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

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.

Fabrication strategies for chiral self-assembly surface

Chiral self-assembly is the spontaneous organization of individual building blocks from chiral (bio)molecules to macroscopic objects into ordered superstructures. Chiral self-assembly is ubiquitous in nature, such as DNA and proteins, which formed the foundation of biological structures. In addition to chiral (bio) molecules, chiral ordered superstructures constructed by self-assembly have also attracted much attention. Chiral self-assembly usually refers to the process of forming chiral aggregates in an ordered arrangement under various non-covalent bonding such as H-bond, π-π interactions, van der Waals forces (dipole-dipole, electrostatic effects, etc.), and hydrophobic interactions. Chiral assembly involves the spontaneous process, which followed the minimum energy rule. It is essentially an intermolecular interaction force. Self-assembled chiral materials based on chiral recognition in electrochemistry, chiral catalysis, optical sensing, chiral separation, etc. have a broad application potential with the research development of chiral materials in recent years.

Discovery and bioinspired total syntheses of unprecedented sesquiterpenoid dimers unveiled bifurcating [4 + 2] cycloaddition and target differentiation of enantiomers

[4 + 2] cycloaddition has led to diverse polycyclic chiral architectures, serving as novel sources for organic synthesis and biological exploration. Here, an unprecedented class of cadinane sesquiterpene [4 + 2] dimers, henryinins A-E (1-5), with a unique 6/6/6/6/6-fused pentacyclic system, were isolated from Schisandra henryi. The divergent total syntheses of compounds 1-5 and their enantiomers (6-10) were concisely accomplished in eight linear steps using a protection-free approach. Mechanistic studies illustrated the origin of selectivity in the key [4 + 2] cycloaddition as well as the inhibition of reaction pathway bifurcation via desymmetrization. The chemical proteomics results showed that a pair of enantiomers shared common targets (PRDX5 C100 and BLMH C73) and had unique targets (USP45 C588 for 4 and COG7 C419 for 9). This work provides experimental evidence for the discovery of unprecedented cadinane dimers from selective Diels-Alder reaction and a powerful strategy to explore the biological properties of natural products.

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.

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.

Chiral selectivity vs. noise in spontaneous mirror symmetry breaking

Mirror symmetry breaking bifurcations, that occur in nonlinear chemical systems leading to final chiral states with very large enantiomeric excess, can be exploited as an efficient chiral signal selector for even the smallest chiral polarizations. This effect of the chiral polarization requires the system's capacity for overcoming thermal noise, which is manifested as fluctuating reaction rate constants. Therefore, we investigate the chiral selectivity across a range of tiny parity-violating energy differences (PVED) in the presence of inevitable non-equilibrium temperature fluctuations. We use a stochastic differential equation simulation methodology (Ito process) that serves as a valuable tool in open systems for identifying the thresholds at which the chiral force induces chiral selectivity in the presence of non-equilibrium temperature fluctuations. This approach enables us to include and analyze chiral selectivity in the presence of other types of fluctuations, such as perturbations in the rate of fluid flow into and out of the reactor and in the clamped input concentrations. These concepts may be of practical interest (i.e., spontaneous deracemizations) but are also useful for a better understanding of the general principles governing the emergence of biological homochirality.

Thermo-/Mechano-Chromic Chiral Coordination Dimer: Formation of Switchable and Metastable Discrete Structure through Chiral Self-Sorting

Although strong chiral self-sorting often emerges in extended covalent or supramolecular polymers, the phenomenon is generally weak in discrete assemblies (e.g., dimers and oligomers) of small molecules due to the lack of a cooperative growth mechanism. Consequently, chiral self-sorting has been overlooked in the design of switchable and metastable discrete supramolecular structures. Here, we report a butyl-benzo[h]quinoline-based iridium(III) complex (Bu-Ir) with helical chirality at its metal center, which forms preferentially a homochiral dimer and exhibits thermo-/mechano-chromism based on a monomer-dimer transformation. While a five-coordinate monomer is formed in a racemic or an enantiopure Bu-Ir solution at 25 °C, a six-coordinate homochiral dimer complex is formed almost exclusively at low temperatures, with a higher degree of dimerization in enantiopure Bu-Ir solution. Estimation of apparent dimerization binding constants (K) and thermodynamic parameters (ΔH and ΔS) based on variable temperature ultraviolet-visible (UV-vis) and 1H NMR spectra reveals a strong preference for homochiral dimerization (largest known value for the coordination complex, Khomo/Khetero > 50). Notably, crystals of the homochiral dimer are metastable, undergoing a distinct color change upon grinding (from yellow to red) due to mechanical cleavage of coordination bonds (i.e., a dimer to monomer transformation). A comparison with control compounds having different substituents (proton, methyl, isopropyl, and phenyl groups) reveals that Bu-Ir dimerization involves both strong homochiral self-sorting preference and connected thermo-/mechano-chromic behavior, which is based on matched propeller-shaped chirality and subtle steric repulsion between alkyl substituents that render the homochiral dimer switchable and metastable. These findings provide substantial insights into the emergence of dynamic functionality based on the rational design of discrete chiral assemblies.

