Combined multidimensional anharmonic and parity violating effects in CDBrClF

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.

Toward Detection of the Molecular Parity Violation in Chiral Ru(acac)3 and Os(acac)3

We present a theory-experiment investigation of the helically chiral compounds Ru(acac)₃ and Os(acac)₃ as candidates for next-generation experiments for detection of molecular parity violation (PV) in vibrational spectra. We used relativistic density functional theory calculations to identify optimal vibrational modes with expected PV effects exceeding by up to 2 orders of magnitude the projected instrumental sensitivity of the ultrahigh resolution experiment under construction at the Laboratoire de Physique des Lasers in Paris. Preliminary measurements of the vibrational spectrum of Ru(acac)₃ carried out as the first steps toward the planned experiment are presented.

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.

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 purity and its violation and has a fundamental relation to stereochemistry and molecular chirality.

Separation of Isomers and Mechanisms of Inversion of Stereochemistry of Group 9 d6 Tris-Chelate Complexes of Hinokitiol

Tris-chelate complexes of Co(III), Rh(III), and Ir(III) with 4-isopropyltropolone (hinokitiol or β-thujaplicin) form by the substitution of carbonate and chloride ligands from group 9 trivalent metal salts. The new complexes are neutral, are readily soluble in most organic solvents, and are brightly colored with strong charge transfer bands. The fac isomers of Co(hino)₃ and Rh(hino)₃ were isolated from the mixture by fractional recrystallization from ethanol. The remaining mixtures were respectively enriched by 5:3 and 4.4:3 for the mer isomer. The ¹H NMR data show that the complexes exhibit remarkable stereochemical lability, which is unusual for diamagnetic d⁶ group 9 metals, with rotational barriers of 14.2 and 18.2 kcal/mol found for the inversion of stereochemistry of Co(hino)₃ and Rh(hino)₃. The low activation barriers, as well as the analysis of some key structural parameters, suggest that the inversion of stereochemistry occurs via a trigonal-twist (Bailar) mechanism. Facile substitution of a single hinokitiol ligand in the cobalt complex with ethylenediamine to form [Co(en)(hino)₂]Cl also indicates that the tris-chelates are substitutionally and configurationally labile.

Chiral Molecules as Sensitive Probes for Direct Detection of P-Odd Cosmic Fields

Potential advantages of chiral molecules for a sensitive search for parity violating cosmic fields are highlighted. Such fields are invoked in different models for cold dark matter or in the Lorentz-invariance violating standard model extensions and thus are signatures of physics beyond the standard model. The sensitivity of a 20-year-old experiment with the molecule CHBrClF to pseudovector cosmic fields as characterized by the parameter |b_{0}^{e}| is estimated to be O(10^{-12}  GeV) employing ab initio calculations. This allows us to project the sensitivity of future experiments with favorable choices of chiral heavy-elemental molecular probes to be O(10^{-17}  GeV), which will be an improvement of the present best limits by at least two orders of magnitude.

Homochirality: A Perspective from Fundamental Physics

In this brief review, possible mechanisms which could lead to complete biological homochirality are discussed from the viewpoint of fundamental physics. In particular, the role played by electroweak parity violation, including neutrino-induced homochirality, and contributions from the gravitational interaction, will be emphasized.

An oxorhenium complex bearing a chiral cyclohexane-1-olato-2-thiolato ligand: Synthesis, stereochemistry, and theoretical study of parity violation vibrational frequency shifts

In our effort towards measuring the parity violation energy difference between two enantiomers, a simple chiral oxorhenium complex 5 bearing enantiopure 2-mercaptocyclohexan-1-ol has been prepared as a potential candidate species. Vibrational circular dichroism revealed a chiral environment surrounding the rhenium atom, even though the rhenium is not a stereogenic center itself, and enabled to assign the (1S,2S)-(-) and (1R,2R)-(+) absolute configuration for 5. For both compound 5 and complex 4, previously studied by us and bearing a propane-2-olato-3-thiolato ligand, relativistic calculations predict parity violating vibrational frequency differences of a few hundreds of millihertz, above the expected sensitivity attainable by a molecular beam Ramsey interferometer that we are constructing.

