Exact Two-Component Theory Becoming an Efficient Tool for NMR Shieldings and Shifts with Spin-Orbit Coupling

25 August 2023, Version 3
This content is a preprint and has not undergone peer review at the time of posting.


We present a gauge-origin invariant exact two-component (X2C) approach within a modern density functional framework, supporting meta-generalized gradient approximations (meta-GGAs) such as TPSS and range-separated hybrid functionals such as CAM-B3LYP. The complete exchange-correlation kernel is applied, including the direct contribution of the field-dependent basis functions and the reorthonormalization contribution from the perturbed overlap matrix. Additionally, the finite nucleus model is available for the electron-nucleus potential and the vector potential throughout. Efficiency is ensured by the diagonal local approximation to the unitary decoupling transformation (DLU) in X2C as well as the (multipole-accelerated) resolution of the identity approximation for the Coulomb term (MARI-J, RI-J) and the seminumerical exchange approximation. Errors introduced by these approximations are assessed and found to be clearly negligible. The applicability of our implementation to large-scale calculations is demonstrated for for a tin pincer-type system as well as low-valent tin and lead complexes. Here, the calculation of the Sn NMR shifts for the pincer-type ligand with about 2400 basis functions requires less than one hour for hybrid density functionals. Further, the impact of spin-orbit coupling on the nucleus-independent chemical shifts and the corresponding ring currents of all-metal aromatic systems is studied.


NMR spectroscopy
Relativistic Effects
Density Functional Theory
Spin-orbit coupling
Nucleus-independent chemical shift
119Sn NMR

Supplementary materials

Shieldings and Shifts
Original data to compute the NMR chemical shifts
Cartesian Coordinates
Cartesian coordinates in xyz format for new optimized structures


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