Parity non-conservation and NMR parameters

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.

Relayed hyperpolarization for zero-field nuclear magnetic resonance

Zero- to ultralow-field nuclear magnetic resonance (ZULF NMR) is a rapidly developing form of spectroscopy that provides rich spectroscopic information in the absence of large magnetic fields. However, signal acquisition still requires a mechanism for generating a bulk magnetic moment for detection, and the currently used methods only apply to a limited pool of chemicals or come at prohibitively high cost. We demonstrate that the parahydrogen-based SABRE (signal amplification by reversible exchange)-Relay method can be used as a more general means of generating hyperpolarized analytes for ZULF NMR by observing zero-field J-spectra of [13C]-methanol, [1-13C]-ethanol, and [2-13C]-ethanol in both 13C-isotopically enriched and natural abundance samples. We explore the magnetic field dependence of the SABRE-Relay efficiency and show the existence of a second maximum at 19.0 ± 0.3 mT. Despite presence of water, SABRE-Relay is used to hyperpolarize ethanol extracted from a store-bought sample of vodka (%PH ~ 0.1%).

Coordination Chemistry of the Parent Dithiocarbamate H2NCS2-: Organometallic Chemistry and Tris-Chelates of Group 9 Metals

Two tris-chelate complexes of cobalt and rhodium and two complexes of Ru(II) of dithiocarbamate, [S₂CNH₂]^-, were synthesized. The complexes were spectroscopically characterized by IR, NMR, UV-vis, and MS and structurally characterized by X-ray diffraction. The structural features of the rhodium complex were compared to those of other tris-chelate Rh(III) dithiocarbamate complexes and are characterized by a change in the ground-state geometry in comparison to expected octahedral tris-chelate complexes. This was confirmed both experimentally by X-ray diffraction and theoretically using DFT calculations. The inversion barriers of Rh(Bz₂dtc)₃, Ir(Bz₂dtc)₃, and Rh(Et₂dtc)₃ were determined using VT-NMR in DMSO. These barriers were found to be surprisingly low for heavy group 9 elements of d⁶ tris-chelate complexes: values of 16.7, 17.1, and 16.4 kcal/mol were calculated, respectively. By comparing structural features, we are able to determine that the activation barrier for the inversion of stereochemistry of Rh(H₂dtc)₃ must have a similarly low value. A modified version of the Bailar twist involving an intermediate with C_3h geometry was proposed as the mechanism of inversion.

Relativistic study of parity-violating nuclear spin-rotation tensors

We present a four-component relativistic approach to describe the effects of the nuclear spin-dependent parity-violating (PV) weak nuclear forces on nuclear spin-rotation (NSR) tensors. The formalism is derived within the four-component polarization propagator theory based on the Dirac-Coulomb Hamiltonian. Such calculations are important for planning and interpretation of possible future experiments aimed at stringent tests of the standard model through the observation of PV effects in NSR spectroscopy. An exploratory application of this theory to the chiral molecules H₂X₂ (X = ¹⁷O, ³³S, ⁷⁷Se, ¹²⁵Te, and ²⁰⁹Po) illustrates the dramatic effect of relativity on these contributions. In particular, spin-free and spin-orbit effects are even of opposite signs for some dihedral angles, and the latter fully dominate for the heavier nuclei. Relativistic four-component calculations of isotropic nuclear spin-rotation constants, including parity-violating electroweak interactions, give frequency differences of up to 4.2 mHz between the H₂Po₂ enantiomers; on the nonrelativistic level of theory, this energy difference is 0.1 mHz only.

Direct enantiomeric discrimination through antisymmetric hyperfine coupling

Chiral open-shell molecules possessing permanent electric dipole moments have an EPR signal at the difference frequency of the electron and nuclear resonances, allowing direct enantiomeric discrimination by signal phase. The effect depends on the vector antisymmetry of the hyperfine coupling. Quantum chemistry suggests chiral bisfluorene methyl radical derivatives as promising for experiments.

