Parity violation

Strong parity-violation effects induced by large-amplitude motions: A quantum-dynamics study of substituted chiral methanols

An enhanced mechanism is proposed for the large-amplitude-motion-induced parity-violating frequency by integrating the exact quantum dynamics method with the relativistic electronic structure theory. The torsional wavefunctions and parity-violating (PV) frequency shifts are obtained by using the exact quantum dynamics method. The potential energy curve and PV energy along the torsional coordinates are calculated using the extended atomic mean-field two-component Hamiltonian. The predicted PV frequency shift for the torsional transition of CFClBrOH is ∼100 times larger than that of the conventional C-F stretching mode of CHFClBr. The maximum PV frequency shift (3.2 Hz) is obtained in the CHBrIOH molecule.

Opportunities for fundamental physics research with radioactive molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

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%.

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.

A Relationship between the Molecular Parity-Violation Energy and the Electronic Chirality Measure

When the weak forces producing parity-violating effects are taken into account, there is a tiny energy difference between the total electronic energies of two enantiomers (ΔEPV), which might be the key to understanding the evolution of the biological homochirality. We focus on the electronic chirality measure (ECM), a powerful descriptor based on the electronic charge density, for quantifying the chirality degree of a molecule, in a representative set of chiral molecules, together with their EPV energies. Our results show a novel, strong, and positive correlation between ΔEPV and ECM, supporting a subtle interplay between the weak forces acting within the nuclei of a given molecule and its chirality. These findings suggest that experimental investigations for molecular parity violation detection should consider molecules with ECM values as large as possible and may support that a chiral signature is imprinted on life by fundamental physics via the parity-violating weak interactions.

Extending Chirality in Group XIV Metallatranes

The syntheses of the racemic amino alcohol rac-N(CH₂CMe₂OH)(CMe₂CH₂OH)(CH₂CHMeOH) (L^22'1*H₃, 2) and its representative N(CH₂CMe₂OH)(CMe₂CH₂OH)(CH₂C(R)HMeOH) (L^22'1RH₃, 3) with the stereogenic carbon center being R-configured are reported. Also reported are the stannatranes L^22'1*SnOt-Bu (4) L^22'1RSnOt-Bu (6) and germatranes L^22'1*GeOEt (5) and L^22'1RGeOEt (7) as well as the trinuclear tin oxocluster [(μ₃-O)(μ₃-O-t-Bu){SnL^22'1R}₃] (8). NMR and IR spectroscopy, electrospray ionization mass spectrometry (ESI MS), and single crystal X-ray diffraction analysis characterize these compounds. Computational studies accompany the experimental work and help understand the diastereoselectivity observed in the course of the metallatrane syntheses.

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.

Instanton calculations of tunneling splittings in chiral molecules

We report the ground state tunneling splittings (ΔE_± ) of a number of axially chiral molecules using the ring-polymer instanton (RPI) method (J. Chem. Phys., 2011, 134, 054109). The list includes isotopomers of hydrogen dichalcogenides H₂ X₂ (X = O, S, Se, Te, and Po), hydrogen thioperoxide HSOH and dichlorodisulfane S₂ Cl₂ . Ab initio electronic-structure calculations have been performed on the level of second-order Møller-Plesset perturbation (MP2) theory either with split-valance basis sets or augmented correlation-consistent basis sets on H, O, S, and Cl atoms. Energy-consistent pseudopotential and corresponding triple zeta basis sets of the Stuttgart group are used on Se, Te, and Po atoms. The results are further improved using single point calculations performed at the coupled cluster level with iterative singles and doubles and perturbative triples amplitudes. When available for comparison, our computed values of ΔE_± are found to lie within the same order of magnitude as values reported in the literature, although RPI also provides predictions for H₂ Po₂ and S₂ Cl₂ , which have not previously been directly calculated. Since RPI is a single-shot method which does not require detailed prior knowledge of the optimal tunneling path, it offers an effective way for estimating the tunneling dynamics of more complex chiral molecules, and especially those with small tunneling splittings.

Lower than low: Perspectives on zero- to ultralow-field nuclear magnetic resonance

The less-traveled low road in nuclear magnetic resonance is discussed, honoring the contributions of Prof. Bernhard Blümich, aspiring towards reaching 'a new low.' A history of the subject and its current status are briefly reviewed, followed by an effort to prophesy possible directions for future developments.

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.

Parity Violation Energy of Biomolecules - V: Protein Metal Centers

The parity-violation difference between mirror images of chiral metal centers found in naturally occurring proteins and enzymes is computed at the Dirac-Hartree-Fock level, for both equilibrium and transition state configurations. The systems, selected on the likelihood of yielding high parity violation energies based on atomic mass and coordination geometry, are extracted from: type I Blue Copper Protein active site, Zn and Cd Carbon Anhydrase, Ni Acetyl-Coenzyme-A Synthase, and Mo based CO-Dehydrogenase. Our values provide an approximate upper limit to possible parity-violation effects in biological systems based on static effects.

Spectroscopy of short-lived radioactive molecules

Molecular spectroscopy offers opportunities for the exploration of the fundamental laws of nature and the search for new particle physics beyond the standard model1-4. Radioactive molecules-in which one or more of the atoms possesses a radioactive nucleus-can contain heavy and deformed nuclei, offering high sensitivity for investigating parity- and time-reversal-violation effects5,6. Radium monofluoride, RaF, is of particular interest because it is predicted to have an electronic structure appropriate for laser cooling6, thus paving the way for its use in high-precision spectroscopic studies. Furthermore, the effects of symmetry-violating nuclear moments are strongly enhanced5,7-9 in molecules containing octupole-deformed radium isotopes10,11. However, the study of RaF has been impeded by the lack of stable isotopes of radium. Here we present an experimental approach to studying short-lived radioactive molecules, which allows us to measure molecules with lifetimes of just tens of milliseconds. Energetically low-lying electronic states were measured for different isotopically pure RaF molecules using collinear resonance ionisation at the ISOLDE ion-beam facility at CERN. Our results provide evidence of the existence of a suitable laser-cooling scheme for these molecules and represent a key step towards high-precision studies in these systems. Our findings will enable further studies of short-lived radioactive molecules for fundamental physics research.