Creating a Defined Chirality in Amino Acids and Cyclic Dipeptides by Photochemical Deracemization

2,5-Diketopiperazines are cyclic dipeptides displaying a wide range of applications. Their enantioselective preparation has now been found possible from the respective racemates by a photochemical deracemization (53 examples, 74 % to quantitative yield, 71-99 % ee). A chiral benzophenone catalyst in concert with irradiation at λ=366 nm enables to establish the configuration at the stereogenic carbon atom C6 at will. If other stereogenic centers are present in the diketopiperazines they remain unaffected and a stereochemical editing is possible at a single position. Consecutive reactions, including the conversion into N-aryl or N-alkyl amino acids or the reduction to piperazines, occur without compromising the newly created stereogenic center. Transient absorption spectroscopy revealed that the benzophenone catalyst processes one enantiomer of the 2,5-diketopiperazines preferentially and enables a reversible hydrogen atom transfer that is responsible for the deracemization process. The remarkably long lifetime of the protonated ketyl radical implies a yet unprecedented mode of action.

Chiral molecule candidates for trapped ion spectroscopy by ab initio calculations: From state preparation to parity violation

Parity non-conservation (PNC) due to the weak interaction is predicted to give rise to enantiomer dependent vibrational constants in chiral molecules, but the phenomenon has so far eluded experimental observation. The enhanced sensitivity of molecules to physics beyond the Standard Model (BSM) has led to substantial advances in molecular precision spectroscopy, and these may be applied to PNC searches as well. Specifically, trapped molecular ion experiments leverage the universality of trapping charged particles to optimize the molecular ion species studied toward BSM searches, but in searches for PNC, only a few chiral molecular ion candidates have been proposed so far. Importantly, viable candidates need to be internally cold, and their internal state populations should be detectable with high quantum efficiency. To this end, we focus on molecular ions that can be created by near threshold resonant two-photon ionization and detected via state-selective photo-dissociation. Such candidates need to be stable in both charged and neutral chiral versions to be amenable to these methods. Here, we present a collection of suitable chiral molecular ion candidates we have found, including CHDBrI+ and CHCaBrI+, that fulfill these conditions according to our ab initio calculations. We find that organo-metallic species have low ionization energy as neutrals and relatively high dissociation thresholds. Finally, we compute the magnitude of the PNC values for vibrational transitions for some of these candidates. An experimental demonstration of state preparation and readout for these candidates will be an important milestone toward measuring PNC in chiral molecules for the first time.

A relativistic relationship between parity-violating nuclear spin-rotation tensors and parity-violating NMR shielding tensors

The nuclear-spin-dependent parity-violation contributions to the nuclear magnetic resonance shielding and nuclear spin-rotation tensors (σ^PV and M^PV, respectively) are known to be formally related to one another in the non-relativistic regime. In this work, the polarization propagator formalism and the linear response within the elimination of small components model are used to show a new and more general relationship between them, which is valid within the relativistic framework. The full set of the zeroth- and first-order relativistic contributions to σ^PV and M^PV are also given here for the first time, and these results are compared with previous findings. According to four-component relativistic calculations, the electronic spin-orbit effects are the most significant ones for the isotropic values of σ^PV and M^PV in the H₂X₂ series of molecules (with X = O, S, Se, Te, and Po). When only scalar relativistic effects are taken into account, the non-relativistic relationship between σ^PV and M^PV does hold. However, when the spin-orbit effects are taken into consideration, this old non-relativistic relationship breaks down, and therefore, the new one must be considered.