Theoretical study of the nuclear spin-molecular rotation coupling for relativistic electrons and non-relativistic nuclei

Abstract

A theoretical study of the relation between the relativistic formulation of the nuclear magnetic shielding and spin-rotation tensors is presented. To this end a theoretical expression of the relativistic spin-rotation tensor is formulated, considering a molecular Hamiltonian of relativistic electrons and non-relativistic nuclei. Molecular rotation effects are introduced considering the terms of the Born-Oppenheimer decomposition, which couple the electrons and nuclei dynamics. The loss of the simple relation linking both spectral parameters in the non-relativistic formulation is further analyzed carrying out a perturbative expansion of relativistic effects by means of the linear response within the elimination of the small component approach. It is concluded that relativistic effects on the spin-rotation tensor are less important than those of the nuclear magnetic shielding tensor.

Breit interaction effects in relativistic theory of the nuclear spin-rotation tensor

“…In Ref. 6, we developed a theoretical formalism based on first order corrections to the BO approximation. 8 The zeroth order molecular wave function is expressed as the product…”

“…Taking the equilibrium configuration as starting point and neglecting vibrational effects, the Hamiltonian for the nuclei is the one corresponding to a purely rotating system described by the rigid rotor Hamiltonian, 6, 11…”

“…Even though 4-component relativistic theory of NMR parameters was developed several years ago, only recently the relativistic theory of the SR tensor has been treated in detail by different authors. [5][6][7] In particular our rea) Electronic mail: azua@df.uba.ar search group has developed a formal theory considering an approximation of non-relativistic nuclei and relativistic electrons, taking into account that nuclei in molecular bound states are by far much slower than the speed of light c (in the molecule center of mass system). The starting point is a molecular Hamiltonian defined entirely in the laboratory system.…”

“…6 and explicitly presented in Ref. 7, the full consistency of this approach requires to take account of the interactions between moving electrons and moving nuclei, given by the Breit electron-nucleus interaction.…”

Relativistic calculations of magnetic resonance parameters: background and some recent developments

“…In this work, the authors also addressed the correspondence between the paramagnetic shielding and the nuclear-spinmolecular-rotation coupling constant [180]. The latter point was more thoroughly investigated in a follow-up study [181]. Within the applied approximations, it was found that the analogy between the two properties does not extend into the relativistic regime.…”