# All-electron density functional calculations for electron and nuclear spin interactions in molecules and solids

## TL;DR

This paper presents a first-principles approach using all-electron density functional theory with finite element methods to accurately compute spin interaction parameters in molecules and solids, including hyperfine and quadrupole tensors.

## Contribution

It introduces a systematic all-electron FE-based DFT method for calculating spin Hamiltonian parameters, providing a benchmark for accuracy and convergence.

## Key findings

- FE calculations can be systematically converged for spin parameters
- Results agree well with Gaussian and plane-wave methods
- Establishes reference values for spin Hamiltonian parameters

## Abstract

The interaction between electronic and nuclear spins in the presence of external magnetic fields can be described by a spin Hamiltonian, with parameters obtained from first principles, electronic structure calculations. We describe an approach to compute these parameters, applicable to both molecules and solids, which is based on Density Functional Theory (DFT) and real-space, all-electron calculations using finite elements (FE). We report results for hyperfine tensors, zero field splitting tensors (spin-spin component) and nuclear quadrupole tensors of a series of molecules and of the nitrogen-vacancy center in diamond. We compare our results with those of calculations using Gaussian orbitals and plane-wave basis sets, and we discuss their numerical accuracy. We show that calculations based on FE can be systematically converged with respect to the basis set, thus allowing one to establish reference values for the spin Hamiltonian parameters, at a given level of DFT.