Analysis of parity violation in chiral molecules

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.

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.

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.

Assessing MP2 frozen natural orbitals in relativistic correlated electronic structure calculations

The high computational scaling with the basis set size and the number of correlated electrons is a bottleneck limiting applications of coupled cluster algorithms, in particular for calculations based on two- or four-component relativistic Hamiltonians, which often employ uncontracted basis sets. This problem may be alleviated by replacing canonical Hartree-Fock virtual orbitals by natural orbitals (NOs). In this paper, we describe the implementation of a module for generating NOs for correlated wavefunctions and, in particular, second order Møller-Plesset perturbation frozen natural orbitals (MP2FNOs) as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [Pototschnig et al. J. Chem. Theory Comput. 17, 5509, (2021)]. Our implementation can manipulate complex or quaternion density matrices, thus allowing for the generation of both Kramers-restricted and Kramers-unrestricted MP2FNOs. Furthermore, NOs are re-expressed in the parent atomic orbital (AO) basis, allowing for generating coupled cluster singles and doubles NOs in the AO basis for further analysis. By investigating the truncation errors of MP2FNOs for both the correlation energy and molecular properties-electric field gradients at the nuclei, electric dipole and quadrupole moments for hydrogen halides HX (X = F-Ts), and parity-violating energy differences for H₂Z₂ (Z = O-Se)-we find MP2FNOs accelerate the convergence of the correlation energy in a roughly uniform manner across the Periodic Table. It is possible to obtain reliable estimates for both energies and the molecular properties considered with virtual molecular orbital spaces truncated to about half the size of the full spaces.

Systematic study and uncertainty evaluation of P, T-odd molecular enhancement factors in BaF

A measurement of the magnitude of the electric dipole moment of the electron (eEDM) larger than that predicted by the Standard Model (SM) of particle physics is expected to have a huge impact on the search for physics beyond the SM. Polar diatomic molecules containing heavy elements experience enhanced sensitivity to parity (P) and time-reversal (T)-violating phenomena, such as the eEDM and the scalar-pseudoscalar (S-PS) interaction between the nucleons and the electrons, and are thus promising candidates for measurements. The NL-eEDM collaboration is preparing an experiment to measure the eEDM and S-PS interaction in a slow beam of cold BaF molecules [P. Aggarwal et al., Eur. Phys. J. D 72, 197 (2018)]. Accurate knowledge of the electronic structure parameters, W_d and W_s, connecting the eEDM and the S-PS interaction to the measurable energy shifts is crucial for the interpretation of these measurements. In this work, we use the finite field relativistic coupled cluster approach to calculate the W_d and W_s parameters in the ground state of the BaF molecule. Special attention was paid to providing a reliable theoretical uncertainty estimate based on investigations of the basis set, electron correlation, relativistic effects, and geometry. Our recommended values of the two parameters, including conservative uncertainty estimates, are 3.13 ±0.12×10²⁴Hzecm for W_d and 8.29 ± 0.12 kHz for W_s.

Chirality and Relativistic Effects in Os3(CO)12

The energy and structural parameters were obtained for all forms of the carbonyl complex of osmium Os₃(CO)₁₂ with D_3h and D₃ symmetries using density functional theory (DFT) methods. The calculations took into account various levels of relativistic effects, including those associated with nonconservation of spatial parity. It was shown that the ground state of Os₃(CO)₁₂ corresponds to the D₃ symmetry and thus may be characterized either as left-twisted (D_3S) or right-twisted (D_3R). The D_3S↔D_3R transitions occur through the D_3h transition state with an activation barrier of ~10^–14 kJ/mol. Parity violation energy difference (PVED) between D_3S and D_3R states equals to ~5 × 10⁻¹⁰ kJ/mol. An unusual three-center exchange interaction was found inside the {Os₃} fragment. It was found that the cooperative effects of the mutual influence of osmium atoms suppress the chirality of the electron system in the cluster.

Can One Hear the Shape of a Molecule (from its Coulomb Matrix Eigenvalues)?

