Nuclear spin–spin coupling density functions and the Fermi hole

Abstract

Nuclear spin–spin coupling density functions yield a three-dimensional picture of the interaction between two nuclear dipole moments mediated by electron spin density. A physical interpretation of the Fermi contact coupling density maps can be readily arrived at on account of the Fermi correlation between same-spin electrons as the mechanism whereby the spin polarization induced about one nucleus is transmitted to another nucleus coupled to it. It is shown that the Fermi hole density function, evaluated by an opportune choice of the reference electron, is characterized by morphological aspects very similar to those appearing in the plots of one- and two-bonds Fermi contact density functions. A comparison has been made for hydrogen fluoride, water, ammonia, and methane molecules at the Hartree–Fock level of theory. The results confirm the role of the Fermi correlation as the fundamental vehicle propagating nuclear-spin/electron-spin contact interaction, i.e., the process mainly responsible for nuclear spin–spin coupling. The plots of Fermi hole density show that the geminal H–H coupling would not be possible without the essential contribution of the spin density in the vicinity of the heavier nucleus. The combined use of Fermi contact density functions and Fermi hole distributions yields a very promising approach to the study of nuclear magnetic resonance coupling constants, and provides a sound physical basis for their interpretation.