Nuclear charge-distribution effects on the NMR spectroscopy parameters

Relativistic and QED effects on NMR magnetic shielding constant of neutral and ionized atoms and diatomic molecules

We show here results of four-component calculations of nuclear magnetic resonance σ for atoms with 10 ≤ Z ≤ 86 and their ions, within the polarization propagator formalism at its random phase level of approach, and the first estimation of quantum electrodynamic (QED) effects and Breit interactions of those atomic systems by using two theoretical effective models. We also show QED corrections to σ(X) in simple diatomic HX and X₂ (X = Br, I, At) molecules. We found that the Z dependence of QED corrections in bound-state many-electron systems is proportional to Z⁵, which is higher than its dependence in H-like systems. The analysis of relativistic ee (or paramagneticlike) and pp (or diamagneticlike) terms of σ exposes two different patterns: the pp contribution arises from virtual electron-positron pair creation/annihilation and the ee contribution is mainly given by 1s → ns and 2s → ns excitations. The QED effects on shieldings have a negative sign, and their magnitude is larger than 1% of the relativistic effects for high-Z atoms such as Hg and Rn, and up to 0.6% of its total four-component value for neutral Rn. Furthermore, percentual contributions of QED effects to the total shielding are larger for ionized than for neutral atoms. In a molecule, the contribution of QED effects to σ(X) is determined by its highest-Z atoms, being up to -0.6% of its total σ value for astatine compounds. It is found that QED effects grow faster than relativistic effects with Z.

QED effects on individual atomic orbital energies

Several issues, concerning QED corrections, that are important in precise atomic calculations are presented. The leading QED corrections, self-energy and vacuum polarization, to the orbital energy for selected atoms with 30 ≤ Z ≤ 118 have been calculated. The sum of QED and Breit contributions to the orbital energy is analyzed. It has been found that for ns subshells the Breit and QED contributions are of comparative size, but for np and nd subshells the Breit contribution takes a major part of the QED+Breit sum. It has also, been found that the Breit to leading QED contributions ratio for ns subshells is almost independent of Z. The Z-dependence of QED and Breit+QED contributions per subshell is shown. The fitting coefficients may be used to estimate QED effects on inner molecular orbitals. We present results of our calculations for QED contributions to orbital energy of valence ns-subshell for group 1 and 11 atoms and discuss about the reliability of these numbers by comparing them with experimental first ionization potential data.

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.

Relativistic and electron-correlation effects on the nuclear magnetic resonance shieldings of molecules containing tin and lead atoms

The reference values for NMR magnetic shieldings, σ(ref), are of the highest importance when theoretical analysis of chemical shifts are envisaged. The fact that the nonrelativistically valid relationship among spin-rotation constants and magnetic shieldings is not any longer valid for heavy atoms requires that the search for σ(ref) for such atoms needs new strategies to follow. We present here results of σ(ref) that were obtained by applying our own simple procedure which mixes accurate experimental chemical shifts (δ) and theoretical magnetic shieldings (σ). We calculated σ(Sn) and σ(Pb) in a family of heavy-halogen-containing molecules. We found out that σ(ref)[Sn;Sn(CH3)4] in gas phase should be close to 3864.11 ± 20.05 ppm (0.5%). For Pb atom, σ(ref)[Pb;Pb(CH3)4] should be close to 14475.1 ± 500.7 ppm. Such theoretical values correspond to calculations with the relativistic polarization propagator method, RelPPA, at the RPA level of approach. They are closer to experimental values as compared to those obtained applying few different functionals such as PBE0, B3LYP, BLYP, BP86, KT2, and KT3 of the density functional theory, DFT. We studied tin and lead shieldings of the XY(4-n)Z(n) (X = Sn, Pb; Y, Z = H, F, Cl, Br, I) and PbH(4-n)I(n) (n = 0, 1, 2, 3, 4) family of compounds with four-component functionals as implemented in the DIRAC code. For these systems results of calculations with RelPPA-RPA are more reliable than DFT ones. We argue about why those DFT functionals must be modified in order to obtain more accurate results of NMR magnetic shieldings within the relativistic regime: first, there is a dependence among both electron-correlation and relativistic effects that should be introduced in some way in the functionals; and second, the DIRAC code uses standard nonrelativistic functionals and the functionals B3LYP and PBE0 were parametrized only with data taken from light elements. It can explain why they are not able to properly introduce relativistic effects on nuclear magnetic shieldings. We finally show that in the analysis of magnetic shieldings for the family of compounds mentioned above, one must consider the newest and so-called heavy-atom effect on vicinal heavy atoms, HAVHA. Such effects are among the most important relativistic effects in these kind of compounds.

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

This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.