Electronic Current Densities Induced by Magnetic Fields and Nuclear Magnetic Dipoles: Theory and Computation of NMR Spectral Parameters

The Ramsey approach to nuclear magnetic resonance (NMR) spectral parameters, nuclear magnetic shielding (NMS) [1–3], and indirect nuclear spin–spin coupling (NSSC) [4,5], based on quantum mechanical Rayleigh– Schro¨dinger perturbation theory (RSPT), can be reformulated in terms of induced electronic current densities via “phenomenological” relationships that restate the Biot–Savart law (BSL) and other theorems of classical electrodynamics [6] in a quantum context. NMS [1–3] can therefore be expressed via the quantum mechanical electronic current density JB, induced by an applied magnetic field with flux density B. Analogously, the electron-coupled NSSC [4,5] between two nuclei I and J can be described as a result of linear superposition, that is, interference, of two current density vector fields, JmI and JmJ , induced by permanent nuclear magnetic dipoles mI and mJ in the electrons of a molecule [7,8].