An alternative route to detect parity violating energy differences through Bose-Einstein condensation of chiral molecules

Interactions which do not conserve parity might influence chiral compounds giving rise to a parity violating energy difference (PVED) that might have affected the evolution towards homochirality. However, this tiny effect predicted by electroweak-quantum chemistry calculations is easily masked by thermal effects, making it desirable to reach cold regimes in the laboratory. As an alternative route to the detection of the PVED, we study a simplified model of Bose-Einstein condensation of a sample of non-interacting chiral molecules, showing that it leads to a nonzero optical activity of the condensate and also to a subcritical temperature in the heat capacity, due to the internal structure of the molecule characterized by tunneling and parity violation. This predicted singular behavior found for the specific heat, below the condensation temperature, might shed some light on the existence of the thus far elusive PVED between enantiomers.     

Quantum optimal control of electron ring currents in chiral aromatic molecules

We report the results of optimal control simulations of pi-electron rotation (ring current) in a six-membered chiral aromatic molecule, 2,5-dichloro[n](3,6)pyrazinophane (DCP), attached at a surface and excited by a linearly polarized UV laser. DCP has a pair of optically allowed, quasidegenerate pi-electronic excited states. The laser pulse to generate an approximate angular momentum eigenstate consisting of the quasidegenerate states was designed using the global optimal control theory. For both counterclockwise and clockwise pi-electron rotations, the calculated objective functional and target yield as a function of the angle of the photon polarization vector show two maxima and two minima. The origin of the two minima is coherent excitation to only one of the quasidegenerate states. The two maxima arise from creation of a superposition of the quasidegenerate states. The optimal control pulse at the maxima is a two-color laser field resonant with the quasidegenerate states. The electric field of the optimal control pulse consists of two parts: a slowly oscillating part with phase phi(env) and a rapidly oscillating one. The phase phi(env) is a crucial parameter for determination of the rotation direction of pi electrons at the end of control. The results of the optimal control simulations suggest that pi-electron rotation can be controlled by applying a two-color laser field with adjusted phases.     

High resolution spectroscopy of methyltrioxorhenium: towards the observation of parity violation in chiral molecules

Originating from the weak interaction, parity violation in chiral molecules has been considered as a possible origin of biohomochirality. We have proposed the observation of molecular parity violation using the two-photon Ramsey fringes technique on a supersonic beam. As a first step in this direction, a detailed spectroscopic study of methyltrioxorhenium (MTO) has been undertaken. It is an ideal test molecule as the achiral parent molecule of chiral candidates for a parity violation experiment. For the (187)Re MTO isotopologue, a combined analysis of Fourier transform microwave and infrared spectra as well as ultra-high resolution CO(2) laser absorption spectra enabled the assignment of 28 rotational lines and 71 rovibrational lines, some of them with a resolved hyperfine structure. A set of spectroscopic parameters in the ground and first excited state, including hyperfine structure constants, was obtained for the ν(as) antisymmetric Re=O stretching mode of this molecule. This result validates the experimental approach to be followed once a chiral derivative of MTO is synthesized, and shows the benefit of the combination of several spectroscopic techniques in different spectral regions, with different set-ups and resolutions. The first high resolution spectra of jet-cooled MTO, obtained on a set-up being developed for the observation of molecular parity violation, are shown, which constitutes a major step towards the targeted objective.     

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

In view of exploring possibilities for an experimental investigation of molecular parity violation we report quantum-chemical calculations of the parity-conserving and parity-violating potentials in the framework of electroweak quantum chemistry in allene C3H4 and 1,3-difluoroallene C3H2F2, which is nonplanar and axially chiral in the electronic ground state but expected to be nearly planar and achiral in several electronically excited states. The parity-violating potentials Epv for allene and 1,3-difluoroallene calculated with the multiconfiguration linear-response (MC-LR) approach of Berger and Quack [J. Chem. Phys. 112, 3148 (2000)] show qualitatively similar behavior as a function of torsional angle tau with maximum values of about 0.5 pJ mol(-1) for C3H4 and 2 pJ mol(-1) for C3H2F2. However, in the latter case they are asymmetrically shifted around tau=90 degrees , with a nonzero value at the chiral equilibrium geometry resulting in a parity-violating energy difference between enantiomers DeltapvE=Epv(P)-Epv(M)=1.2 pJ mol(-1) (equivalent to about 10(-13) cm(-1)). The calculated barrier heights corresponding to the nonrigid (multiple, and in part chiral) transition states in 1,3-difluoroallene fall in the range of 180-200 kJ mol(-1). These high barriers result in hypothetical tunneling splittings much smaller than DeltapvE and thus parity violation dominates over tunneling for the stereomutation dynamics in 1,3-difluoroallene. Therefore, DeltapvE is predicted to be a spectroscopically measurable energy difference. Two of the lower excited electronic states of C3H2F2 (1A and 3A) are calculated to be planar or quasiplanar, allowing, in principle, for spectroscopic state selection of states of well-defined parity. The results are discussed in relation to possible schemes of measuring parity violation in chiral molecules.     

