Zero-Field Splitting Parameters within Exact Two-Component Theory and Modern Density Functional Theory Using Seminumerical Integration

11 September 2023, Version 2
This content is a preprint and has not undergone peer review at the time of posting.


An efficient implementation of zero-field splitting parameters based on the work of Schmitt et al. [J. Chem. Phys. 134, 194113 (2011)] is presented. Seminumerical integration techniques are used for the two-electron spin–dipole contribution and the response equations of the spin–orbit perturbation. The original formulation is further generalized. First, it is extended to meta-generalized gradient approximations (meta-GGAs) and local hybrid functionals. For these functional classes, the response of the paramagnetic current density is considered in the coupled-perturbed Kohn–Sham (CPKS) equations for the spin–orbit perturbation term. Second, the spin–orbit perturbation is formulated within relativistic exact two-component (X2C) theory and the screened nuclear spin–orbit (SNSO) approximation. Accuracy of the implementation is demonstrated for transition-metal and diatomic main-group compounds. The efficiency is assessed for Mn and Mo complexes. Here, it is found that coarse integration grids for the seminumerical schemes lead to drastic speedups while introducing clearly negligible errors. Additionally, the SNSO approximation substantially reduces the computational demands and leads to very similar results as the spin–orbit mean field (SOMF) ansatz.


Zero-field splitting
EPR spectroscopy
Density Functional Theory
Relativistic Effects
Current Density
Seminumerical Integration
Local Hybrid Functionals
Transition-metal complexes

Supplementary materials

Complete Data
All ZFS parameters of this study
Molecular Structures
Newly optimized structures


Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.