Coulomb matrix eigenvalues (CMEs) are global 3D representations of molecular structure, which have been previously used to predict atomization energies, prioritize geometry searches, and interpret rotational spectra. The properties of the CME representation and its relationship to molecular structure are established using the Gershgorin circle theorem. Numerical bounds are studied using a data set of 309 000 conformational samples of all constitutional isomers of acyclic alkanes, C_nH_2n+2, from methane (n = 1) to undecane (n = 11), to establish the extent to which the CME preserves chemical intuitions about isomer and conformer similarity and its ability to distinguish constitutional isomers. Neither supervised nor unsupervised machine-learning algorithms can perfectly distinguish constitutional isomers as the molecular size increases, but the misclassification rate can be kept below 1%.

The DIRAC code for relativistic molecular calculations

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

False Chirality, Absolute Enantioselection and CP Violation: Pierre Curie’s Legacy

The 1884 suggestion of Pierre Curie (1859–1906) that the type of dissymmetry shown by collinear electric and magnetic fields may induce an enantiomeric excess, in a chemical reaction that would otherwise produce a racemic mixture, is explored in the context of fundamental symmetry arguments. Curie’s arrangement exhibits false chirality (time-noninvariant enantiomorphism), and so it may not induce absolute enantioselection (ae) in a process that has reached thermodynamic equilibrium, since it does not lift the degeneracy of chiral enantiomers. However, it may do so in far-from-equilibrium processes via a breakdown in microscopic reversibility analogous to that observed in elementary particle processes under the influence of CP violation, the associated force possessing false chirality with respect to CP enantiomorphism. In contrast, an influence like circularly polarized light exhibiting true chirality (time-invariant enantiomorphism) lifts the degeneracy of enantiomers, and so may induce ae in all circumstances. Although to date, ae has not been observed under the influence of Curie’s arrangement of collinear electric and magnetic fields, it is argued that two different experiments have now demonstrated ae under a falsely chiral influence in systems far from equilibrium, namely in a spinning sample under a gravitational field, and in the separation of enantiomers at a ferromagnetic surface.

Parity violating energy difference for mirror conformers of DABCO linker between two M2+ cations (M = Zn, Cd, and Hg)

We have studied the potential energy surface of [ M 2 D A B C O ] 4 + cations (M = Zn, Cd, and Hg), which are considered as a model for the DABCO linker in metal-organic frameworks, a new prospective class of materials. Relativistic four-component and two-component calculations of parity violating energy difference (PVED) for twisted isomers of [ M 2 D A B C O ] 4 + cations have been performed. The right-twisted conformers of [ M 2 D A B C O ] 4 + are more stable than the left-twisted ones. The increase in PVED with the nuclear charge of the transition metal atom M (Z _M ) is discussed.

Antisymmetric Couplings Enable Direct Observation of Chirality in Nuclear Magnetic Resonance Spectroscopy

Here we demonstrate that a term in the nuclear spin Hamiltonian, the antisymmetric J-coupling, is fundamentally connected to molecular chirality. We propose and simulate a nuclear magnetic resonance (NMR) experiment to observe this interaction and differentiate between enantiomers without adding any additional chiral agent to the sample. The antisymmetric J-coupling may be observed in the presence of molecular orientation by an external electric field. The opposite parity of the antisymmetric coupling tensor and the molecular electric dipole moment yields a sign change of the observed coupling between enantiomers. We show how this sign change influences the phase of the NMR spectrum and may be used to discriminate between enantiomers.

Advances in spectroscopy and dynamics of small and medium sized molecules and clusters

Investigations of the spectroscopy and dynamics of small- and medium-sized molecules and clusters represent a hot topic in atmospheric chemistry, biology, physics, atto- and femto-chemistry and astrophysics.

Nuclear size effects in vibrational spectra

A theoretical study confirms that rovibrational spectroscopy can find bond length changes on the order of 1% of the nuclear radius.

