Understanding NMR J-couplings by the Theory of Polarization Propagators

GUSTAVO A. AUCAR

Concepts in Magnetic Resonance Part A

Wiley InterScience

Año: 2008 vol. 32A p. 88 - 116

Polarization propagators are powerful theoretical tools that were first developed within the non relativistic regime and applied in atomic and molecular physics more than thirty years ago. Electric and magnetic molecular response properties are between that properties that were most studied with them. Whence they were generalized for being applied in a {it full} relativistic framework it became apparent their special role for describing the quantum origin of any molecular property and the coherence of both, their definition and the proposed aproximate solutions of the corresponding equation of motions. Then the finding of a QED based theory of polarization propagators was a natural generalization of the relativistic polarization propagator theory given that propagators summarises the quantum behavior of molecular systems. Furthermore polarization propagators are special theoretical devices from which one can do a deep analysis of the electronic mechanisms that underlies to any molecular response property from basic theoretical elements, like molecular orbitals, electronic excitation energies, {it coupling pathways}, {it entanglement}, contributions within different levels of theory, etc. All that is obtained in a natural way in both regimes: relativistic and non relativistic. 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 indirect nuclear spin - nuclear spin coupling mediated by the electronic system (the NMR J parameter) within both regimes: relativistic and non relativistic. This presentation is given in a level that can be followed having a basic knowledge of quantum mechanics. Our aim is to show what one can learn about molecular electronic configurations, and also about the transmission and influence of magnetic perturbations on electronic systems by using propagators with: i) {it semiempirical} models and ii) {it ab initio} calculations at different level of approachs. We stress every time that is needed the similarities between all models applied and the news that each of them gives to our understanding of the NMR J magnetic molecular property. We give in the first part a global overview about polarization propagators that include models within completely different levels of theory and different implementations of them in schemes that may be {it semiempirical} or {it ab initio}. In the second part we show how some special characteristics of the NMR J spectroscopic parameter are understandable within the polarization propagator theory: the electronic origin of the Karplus´ rule, the sign of indirect nuclear spin couplings, unusually large longe range couplings, cooperativity effects, relativistic effects and the origin of diamagnetism. Some of these analysis are based in previous publications and some others are presented here for the first time.