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

A relativistic relationship between parity-violating nuclear spin-rotation tensors and parity-violating NMR shielding tensors

The nuclear-spin-dependent parity-violation contributions to the nuclear magnetic resonance shielding and nuclear spin-rotation tensors (σ^PV and M^PV, respectively) are known to be formally related to one another in the non-relativistic regime. In this work, the polarization propagator formalism and the linear response within the elimination of small components model are used to show a new and more general relationship between them, which is valid within the relativistic framework. The full set of the zeroth- and first-order relativistic contributions to σ^PV and M^PV are also given here for the first time, and these results are compared with previous findings. According to four-component relativistic calculations, the electronic spin-orbit effects are the most significant ones for the isotropic values of σ^PV and M^PV in the H₂X₂ series of molecules (with X = O, S, Se, Te, and Po). When only scalar relativistic effects are taken into account, the non-relativistic relationship between σ^PV and M^PV does hold. However, when the spin-orbit effects are taken into consideration, this old non-relativistic relationship breaks down, and therefore, the new one must be considered.

Relativistic study of parity-violating nuclear spin-rotation tensors

We present a four-component relativistic approach to describe the effects of the nuclear spin-dependent parity-violating (PV) weak nuclear forces on nuclear spin-rotation (NSR) tensors. The formalism is derived within the four-component polarization propagator theory based on the Dirac-Coulomb Hamiltonian. Such calculations are important for planning and interpretation of possible future experiments aimed at stringent tests of the standard model through the observation of PV effects in NSR spectroscopy. An exploratory application of this theory to the chiral molecules H₂X₂ (X = ¹⁷O, ³³S, ⁷⁷Se, ¹²⁵Te, and ²⁰⁹Po) illustrates the dramatic effect of relativity on these contributions. In particular, spin-free and spin-orbit effects are even of opposite signs for some dihedral angles, and the latter fully dominate for the heavier nuclei. Relativistic four-component calculations of isotropic nuclear spin-rotation constants, including parity-violating electroweak interactions, give frequency differences of up to 4.2 mHz between the H₂Po₂ enantiomers; on the nonrelativistic level of theory, this energy difference is 0.1 mHz only.

Influence of the nuclear charge distribution and electron correlation effects on magnetic shieldings and spin-rotation tensors of linear molecules

The nuclear charge distribution effects (NChDE) on two response properties, the NMR magnetic shielding (σ) and the nuclear spin-rotation (SR) constants (M), are analyzed. We do it employing point-like and Gaussian-like models for describing the nuclear charge density of three linear molecules: HBr, HI and HAt. According to our results, both properties are sensitive to the NChDE. We show that the NChDE are almost completely relativistic, i.e., they nearly vanish in the non-relativistic limit of both properties. We calculated the NChDE on σ and M, and analyzed the differences between them in terms of a relativistic relation between these two properties. Using that relation we found that the electronic core mechanisms are the main ones for the NChDE on the shielding of nuclei of both, molecules and free atoms. The NChDE are smaller on SR constants than on shieldings. Nevertheless, within the relativistic polarization propagator formalism at the RPA level of approach they are very important for SR constants of nuclei in heavy-atom-containing compounds. Astatine in HAt has the largest influence: M_At = −9.95 kHz for a point-like model and −50.10 kHz for a Gaussian-like model. Correlation effects must be included and we do it using different DFT schemes. The PBE0 functional gives results that are closest to experiments for Br and I, though the LDA gives the closest for hydrogen. The value of the SR constant of At is reduced among 350 kHz and 500 kHz from its RPA value, when different and usual functionals are applied. Given that the NChDE on M and σ are mostly relativistic in their origin, these effects are also dependent on electron correlation. They have also a nonvanishing dependence with the Gaunt electron–electron interactions.

The origin and the size of both, electron correlation and nuclear charge distribution on shieldings and spin-rotations of heavy-atom containing linear molecules are shown. The analysis is performed on the relativistic and non relativistic regimes.

Toward an absolute NMR shielding scale using the spin-rotation tensor within a relativistic framework

How can one extend Flygare's rule to the relativistic framework? Three models are proposed here. The best of them shows that σ is related with the spin-rotation tensor, the atomic shielding and a new term coined as σ^SO-S.

New Experimental NMR Shielding Scales Mapped Relativistically from NSR: Theory and Application

The recently proposed relativistic mapping between nuclear magnetic resonance (NMR) shielding and nuclear spin-rotation (NSR) coupling tensors [J. Chem. Phys. 2013, 138, 134104] is employed to establish new experimental (more precisely, experimentally derived) absolute shielding constants for H and X in HX (X = F, Cl, Br, and I). The results are much more accurate than the old "experimental" values that were based on the well-known nonrelativistic mapping. The relativistic mapping is very robust in the sense that it is rather insensitive to the quality of one-particle basis sets and the treatment of electron correlation. Relativistic effects in the NSR coupling constants are also elucidated in depth.