Parity Violation In Chiral Molecules Research Articles

Near-complete chiral selection in rotational quantum states

Controlling the internal quantum states of chiral molecules for a selected enantiomer has a wide range of fundamental applications from collision and reaction studies, quantum information to precision spectroscopy. Achieving full enantiomer-specific state transfer is a key requirement for such applications. Using tailored microwave fields, a chosen rotational state can be enriched for a selected enantiomer, even starting from a racemic mixture. This enables rapid switching between samples of different enantiomers in a given state, holding great promise, for instance, for measuring parity violation in chiral molecules. Although perfect state-specific enantiomeric enrichment is theoretically feasible, achieving the required experimental conditions seemed unrealistic. Here, we realize near-ideal conditions, overcoming both the limitations of thermal population and spatial degeneracy in rotational states. We achieve over 92% enantiomer-specific state transfer efficiency using enantiopure samples. This indicates that 96% state-specific enantiomeric purity can be obtained from a racemic mixture, in an approach that is universally applicable to all chiral molecules of C1 symmetry. Our work integrates the control over internal quantum states with molecular chirality, thus expanding the field of state-selective molecular beams studies to include chiral research.

The Interplay between Tunneling and Parity Violation in Chiral Molecules.

In this review, the concepts of quantum tunneling and parity violation are introduced in the context of chiral molecules. A particle moving in a double well potential provides a good model to study the behavior of chiral molecules, where the left well and right well represent the L and R enantiomers, respectively. If the model considers the quantum behavior of matter, the concept of quantum tunneling emerges, giving place to stereomutation dynamics between left- and right-handed chiral molecules. Parity-violating interactions, like the electroweak one, can be also considered, making possible the existence of an energy difference between the L and R enantiomers, the so-called parity-violating energy difference (PVED). Here we provide a brief account of some theoretical methods usually employed to calculate this PVED, also commenting on relevant experiments devoted to experimentally detect the aforementioned PVED in chiral molecules. Finally, we comment on some ways of solving the so-called Hund's paradox, with emphasis on mean-field theory and decoherence.

Highlighting the DCO‐SCF 2020 Award Winners – A Valuable Collaboration with EurJOC

Highlighting the DCO‐SCF 2020 Award Winners – A Valuable Collaboration with EurJOC

Perspectives on parity violation in chiral molecules: theory, spectroscopic experiment and biomolecular homochirality.

The reflection (or 'mirror') symmetry of space is among the fundamental symmetries of physics. It is connected to the conservation law for the quantum number parity and a fundamental 'non-observable' property of space (as defined by an absolute 'left-handed' or 'right-handed' coordinate system). The discovery of the violation of this symmetry - the non-conservation of parity or 'parity violation' - in 1956/1957 had an important influence on the further development of physics. In chemistry the mirror symmetry of space is connected to the existence of enantiomers as isomers of chiral ('handed') molecules. These isomers would relate to each other as idealized left or right hand or as image and mirror image and would be energetically exactly equivalent with perfect space inversion symmetry. Parity violation results in an extremely small 'parity violating' energy difference between the ground states of the enantiomers which can be theoretically calculated to be about 100 aeV to 1 feV (equivalent to 10-11 to 10-10 J mol-1), depending on the molecule, but which has not yet been detected experimentally. Its detection remains one of the great challenges of current physical-chemical stereochemistry, with implications also for fundamental problems in physics. In biochemistry and molecular biology one finds a related fundamental question unanswered for more than 100 years: the evolution of 'homochirality', which is the practically exclusive preference of one chiral, enantiomeric form as building blocks in the biopolymers of all known forms of life (the l-amino acids in proteins and d-sugars in DNA, not the reverse d-amino acids or l-sugars). In astrobiology the spectroscopic detection of homochirality could be used as strong evidence for the existence of extraterrestrial life, if any. After a brief conceptual and historical introduction we review the development, current status, and progress along these three lines of research: theory, spectroscopic experiment and the outlook towards an understanding of the evolution of biomolecular homochirality.