Chiral discrimination in nuclear magnetic resonance spectroscopy

Chirality is a fundamental property of molecules whose spatial symmetry is characterized by the absence of improper rotations, making them not superimposable to their mirror image. Chiral molecules constitute the elementary building blocks of living species and one enantiomer is favoured in general (e.g. L-aminoacids and D-sugars pervade terrestrial homochiral biochemistry) because most chemical reactions producing natural substances are enantioselective. Since the effect of chiral chemicals and drugs on living beings can be markedly different between enantiomers, the quest for practical spectroscopical methods to scrutinize chirality is an issue of great importance and interest. Nuclear magnetic resonance (NMR) is a topmost analytical technique, but spectrometers currently used are 'blind' to chirality, i.e. unable to discriminate the two mirror-image forms of a chiral molecule, because, in the absence of a chiral solvent, the spectral parameters, chemical shifts and spin-spin coupling constants are identical for enantiomers. Therefore, the development of new procedures for routine chiral recognition would offer basic support to scientists. However, in the presence of magnetic fields, a distinction between true and false chirality is mandatory. The former epitomizes natural optical activity, which is rationalized by a time-even pseudoscalar, i.e. the trace of a second-rank tensor, the mixed electric dipole/magnetic dipole polarizability. The Faraday effect, magnetic circular dichroism and magnetic optical activity are instead related to a time-odd axial vector. The present review summarizes recent theoretical and experimental efforts to discriminate enantiomers via NMR spectroscopy, with the focus on the deep connection between chirality and symmetry properties under the combined set of fundamental discrete operations, namely charge conjugation, parity (space inversion) and time (motion) reversal.

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.

Analysis of parity violation in chiral molecules

In order to guide the experimental search for parity violation in molecular systems, in part motivated by the possible link to biomolecular homochirality, we present a detailed analysis in a relativistic framework of the mechanism behind the tiny energy difference between enantiomers induced by the weak force. A decomposition of the molecular expectation value into atomic contributions reveals that the effect can be thought of as arising from a specific mixing of valence s(1/2) and p(1/2) orbitals on a single center induced by a chiral molecular field. The intra-atomic nature of the effect is further illustrated by visualization of the electron chirality density and suggests that a simple model for parity violation in molecules may be constructed by combining pre-calculated atomic quantities with simple bonding models. A 2-component relativistic computational procedure is proposed which bridges the relativistic and non-relativistic approaches to the calculation of parity violation in chiral molecules and allows us to explore the single-center theorem in a variational setting.

Chiral discrimination via nuclear magnetic shielding polarisabilities from NMR spectroscopy: Theoretical study of (Ra)-1,3-dimethylallene, (2R)-2-methyloxirane, and (2R)-N-methyloxaziridine

Three medium-size optically active molecules have been studied to make a guess at candidates suitable for chiral discrimination in an isotropic medium via nuclear magnetic resonance spectroscopy. The criterion for experimental detection is given by the magnitude of the isotropic part of nuclear magnetic shielding polarisability tensors, related to a pseudoscalar of opposite sign for the two enantiomers. The pseudoscalar shielding polarisability at the (17)O nucleus in N-methyloxaziridine, calculated at the Hartree-Fock level, is approximately 7.8 x10(-)(17) mV(-)(1). To obtain an experimentally observable magnetic field induced at the (17)O nucleus in N-methyloxaziridine, electric fields as large as approximately 10(7) - 10(8) Vm(-)(1) should be applied to the probe. The molecular electric dipole moment induced by precession of the magnetic dipole of the (17)O nucleus in a magnetic field of 10 T is, in absolute value, approximately 8.8 x 10(-)(42) Cm. The estimated rf-voltage at a resonance circuit is approximately 10 nV. Smaller values have been estimated for N, C, and H nuclei in 1,3-dimethylallene and 2-methyloxirane.

Theoretical determination of parity-violating vibrational frequency differences between the enantiomers of chiral molecules

A perturbation treatment has been used to compute the leading first- and second-order parity-violating corrections to the vibrational energy levels of a chiral molecule. Assuming the molecular equilibrium geometry as expansion point of both parity-violating and parity-conserving potential-energy surfaces, it is shown that these corrections, i.e., harmonic and anharmonic contributions, are of the same order of magnitude and that none of them can be neglected for a realistic determination of vibrational frequency differences. Numerical tests based on ab initio MP2 force fields and quantum-relativistic calculations of the parity-violating potential for each normal mode of PHBrF and AsHBrF molecules confirm this conclusion. In particular, it is shown that a normal mode of AsHBrF is characterized by one of the largest vibrational frequency difference ever found--the prediction is approximately 0.1 Hz--only one order of magnitude less than the presumed resolution limit of current experimental investigations.

