Understanding NMR J-couplings by the theory of polarization propagators

Abstract

Propagators are powerful theoretical tools that were first developed within the nonrelativistic (NR) regime and were applied to calculate atomic and molecular properties more than 30 years ago. The recent relativistic generalization of polarization propagators has shown that these propagators play a special role in describing the quantum origin of any molecular property and the broad implication of their particular definition. In this article, we give a general overview on fundamentals and applications of polarization propagators to one of the most important NMR spectroscopic parameters, the nuclear spin coupling mediated by the electronic system within both regimes: relativistic and NR. This presentation is given in a level that can be followed with a basic knowledge of quantum mechanics. Our aim is to show what one can learn about molecular electronic configurations, and also the transmission and influence of magnetic perturbations on electronic systems from basic theoretical elements like molecular orbitals, electronic excitation energies, coupling pathways, entanglement, etc. by using propagators. We shall use i) semiempirical models and ii) ab initio calculations at different levels of approach. We give a deep insight on the electronic origin of the Karplus' rule, the sign of indirect nuclear spin couplings, unusually large long-range couplings, cooperativity effects, relativistic effects, and the origin of diamagnetism. Some of these analysis are based on previous publications, and some others are presented here for the first time.