Towards highly accurate calculations of parity violation in chiral molecules: relativistic coupled-cluster theory including QED-effects

Parity-violating energies of the H2X2 (X = O, S, Se, Te, Po) molecules are reported, calculated as analytical expectation values at the relativistic coupled-cluster singles-and-doubles (CCSD) level using property-optimised basis sets. Radiative corrections to the was investigated using effective QED-potentials and found to reach a maximal value of 2.38% for H2Po2. However, this result depends on the choice of effective self-energy potential and may indicate limitations to their domain of validity.

Parity-violation effects in the vibrational spectra of CHFClBr and CDFClBr

Relativistic four-component electronic structure calculations at the density functional level have been carried out to describe parity-violation (PV) energy shifts to the total electronic energy for the chiral molecule CHFClBr. An $n$-mode ($n=3,4$) expansion of the complete potential energy surface at the explicitly correlated coupled-cluster level has been used for the vibrational analysis of PV effects for CHFClBr and CDFClBr. The vibrational spectrum and corresponding absolute intensities for fundamental, overtone, and combination band transitions obtained from a variational configuration interaction treatment are in excellent agreement with experimental data and the most accurate so far obtained. The results show that a 3-mode expansion is sufficient for the vibrational analysis. The PV energy shifts for the fundamental, overtone, and combination bands are all in the mHz region. The data provided will be useful for future detection of PV in chiral molecules.

Studying fundamental physics using quantum enabled technologies with trapped molecular ions

The text below was written during two visits that Daniel Segal made at Université Paris 13. Danny stayed at Laboratoire de Physique des Lasers the summers of 2008 and 2009 to participate in the exploration of a novel lead in the field of ultra-high resolution spectroscopy. Our idea was to probe trapped molecular ions using Quantum Logic Spectroscopy (QLS) in order to advance our understanding of a variety of fundamental processes in nature. At that time, QLS, a ground-breaking spectroscopic technique, had only been demonstrated with atomic ions. Our ultimate goals were new approaches to the observation of parity violation in chiral molecules and tests of time variations of the fundamental constants. This text is the original research proposal written eight years ago. We have added a series of notes to revisit it in the light of what has been since realized in the field.

Enantiomer-Specific State Transfer of Chiral Molecules

State-selective enantiomeric excess is realized using microwave-driven coherent population transfer. The method selectively promotes either R or S molecules to a higher rotational state by phase-controlled microwave pulses that drive electric-dipole allowed rotational transitions. We demonstrate the enantiomer-specific state transfer method using enantiopure samples of 1,2-propanediol. This method of state-specific enantiomeric enrichment can be applied to a large class of asymmetric, chiral molecules that can be vaporized and cooled to the point where rotationally resolved spectroscopy is possible, including molecules that rapidly racemize. The rapid chiral switching demonstrated here allows for new approaches in high-precision spectroscopic searches for parity violation in chiral molecules.

Characterising molecules for fundamental physics: an accurate spectroscopic model of methyltrioxorhenium derived from new infrared and millimetre-wave measurements.

Precise spectroscopic analysis of polyatomic molecules enables many striking advances in physical chemistry and fundamental physics. We use several new high-resolution spectroscopic devices to improve our understanding of the rotational and rovibrational structure of methyltrioxorhenium (MTO), the achiral parent of a family of large oxorhenium compounds that are ideal candidate species for a planned measurement of parity violation in chiral molecules. Using millimetre-wave and infrared spectroscopy in a pulsed supersonic jet, a cryogenic buffer gas cell, and room temperature absorption cells, we probe the ground state and the Re[double bond, length as m-dash]O antisymmetric and symmetric stretching excited states of both CH3187ReO3 and CH3185ReO3 isotopologues in the gas phase with unprecedented precision. By extending the rotational spectra to the 150-300 GHz range, we characterize the ground state rotational and hyperfine structure up to J = 43 and K = 41, resulting in refinements to the rotational, quartic and hyperfine parameters, and the determination of sextic parameters and a centrifugal distortion correction to the quadrupolar hyperfine constant. We obtain rovibrational data for temperatures between 6 and 300 K in the 970-1015 cm-1 range, at resolutions down to 8 MHz and accuracies of 30 MHz. We use these data to determine more precise excited-state rotational, Coriolis and quartic parameters, as well as the ground-state centrifugal distortion parameter DK of the 187Re isotopologue. We also account for hyperfine structure in the rovibrational transitions and hence determine the upper state rhenium atom quadrupole coupling constant eQq'.

