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Perspective
Discovery
Introduction
High-resolution nuclear magnetic resonance spectroscopy is an important technique for determining the structure of molecules in solution. The molecular properties that determine an NMR spectrum, namely the chemical shift and the nuclear spin-spin coupling constant, are identical for a molecule and its mirror image. These second-rank tensor properties [formula omitted, refer to PDF] and [formula omitted, refer to PDF], where N and N' are two nuclei with spin, are even under the parity operator [formula omitted, refer to PDF] that inverts the coordinates of all particles in the molecule and therefore converts one enantiomer of a chiral molecule into the other. For chiral sensitivity one looks for properties that are even under time-reversal [formula omitted, refer to PDF] and odd under [formula omitted, refer to PDF], like the optical rotational strength, which is the imaginary part of the scalar product of electric and magnetic transition dipole moments (Barron, 2004). The linear dependence of [formula omitted, refer to PDF] on an electric field E is determined by the third-rank tensor [formula omitted, refer to PDF] which is odd under [formula omitted, refer to PDF] and even under [formula omitted, refer to PDF]. It has been shown (Buckingham, 2004; Buckingham & Fischer, 2006) that the isotropic part of [formula omitted, refer to PDF], viz. [formula omitted, refer to PDF], where [...] [...] [...] is the third-rank skew-symmetric unit tensor and [formula omitted, refer to PDF] is a pseudoscalar which vanishes for achiral molecules, leads to a rotating electric polarization perpendicular to the precessing nuclear magnetic moment and to the applied magnetic field B (0). Each line in the NMR spectrum of a chiral molecule has an associated positive or negative signal at the same frequency, as occurs in circular dichroism and vibrational circular dichroism (Stephens et al. 2012) but these chirally sensitive spectral lines are yet to be observed in NMR.
Computations of [formula omitted, refer to PDF] (Buckingham & Fischer, 2006; Lazzeretti et al. 2008; Monaco & Zanasi 2011; Pelloni et al. 2013; Zanasi et al. 2007) have shown that its contribution to the electric polarization is likely to be too small for easy detection, even for heavier...