I'm having a hard time understanding the mechanism of J coupling in NMR. Why is coupling information only transmitted through bonding electrons with nonzero s-character? For example, why can't coupling information be transmitted through a bond with no s-character, e.g. a retrodative bond between a metal and a ligand? It's been explained to me that J coupling occurs through the Fermi contact interaction, in which the magnetic moment of the nucleus interacts with those of bonding electrons, and that this interaction can only occur with s-electrons since they are the only electrons with nonzero probability density at the nucleus. However, if the nucleus makes a magnetic moment in space, why shouldn't that magnetic moment interact with p or d electrons? I found the following formula for the magnitude of the Fermi contact interaction on Wikipedia. Do these brackets <> represent an inner product? And if so, is the Fermi contact interaction zero for p electrons because this inner product is somehow zero?