Controlling ⟨Ŝ2⟩ in broken-symmetry density functional theory calculations via constrained optimization

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Accurate calculation of magnetic exchange coupling constants (J) using density functional theory (DFT) is crucial for understanding magnetic materials.
• Standard DFT methods, particularly broken-symmetry (BS) approaches for open-shell systems, often suffer from spin contamination, leading to exaggerated J values.

Purpose of the Study:

• To develop a new DFT-based method to accurately determine magnetic exchange coupling constants (J) by imposing constraints on the spin-squared expectation value.
• To overcome the limitations of existing methods in handling spin contamination in open-shell systems.

Main Methods:

• A Lagrange multiplier approach was used to impose a constraint on the DFT energy, enforcing a target spin-squared expectation value (⟨Ŝ2⟩).
• Analytical expressions for the gradient of ⟨Ŝ2⟩ were derived for implementation within a generalized Kohn-Sham scheme.
• The spin-constrained approach was applied to calculate J couplings for model systems (H2He, H3He3, Cu(II) complex) and compared with energy-difference-based schemes.

Main Results:

• The spin-constrained DFT method systematically yielded lower and more consistent exchange coupling constants (J) compared to standard BS methods.
• The approach demonstrated robustness across different density functional approximations and various test systems.
• The derived analytical expressions are general for single-determinant methods and arbitrary spin states.

Conclusions:

• The spin-constrained DFT approach provides a robust and general route for accurate calculation of magnetic exchange interactions.
• This method effectively mitigates spin contamination issues in open-shell systems.
• The findings pave the way for more reliable theoretical predictions of magnetic properties in molecular and materials systems.