High-resolution FTIR spectroscopy of trisulfane HSSSH: a candidate for detecting parity violation in chiral molecules.

We report the first successful high-resolution analyses of the Fourier transform infrared (FTIR) spectrum of trisulfane. A band centered at 861.0292 cm-1 can be assigned unambiguously to the chiral trans conformer by means of ground state combination differences in comparison with known rotational spectra. A second band near 864.698 cm-1 is tentatively assigned to the cis conformer by comparison with theory. The results are discussed in relation to their importance for experimental attempts to measure the parity violating energy difference ΔpvE between the ground states of enantiomers of chiral molecules.

Infrared laser induced population transfer and parity selection in (14)NH3: A proof of principle experiment towards detecting parity violation in chiral molecules.

We have set up an experiment for the efficient population transfer by a sequential two photon-absorption and stimulated emission-process in a molecular beam to prepare quantum states of well defined parity and their subsequent sensitive detection. This provides a proof of principle for an experiment which would allow for parity selection and measurement of the time evolution of parity in chiral molecules, resulting in a measurement of the parity violating energy difference ΔpvE between enantiomers of chiral molecules. Here, we present first results on a simple achiral molecule demonstrating efficient population transfer (about 80% on the average for each step) and unperturbed persistence of a selected excited parity level over flight times of about 1.3 ms in the beam. In agreement with model calculations with and without including nuclear hyperfine structure, efficient population transfer can be achieved by a rather simple implementation of the rapid adiabatic passage method of Reuss and coworkers and considering also the stimulated Raman adiabatic passage technique of Bergmann and coworkers as an alternative. The preparation step uses two powerful single mode continuous wave optical parametric oscillators of high frequency stability and accuracy. The detection uses a sensitive resonantly enhanced multiphoton ionization method after free flight lengths of up to 0.8 m in the molecular beam. Using this technique, we were able to also resolve the nuclear hyperfine structure in the rovibrational levels of the ν1 and ν3 fundamentals as well as the 2ν4 overtone of (14)NH3, for which no previous data with hyperfine resolution were available. We present our new results on the quadrupole coupling constants for the ν1, ν3, and 2ν4 levels in the context of previously known data for ν2 and its overtone, as well as ν4, and the ground state. Thus, now, (14)N quadrupole coupling constants for all fundamentals and some overtones of (14)NH3 are known and can be used for further theoretical analysis.

Tunneling and Parity Violation in Trisulfane (HSSSH): An Almost Ideal Molecule for Detecting Parity Violation in Chiral Molecules.

Measuring the parity-violating energy difference Δpv E between the enantiomers of chiral molecules is a major challenge of current physical-chemical stereochemistry. An important step towards this goal is to identify suitable molecules for such experiments by means of theory. This step has been made by calculations for the complex dynamics of tunneling and electroweak quantum chemistry of parity violation in the "classic" molecule trisulfane, HSSSH, which satisfies the relevant conditions for experiments almost ideally, as the molecule is comparatively simple and parity violation clearly dominates over tunneling in the ground state. At the same time, the barrier for stereomutation is easily overcome by the S-H infrared chromophore.

Investigation of parity violation in nuclear spin-rotation interaction of fluorooxirane

When it comes to the question of how signatures from parity violation in chiral molecules can be revealed, then ultra-high resolution spectroscopy techniques play a crucial role in attempts to detect such effects via line shifts. A prerequisite for this approach towards molecular parity violation is a detailed understanding of the corresponding conventional spectroscopy, including even small effects that are often neglected. Nuclear spin-rotation (NSR) interaction is one such effect that becomes appreciable only at high to ultra-high resolution and is often masked by nuclear electric quadrupole interactions (NQI) if nuclei are present with nuclear spin quantum number I larger than 1/2. Herein, NSR interactions are studied theoretically for the chiral molecules fluorooxirane and bromochlorofluoromethane (CHBrClF). For the latter molecule, NSR interactions are compared to nuclear electric quadrupole coupling contributions. The former molecule is devoid of I > 1/2 nuclei such that NSR interactions are not masked by NQI. Parity-odd contributions to NSR of 19F are computed that give rise to additional line shifts in hyperfine transitions. A detection of these nuclear spin-dependent P-odd terms could in principle give information on the nuclear anapole moment in fluorine, which arises due to parity violating interactions within the nucleus.

