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Magnetic Resonance Observables in FHI-aims: Shieldings, Magnetizabilities, and J-Couplings

Magnetic resonance spectroscopies, especially nuclear magnetic resonance (NMR), are a key set of techniques to probe the structure of molecules and solids.

At the time of writing, FHI-aims implements computations of

  • Molecular magnetizabilities
  • NMR shielding tensors (and, consequently, chemical shifts) of nuclear spins in molecules
  • J-couplings (also called indirect dipole-dipole couplings or spin-spin couplings) between nuclear spins in molecules.

These quantities can be calculated using density-functional theory with non-relativistic or scalar relativistic treatments. The code can handle systen sizes up to at least thousands of atoms with high numerical precision.

This tutorial demonstrates how to compute reliable magnetic resonance observables with FHI-aims. The technical underpinnings and detailed data on basis set convergence are documented in the following reference:

Laasner et al., Electronic Structure 6 (2), 027002 (2024), DOI: 10.1088/2516-1075/ad45d4

In particular, this reference contains detailed benchmarks of NAO basis sets appropriate for well converged magnetizabilities, chemical shifts and shieldings.

Another key use of NMR data is the interpretation of NMR spectra. Even given a set of shieldings, matching them to the experimental spectrum of a particular molecule may not be trivial since experimental NMR spectra represent a continuous average over molecular motions. We therefore also explain how calculated shieldings can be employed to match and/or interpret the NMR spectra of a molecule.

This tutorial is divided into five parts:

  • Calculating NMR shieldings and chemical shifts

  • Calculating molecular magnetizabilities

  • Calculating spin-spin coupling constants (J-couplings)

  • Efficiency considerations

  • Using shieldings to predict approximate NMR spectra with Ethanol as an example

Each part is accessed in the sidebar on the left.

They are briefly described below.

Overview

Shieldings

Example Molecule: Pyrazole (Geometry from NS372 database, Schattenberg and Kaupp)

Basis set used: NAO-VCC-nZ, FHI-aims-09, NAO-J-n

The computation of shielding tensors is the first step to simulating entire NMR spectra as is described in the NMR section of this tutorial. In this tutorial we will compute the shielding tensors of pyrazole using a wide range of different basis sets. These shielding tensors are then compared against reference values computed in Schattenberg and Kaupp. From this set of calculations, we can observe the tradeoff between the increased accuracy of the NAO-J-n and NAO-VCC-nZ basis sets and the computational efficiency of the FHI-aims-09 standard basis sets.

Magnetizabilities

Example Molecule: H2C2O (Geometry from Lutnaes et al.)

Basis set used: FHI-aims-09 (the standard FHI-aims "tier" basis sets for DFT)

Spin-Spin Couplings

Example Molecule: CH2O (Geometry optimization technique from San Fabian et al.)

Basis set used: NAO-J-n

Spin-spin couplings represent the coupling of nuclear magnetic spins. The magnitude is extremely sensitive to the local chemical environment and thus can reveal detailed information about bond lengths and angles. However, interpretation of spin-spin couplings is difficult making simulation a valuable tool to verify the link between geometry and coupling. Even beyond NMR spectra, these couplings are also generally responsible for the time evolution of coupled nuclear spins which is valuable for a variety of techniques. This tutorial provides a guide for computing spin-spin couplings and a comparison against reference values.

Efficiency Considerations

The correct choice of basis set for a given calculation often depends both on the NMR observable being computed and your desired level of accuracy. This section provides comments on the appropriate basis set choices for different types of NMR calculations and some comments on runtime. For a quantification of the runtime and accuracy differences between basis set choices see the Shieldings section of this tutorial as well as Laasner et al..

From Shieldings and J-couplings to Actual NMR Spectra

Example Molecule: CH3CH2OH (Geometry from PubChem)

Basis set used: NAO-VCC-5Z and FHI-aims-09 "tight"

Real NMR spectra are based on chemical shieldings and spin-spin couplings but the actual spectra are shaped by other effects as well, most importantly the motions of individual nuclei over the period of their interaction with the magnetic field. Field frequencies can be in the 100 MHz range and so the interaction time can extend to 10 ns or more, i.e., much longer than typical timescales of local nuclear motions. This segment provides a beginning for how to tackle NMR spectra by computations in practice.

How to use this documentation

Individual sections of this tutorial can be accessed via the panel on the left. A table of contents of the present page is shown on the right.

Prerequisites

This tutorial is written for FHI-aims release version 240920.