Spatial contributions to nuclear magnetic shieldings

TL;DR

This paper introduces a new methodology for calculating and visualizing nuclear magnetic shielding densities, enabling detailed analysis of atomic contributions and spatial origins of shielding effects in molecules.

Contribution

The authors develop a novel approach to analyze and visualize nuclear magnetic shielding densities, including atomic contributions, implemented in the GIMIC program, and demonstrate its application to benzene and cyclobutadiene.

Findings

Shielding densities reveal diatropic and paratropic current effects.

Shielding contributions mainly originate from the studied atom and neighbors.

The method allows visual inspection of shielding origins.

Abstract

We develop a methodology for calculating, analyzing and visualizing nuclear magnetic shielding densities, which are calculated from the current density via the Biot-Savart relation. Atomic contributions to nuclear magnetic shielding constants can be estimated within our framework with a Becke partitioning scheme. The new features have been implemented in the GIMIC program and are applied in this work to the study of the $^1$H and $^{13}$C nuclear magnetic shieldings in benzene (C$_6$H$_6$) and cyclobutadiene (C$_4$H$_4$). The new methodology allows a visual inspection of the spatial origins of the positive (shielding) and negative (deshielding) contributions to the nuclear magnetic shielding constant of a single nucleus, something which has not been hitherto easily accomplished. Analysis of the shielding densities shows that diatropic and paratropic current-density fluxes yield both shielding as well as deshielding contributions, as the shielding or deshielding is determined by the direction of the current-density flux with respect to the studied nucleus instead of the tropicity. Becke partitioning of the magnetic shieldings shows that the magnetic shielding contributions mainly originate from the studied atom and its nearest neighbors, confirming the localized character of nuclear magnetic shieldings.