Pseudotetrahedral polyhalocubanes: synthesis, structures, and parity violating energy differences

All possible pseudotetrahedral, stable polyhalocubanes were prepared, and their structures were proven by NMR spectroscopy and X-ray crystallography. Parity violating energy differences (DeltaEpv) and vibrational frequency shifts were computed. The DeltaEpv values are predicted to be one to two orders of magnitude smaller than those for the corresponding polyhalomethanes. However, the DeltaEpv energy ordering is the same as that for the methane analogues. For both substance classes, the (S) isomers are, with the exception of the bromochlorofluoroiodo derivatives, more stable than the (R) forms.     

Classification of topologically chiral molecules

Graphs are partitioned into six classes from the perspective of chirality, depending on whether they are topologically achiral, whether there is at least one topologically achiral embedding, whether there is at least one rigidly achiral embedding, and whether there is at least one rigidly achiral presentation. Three of these classes are well represented by a variety of chemical structures: topologically chiral molecular graphs with no topologically achiral embeddings, topologically chiral molecular graphs with at least one rigidly achiral embedding, and topologically achiral molecular graphs with at least one rigidly achiral presentation. Known representatives of these three classes are described. Various meanings associated with the concepts molecular graph and intrinsic chirality are critically discussed. Previous arrangements of molecular graphs and molecules in a hierarchical order, ranging from the most to the least chiral, are interpreted in terms of the graph's and molecule's chiral persistence.     

Packing of chiral molecules of metal TRIS-acetylacetonates

The Cambridge Crystallographic Data Centre (CCDC) is searched to organize packings of metal tris-acetylacetonates M(aa)₃ (about 70 structures over the last 50 years). In all structures, planes with a hexagonal molecular environment are found. Three types of the nearest hexagonal environment are revealed in these planes with allowance for the chirality of molecules. Different superposition of these planes produces five types of packing of metal tris-acetylacetonates: α, β, γ, jg, and pg. Spectrally pure Al(aa)₃, Cr(aa)₃, Mn(aa)₃, and Fe(aa)₃ complexes are synthesized and their solid solutions are studied. The effect of impurities on crystallization is established. A temperature range of 210 K to 100 K, in which we have previously detected thermochromism of metal β-diketonates is distinguished. In the same range, a symmetry change was previously found for Al(aa)₃ and Mn(aa)₃, however, Cr(aa)₃ symmetry did not change in this temperature range. The ratios of components in solid solutions, at which low temperature symmetry change is observed in the complexes, are found experimentally. The relation between thermochromism and the symmetry change is discussed.     

Palladium-catalyzed asymmetric synthesis of axially chiral molecules

The asymmetric synthesis of chiral 3-alkylidene bicyclo[3.3.0]octane and 4-substituted 1-alkylidene cyclohexane systems has been carried out (in up to 40% ee) by the palladium-catalyzed reaction of allylic acetates with sodium dimethyl malonate or morpholine.     

Applications of chiral C3-symmetric molecules

Throughout history symmetry and chirality have inspired artists and scientists alike. Given that rotational axes are the only elements of symmetry compatible with chirality, it is not surprising that C2- and C3-symmetrical molecules have attracted considerable attention. In recent years, the aesthetic appeal of C2-symmetrical molecules has been translated into many widely-used applications some of which are of commercial importance by its exploitation in the area of asymmetric catalysis. In contrast, exploitation of the arguably greater aesthetic appeal of C3-symmetric molecules is still in its infancy. This review, which surveys the applications of chiral C3-symmetrical molecules in the areas of asymmetric catalysis, molecular recognition and nanoarchitecture, has been designed with a view to identifying some of the most promising areas of application of these very beautiful molecules.     

Dissipative geometric phase and decoherence in parity-violating chiral molecules

Within a generalized Langevin framework for open quantum systems, the cyclic evolution of a two-level system is analyzed in terms of the geometric phase extended to dissipative systems for Ohmic friction. This proposal is applied to the dynamics of chiral molecules where the tunneling and parity violating effects are competing. The effect of different system-bath coupling functions in the dissipated energy is shown to be crucial to understand the behavior of the geometric phase as well as the decoherence displayed by the corresponding interference patterns.     