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

We present the first analysis of high resolution infrared spectra for trisulfane, a candidate to measure molecular parity violation.

High resolution GHz and THz (FTIR) spectroscopy and theory of parity violation and tunneling for 1,2-dithiine (C4H4S2) as a candidate for measuring the parity violating energy difference between enantiomers of chiral molecules

Our results show that this molecule is a suitable candidate for a possible first determination of the parity violating energy difference Δ_pvE between enantiomers.

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.

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 Spectroscopic Studies and Theory of Parity Violation in Chiral Molecules

We review the high-resolution spectroscopic approach toward the study of intramolecular dynamics, emphasizing molecular parity violation. Theoretical work in the past decade has shown that parity-violating potentials in chiral molecules are much larger (typically one to two orders of magnitude) than anticipated on the basis of older theories. This makes experimental approaches toward small molecular parity-violating effects promising. The concepts and results of intramolecular dynamics derived from spectroscopy are analyzed as a sequence of symmetry breakings. We summarize the concepts of symmetry breakings (de facto and de lege) in view of parity violation in chiral molecules. The experimental schemes and the current status of spectroscopic experiments on molecular parity violation are established. We discuss the promises of detecting and accurately measuring parity-violating energy differences Δpv E on the order of 10−11 J mol−1 (approximately 100 aeV) in enantiomers of chiral molecules with regard to their contribution to fundamental physics in the framework of the standard model of particle physics and more speculative future fundamental symmetry tests such as for the combined charge conjugation, parity, and time-reversal (CPT) symmetry violation.

High Resolution Rovibrational Spectroscopy of Chiral and Aromatic Compounds

The analysis of selected rovibrationally resolved infrared spectra of some relatively heavy and large polyatomic molecules is reviewed. A short historical summary of the development of high resolution interferometric Fourier transform infrared (FTIR) spectrometers is given and the possibilities of the currently most highly resolving FTIR spectrometer, which is commercially available in the Bruker IFS 125 series, are discussed. The computational tools necessary to analyse FTIR spectra are described briefly. As examples of rovibrational analysis the spectra of three selected molecules CHCl(2)F, CDBrClF, and pyridine (C(5)H(5)N) are discussed. The spectrum of CHCl(2)F, a fluorochlorohydrocarbon, is of interest for a better understanding of the chemistry of the Earth's atmosphere. CDBrClF is a chiral molecule and therefore the analysis of its rovibrational spectra provides the basis for carrying out further experiments towards the detection of molecular parity violation. The analysis of the pyridine FTIR spectra illustrates the potential of the new generation of FTIR spectrometers in the study of spectra and rovibrational dynamics of aromatic systems and molecules of potential biological interest.

Theoretical determination of parity-violating vibrational frequency differences between the enantiomers of chiral molecules

A perturbation treatment has been used to compute the leading first- and second-order parity-violating corrections to the vibrational energy levels of a chiral molecule. Assuming the molecular equilibrium geometry as expansion point of both parity-violating and parity-conserving potential-energy surfaces, it is shown that these corrections, i.e., harmonic and anharmonic contributions, are of the same order of magnitude and that none of them can be neglected for a realistic determination of vibrational frequency differences. Numerical tests based on ab initio MP2 force fields and quantum-relativistic calculations of the parity-violating potential for each normal mode of PHBrF and AsHBrF molecules confirm this conclusion. In particular, it is shown that a normal mode of AsHBrF is characterized by one of the largest vibrational frequency difference ever found--the prediction is approximately 0.1 Hz--only one order of magnitude less than the presumed resolution limit of current experimental investigations.

Astrobiology and biological chirality

The emerging discipline of astrobiology could gain valuable support from research dealing with the problems of biological chirality. The most profitable fields of common interest are: (a) living organisms under extraterrestrial conditions, (b) extraterrestrial signatures of life and (c) origin(s) of biological chirality. These areas of complementary and overlapping fields are analysed on the basis of selected references.

