Parity Violation Dominates the Dynamics of Chirality in Dichlorodisulfane

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.

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.

Simple models for the quick estimation of ground state hydrogen tunneling splittings in alcohols and other compounds

Models for the quick estimation of energy splittings caused by coherent tunneling of hydrogen atoms are evaluated with available experimental data for alcohols and improvements are proposed. The discussed models are mathematically simple and require only results from routine quantum chemical computations, i.e. hybrid DFT calculation of the equilibrium geometry and the transition state within the harmonic approximation. A benchmark of experimental splittings spanning four orders of magnitude for 27 alcohol species is captured by three evaluated models with a mean symmetric deviation factor of 1.7, 1.5 and 1.4, respectively, i.e. the calculated values deviate on average by this factor in either direction. Limitations of the models are explored with alcohols featuring uncommon properties, such as an inverted conformational energy sequence, a very light molecular frame, an elevated torsional frequency, or a coupling with a second internal degree of freedom. If the splitting of either the protiated or deuterated form of an alcohol is already experimentally determined, the one of the second isotopolog can be estimated by three additional models with a mean symmetric deviation factor of 1.14, 1.19 and 1.15, respectively. It is shown that this can be achieved with a novel approach without any quantum chemical calculation by directly correlating experimental splittings of isotopologs across related species. This is also demonstrated for other classes of compounds with hydrogen tunneling, such as amines, thiols, and phenols. Furthermore, it is found that the isotope effect can even be anticipated without any further knowledge about the system solely from the size of either splitting with a mean symmetric deviation factor of 1.3. This is based on an extensive sample of 77 pairs of splittings spanning eight orders of magnitude for isotopologs of chemically diverse compounds.

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.

State-Specific Enrichment of Chiral Conformers with Microwave Spectroscopy

An interesting class of molecules is that in which the molecules do not possess a stereogenic center but can become chiral because of their spatial arrangement. These molecules can be seen as chiral conformers, whose two nonsuperimposable forms can interconvert from one to another by rotations about single bonds. Here, we show that an initially racemic mixture of chiral conformers, such as a sample of cyclohexylmethanol, C₇H₁₄O, can be enantiomerically enriched by performing the enantioselective process of coherent population transfer between rotational levels. By first performing a population transfer cycle, followed by a three-wave mixing experiment, we show that an enantiomeric excess in a rotational level of choice can be achieved. This represents the first experimental demonstration of such an effect in a chiral pair of conformers, and it showcases the broad applicability of three-wave mixing not only for analytical applications but also to a wide scope of experiments of fundamental interest.

Chiral Imprinting in the Gas Phase

Undoing the twist: Recent successful attempts to change the relative populations of two otherwise identical enantiomers of a large gas-phase molecule using resonant microwave fields are highlighted. Specifically, the population of a specific enantiomer of a chiral terpene could be enhanced relative to the other enantiomer by the application of a sequence of microwave pulses in a phase- and polarization-controlled manner.

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.

Millimeter-wave spectroscopy of S2Cl2: a candidate molecule for measuring ortho-para transition

S2Cl2 is a candidate for the observation of ortho-para transition. To estimate the ortho-para mixing in a hyperfine-resolved rotational state, pure rotational transitions were measured by millimeter-wave (mm-wave) spectroscopy using two different experimental set-ups. The transitions from the term value around 20 K was measured with a supersonic jet and those around 200 K were measured with a dry ice cooled gas cell. Several hundred peaks were assigned for the naturally abundant S2(35)Cl2 and S2(35)Cl(37)Cl isotopic species and the rotational molecular parameters including the fourth-order and sixth-order centrifugal distortion constants were determined. The hyperfine structures were partly resolved in some Q-branch transitions, which were well described with the hyperfine constants determined by FTMW spectroscopy in the centimeter-wave region. With the new rotational constants determined in our study and the previous hyperfine constants, it will be possible to obtain a more reliable ortho-para mixing ratio and to narrow down the possible candidate transitions in the mm-wave region for the observation of ortho-para transition.

Tunneling and tunneling switching dynamics in phenol and its isotopomers from high-resolution FTIR spectroscopy with synchrotron radiation

Tunneling and chemical reactions by tunneling switching are reported for phenol and ortho-deuterophenol on the basis of high-resolution FTIR spectroscopy. Tunneling splittings are measured for the torsional motion in the ground and several vibrationally excited states of phenol. Tunneling times range from 10 ns to 1 ps, depending on excitation. For more-highly excited torsional levels in ortho-deuterophenol, delocalization and chemical reaction by tunneling switching is found.

Progress toward the first observation of parity violation in chiral molecules by high-resolution laser spectroscopy

Parity violation (PV) effects in chiral molecules have so far never been experimentally observed. To take up this challenge, a consortium of physicists, chemists, theoreticians, and spectroscopists has been established and aims at measuring PV energy differences between two enantiomers by using high-resolution laser spectroscopy. In this article, we present our common strategy to reach this goal, the progress accomplished in the diverse areas, and point out directions for future PV observations. The work of André Collet on bromochlorofluoromethane (1) enantiomers, their synthesis, and their chiral recognition by cryptophanes made feasible the first generation of experiments presented in this article.