New approaches to chiral discrimination in coupling between molecules

Results in the coupling of chiral molecules are reviewed from elementary points of view and some new results are given. We show that interactions between chiral molecules can be treated by using molecular quantum electrodynamics in electric and magnetic dipole approximation in ways different from standard diagrammatic perturbation theory. The interactions are the dispersive coupling of ground-state chiral molecules and excitation transfer, with emphasis on chiral discrimination. For ground-state molecules the coupling is dealt with first by calculating the coupling, at all separation distances, of electric and magnetic dipoles induced in the two molecules by fluctuations in the vacuum radiation field. The second method is the response by one chiral molecule to the field generated by the other. Excitation transfer is treated as the response by the accepting ground-state molecule to the dipole field of the donor. A novel variant in finding the rate of excitation transfer is by using Poynting's theorem. Received: 17 June 1998 / Accepted: 6 October 1998 / Published online: 16 March 1999     

Parity nonconservation contribution to the nuclear magnetic resonance shielding constants of chiral molecules: a four-component relativistic study

A systematic four-component relativistic study of the parity nonconservation (PNC) contribution to the (isotropic) NMR shielding constants of chiral molecules is presented for the P enantiomers of the series H(2)X(2) (X=(17)O,(33)S,(77)Se,(125)Te,(209)Po). The PNC contributions are obtained within a linear response approach at the Hartree-Fock level. A careful design of the basis sets is necessary. The four-component relativistic results based on the Dirac-Coulomb Hamiltonian are compared with the nonrelativistic Levy-Leblond results and those obtained by the spin-free modified Dirac Hamiltonian. The calculations confirm the nonrelativistic scaling law Z(2.4) of the PNC contribution with respect to nuclear charge Z. However, the calculations also show that the overall scaling is significantly modified by relativistic effects. The scalar relativistic effect scales as Z(4.7) for the selected set of molecules, whereas the spin-orbit effect, of opposite sign, scales better than Z(6) and completely dominates the PNC contribution for the heaviest elements. This opens up the intriguing possibility of the experimental observation of PNC effects on NMR parameters of molecules containing heavy atoms. The presented formalism is expected to be valuable in assisting the search for suitable candidate molecules.     

Internal stochastic resonance in two coupled chemical oscillators

The dynamics of two coupled chemical oscillators was investigated numerically when the first subsystem was subjected to external parametric noise. The signal-to-noise ratio (SNR) of the response of each subsystem to external noise shows internal stochastic resonance (SR). In addition, the SNR also shows resonance behavior with the variation of coupling strength.     

Crystal structures of cyclodextrin complexes with chiral molecules

The chiral recognition by cyclodextrins and permethylated cyclodextrins have been investigated on the basis of the X-ray data of crystalline inclusion complexes. The macrocyclic ring of - and -cyclodextrin shows a round and symmetrical structure. -Cyclodextrin includes racemic 1-phenylethanol with the statistical disorder of the hydroxyl group. A pair of the R- and S-isomers of flurbiprofen are included within the cylindrical cavity formed by dimeric -cyclodextrin molecules with a head-to-head arrangement. The macrocyclic ring of permethylated cyclodextrins is remarkably distorted from the regular polygonal symmetry and has more flexibility in the conformational change than cyclodextrins. Owing to the distorted conformation and steric hindrance involving methyl groups, permethylated cyclodextrins do not equally include both isomers, as demonstrated by the permethylated -cyclodextrin complexes with mandelic acids. Permethylated -cyclodextrin binds D-mandelic acid more tightlyvia a host-guest hydrogen bond and induced-fit conformational change. Permethylated -cyclodextrin forms a hydrated crystalline complex with R-flurbiprofen, but S-flurbiprofen forms a non-hydrated crystalline complex. Significant differences between the two complexes are found in the orientation of the phenyl group and hydrogen-bond formation involving the carboxyl group.     

Helical structures induced by laterally-connected chiral twin molecules

A novel chiral twin material, (R)-bis[5-octyloxy-2-(4-octyloxyphenoxycarbonyl)phenyl] 3-methyladipate, has been prepared, where two mesogenic parts are connected laterally by a spacer possessing a chiral centre. A weaker helical structure, in particular in the chiral smectic C (S*_c) phase, was found to be induced by the laterally-connected twin material than by the analogous terminally-connected twin material. If laterally-connected chiral twin molecules prefer to stay in the smectic layer structure so that the two mesogenic parts exist in the same smectic layer, the twist interaction between adjacent layers cannot be produced by direct correlation of motion and directions of two mesogenic parts. Thus, the helical structure in the S*_c phase induced by laterally-connected chiral twin molecules becomes weak. An analogous laterally-branched 'monomeric' compound, (S)-5-octyloxy-2-(4-octyloxyphenoxycarbonyl)phenyl 3-methyl-pentanoate, has also been prepared, and the induced helical structures compared.     

Differential scattering of spin-polarized particles by chiral molecules

It is shown with the help of quantum electrodynamics that the inelastic differential cross section for scattering of any spin-polarized particles with spin ±$\text{1}\text{2}$ by chiral molecules is spin dependent. This effect appears in the first order of the interaction between the particle spin and the magnetic moment of the electrons in the chiral molecules.