Density functional calculations of molecular parity-violating effects within the zeroth-order regular approximation

A (quasirelativistic) two-component density functional theory (DFT) approach to the computation of parity-violating energy differences between enantiomers is presented which is based on the zeroth-order regular approximation (ZORA). This approach is employed herein to compute parity-violating energy differences between several P and M conformations of dihydrogen dichalcogenides (H2X2 with X=O, S, Se, Te, Po), of which some compounds have recently been suggested as potential molecular candidates for the first experimental measurement of parity-violating effects in chiral molecules. The DFT ZORA results obtained in this work with "pure" density functionals are anticipated to deviate by well less than 1% from data that would be computed within related (relativistic) four-component Dirac-Kohn-Sham-Coulomb schemes. In our implementation of the ZORA slightly larger relative deviations are expected for hybrid functionals, depending on the amount of "exact" exchange. For B3LYP (20% exact exchange) differences are estimated to amount to at most 3% in hydrogen peroxide, 2% in disulfane, and 1% or less for the heavier homologs. Thus, the present two-component approach is expected to perform excellently when compared to four-component density functional schemes while being at the same time computationally more efficient. The ZORA approach will therefore be of particular interest for the prediction of parity-violating vibrational frequency shifts, for instance, in isotopomers of H(2)Se(2) and H(2)Te(2).

Pseudotetrahedral Polyhalocubanes: Synthesis, Structures, and Parity Violating Energy Differences

All possible pseudotetrahedral, stable polyhalocubanes were prepared, and their structures were proven by NMR spectroscopy and X-ray crystallography. Parity violating energy differences (DeltaEpv) and vibrational frequency shifts were computed. The DeltaEpv values are predicted to be one to two orders of magnitude smaller than those for the corresponding polyhalomethanes. However, the DeltaEpv energy ordering is the same as that for the methane analogues. For both substance classes, the (S) isomers are, with the exception of the bromochlorofluoroiodo derivatives, more stable than the (R) forms.

Stereomutation Tunneling Switching Dynamics and Parity Violation in Chlorineperoxide Cl−O−O−Cl

In a search for efficient spectroscopic avenues toward experiments on molecular parity violation, we investigate the stereomutation tunneling processes in the axially chiral chlorine isotopomers of Cl2O2 by the quasi-adiabatic channel reaction path Hamiltonian (RPH) approach and the corresponding parity violating potentials by means of quantum chemical calculations including our recently developed Multiconfiguration linear response (MC-LR) approach to electroweak quantum chemistry. The calculated ground-state torsional tunneling splittings for all isotopomers of Cl2O2 are much smaller than the parity violating energy differences Delta(pv)E between the enantiomers of these molecules and therefore parity violation is predicted to dominate the quantum dynamics of stereomutation at low energies. We also compare these with torsional ground-state tunneling splittings and parity violating energy differences of the whole series of axially chiral HXYH(+) isotopomers (with X, Y= Cl(+), O, S, Se, Te). A comparison with our previous results for the homologous molecule Cl2S2 shows that for Cl2O2 a spectroscopic high-resolution analysis should be easier and the energy region of large tunneling splittings should be more easily accessible by IR excitation. We thus propose a scheme using "tunneling switching" with vibrational excitation in order to carry out the measurement of time-dependent parity violation in superposition states of initially well-defined parity. We discuss the advantages and drawbacks of such an experiment that can be carried out entirely in the IR spectral range (for Cl2O2 or related molecules).

Harmonic and anharmonic contributions to parity-violating vibrational frequency difference between enantiomers of chiral molecules

A general perturbative procedure for the computation of harmonic and anharmonic contributions to parity-violating vibrational shifts is introduced and applied to PHBrF and AsHBrF. The results point out the importance of both diagonal and off-diagonal anharmonic contributions and indicate that some parity-violating shift of AsHBrF approaches the resolution forecasted for next generation experiments. The proposed approach is sufficiently general and computationally effective to allow studies of similar and larger molecular systems.

