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

Reformulation of Thermally-Assisted-Occupation Density Functional Theory in the Kohn-Sham Framework

We reformulate the thermally-assisted-occupation density functional theory (TAO-DFT) into the Kohn-Sham single-determinant framework and construct two new post-self-consistent field (post-SCF) static correlation correction schemes, named rTAO and rTAO-1. In contrast to the original TAO-DFT with the density in an ensemble form, in which each orbital density is weighted with a fractional occupation number, the ground-state density is given by a single-determinant wavefunction, a regular Kohn-Sham density, and total ground state energy is expressed in the normal Kohn-Sham form with a static correlation energy formulated in terms of the Kohn-Sham orbitals. In post-SCF calculations with rTAO functionals, an efficient energy scanning to quantitatively determine $\theta$ is also proposed. The rTAOs provide a promising method to simulate systems with strong static correlation as original TAO, but simpler and more efficient.We show that both rTAO and rTAO-1 is capable of reproducing most results from TAO-DFT without the additional functional Eθ used in TAO-DFT. Furthermore, our numerical results support that, without the functional Eθ, both rTAO and rTAO-1 can capture correct static correlation profiles in various systems.

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.

Spontaneous mirror symmetry breaking and origin of biological homochirality

Recent reports on both theoretical simulations and on the physical chemistry basis of spontaneous mirror symmetry breaking (SMSB), that is, asymmetric synthesis in the absence of any chiral polarizations other than those arising from the chiral recognition between enantiomers, strongly suggest that the same nonlinear dynamics acting during the crucial stages of abiotic chemical evolution leading to the formation and selection of instructed polymers and replicators, would have led to the homochirality of instructed polymers. We review, in the first instance, which reaction networks lead to the nonlinear kinetics necessary for SMSB, and the thermodynamic features of the systems where this potentiality may be realized. This could aid not only in the understanding of SMSB, but also the design of reliable scenarios in abiotic evolution where biological homochirality could have taken place. Furthermore, when the emergence of biological chirality is assumed to occur during the stages of chemical evolution leading to the selection of polymeric species, one may hypothesize on a tandem track of the decrease of symmetry order towards biological homochirality, and the transition from the simple chemistry of astrophysical scenarios to the complexity of systems chemistry yielding Darwinian evolution.

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.

Spontaneous mirror symmetry breaking in the limited enantioselective autocatalysis model: abyssal hydrothermal vents as scenario for the emergence of chirality in prebiotic chemistry

The emergence of chirality in enantioselective autocatalysis for compounds unable to transform according to the Frank-like reaction network is discussed with respect to the controversial limited enantioselectivity (LES) model composed of coupled enantioselective and non-enantioselective autocatalyses. The LES model cannot lead to spontaneous mirror symmetry breaking (SMSB) either in closed systems with a homogeneous temperature distribution or in closed systems with a stationary non-uniform temperature distribution. However, simulations of chemical kinetics in a two-compartment model demonstrate that SMSB may occur if both autocatalytic reactions are spatially separated at different temperatures in different compartments but coupled under the action of a continuous internal flow. In such conditions, the system can evolve, for certain reaction and system parameters, toward a chiral stationary state; that is, the system is able to reach a bifurcation point leading to SMSB. Numerical simulations in which reasonable chemical parameters have been used suggest that an adequate scenario for such a SMSB would be that of abyssal hydrothermal vents, by virtue of the typical temperature gradients found there and the role of inorganic solids mediating chemical reactions in an enzyme-like role.

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.

Jahn-Teller effects in molecular cations studied by photoelectron spectroscopy and group theory

The traditional "ball-and-stick" concept of molecular structure fails when the motion of the electrons is coupled to that of the nuclei. Such a situation arises in the Jahn-Teller (JT) effect which is very common in open-shell molecular systems, such as radicals or ions. The JT effect is well known to chemists as a mechanism that causes the distortion of an otherwise symmetric system. Its implications on the dynamics of molecules still represent unsolved problems in many cases. Herein we review recent progress in understanding the dynamic structure of molecular cations that have a high permutational symmetry by using rotationally resolved photoelectron spectroscopy and group theory. Specifically, we show how the pseudo-Jahn-Teller effect in the cyclopentadienyl cation causes electronic localization and nuclear delocalization. The fundamental physical mechanisms underlying the vaguely defined concept of "antiaromaticity" are thereby elucidated. Our investigation of the methane cation represents the first experimental characterization of the JT effect in a threefold degenerate electronic state. A special kind of isomerism resulting from the JT effect has been discovered and is predicted to exist in all JT systems in which the minima on the potential-energy surface are separated by substantial barriers.

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.

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).