Theoretical predictions of properties and volatility of chlorides and oxychlorides of group-4 elements. II. Adsorption of tetrachlorides and oxydichlorides of Zr, Hf, and Rf on neutral and modified surfaces

With the aim to interpret results of gas-phase chromatography experiments on volatility of group-4 tetrachlorides and oxychlorides including those of Rf, adsorption enthalpies of these species on neutral, and modified quartz surfaces were estimated on the basis of relativistic, two-component Density Functional Theory calculations of MCl4, MOCl2, MCl6(-), and MOCl4(2) with the use of adsorption models. Several mechanisms of adsorption were considered. In the case of physisorption of MCl4, the trend in the adsorption energy in the group should be Zr > Hf > Rf, so that the volatility should change in the opposite direction. The latter trend complies with the one in the sublimation enthalpies, ΔH(sub), of the Zr and Hf tetrachlorides, i.e., Zr < Hf. On the basis of a correlation between these quantities, ΔH(sub)(RfCl4) was predicted as 104.2 kJ/mol. The energy of physisorption of MOCl2 on quartz should increase in the group, Zr < Hf < Rf, as defined by increasing dipole moments of these molecules along the series. In the case of adsorption of MCl4 on quartz by chemical forces, formation of the MOCl2 or MOCl4(2-) complexes on the surface can take place, so that the sequence in the adsorption energy should be Zr > Hf > Rf, as defined by the complex formation energies. In the case of adsorption of MCl4 on a chlorinated quartz surface, formation of the MCl6(2-) surface complexes can occur, so that the trend in the adsorption strength should be Zr ≤ Hf < Rf. All the predicted sequences, showing a smooth change of the adsorption energy in the group, are in disagreement with the reversed trend Zr ≈ Rf < Hf, observed in the "one-atom-at-a-time" gas-phase chromatography experiments. Thus, currently no theoretical explanation can be found for the experimental observations.

Strong enhancement of parity violation effects in chiral uranium compounds

A new generation of molecular candidates for parity violation measurements. The chiral UNXYZ compounds are predicted to exhibit strong parity violating effects which are up to an order of magnitude larger than for any of the previously suggested candidates.

From cosmic chirality to protein structure: Lord Kelvin's legacy

A selection of my work on chirality is sketched in two distinct parts of this lecture. Symmetry and Chirality explains how the discrete symmetries of parity P, time reversal T, and charge conjugation C may be used to characterize the properties of chiral systems. The concepts of true chirality (time-invariant enantiomorphism) and false chirality (time-noninvariant enantiomorphism) that emerge provide an extension of Lord Kelvin's original definition of chirality to situations where motion is an essential ingredient thereby clarifying, inter alia, the nature of physical influences able to induce absolute enantioselection. Consideration of symmetry violations reveals that strict enantiomers (exactly degenerate) are interconverted by the combined CP operation. Raman optical activity surveys work, from first observation to current applications, on a new chiroptical spectroscopy that measures vibrational optical activity via Raman scattering of circularly polarized light. Raman optical activity provides incisive information ranging from absolute configuration and complete solution structure of smaller chiral molecules and oligomers to protein and nucleic acid structure of intact viruses.

Stabilization of chiral molecules by decoherence and environment interactions in the gas phase

We study the tunnel dynamics of a chiral molecule between its left (L) and right (R) conformations, under the global effect of collisional decoherence together with the effect of a mean-field generated by the environment where an energetic difference, K, between homochiral and heterochiral interactions is assumed. We show that this decoherence leads unavoidably to equal populations of the L and R chiral conformations even for a high enough value of K which tends to keep localized an initial chiral state. However, we also show that K contributes to the stabilization of an initial L or R state for times that could be many orders of magnitude larger than the tunneling time, in the case the decoherence rate is much greater than the tunneling rate. In this case, an estimation of this stabilization time and a critical tunneling time is made. Even in the case in which the tunneling rate is greater than the decoherence rate, the effect of K is to keep localized the initial chiral state for times greater than the tunneling time. A possible slight chiral asymmetry is also considered.