Chiral oxorhenium(V) complexes as candidates for the experimental observation of molecular parity violation: a structural, synthetic and theoretical study

We report the synthesis and resolution of a series of new chiral "3 + 1" oxorhenium(V) complexes, designed for high-resolution laser spectroscopy experiments probing molecular parity-violation (PV) effects in the Re=O stretching mode frequency. These complexes display a particularly simple chemical structure, with the rhenium atom as the stereogenic center, and show large PV energy differences according to our calculations. They were obtained in the racemic and enantioenriched forms, in the latter case by using either semi-preparative chiral HPLC resolution or enantioselective synthesis. The vibrational transition frequency differences between the enantiomeric pairs due to PV have been calculated with two- and four-component relativistic Hamiltonians using Hartree-Fock (HF) and density functional theory (DFT). For three complexes, including one synthesized in enantioenriched form, our HF calculations predict frequency differences above the present resolution limit of 1 Hz. These results confirm the order of magnitude for the calculated HF PV vibrational frequency differences reported earlier for this class of compounds [P. Schwerdtfeger and R. Bast, J. Am. Chem. Soc., 2004, 126, 1652]. However, at the DFT level the PV vibrational frequency differences are in some cases reduced by an order of magnitude, but are still within the sensitivity of 0.01 Hz, which is the anticipated sensitivity in a new proposed experiment. We therefore believe that the present study represents an important step towards the experimental observation of PV in molecular systems, and emphasizes the extreme sensitivity of the PV vibrational frequency difference to the chemical environment around the rhenium center.

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.

From stochastic pulse optimization to a stereoselective laser pulse sequence: simulation of a chiroptical molecular switch mounted on adamantane

Quantum dynamical simulations for the laser-controlled isomerization of 1-(2-cis-fluoroethenyl)-2-fluorobenzene mounted on adamantane are reported based on a one-dimensional electronic ground-state potential and dipole moment calculated by density functional theory. The model system 1-(2-cis-fluoroethenyl)-2-fluorobenzene supports two chiral and one achiral atropisomers upon torsion around the C-C single bond connecting the phenyl ring and ethylene group. The molecule itself is bound to an adamantyl frame which serves as a model for a linker or a surface. Due to the C3 symmetry of the adamantane molecule, the molecular switch can have three equivalent orientations. An infrared picosecond pulse is used to excite the internal rotation around the chiral axis, thereby controlling the chirality of the molecule. In order to selectively switch the molecules--independent of their orientations-- from their achiral to either their left- or right-handed form, a stochastic pulse optimization algorithm is applied. A subsequent detailed analysis of the optimal pulse allows for the design of a stereoselective laser pulse sequence of analytical form. The developed control scheme of elliptically polarized laser pulses is enantioselective and orientation-selective.

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.

Laser-operated chiral molecular switch: quantum simulations for the controlled transformation between achiral and chiral atropisomers

We report quantum dynamical simulations for the laser controlled isomerization of 1-(2-cis-fluoroethenyl)-2-fluorobenzene based on one-dimensional electronic ground and excited state potentials obtained from (TD)DFT calculations. 1-(2-cis-fluoroethenyl)-2-fluorobenzene supports two chiral and one achiral atropisomers, the latter being the most stable isomer at room temperature. Using a linearly polarized IR laser pulse the molecule is excited to an internal rotation around its chiral axis, i.e. around the C-C single bond between phenyl ring and ethenyl group, changing the molecular chirality. A second linearly polarized laser pulse stops the torsion to prepare the desired enantiomeric form of the molecule. This laser control allows the selective switching between the achiral and either the left- or right-handed form of the molecule. Once the chirality is "switched on" linearly polarized UV laser pulses allow the selective change of the chirality using the electronic excited state as intermediate state.

Detection of the chirality of C alpha-methylated alpha-amino acids with a dynamic helical poly(phenylacetylene) bearing aza-18-crown-6 ether pendants

A stereoregular poly(phenylacetylene) bearing the aza-18-crown-6 ether pendants (poly-1) was found to form a predominantly one-handed helix upon complexation with optically active C(alpha)-methylated alpha-amino acids and their amide derivatives including typical meteoritic C(alpha)-methylated alpha-amino acids such as C(alpha)-methyl norvaline and C(alpha)-methyl valine. The complexes exhibited an induced circular dichroism (ICD) in the UV-visible region of the polymer backbone. Therefore, poly-1 can be used as a novel probe for detection of the chirality of C(alpha)-methylated alpha-amino acids. The effect of the enantiomeric excess (ee) of C(alpha)-methylated alpha-amino acids on the helicity induction in poly-1 was also investigated.

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).

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.

Intramolecular Förster energy transfer in a dendritic system at the single molecule level

The photophysics of a dendrimer containing four donor chromophores and one acceptor chromophore are studied at the single-molecule level. Upon excitation of the donors exclusive acceptor emission is observed due to efficient Förster energy transfer. For 70% of the molecules donor emission is observed after bleaching of the acceptor, leading to a reduction of the Förster energy transfer efficiency. Furthermore, we demonstrate that in this molecular system the donor chromophores do not bleach by a triplet-sensitized photooxidation.