Relativistic heavy-atom effects on heavy-atom nuclear shieldings

Abstract

The principal relativistic heavy-atom effects on the nuclear magnetic resonance (NMR) shielding tensor of the heavy atom itself (HAHA effects) are calculated using ab initio methods at the level of the Breit-Pauli Hamiltonian. This is the first systematic study of the main HAHA effects on nuclear shielding and chemical shift by perturbational relativistic approach. The dependence of the HAHA effects on the chemical environment of the heavy atom is investigated for the closed-shell X(2+), X(4+), XH(2), and XH(3) (-) (X=Si-Pb) as well as X(3+), XH(3), and XF(3) (X=P-Bi) systems. Fully relativistic Dirac-Hartree-Fock calculations are carried out for comparison. It is necessary in the Breit-Pauli approach to include the second-order magnetic-field-dependent spin-orbit (SO) shielding contribution as it is the larger SO term in XH(3) (-), XH(3), and XF(3), and is equally large in XH(2) as the conventional, third-order field-independent spin-orbit contribution. Considering the chemical shift, the third-order SO mechanism contributes two-thirds of the difference of approximately 1500 ppm between BiH(3) and BiF(3). The second-order SO mechanism and the numerically largest relativistic effect, which arises from the cross-term contribution of the Fermi contact hyperfine interaction and the relativistically modified spin-Zeeman interaction (FC/SZ-KE), are isotropic and practically independent of electron correlation effects as well as the chemical environment of the heavy atom. The third-order SO terms depend on these factors and contribute both to heavy-atom shielding anisotropy and NMR chemical shifts. While a qualitative picture of heavy-atom chemical shifts is already obtained at the nonrelativistic level of theory, reliable shifts may be expected after including the third-order SO contributions only, especially when calculations are carried out at correlated level. The FC/SZ-KE contribution to shielding is almost completely produced in the s orbitals of the heavy atom, with values diminishing with the principal quantum number. The relative contributions converge to universal fractions for the core and subvalence ns shells. The valence shell contribution is negligible, which explains the HAHA characteristics of the FC/SZ-KE term. Although the nonrelativistic theory gives correct chemical shift trends in present systems, the third-order SO-I terms are necessary for more reliable predictions. All of the presently considered relativistic corrections provide significant HAHA contributions to absolute shielding in heavy atoms.

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

“…Both give closest results compared with the four-component polarization propagator approach, and in some cases with experimental results [139,140]. Their shortcomings lie in the fact that they can quantitatively reproduce only the leading relativistic effects until elements of the fifth-row [99], though their advantages are on interpretations which in most cases are related with a mix of NR mechanisms [141]. The elimination of the small component reduction is applied directly to 38 G. A. Aucar et al…”

Four-component relativistic theory for nuclear magnetic shielding: Magnetically balanced gauge-including atomic orbitals

“…As such, except for some benchmark results for closed-shell atoms/ions at the Dirac-Slater or the coupled-perturbed Dirac-Hartree-Fock ͑CP-DHF͒ level, 1-3,10,11 most of the four-component relativistic calculations on molecular systems [12][13][14][15][16][17][18][19][20][21] suffer from severe basis set incompleteness errors and/or the use of crude approximations for the contributions of NES. 22 As a matter of fact, very few solid CP-DHF [23][24][25] or coupled-perturbed Dirac-Kohn-Sham ͑CP-DKS͒-type 26 molecular calculations have been carried out up to date. Even so, the CP-DHF-type calculations have invoked a diagonal approximation to the orbital Hessian and sizable discrepancies still exist among the results for systems as simple as hydrogen halides.…”

Theoretical developments and applications of polarization propagators

“…There are several relativistic effects involved in calculations of atomic or molecular systems containing heavy atoms; the most common are the heavy‐atom effec on light‐atom, HALA, and the heavy‐atom effect on heavy‐atom, HAHA . They were studied since 30 years ago for many research groups in a vast variety of molecular systems.…”