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Zero-field splitting parameters within exact two-component theory and modern density functional theory using

Florian Bruder1, Yannick J Franzke1, Christof Holzer2

  • 1Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany.

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This study presents an efficient computational method for calculating zero-field splitting parameters, extending its applicability to various density functional approximations and relativistic theories. The method achieves significant speedups with minimal error, making it practical for complex molecular systems.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Zero-field splitting (ZFS) parameters are crucial for understanding the electronic structure and magnetic properties of molecules.
  • Accurate calculation of ZFS parameters, especially spin-orbit coupling (SOC) and spin-spin (SS) contributions, is computationally demanding.
  • Existing methods often face limitations in handling advanced density functional approximations and relativistic effects.

Purpose of the Study:

  • To develop and implement an efficient computational approach for calculating zero-field splitting parameters.
  • To extend the existing methodology to meta-generalized gradient approximations (meta-GGAs), local hybrid functionals, and relativistic two-component theories.
  • To assess the accuracy and efficiency of the new implementation for various chemical systems.

Main Methods:

  • Utilized seminumerical integration techniques for two-electron spin-dipole and spin-orbit perturbation contributions.
  • Extended the formulation to meta-GGAs and local hybrid functionals, incorporating paramagnetic current density response.
  • Formulated spin-orbit perturbation within relativistic exact two-component (2c) theory and the screened nuclear spin-orbit (SNSO) approximation.

Main Results:

  • Demonstrated the accuracy of the implementation for transition-metal and diatomic main-group compounds.
  • Achieved significant speedups for Mn and Mo complexes using coarse integration grids with negligible error.
  • The SNSO approximation substantially reduced computational cost, yielding results comparable to the spin-orbit mean field (SOMF) Ansatz.

Conclusions:

  • The presented efficient implementation of ZFS parameters is accurate and applicable to a broader range of electronic structure methods.
  • The use of coarse integration grids and the SNSO approximation offers a practical and computationally feasible approach for ZFS calculations.
  • This work advances the capability for accurate theoretical studies of magnetic properties in complex molecules.