Dependence of Magnetic Shielding of Nuclei upon Molecular Orientation

An expression is calculated for the dependence of the magnetic shielding of nuclei in linear molecules upon the magnetic quantum number of the molecule. The expression for the dependence upon orientation is shown to consist of two different terms. The first of these is directly related to the spin-rotational magnetic interaction constant of the molecule. Since the interaction is known experimentally in the important case of molecular hydrogen, this term can directly be evaluated from the experimental measurements. The other term is proportional to $\frac{(3\mathrm{}{\zeta }^2-r^2)}{r^3}$ averaged over the electron coordinates in the molecule. This term can be calculated from the wave function of the hydrogen molecule. For molecular hydrogen, the dependence of the nuclear shielding upon the molecular orientation is in principle measurable. Such a measurement, combined with the theory of the paper, provides an important check on the molecular hydrogen wave function.