Steps towards molecular parity violation in axially chiral molecules. I. Theory for allene and 1,3-difluoroallene

In view of exploring possibilities for an experimental investigation of molecular parity violation we report quantum-chemical calculations of the parity-conserving and parity-violating potentials in the framework of electroweak quantum chemistry in allene C3H4 and 1,3-difluoroallene C3H2F2, which is nonplanar and axially chiral in the electronic ground state but expected to be nearly planar and achiral in several electronically excited states. The parity-violating potentials Epv for allene and 1,3-difluoroallene calculated with the multiconfiguration linear-response (MC-LR) approach of Berger and Quack [J. Chem. Phys. 112, 3148 (2000)] show qualitatively similar behavior as a function of torsional angle tau with maximum values of about 0.5 pJ mol(-1) for C3H4 and 2 pJ mol(-1) for C3H2F2. However, in the latter case they are asymmetrically shifted around tau=90 degrees , with a nonzero value at the chiral equilibrium geometry resulting in a parity-violating energy difference between enantiomers DeltapvE=Epv(P)-Epv(M)=1.2 pJ mol(-1) (equivalent to about 10(-13) cm(-1)). The calculated barrier heights corresponding to the nonrigid (multiple, and in part chiral) transition states in 1,3-difluoroallene fall in the range of 180-200 kJ mol(-1). These high barriers result in hypothetical tunneling splittings much smaller than DeltapvE and thus parity violation dominates over tunneling for the stereomutation dynamics in 1,3-difluoroallene. Therefore, DeltapvE is predicted to be a spectroscopically measurable energy difference. Two of the lower excited electronic states of C3H2F2 (1A and 3A) are calculated to be planar or quasiplanar, allowing, in principle, for spectroscopic state selection of states of well-defined parity. The results are discussed in relation to possible schemes of measuring parity violation in chiral molecules.

Perturbational calculations of parity-violating effects in nuclear-magnetic-resonance parameters

We investigate the effects of the parity-violating electroweak interaction in the spectral parameters of nuclear magnetic resonance. Perturbational theory of parity-violating effects in the nuclear magnetic shielding is presented to the order of G(F)alpha, and in the indirect spin-spin coupling, to the order of G(F)alpha3. These leading-order parity-violating corrections are evaluated using analytical linear-response theory methods based on Hartree-Fock and density-functional theory reference states. Parity-violating contributions to spin-spin couplings are evaluated for the first time at the first-principles level. Calculations are carried out for two chiral halomethanes, bromochlorofluoromethane and bromofluoroiodomethane.

The Chiral Molecule CHClFI: First Determination of Its Molecular Parameters by Fourier Transform Microwave and Millimeter-Wave Spectroscopies Supplemented by ab Initio Calculations

The rotational spectrum of chlorofluoroiodomethane (CHClFI) has been investigated. Because its rotational spectrum is extremely crowded, extensive ab initio calculations were first performed in order to predict the molecular parameters. The low J transitions were measured using a pulsed-molecular-beam Fourier transform spectrometer, and the millimeter-wave spectrum was measured to determine accurate centrifugal distortion constants. Because of the high resolution of the experimental techniques, the analysis yielded accurate rotational constants, centrifugal distortion corrections, and the complete quadrupole coupling tensors for the iodine and chlorine nuclei, as well as the contribution of iodine to the spin-rotation interaction. These molecular parameters were determined for the two isotopologs CH35ClFI and CH37ClFI. They reproduce the observed transitions within the experimental accuracy. Moreover, the ab initio calculations have provided a precise equilibrium molecular structure. Furthermore, the ab initio molecular parameters are found in good agreement with the corresponding experimental values.

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.

Large parity violation effects in the vibrational spectrum of organometallic compounds

Large parity violation effects of the order of 1 Hz are predicted for the vibrational spectrum of two organometallic species, Os(eta5-C5H5)(=CCl2)Cl(PH3) and Re(eta5-Cp*)(=O)(CH3)Cl. It should therefore be possible to detect such effects in molecules by high-resolution spectroscopy for the first time.