an electroweak origin of meteorite L-enantiomeric excesses

In 1996, four alpha-methyl amino acids in the Murchison meteorite--L-isovaline, L-alpha-methylnorvaline, L-alpha-methyl-allo-isoleucine and L-alpha-methyl-isoleucine--were found to show significant enantiomeric excesses of the L form, ranging from 2% to 9%. Their deuterium to hydrogen isotope ratios suggest they formed in the pre-solar interstellar gas cloud rather than during a later aqueous processing phase on the asteroid parent body. In this paper we apply the techniques of the preceding two papers to compute the parity-violating energy shifts of these amino acids. We find that, in the gas phase, the PVESs of the neutral L forms of all four Murchison alpha-methyl amino acids are decisively negative, and there is even some correlation between the magnitudes of the L-excesses and the magnitudes of the PVESs--all of which is at least consistent with an electroweak origin of the Murchison enantiomeric excesses.

A photochemical mechanism for homochirogenesis

Theoretical analysis of one-step and multiple-step photoreactions initiated with circularly polarized light shows that the enantiomeric excess of a chiral reactant approaches +/- 1 as the amount of unreacted reactant approaches 0. The final product never has a large enantiomeric excess at any stage of its formation and slowly decreases to 0 at the completion of the reaction. For multiple-step reactions the behavior of the intermediate photoproducts is much more interesting. During certain stages of the overall reaction both the size of the enantiomer excess and the amount of a given intermediate photoproduct are large. Furthermore, the sign of the enantiomeric excess of an intermediate may change during the course of the reaction. Multiple-step photoreactions initiated with circularly polarized light may be a method by which the exogenous and endogenous synthesis of optically active molecules occurred in the prebiotic universe.

Computational study of ground-state chiral induction in small peptides: comparison of the relative stability of selected amino acid dimers and oligomers in homochiral and heterochiral combinations

The relative stabilities of homochiral and heterochiral forms of selected dipeptides, AA, AS, AC, AV, AF, AD, AK, tripeptides, AAA, AVA, and an acetylpentapeptide, AcGLSFA, have been calculated using thermodynamic integration protocols and the GROMOS 53A6 force field. Integration pathways have been designed that produce minimal disturbance to the system, including the use of soft atoms, low-energy intermediates, and chiral inversion of the smaller amino acid in the peptide. Comparison of the results obtained by thermodynamic integration between the diastereomeric forms (in explicit water, at 300 K) and from exhaustive global minimum-energy searches for the individual dipeptides (implicit water, epsilon = 78, 0 K) suggests that entropic contributions to the relative stability of the chiral forms are important. This conclusion is supported by the results of explicit calculation of the effect of temperature on the relative stability of alanylvalylalanine diastereomers. The Gibbs free energy calculations predict that at ambient temperature and pressure homochiral dipeptides with small side chains or polar groups in the vicinity of the peptide backbone, AA, AS, and AD, are more stable than their heterochiral counterparts by fractions of a kJ/mol. For bigger side chains, AC, AV, AF, and AK, the heterochiral diastereomers appear to be more stable. Predicted relative stabilities are in line with observations reported in the literature for AE and YY. Excellent agreement is found for the calculated and experimentally determined relative stabilities of the diastereomers of the dipeptide AA and of all-L AcGLSFA and its diastereomer containing D-serine in the central position. Addition of counterions to the solvent box has no significant effects on charged and neutral forms. From the present findings it would appear unlikely that the intrinsic stability difference between homo- and heterochiral dipeptides has been a driving force in a primordial selection process leading to the incorporation of amino acids with a single enantiomeric configuration in natural proteins.

Serine octamers: cluster formation, reactions, and implications for biomolecule homochirality

The emergence of homochirality continues to be one of the most challenging topics associated with the origin of life. One possible scenario is that aggregates of amino acids might have been involved in a sequence of chemical events that led to chiral biomolecules in self-replicating systems, that is, to homochirogenesis. Serine is the amino acid of principal interest, since it forms "magic-number" ionic clusters composed of eight amino acid units, and the clusters have a remarkable preference for homochirality. These serine octamer clusters (Ser8) can be generated under simulated prebiotic conditions and react selectively with other biomolecules. These observations led to the hypothesis that serine reactions were responsible for the first chiral selection in nature which was then passed through chemical reactions to other amino acids, saccharides, and peptides. This Review evaluates the chemistry of Ser8 clusters and the experimental evidence that supports their possible role in homochirogenesis.

