Nuclear spin-spin coupling density in molecules

It is shown that nuclear spin-spin coupling in a molecule can be rationalized in terms of property density functions which depend on the position in three-dimensional space. The spin-spin coupling density surface, calculated as a table of values for a grid of coordinates on a plane through the molecular domain, yields a direct physical picture and offers a physical interpretation of the phenomenology, by showing the path whereby coupling takes place. The different role and the relative importance of the Fermi contact, spin-dipolar, and diamagnetic and paramagnetic spin-orbit mechanisms is readily assessed. The display of the spin-spin density reveals that the major contribution comes from the electrons close to the coupled nuclei. The economy of thinking achieved by the use of functions of three coordinates in real space, instead of n-electron wave functions depending on 3n coordinates in Hilbert space, is evident in the present case. The utility of spin-spin coupling densities has been discussed for the molecules of hydrogen fluoride, water, ammonia, and methane.