Recent experimental and theoretical developments towards the observation of parity violation (PV) effects in molecules by spectroscopy

Parity violation (PV) at the molecular level is known to be responsible for a tiny energy difference between the two enantiomers of a chiral molecule. This parity violation energy difference (PVED) has not yet been detected by experiment. In the last few years, the search for PV effects in molecules has made important steps ahead for several reasons. On one hand, very accurate infra-red spectroscopy measurements were performed by metrologists on bromochlorofluoromethane (CHFClBr) with a 10 Hz accuracy, which so far is the most precise. On the other hand, relativistic calculations were used for the evaluation of DeltaE(PV) allowing for a screening of favorable molecules for future measurements. The synthesis of such chiral molecules with high parity violation effects is currently being investigated. In memory of Professor Jean-Bernard Robert.

Search for resolution of chiral fluorohalogenomethanes and parity-violation effects at the molecular level

The first observation of a parity-violation effect in molecules induced by weak interactions is still a dream that requires the synthesis and, eventually, the resolution of the enantiomers of well-chosen simple chiral molecules together with an appropriate experimental set-up for high-resolution spectroscopy. Performing IR spectroscopy on highly enantiomerically enriched samples of bromochlorofluoromethane succeeded in giving an upper limit of 10(-13) for the relative vibrational energy difference between the two enantiomers. These results led us to conceive a new experimental set-up based on a supersonic molecular beam and to work on other chiral molecules, such as chlorofluoroiodomethane. A synthesis of (+/-)-CHCIFI from racemic chlorofluoroiodoacetic acid should, in the near future permit the preparation of optically active samples of this haloform. The development of molecular beam spectroscopy using a two-photon Ramsey-fringes experiment should allow us to reach the precision needed to observe parity violation. These experimental challenges, which stimulate a close collaboration between chemists and physicists, are presented. The success of these projects would open the route to new information on the molecular Hamiltonian, a better knowledge of the electroweak interaction, and a better control of the various chirality-related properties of simple molecules.

NMR and parity violation: low-temperature dependence in 1H CRAMPS and 13C CP/MAS ssNMR spectra of alanine enantiomer

Life is based on L-amino acids and D-sugars rather than the enantiomeric D-amino acids and L-sugars. This broken symmetry is now believed to be a feature of fundamental physics-a result of symmetry-breaking induced by the weak force, which makes one enantiomer slightly more stable than the other. An amplification mechanism based on quantum mechanical tunneling could give rise to a second-order phase transition. In order to understand the transition mechanism, we measured the temperature dependence of 1H CRAMPS solid state NMR and 13C CP/MAS spectra of D- and L-alanine crystals from 295 K through to 220 K. Obvious difference of NMR behaviors between two enantiomers was observed in the phase transition which may be related to one suggested by Salam, caused biochirality among twenty amino acids.

NMR and parity nonconservation. Experimental requirements to observe a difference between enantiomer signals

The possibility of observing a difference in the high-resolution NMR spectra of two enantiomers as due to parity nonconservation is discussed. Proposals to minimize the NMR linewidths are presented. It is concluded that, using the ultra- high-resolution technique, a difference could be observed with high Z value spin one- half nuclei such as Pt, T1, Xe. Other nuclei can also be considered.

Influence of parity violating weak nuclear potentials on vibrational and rotational frequencies in chiral molecules

We study the effect of parity violation on the vibrational and rotational frequencies of CHBrClF. We report the parity violating potentials as a function of reduced normal coordinates for all nine internal vibrational modes omega(1) to omega(9), using our new, accurate multiconfigurational-linear response (RPA and complete-active-space self-consistent field) approach. All modes omega(i) show a strongly mode dependent relative shift Delta(pv)omega(i)/omega(i) (between 0.08x10(-16) and 13.3x10(-16), much smaller than all previous experimental tests could detect, including the most recent ones). The results are discussed in relation to other tests of parity violation.

Energetic stabilization of d-camphor via weak neutral currents

It is shown via a series of numerical tests on the camphor molecule, C10H16O, that the naturally occurring d-enantiomer is energetically stabilized with respect to its mirror image by electroweak force. The calculated energy difference between enantiomers, about 1.5 x 10(-19) hartree, is roughly eight orders of magnitude smaller than the upper bound suggested by available spectroscopic investigations on the frequency of a spectroscopic transition. However, such a difference is about ten times larger than previous estimates of parity-violating energy contributions reported in the literature for other chiral molecules, which makes the idea of electroweak stabilization of one enantiomer more reliable than expected before.