Intrinsic asymmetries of amino acid enantiomers and their peptides: A possible role in the origin of biochirality

L-amino acids and D-carbohydrates were incorporated into the first forms of life over 3.5 billion years ago, presumably from racemic mixtures of organic solutes produced by abiotic synthetic pathways. The process by which this choice occurred has not been established, but a consensus view is that it was a chance event, such that life could equally well have used D-amino acids and L sugars. In this review we will explore a second, less plausible alternative that minute differences in the physical properties of certain enantiomers made it more likely that L-amino acids and D-carbohydrates would be incorporated into early life. By all classical criteria, chiral isomers are perfect mirror image structures and, therefore, are expected to be identical in their macroscopic properties. However, scattered reports in the literature suggest that there may be slight differences in the physical properties of L- and D-amino acids and their polymers, which could lead to a preferred incorporation of L-amino acids into primitive forms of life. Here we present a literature survey of this issue and discuss its possible role in the origin of biochirality.

Stochastic Analysis of the Parity-Violating Energy Differences between Enantiomers and Its Implications for the Origin of Biological Chirality

A stochastic description of a racemic mixture is developed taking into account the slight energy difference between enantiomers originating from parity violation (DeltaE(PV) approximately equal to 10(-13) Jmol(-1)). The system can be described by an asymmetric binomial distribution. A method is developed to calculate the probability of forming the more-stable isomer in excess, which is not significantly larger than 50% under normal conditions. It is concluded that the parity-violating energy difference between enantiomers is very unlikely to be relevant in considerations about the origin of biological chirality.

Parity nonconservation contribution to the nuclear magnetic resonance shielding constants of chiral molecules: A four-component relativistic study

A systematic four-component relativistic study of the parity nonconservation (PNC) contribution to the (isotropic) NMR shielding constants of chiral molecules is presented for the P enantiomers of the series H(2)X(2) (X=(17)O,(33)S,(77)Se,(125)Te,(209)Po). The PNC contributions are obtained within a linear response approach at the Hartree-Fock level. A careful design of the basis sets is necessary. The four-component relativistic results based on the Dirac-Coulomb Hamiltonian are compared with the nonrelativistic Levy-Leblond results and those obtained by the spin-free modified Dirac Hamiltonian. The calculations confirm the nonrelativistic scaling law Z(2.4) of the PNC contribution with respect to nuclear charge Z. However, the calculations also show that the overall scaling is significantly modified by relativistic effects. The scalar relativistic effect scales as Z(4.7) for the selected set of molecules, whereas the spin-orbit effect, of opposite sign, scales better than Z(6) and completely dominates the PNC contribution for the heaviest elements. This opens up the intriguing possibility of the experimental observation of PNC effects on NMR parameters of molecules containing heavy atoms. The presented formalism is expected to be valuable in assisting the search for suitable candidate molecules.

Parity violating energetic difference and enantiomorphous crystalsp-caveats; reinvestigation of tyrosine crystallization

The present article challenges reports claiming to have demonstrated the Parity Violating Energetic Difference (PVED) between enantiomorphous D- and L-crystals. Apart from PVED, the presence of minute quantities and differing profiles of impurities incorporated during their different history of preparation will affect the physical properties of D- and L-crystals. These impurities are anticipated to play a much greater role in affecting crystallization behavior than PVED. The effect of impurities on the growth and dissolution of enantiomorphous crystals is illustrated with some representative examples. Shinitzky et al. (2002) reported recently dramatic differences in the growth and dissolution properties of the D- and L-crystals of tyrosine. We have repeated these experiments using commercial samples from different sources and employing a validated enantioselective gas chromatographic technique. We attribute Shinitzky's findings either to the use of inappropriate analytical techniques for the determination of enantiomeric composition and/or to the presence of unidentified contaminants in the commercial tyrosine samples. Related caveats hold also for the recently published claims by Shinitzky (2006) and Scolnik et al. (2006) to have observed experimentally PVED between enantiomeric helices of poly-glutamic acid composed of 24 repeating units.

Recent experimental and theoretical developments towards the observation of parity violation (PV) effects in molecules by spectroscopy

Parity violation (PV) at the molecular level is known to be responsible for a tiny energy difference between the two enantiomers of a chiral molecule. This parity violation energy difference (PVED) has not yet been detected by experiment. In the last few years, the search for PV effects in molecules has made important steps ahead for several reasons. On one hand, very accurate infra-red spectroscopy measurements were performed by metrologists on bromochlorofluoromethane (CHFClBr) with a 10 Hz accuracy, which so far is the most precise. On the other hand, relativistic calculations were used for the evaluation of DeltaE(PV) allowing for a screening of favorable molecules for future measurements. The synthesis of such chiral molecules with high parity violation effects is currently being investigated. In memory of Professor Jean-Bernard Robert.

Quantum mechanical considerations on the algebraic structure of central molecular chirality

The chiral algebra of tetrahedral molecules, derived from Fischer's projections, is discussed in the framework of quantum mechanics. A "quantum chiral algebra" is obtained whose operators, acting as rotations or inversions, commute with the Hamiltonian of the system. It is shown that energy and chirality eigenstates are strictly related through the Heisenberg relations, while chirality operators "conserve" parity eigenstates.