Investigating solvent effects on the magnetic properties of molybdate ions (MoO$_{4}^{2-}$) with relativistic embedding

TL;DR

This study evaluates relativistic embedding methods to accurately model solvent effects on NMR shielding constants of molybdate ions, highlighting the importance of spin-orbit coupling and electronic contributions for precise magnetic property predictions.

Contribution

It demonstrates that scalar relativistic treatments are sufficient for solvent effects on NMR shielding in molybdate ions, and emphasizes the role of electronic contributions in embedding calculations.

Findings

Spin-orbit coupling significantly affects absolute shielding values.

Scalar relativistic methods adequately estimate solvent effects for relative quantities.

Electronic contributions are crucial for accurate magnetic response predictions.

Abstract

We investigate the ability of mechanical and electronic density functional theory (DFT)-based embedding approaches to describe the solvent effects on nuclear magnetic resonance (NMR) shielding constants of the $^{95}$Mo nucleus in the molybdate ion in aqueous solution. From the description obtained from calculations with two- and four-component relativistic Hamiltonians, we find that for such systems spin-orbit coupling effects are clearly important for absolute shielding values, but for relative quantities a scalar relativistic treatment provides a sufficient estimation of the solvent effects. We find that the electronic contributions to the solvent effects are relatively modest yet decisive to provide a more accurate magnetic response of the system, when compared to reference supermolecular calculations. We analyze the errors in the embedding calculations by statistical methods as well as through a real-space representation of NMR shielding densities, which are shown to provide a clear picture of the physical processes at play.