ChemInform Abstract: Progress Toward the First Observation of Parity Violation in Chiral Molecules by High‐Resolution Laser Spectroscopy

AbstractReview: 104 refs.

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.

High resolution spectroscopy of methyltrioxorhenium: towards the observation of parity violation in chiral molecules

Originating from the weak interaction, parity violation in chiral molecules has been considered as a possible origin of the biohomochirality. It was predicted in 1974 but has never been observed so far. Parity violation should lead to a very tiny frequency difference in the rovibrational spectra of the enantiomers of a chiral molecule. We have proposed to observe this predicted frequency difference using the two photon Ramsey fringes technique on a supersonic beam. Promising candidates for this experiment are chiral oxorhenium complexes, which present a large effect, can be synthesized in large quantity and enantiopure form, and can be seeded in a molecular beam. As a first step towards our objective, a detailed spectroscopic study of methyltrioxorhenium (MTO) has been undertaken. It is an ideal test molecule as the achiral parent molecule of chiral candidates for the parity violation experiment. For the 187Re MTO isotopologue, a combined analysis of Fourier transform microwave and infrared spectra as well as ultra-high resolution CO2 laser absorption spectra enabled the assignment of 28 rotational lines and 71 rovibrational lines, some of them with a resolved hyperfine structure. A set of spectroscopic parameters in the ground and first excited state, including hyperfine structure constants, was obtained for the antisymmetric Re=O stretching mode of this molecule. This result validates the experimental approach to be followed once a chiral derivative of MTO will be synthesized, and shows the benefit of the combination of several spectroscopic techniques in different spectral regions, with different set-ups and resolutions. First high resolution spectra of jet-cooled MTO, obtained on the set-up being developed for the observation of molecular parity violation, are shown, which constitutes a major step towards the targeted objective.

Tailored molecular samples for precision spectroscopy experiments

The resolution of any spectroscopy experiment is ultimately limited by the observation time. The ability to produce slow, yet intense molecular beams significantly increases the attainable observation time and thus the resolution in the spectroscopic experiment. Such slow molecular samples are ideal starting points for novel precision spectroscopy experiments aiming at, for example, determining the time variation of fundamental constants or the effect of parity violation in chiral molecules. We consider the use of decelerated chiral polar molecules to perform very high-resolution rotational spectroscopy aiming at measuring the energy difference of the two enantiomers due to parity violation. Using molecule velocities around 20 m s(-1) and a microwave resonator consisting of 50 cm-reflectors (in diameter) and a reflector distance of up to one meter, spectral resolutions on the order of only a few Hz become feasible using Fourier transform microwave spectroscopy. This should be sufficient to resolve the parity-violation effect for species containing heavy atoms, such as SOCH3Ph and SeOFI. We also discuss the possibilities to use trapped molecules for high-resolution spectroscopy--and work out their advantages, such as long observation times, and their disadvantages, such as line broadening due to the inhomogeneous trapping fields.

Frontiers in spectroscopy

We review the frontiers of spectroscopy from a historical perspective, starting with the development of atomic spectroscopy about 150 years ago, followed by some comments on selected previous Faraday Discussions. As the spectrum of frontiers at the Faraday Discussion 150 is very broad, we give only a brief survey providing a map of the various frontiers approached today. This is followed by an exemplary discussion of one particular frontier towards the spectroscopic detection of symmetry violations in fundamental physics. In particular the understanding of parity violation in chiral molecules has recently made great progress. We briefly describe the advances made in recent decades as well as the current status of theory and experiments in this exciting field of research. We conclude with an outlook on open questions and frontiers of the future in spectroscopy.

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.

Detection of parity violation in chiral molecules by external tuning of electroweak optical activity

A proposal is made to measure the parity-violating energy difference between enantiomers of chiral molecules by modifying the dynamics of the two-state system using an external chiral field, in particular, circularly polarized light. The intrinsic molecular parity-violating energy could be compensated by this external chiral field, with the subsequent change in the optical activity. From the observation of changes in the time-averaged optical activity of a sample with initial chiral purity and minimized environment effects, the value of the intrinsic parity-violating energy could be extracted. A discussion is made on the feasibility of this measurement.