Magnetic shielding of nuclei in molecules

Abstract An expression is developed for the magnetic field at a nucleus of a poly-atomic molecule with zero resultant orbital and spin angular momenta in an external magnetic field. The field at the nucleus is not the same as the externally applied field because of the field arising from the motion of the electrons in the molecule. The expression for the electron contribution to the magnetic field is shown to consist of two parts. The first is a simple term that is similar to the diamagnetic correction developed by Lamb for atoms. The second is a complicated one arising from second order paramagnetism and is analogous to the term dependent on the high frequency matrix elements in the theory of molecular diamagnetism. Under certain circumstances the second order paramagnetism term could become quite large. Since both of these terms are altered when the same nucleus is in different molecules, they at least partially and perhaps completely explain the chemical effect in nuclear moment measurements that has been reported by various observers. For linear molecules, the second order paramagnetism term is shown to be directly related to the experimentally measurable spin-rotational magnetic interaction constant of the molecule. This relation is particularly valuable in the important case of molecular hydrogen where it is shown that the correction for second order paramagnetism is −0.56 × 10−5. When this is added to the Lamb type term as calculated by Anderson, the total magnetic shielding constant for molecular H2 becomes 2.68 × 10−5