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 ime.

NMR and DFT calculation study on structures of 2‐[2‐nitro‐4‐(trifluoromethyl)benzoyl]cyclohexane‐1,3‐dione (NTBC) and its two metabolites isolated from urine of patients suffering from tyrosinemia type I

“…These tables also contain theoretical coupling constants calculated for the selected conformers of the investigated compounds. In accord with the expectations, the vicinal coupling constants between aliphatic protons are strongly dependent on the appropriate dihedral angles 27. On the other hand, the coupling constants are almost independent on A ⇆ B transition and only marginally dependent on endo ⇆ exo tautomerization.…”

Polarization propagators: A powerful theoretical tool for a deeper understanding of NMR spectroscopic parameters

“…LMOs intervening in the given coupling pathways at the site of the nuclei involved [76]. The CLOPPA model generalizes the previous Dirac-Peeney model in a natural manner.…”

“…The origin of this rule is more related to the description of the molecule as a whole than on the precise local interactions like those defining the sign of J. Since an extensive explanation was given elsewhere [76,86] we shall give only a sketchy presentation of the CLOPPA model explanation of the Karplus rule.…”

“…There is an old model that was used for decades by experimentalists [76], the Dirac-Peeney model. It is known that it fails to explain the sign of several couplings, e.g.…”

Theoretical developments and applications of polarization propagators

“…In other words, the principal propagator matrix, that should be positive, is not as positive as necessary to overcome that problem, which is also known in perturbative calculations using perturbation theory. Within the Schrödinger formulation of quantum mechanics, it happens when the restricted Hartree–Fock electronic ground‐state of the given molecular system is not (or is quite close to) the lowest energy state, but a triplet state is (quite close to) the lowest …”