Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

Abstract

A spherical Gaussian nuclear charge distribution model has been implemented for spin-free (scalar) and two-component (spin-orbit) relativistic density functional calculations of indirect NMR nuclear spin-spin coupling (J-coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J-couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg(2) (2+), and Tl--X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite-nucleus effects.

Perspective: Relativistic effects

“…The difference between the relativistic calculation result and experiment was later shown to be due to solvent effects. 166 Finite nucleus effects on J-coupling constants between Hg and a light atom were shown to be comparable to those of the HFCCs, 155 also reducing the magnitude of the coupling, and of comparable magnitude for Pb (below 10% for Pt). For the Hg-Hg coupling in a crown-ether complex of [Hg-Hg] 2 + , the finite nucleus effects reached 19%, and went up to 28% for the coupling in the free [Hg-Hg] 2 + ion.…”

“…The matrix elements of the ZORA FC operator remain finite for moderately large Z and the operator matrix elements can be converged in a meaningful way with respect to the basis set size. 154,155 Instead of sampling a finite electron density at a point nucleus, the quasi-relativistic form of the FC operator samples the density and its slope very close to the nucleus. If one were to use a hyperfine operator that is inconsistent with the approximate or an exact two-component method, such as the nonrelativistic form of the FC term, the results would not be meaningful and become singular in a complete basis.…”

“…For the Hg-Hg coupling in a crown-ether complex of [Hg-Hg] 2 + , the finite nucleus effects reached 19%, and went up to 28% for the coupling in the free [Hg-Hg] 2 + ion. 155 As far as the magnitude of the Hg-Hg coupling in the crownether complex is concerned, a calculation at the hybrid DFT level with finite nuclei 155 determined K = 771 × 10 22 T 2 /J versus an experimental value of 721. The experimental value translates into the world record for a J-coupling constant: 284 kHz.…”

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

“…The 1 J(Pb-H) value obtained for this system with the BP non-hybrid density functional was 2345 Hz with the four-component method, compared to an experimental estimate of around 2600-2800 Hz from extrapolations of measured couplings for methyl-substituted plumbanes. For comparison, a point-nucleus result from [201] obtained with ZORA and the PBE non-hybrid functional and converted to Hz ( 1 H, 207 Pb) would be 2836 Hz. In [201], it was shown that the use of a hybrid functional strongly increases the Pb-H J-coupling in plumbanes, while finite-nucleus corrections lead to a reduction again.…”

“…The effects were found to be of comparable magnitude for Pb, but below 10% for Pt. For the Hg-Hg coupling in a crown ether complex of [Hg-Hg] 2+ , the finite-nucleus effects reached 19%, and went up to 28% for the coupling in the free [HgHg] 2+ ion [201]. The finite-nucleus effect on 'nuclear properties' has two aspects.…”