Direct chiral discrimination in NMR spectroscopy

Conventional nuclear magnetic resonance spectroscopy is unable to distinguish between the two mirror-image forms (enantiomers) of a chiral molecule. This is because the NMR spectrum is determined by the chemical shifts and spin–spin coupling constants which – in the absence of a chiral solvent – are identical for the two enantiomers. We discuss how chirality may nevertheless be directly detected in liquid-state NMR spectroscopy: In a chiral molecule, the rotating nuclear magnetic moment induces an electric dipole moment in the direction perpendicular to itself and to the permanent magnetic field of the spectrometer. We present computations of the precessing electric polarization following a π/2 pulse. Our estimates indicate that the electric polarization should be detectable in favourable cases. We also predict that application of an electrostatic field induces a chirally sensitive magnetization oscillating in the direction of the permanent magnetic field. We show that the electric-field-perturbed chemical shift tensor, the nuclear magnetic shielding polarizability, underlies these chiral NMR effects.     

Comparison of some vibrational features of FArH...Rg and FHc...Rg complexes (Rg=He, Ne, Ar, Kr)

The shift in the harmonic vibrational frequency of the ArH stretch of FArH on formation of the linear FArH...Rg complexes (Rg=He, Ne, Ar, Kr), and of the FH stretch on formation of the linear FH...Rg complexes, has been determined by ab initio computations. These shifts are in agreement with predictions from a model based on perturbation theory and involving the first and second derivatives of the interaction energy with respect to displacement of the ArH (FH) bond length from its equilibrium value in the monomer. In the FH...Rg dimers, small blue shifts were obtained for the He and Ne complexes and red shifts for those with Ar and Kr. In the FArH...Rg dimers, blue shifts were obtained for all four complexes. These vibrational characteristics are rationalized by considering the balance between the interaction energy derivatives obtained from the perturbative model. The bond length changes on complexation are also well predicted by the model. Our computations were restricted to the linear geometry since the objective was to investigate the validity of the perturbation model and to illuminate the causes of the red and blue shifts.     

On finding the rate constants of linear and nonlinear systems

In lowest approximation, a certain chemical reaction is described by a system of first-order linear differential equations with unknown constant coefficients. One can therefore write down an expression for the state of the system at time t, and from this find the endpoint of the reaction in terms of the initial state and the rate constants. The relative values of some rate constants can then be estimated from experimental data. A better approximation in which the differential equations are nonlinear is also considered, and it turns out that because of symmetry in the reaction, the relationship between the final state and the ratios of the rate constants is unchanged. Although the differential equations now appear much less tractable, the problem of relating the rate constants to the endpoint of the reaction can be formulated and solved in terms of probabilities. The results illustrate an important property of reaction schemes in which some of the steps are reversible. More generally, this is a property of differential equations: provided that they continue to satisfy certain linear constraints, the parameters of a linear system of ordinary differential equations can vary without affecting the asymptotic solution.     

Relaxation of the individual vibrational levels of carbon monoxide following shock heating at 2100 K

The increases in the populations of the vibrational levels v = 1 to v = 5 in CO which is undergoing thermal vibrational relaxation at 2100 K have been monitored using a cw CO laser. The experiments have been carried out in a very narrow temperature range for mixtures of CO, Ar and He. Under these conditions the first part of the relaxation region is clearly visible, and it has been possible to compare the population growths of different vibrational levels under the same conditions. We have shown that the curve for the increase in the population of the level v = 1 with time is clearly different from those of the higher levels. It has been shown that all of the vibrational levels studied in this work on CO relax with a common vibrational temperature, as postulated in the model of Shuler and co-workers. The results reported here are qualitatively different from those presented by Chow and Greene on HI.