Combined high resolution infrared and microwave study of bromochlorofluoromethane

Electric Field Gradient in Chiral and Tetrahedral Molecules within High-Order LRESC Formalism

In this work, we present the electric field gradient (EFG) given by the linear response elimination of the small component (LRESC) scheme up to the 1/c4 order (c is the speed of light in vacuum) in CHFClX (X = Br, I, At) chiral molecules, together with CHF2Br and CH2FX (X = Br, I, At) tetrahedral systems. The former could be good candidates for further parity violation studies, especially when heavy atoms are surrounding. In this context, the LRESC scheme demonstrates effective applicability to large tetrahedral and chiral molecules that incorporate heavy elements, with relativistic effects playing a crucial role. The LRESC results of EFG exhibit an excellent agreement with those calculated at the four-component level, giving differences of only hundredths order in a.u. (atomic units) for the bromine nucleus and less than 0.1 a.u. for the iodine nucleus. Regarding the other nuclei, for the chiral molecules, there is a heavy atom effect on the light atom (HALA) for chlorine and fluorine atoms as the substituent halogen atom becomes heavier. Furthermore, the electronic part of the EFG for the central carbon and the fluorine nuclei presents an important dependence with the environment in the molecules under study. With accurate calculations of the EFG and tabulated nuclear quadrupole moment, the nuclear quadrupole coupling constant is obtained within the LRESC scheme, including for the first time correlation effects on the spin-dependent corrections with this methodology, providing results close to the experimental ones for Cl, Br, and I atoms. At the Hartree-Fock level, the differences are around 6% for Br and I nuclei, and at the density functional theory level with the LDA and PBE0 functionals, the differences are no more than 2%.

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.

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.

Synchrotron-Based Highest Resolution Terahertz Spectroscopy of the ν24 Band System of 1,2-Dithiine (C4H4S2): A Candidate for Measuring the Parity Violating Energy Difference between Enantiomers of Chiral Molecules

The chiral C₂ symmetric molecule 1,2-dithiine (1,2-dithia-3,5-hexadiene, C₄H₄S₂) has been identified as a possible candidate for measuring the parity violating energy difference between enantiomers. We report here the observation and analysis of the low-frequency fundamental ν₂₄ using highest resolution synchrotron-based interferometric Fourier transform infrared (FTIR) spectroscopy in the terahertz range with a band center of ν₀ = 6.95375559 THz (ν̃₀ = 231.952319 (10) cm^-1) and two related hot bands, the (ν₁₃ + ν₂₄) ← ν₁₃ band at ν₀ = 6.97256882 THz (ν̃₀ = 232.579861 (33) cm^-1) and the 2ν₂₄ ← ν₂₄ band at ν₀ = 7.01400434 THz (ν̃₀ = 233.962001 (14) cm^-1). This success in the difficult analyses of the THz spectrum of a complex chiral molecule of importance for fundamental tests on molecular parity violation is enabled by the ideal setup of an FTIR experiment of currently unique resolution with the very stable and bright synchrotron radiation at the Swiss Light Source (SLS).

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.

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.

Vibrational analyses for CHFClBr and CDFClBr based on high levelab initiocalculations

Anharmonicity corrections to the harmonic vibrational spectra of CHFClBr and its deuterated isotopomer were computed by means of variational and perturbational approaches. A comparison of both methods is provided. Based on CCSD(T)/aug-cc-pVTZ electronic structure calculations excellent agreement with experimental data was obtained. Absolute mean deviations are in the range of about 4 cm(-1) for the fundamental modes, while slightly larger values of about 7 cm(-1) were found for the first vibrational overtones. In addition, vibrationally averaged structural parameters are provided for both molecules. The calculations will serve as a future starting point for parity-violation effects in vibrational transitions in these chiral molecules.

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).

Chlorofluoroiodomethane as a potential candidate for parity violation measurements

CHFClI is among the more favorable molecules for parity violation (PV) measurements in molecules. Despite the fact that calculated PV effects are two orders of magnitude smaller than in some organometallic compounds, CHFClI displays interesting features which could make possible a new experimental PV test on this molecule. Indeed, ultrahigh resolution spectroscopy using an ultrastable CO(2) laser is favored by several intrinsic properties of this molecule. For example, the high vapor pressure of CHFClI allows investigation by supersonic beam spectroscopy. Indeed, the spectroscopic constants have been accurately determined by microwave and millimetre wave spectroscopy. This is important for the subsequent selection of an appropriate absorption band of CHFClI that could be brought to coïncide with the absorption of CO(2). Partially resolved (+)- and (-)-CHFClI enantiomers with respectively 63.3 and 20.5% ee's have been recently prepared and analyzed by molecular recognition using chiral hosts called cryptophanes. Finally, the S-(+)/R-(-) absolute configuration was ascertained by vibrational circular dichroïsm (VCD) in the gas phase.

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.

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.

Search for resolution of chiral fluorohalogenomethanes and parity-violation effects at the molecular level

The first observation of a parity-violation effect in molecules induced by weak interactions is still a dream that requires the synthesis and, eventually, the resolution of the enantiomers of well-chosen simple chiral molecules together with an appropriate experimental set-up for high-resolution spectroscopy. Performing IR spectroscopy on highly enantiomerically enriched samples of bromochlorofluoromethane succeeded in giving an upper limit of 10(-13) for the relative vibrational energy difference between the two enantiomers. These results led us to conceive a new experimental set-up based on a supersonic molecular beam and to work on other chiral molecules, such as chlorofluoroiodomethane. A synthesis of (+/-)-CHCIFI from racemic chlorofluoroiodoacetic acid should, in the near future permit the preparation of optically active samples of this haloform. The development of molecular beam spectroscopy using a two-photon Ramsey-fringes experiment should allow us to reach the precision needed to observe parity violation. These experimental challenges, which stimulate a close collaboration between chemists and physicists, are presented. The success of these projects would open the route to new information on the molecular Hamiltonian, a better knowledge of the electroweak interaction, and a better control of the various chirality-related properties of simple molecules.

How important is parity violation for molecular and biomolecular chirality?

Parity violation leads to energy differences delta(pv)H(o)(0)=N(A)delta(pv)E of enantiomers in the femtojoule to picojoule per mole range. Recently introduced methods of electroweak quantum chemistry predict such energy differences to be one to two orders of magnitude larger than previously accepted-but still very small. How can such small energies be measured and what are the consequences for our understanding of molecular chirality, biomolecular homochirality, and perhaps fundamental physics? The review gives some tentative answers to these questions. We discuss the current status of theory and some of the current experimental approaches.